Philosophical MulticoreWritings on philosophy, investing, and altruism from a person with some thoughts on philosophy, investing, and altruism
http://mdickens.me
Index Funds That Vote Are Active, Not Passive<p>As an investor, you might invest in an index fund because you want to get unbiased, diversified exposure to the market. You don’t have to figure out which stocks will beat the market if you simply buy every stock.</p>
<p>But when you invest in an index fund, usually that means the fund can now vote on your behalf. The more stock an index fund owns, the more voting power it has. Generally speaking, the big index fund providers (including <a href="https://corporate.vanguard.com/content/dam/corp/advocate/investment-stewardship/pdf/policies-and-reports/2021_proxy_voting_policies.pdf">Vanguard</a> and <a href="https://www.blackrock.com/corporate/literature/fact-sheet/blk-responsible-investment-guidelines-us.pdf">BlackRock</a>) will vote in ways that align with their own corporate values—their top (stated) priorities are to increase climate change mitigation and workforce gender/racial diversity.</p>
<p>Regardless of whether you <em>want</em> this voting behavior, it means these index funds are not passive. By putting your money in an index fund that votes, you are implicitly claiming that it will make better voting decisions than the market.</p>
<p>(For that matter, any time you hold something other than the global market portfolio, you’re making an active bet. Sadly (and surprisingly), there aren’t any single index funds that offer the global market portfolio. But I digress.)</p>
Wed, 20 Apr 2022 00:00:00 -0500
http://mdickens.me/2022/04/20/index_funds_that_vote_are_active/
http://mdickens.me/2022/04/20/index_funds_that_vote_are_active/A Preliminary Model of Mission-Correlated Investing<h2 id="summary">Summary</h2>
<p><strong>TLDR:</strong> According to my preliminary model, the altruistic investing portfolio should ultimately allocate 5–20% on a risk-adjusted basis to mission-correlated investing. But for the current EA portfolio, it’s better on the margin to increase its risk-adjusted return than to introduce mission-correlated investments.</p>
<p><em>Last updated 2022-04-06.</em></p>
<p>The purpose of <a href="https://forum.effectivealtruism.org/posts/YApaCr98Q7wSYcaoB/mission-correlation-more-than-just-hedging">mission-correlated investing</a> is to earn more money in worlds where your money matters more. For instance, if you’re working to prevent climate change, you could buy stock in oil companies. In worlds where oil companies are more successful and climate change gets worse, you make more money.</p>
<p>Previous work by <a href="https://pubs.aeaweb.org/doi/pdfplus/10.1257/aeri.20180347">Roth Tran (2019)</a><sup id="fnref:3"><a href="#fn:3" class="footnote">1</a></sup> proved that, under certain weak assumptions, philanthropists should invest more in so-called “evil” companies than they would from a pure profit-making standpoint. This result follows from the assumption that a philanthropist’s actions become more cost-effective when the world gets worse along some dimension.</p>
<p>That’s an interesting result. But all it says is altruists should invest more than zero in mission hedging. How much more? Am I supposed to allocate 1% of my wealth to mission-correlated assets? 5%? 100%?</p>
<p>To answer this question, I extended the <a href="https://en.wikipedia.org/wiki/Modern_portfolio_theory">standard</a> portfolio choice problem to allow for mission-correlated investing. This model makes the same assumptions as the standard problem—asset prices follow lognormal distributions, people experience constant relative risk aversion, etc.—plus the assumption that utility of money increases linearly with the quantity of the mission target, e.g., because the more CO2 there is in the atmosphere, the cheaper it is to extract.</p>
<p>I used this model to find some preliminary results. Future work should further explore the <a href="#how-accurate-is-this-model">model setup</a> and the relevant empirical questions, which I discuss further in the <a href="#future-work">future work</a> section.</p>
<p>Here are the answers the model gives, with my all-things-considered <a href="https://mdickens.me/confidence_tags/">confidence</a> in each:</p>
<ul>
<li>Given no constraints, philanthropists should allocate somewhere between 2% and 40% to mission hedging on a risk-adjusted basis,<sup id="fnref:8"><a href="#fn:8" class="footnote">2</a></sup> depending on what assumptions we make. <em>Confidence: Somewhat likely.</em>
<a href="#unconstrained-results">[More]</a></li>
<li>Given no constraints, and using my best-guess input parameters:
<ul>
<li>Under this model, a philanthropist who wants to hedge a predictable outcome, such as CO2 emissions, should allocate ~5% (risk-adjusted) to mission hedging.</li>
<li>Under this model, a philanthropist who wants to hedge a more volatile outcome, for example AI progress, should allocate ~20% to mission hedging on a risk-adjusted basis.</li>
</ul>
</li>
<li>If you can’t use leverage, then you shouldn’t mission hedge unless mission hedging looks especially compelling. <em>Confidence: Likely.</em>
<a href="#results-with-a-leverage-constraint">[More]</a></li>
<li>If you currently invest most of your money in a legacy investment that you’d like to reduce your exposure to, then it’s more important on the margin to seek high expected return than to mission hedge. <em>Confidence: Likely.</em>
<a href="#results-with-a-legacy-investment">[More]</a></li>
<li>The optimal allocation to mission hedging is proportional to: (<em>Confidence: Likely</em>)
<ol>
<li>the correlation between the hedge and the mission target being hedged;</li>
<li>the standard deviation of the mission target;</li>
<li>your degree of risk tolerance;</li>
<li>the inverse of the standard deviation of the hedge.</li>
</ol>
</li>
</ul>
<p><em>Cross-posted to the <a href="https://forum.effectivealtruism.org/posts/6wwjd8kZWY5ew9Zvy/a-preliminary-model-of-mission-correlated-investing">Effective Altruism Forum</a>.</em></p>
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<h2 id="contents">Contents</h2>
<ul id="markdown-toc">
<li><a href="#summary" id="markdown-toc-summary">Summary</a></li>
<li><a href="#contents" id="markdown-toc-contents">Contents</a></li>
<li><a href="#setup" id="markdown-toc-setup">Setup</a> <ul>
<li><a href="#the-goal" id="markdown-toc-the-goal">The goal</a></li>
<li><a href="#the-utility-function" id="markdown-toc-the-utility-function">The utility function</a></li>
<li><a href="#some-more-assumptions" id="markdown-toc-some-more-assumptions">Some more assumptions</a></li>
<li><a href="#table-of-variables" id="markdown-toc-table-of-variables">Table of variables</a></li>
</ul>
</li>
<li><a href="#results" id="markdown-toc-results">Results</a> <ul>
<li><a href="#unconstrained-results" id="markdown-toc-unconstrained-results">Unconstrained results</a> <ul>
<li><a href="#general-solution" id="markdown-toc-general-solution">General solution</a></li>
<li><a href="#specific-numeric-results" id="markdown-toc-specific-numeric-results">Specific numeric results</a></li>
</ul>
</li>
<li><a href="#results-with-a-leverage-constraint" id="markdown-toc-results-with-a-leverage-constraint">Results with a leverage constraint</a></li>
<li><a href="#results-with-a-legacy-investment" id="markdown-toc-results-with-a-legacy-investment">Results with a legacy investment</a></li>
</ul>
</li>
<li><a href="#how-accurate-is-this-model" id="markdown-toc-how-accurate-is-this-model">How accurate is this model?</a></li>
<li><a href="#future-work" id="markdown-toc-future-work">Future work</a></li>
<li><a href="#acknowledgments" id="markdown-toc-acknowledgments">Acknowledgments</a></li>
<li><a href="#appendices" id="markdown-toc-appendices">Appendices</a> <ul>
<li><a href="#appendix-a-mission-leveraging" id="markdown-toc-appendix-a-mission-leveraging">Appendix A: Mission leveraging</a></li>
<li><a href="#appendix-b-why-use-this-approach" id="markdown-toc-appendix-b-why-use-this-approach">Appendix B: Why use this approach?</a></li>
<li><a href="#appendix-c-proof-of-analytic-solution" id="markdown-toc-appendix-c-proof-of-analytic-solution">Appendix C: Proof of analytic solution</a></li>
<li><a href="#appendix-d-tables-of-optimization-results" id="markdown-toc-appendix-d-tables-of-optimization-results">Appendix D: Tables of optimization results</a></li>
<li><a href="#appendix-e-numeric-approximation-of-the-optimal-solution" id="markdown-toc-appendix-e-numeric-approximation-of-the-optimal-solution">Appendix E: Numeric approximation of the optimal solution</a></li>
</ul>
</li>
<li><a href="#notes" id="markdown-toc-notes">Notes</a></li>
</ul>
<h1 id="setup">Setup</h1>
<h2 id="the-goal">The goal</h2>
<p>We have some utility function that says how much we value the state of the world. Our utility function cares about two things: (1) our wealth and (2) some mission target. The mission target is a measure of an outcome we care about. For example, if we want to hedge climate change, the mission target is the level of CO2 in the atmosphere. If we’re hedging factory farming, the mission target could be the number of animals on factory farms.</p>
<p>Suppose there are two things we can invest in: an MVO (mean-variance optimal) asset and a hedge asset. (Note: usually MVO stands for <a href="https://www.effisols.com/basics/MVO.htm">“mean-variance optimization”</a>, but I’m using it to mean “mean-variance optimal”.) Let the MVO asset be the investment that maximizes expected utility of wealth without regard to the mission target<sup id="fnref:14"><a href="#fn:14" class="footnote">3</a></sup>. Let the hedge asset be an investment that’s correlated with the mission target and uncorrelated with the MVO asset—for example, a climate change hedge could consist of buying oil stocks + shorting the S&P 500. We choose some proportions of our wealth to invest in each of the MVO asset and the hedge asset. This total could add up to more than 100% (by using leverage) or it could be negative (by short selling).</p>
<p>Then we want to find the asset proportions that maximize expected utility.</p>
<p>As an example, say we can invest in two securities: XOM (Exxon Mobil) and SPY (S&P 500 index fund). The MVO asset might be {90% SPY, 10% XOM}, and the hedge asset might be {100% XOM, –100% SPY}. That means, by assumption, {90% SPY, 10% XOM} maximizes expected utility when holding the mission target constant.</p>
<p>If we invest 90% in the MVO asset and 10% in the hedge asset, then our allocation becomes</p>
<pre><code> 0.9 (90% SPY + 10% XOM) + 0.1 (100% XOM – 100% SPY)
= 71% SPY + 19% XOM
</code></pre>
<p>That is, 71% long SPY and 19% long XOM, with the remaining 10% in cash.</p>
<p>The hedge asset is a combination of positions that (by definition) has no correlation to the MVO asset. But we might never invest directly in the hedge asset. In the example above, even though the hedge includes both long and short positions, our final allocation doesn’t require short-selling. And in practice, you probably wouldn’t think about how to allocate between (90% SPY, 10% XOM) and (100% XOM, -100% SPY). You’d just think about how to allocate between SPY and XOM. But for the sake of analyzing the problem, it’s easier to think in terms of a mean-variance optimal asset vs. an uncorrelated hedge asset.</p>
<p>Importantly, mission hedging climate change doesn’t just mean we allocate more than 0% to oil stocks. It means we allocate <em>more to oil stocks than a typical investor would</em>. In this example, a normal investor allocates 10% to XOM, while a mission hedger allocates 19%.</p>
<p>Note A: Mission hedging is a special case of <a href="https://forum.effectivealtruism.org/posts/YApaCr98Q7wSYcaoB/mission-correlation-more-than-just-hedging">mission-correlated investing</a>. It’s the most intuitive case, so I will focus on it in this essay, but the model I present could be adapted to apply to other types of mission-correlated investing. See <a href="#appendix-a-mission-leveraging">Appendix A</a> for how this could be done.</p>
<p>Note B: This model of mission hedging uses an extension of mean-variance optimization, but it’s not obvious that this is a good approach. See <a href="#appendix-b-why-use-this-approach">Appendix B</a> for more on why I used this method.</p>
<h2 id="the-utility-function">The utility function</h2>
<p>Following <a href="https://pubs.aeaweb.org/doi/pdfplus/10.1257/aeri.20180347">Roth Tran (2019)</a>, we want our utility function to meet the following criteria. Plain descriptions on the left, mathematical definitions on the right, with U = utility, W = wealth, b = mission target (which Roth Tran called a “bad activity”, although in my model, it’s not necessarily bad):</p>
<table>
<tbody>
<tr>
<td>More wealth is better</td>
<td><script type="math/tex">\displaystyle\frac{dU}{dW} > 0</script></td>
</tr>
<tr>
<td>More of the mission target is worse</td>
<td><script type="math/tex">% <![CDATA[
\displaystyle\frac{dU}{db} < 0 %]]></script></td>
</tr>
<tr>
<td>More of the mission target makes wealth more valuable</td>
<td><script type="math/tex">\displaystyle\frac{d^2U}{dW db} > 0</script></td>
</tr>
</tbody>
</table>
<p>This describes a broad class of utility functions—so broad that it can’t give much practical guidance. Let’s pin down some more requirements:</p>
<table>
<tbody>
<tr>
<td>Wealth has diminishing marginal utility</td>
<td><script type="math/tex">% <![CDATA[
\displaystyle\frac{d^2 U}{dW^2} < 0 %]]></script></td>
</tr>
<tr>
<td>Sufficient wealth can eliminate almost all of the mission target, but never quite all of it</td>
<td><script type="math/tex">\displaystyle\lim\limits_{W \rightarrow \infty} \displaystyle\frac{dU}{db} = 0</script></td>
</tr>
<tr>
<td>We have <a href="https://en.wikipedia.org/wiki/Isoelastic_utility">constant relative risk aversion</a> with respect to wealth</td>
<td><script type="math/tex">-W \displaystyle\frac{d^2 U}{dW^2} / \frac{dU}{dW} = \gamma</script></td>
</tr>
</tbody>
</table>
<p>A constant relative risk aversion (CRRA) utility function looks like</p>
<p>\begin{align}
U(W) = \displaystyle\frac{W^{1 - \gamma} - 1}{1 - \gamma}
\end{align}</p>
<p>where <script type="math/tex">\gamma</script> (that’s the Greek letter gamma) is a constant that’s greater than 1. For our utility function to account for the mission target, we need to ensure (a) utility decreases with the mission target and (b) wealth mitigates the mission target, up to a maximum of 100% mitigation.</p>
<p>So we can define</p>
<p>\begin{align}
U(W, b) = f(b) \displaystyle\frac{W^{1 - \gamma} - 1}{1 - \gamma} - \frac{f(b)}{\gamma - 1}
\end{align}</p>
<p>given some function <script type="math/tex">f(b)</script> that defines how utility scales with the mission target.<sup id="fnref:1"><a href="#fn:1" class="footnote">4</a></sup></p>
<p>The <script type="math/tex">\frac{W^{1 - \gamma} - 1}{1 - \gamma}</script> term says that the utility of wealth scales with <script type="math/tex">f(b)</script>. The <script type="math/tex">\frac{f(b)}{\gamma - 1}</script> term says that total utility decreases with <script type="math/tex">f(b)</script>.</p>
<p>What is the shape of the badness function? As an example, consider climate change. If the atmosphere contains twice as much CO2, you can remove it approximately twice as quickly.<sup id="fnref:21"><a href="#fn:21" class="footnote">5</a></sup> In general, interventions to prevent a bad activity are plausibly twice as effective when there’s twice as much of the bad thing. So we can say <script type="math/tex">f(b) = b</script>.</p>
<p>Our utility function simplifies to</p>
<p>\begin{align}
U(W, b) = b \displaystyle\frac{W^{1 - \gamma}}{1 - \gamma}
\end{align}</p>
<p>For example, <script type="math/tex">\gamma = 1.5</script> gives</p>
<p>\begin{align}
U(W, b) = \displaystyle\frac{-2 b}{\sqrt{W}}
\end{align}</p>
<p>If we wanted to, we could generalize this to <script type="math/tex">U(W, b) = \displaystyle\frac{b^\lambda W^{1 - \gamma}}{1 - \gamma}</script> for some constant <script type="math/tex">\lambda</script>. That would allow utility to change non-linearly with <script type="math/tex">b</script>, which more accurately describes many real-world situations. For this essay, to keep things simple, I will stick with <script type="math/tex">\lambda = 1</script>.</p>
<p>These assumptions imply that we should mission hedge rather than <a href="#appendix-a-mission-leveraging">mission leverage</a>. But there are related assumptions that suggest we should mission leverage. For example, if we change the third condition to <script type="math/tex">% <![CDATA[
\displaystyle\frac{d^2U}{dW db} < 0 %]]></script>, that means wealth becomes more valuable as the mission target increases, so we should mission leverage.</p>
<p><strong>Why this utility function?</strong></p>
<p>Most of the listed criteria make perfect sense—e.g., of course more wealth is better and more of the mission target is worse. It’s not always true that when the mission target gets worse, our spending becomes more cost-effective. But it’s true in some cases, and those are the cases where we’d want to consider mission hedging.</p>
<p>The weirdest thing about this utility function: it has an upper bound. Why is that? Couldn’t we produce arbitrarily high value for the world if we had sufficient wealth?</p>
<p>A bounded utility function makes sense if we think of ourselves as committed to minimizing the harm of a particular mission target. For instance, there’s an upper bound to how much climate change we can prevent, namely, all of it. If we mitigate 100% of climate change, that provides an upper bound on how much good we can do.</p>
<p>Note: This utility function implies that impact investing doesn’t work—the way you invest doesn’t directly change the world. That might be false, but I’ll treat it as true for now.</p>
<h2 id="some-more-assumptions">Some more assumptions</h2>
<p><strong>The philanthropist doesn’t care about anyone else’s investment portfolio.</strong></p>
<p>In reality, <a href="https://mdickens.me/2022/03/18/altruistic_investors_care_about_aggregate_altruistic_portfolio/">philanthropists should value</a> the investments of other like-minded people. Instead of maximizing the expected utility of their personal portfolio, they should consider the aggregate portfolio across all value-aligned investors. They should invest in whatever way best improves the aggregate portfolio on the margin.</p>
<p>However, it makes more sense to start by modeling what philanthropists should do in the aggregate, and then later use that to figure out what to do on the margin. This post focuses on that first step.</p>
<p><strong>The risk-free rate is 0%.</strong></p>
<p>A more sophisticated model should include a term for the risk-free rate, but it’s simpler to assume that the rate is 0%, and this simplification doesn’t change much.</p>
<p><strong>All random variables are lognormally distributed.</strong></p>
<p>It’s common to assume that asset prices follow <a href="https://en.wikipedia.org/wiki/Log-normal_distribution">lognormal distributions</a>. I also assume that the quantity of mission target is lognormally distributed, which makes sense if it’s something that tends to grow exponentially (CO2 emissions, AI progress, and numbers of farmed animals probably all behave this way).</p>
<p><strong>The MVO asset has an arithmetic mean return of 8% and a standard deviation of 18%.</strong></p>
<p>I could spend all day talking about market expectations, but in short, I believe these numbers appropriately represent an aggressive but appropriately-diversified portfolio (e.g., a global equity index fund).</p>
<p>The optimal degree of mission hedging isn’t determined by the expected return or standard deviation alone, but by the ratio between the two.</p>
<p>(I wrote more about market expectations in <a href="https://mdickens.me/2022/04/01/how_I_estimate_future_investment_returns/">a previous essay</a>.)</p>
<p><strong>The hedge asset has an arithmetic mean return of 0% and a standard deviation of 18%.</strong></p>
<p>By assumption, the MVO asset is the optimal selfish portfolio, and the hedge asset has zero correlation with the MVO asset. That means the optimal selfish portfolio contains no allocation to the hedge, and therefore the hedge asset <em>cannot</em> have an expected return greater than 0%.</p>
<p>If expected return equals 0%, then you can add leverage or mix in cash to get whatever standard deviation you want. I set the standard deviation at 18% so it’s the same as the MVO asset.</p>
<p><strong>The MVO asset has zero correlation to the mission target.</strong></p>
<p>This might not actually be true, but it keeps things simple. To the extent that the MVO asset is positively correlated with the mission target, that makes investing in the MVO asset look more compelling. It does not reduce the optimal allocation to the hedge, but it does reduce the optimal <em>relative</em> allocation. For example, increasing the correlation might change the optimal allocation of (MVO, hedge) from (200%, 30%) to (210%, 30%).</p>
<h2 id="table-of-variables">Table of variables</h2>
<p>The model uses the following variables. <em>m, h, b</em> follow lognormal distributions (and thus their logarithms follow normal distributions), and <em>x</em> can refer to any one of <em>m, h, b</em>.</p>
<table>
<tbody>
<tr>
<td>m</td>
<td>MVO asset price</td>
</tr>
<tr>
<td>h</td>
<td>hedge asset price</td>
</tr>
<tr>
<td>b</td>
<td>mission target</td>
</tr>
<tr>
<td>W</td>
<td>wealth</td>
</tr>
<tr>
<td><script type="math/tex">\alpha_x</script></td>
<td>log(mean of x)</td>
</tr>
<tr>
<td><script type="math/tex">\mu_x</script></td>
<td>mean of log(x) = log(geometric mean of x)</td>
</tr>
<tr>
<td><script type="math/tex">\sigma_x</script></td>
<td>standard deviation of log(x)</td>
</tr>
<tr>
<td><script type="math/tex">\sigma_{xy}</script></td>
<td>covariance between log(x) and log(y)</td>
</tr>
<tr>
<td><script type="math/tex">\rho</script></td>
<td>correlation between log(h) and log(b)</td>
</tr>
<tr>
<td><script type="math/tex">\gamma</script></td>
<td>coefficient of risk aversion</td>
</tr>
<tr>
<td><script type="math/tex">\omega_x</script></td>
<td>proportion of wealth allocated to asset x</td>
</tr>
</tbody>
</table>
<h1 id="results">Results</h1>
<p>We now have a model of the expected utility of mission hedging. What does this model say a philanthropist should do?</p>
<p>That depends on the inputs. This model has four free variables:</p>
<ol>
<li><script type="math/tex">\rho</script>: correlation between the hedge asset and the mission target</li>
<li><script type="math/tex">\gamma</script>: risk aversion</li>
<li><script type="math/tex">\alpha_b</script>: arithmetic mean growth rate of the mission target</li>
<li><script type="math/tex">\sigma_b</script>: standard deviation of the growth rate of the mission target</li>
</ol>
<p>The model outputs are <script type="math/tex">\omega_m</script> and <script type="math/tex">\omega_h</script>: the optimal allocations to the MVO asset and the hedge asset, respectively.</p>
<h2 id="unconstrained-results">Unconstrained results</h2>
<p>In this section, I provide a formula for the solution, then I offer some <a href="#specific-numeric-results">concrete answers</a> for particular numeric inputs.</p>
<h3 id="general-solution">General solution</h3>
<p>The MVO asset’s optimal portfolio allocation <script type="math/tex">\omega_m</script> is given by</p>
<p>\begin{align}
\omega_m = \displaystyle\frac{\alpha_m}{\sigma_m^2 \gamma}
\end{align}</p>
<p>where <script type="math/tex">\alpha_m</script> and <script type="math/tex">\sigma_m</script> are the arithmetic mean and standard deviation of the MVO asset, respectively.</p>
<p>(This is identical to the solution to <a href="https://www.gordoni.com/lifetime_portfolio_selection.pdf">Merton’s portfolio problem</a> for an ordinary investor.)</p>
<p>And optimal hedge allocation <script type="math/tex">\omega_h</script> equals</p>
<p>\begin{align}
\omega_h = \displaystyle\frac{\sigma_{bh}}{\sigma_h^2 \gamma}
\end{align}</p>
<p>where <script type="math/tex">\sigma_{bh}</script> is the covariance of the mission target and the hedge, and <script type="math/tex">\sigma_h</script> is the standard deviation of the hedge.</p>
<p>We could also write this as</p>
<p>\begin{align}
\omega_h = \displaystyle\frac{\rho \sigma_b}{\sigma_h \gamma}
\end{align}</p>
<p>where <script type="math/tex">\sigma_b</script> is the standard deviation of the mission target.</p>
<p>That means the optimal allocation to the hedge asset is proportional to its correlation with the mission target, proportional to the mission target’s standard deviation, and inversely proportional to the standard deviation of the hedge and to the philanthropist’s degree of risk aversion.</p>
<p>(See <a href="#appendix-c-proof-of-analytic-solution">Appendix C</a> for proof.)</p>
<p>Some qualitative observations:</p>
<ul>
<li><script type="math/tex">\omega_m</script> and <script type="math/tex">\omega_h</script> are independent, except that they both depend on risk aversion <script type="math/tex">\gamma</script>.</li>
<li><script type="math/tex">\omega_h</script> increases with <script type="math/tex">\rho</script> and <script type="math/tex">\sigma_b</script>, decreases with <script type="math/tex">\sigma_h</script> and <script type="math/tex">\gamma</script>, and does not change with <script type="math/tex">\alpha_b</script>. This makes intuitive sense:
<ul>
<li>We want to mission hedge more when our hedge is more effective (higher covariance with the mission target), including when the mission target is more volatile.</li>
<li>We want to mission hedge less when the hedge is more volatile. We get more “bang for our buck” with each dollar we put in the hedge, so we don’t need as much.</li>
<li>We want to mission hedge less when we’re more risk-averse, because we prefer a safer (less volatile) portfolio.</li>
</ul>
</li>
<li>It’s perhaps not immediately obvious why <script type="math/tex">\omega_h</script> varies with <script type="math/tex">\sigma_b</script> but not <script type="math/tex">\alpha_b</script>. The explanation is that we’re trying to hedge against future worlds where the mission target is <em>unexpectedly</em> prevalent, which is more likely to happen when <script type="math/tex">\sigma_b</script> is large.<sup id="fnref:9"><a href="#fn:9" class="footnote">6</a></sup> <script type="math/tex">\alpha_b</script> doesn’t affect how the hedge covaries with the mission target.</li>
<li>The optimal relative allocation <script type="math/tex">\displaystyle\frac{\omega_h}{\omega_m + \omega_h}</script> does not depend on risk aversion <script type="math/tex">\gamma</script>. In other words, risk aversion doesn’t change our relative preference for hedging vs. traditional investing.</li>
</ul>
<h3 id="specific-numeric-results">Specific numeric results</h3>
<p>When provided reasonable inputs, what output does this model give?</p>
<p>Within a reasonable range of inputs, the optimal relative allocation to the hedge asset <script type="math/tex">\displaystyle\frac{\omega_h}{\omega_m + \omega_h}</script> falls between 1.7% and 29%. So, at least given the model assumptions described previously, we know that 50% is too much and 0.1% is not enough.</p>
<p>Specifically, I tested input values within these ranges:</p>
<ul>
<li><script type="math/tex">\rho</script> (correlation) from 0.25 (weak hedge) to 0.9 (very strong hedge)</li>
<li><script type="math/tex">\gamma</script> (risk aversion) from 1.1 (approximately logarithmic) to 2 (substantially risk-averse)</li>
<li><script type="math/tex">\sigma_b</script> (mission target volatility) from 3% (highly stable thing, e.g., CO2 emissions<sup id="fnref:6"><a href="#fn:6" class="footnote">7</a></sup>) to 20% (volatile or hard-to-predict thing, e.g., AI progress<sup id="fnref:7"><a href="#fn:7" class="footnote">8</a></sup>)</li>
</ul>
<p>Mission hedging looks most favorable when <script type="math/tex">\rho = 0.9, \sigma_b = 20\%</script>. With those parameters, the optimal portfolio allocates 71% to the MVO asset and 29% to the hedge in relative terms. The absolute allocations depend on <script type="math/tex">\gamma</script>. With <script type="math/tex">\gamma = 1.1</script>, the optimal allocation is 227% MVO, 91% hedge (giving 3.18:1 leverage). <script type="math/tex">\gamma = 2</script> gives 124% MVO, 50% hedge.</p>
<p>(I do think it’s plausible that <script type="math/tex">\sigma_b > 20\%</script> for some causes, so the optimal relative allocation to mission hedging could perhaps be higher than 29%. <script type="math/tex">\sigma_b = 30\%</script> gives a relative allocation of up to 38%.)</p>
<p>Mission hedging looks least favorable when <script type="math/tex">\rho = 0.25, \sigma_b = 3\%</script>. In that case, the optimal relative allocation is 98.3% MVO, 1.7% hedge.</p>
<p>Mission hedging boosts expected utility by 0.01% on the low end and 0.3% on the high end.</p>
<p>It’s still an open question as to whether we should invest closer to 1.7% or closer to 29% in mission hedging. That depends on (a) the correlation between the hedge and the mission target and (b) the volatility of the mission target, which I will leave as questions for future research.</p>
<p>For bigger tables of results, see <a href="#appendix-d-tables-of-optimization-results">Appendix D</a>.</p>
<h2 id="results-with-a-leverage-constraint">Results with a leverage constraint</h2>
<p>All the optimal portfolios so far have required us to use leverage—sometimes a lot of leverage. But many investors can’t, at least not easily. What happens if we constrain the solution to disallow leverage?</p>
<p>This changes the results in one key way: Unless we’re particularly risk-averse, we can’t take on as much risk as we want to. If we want to mission hedge, we have to give up some expected return. That doesn’t mean we should <em>never</em> mission hedge, but it does change the tradeoffs.</p>
<p>Specifically, it means we should allocate 0% to mission hedging unless (a) mission hedging looks particularly compelling (high volatility of the mission target, high correlation) or (b) we’re very risk-averse, to the point that we wouldn’t want to use leverage anyway (given the return/risk expectations I used, this happens when <script type="math/tex">\gamma > 3</script>). At <script type="math/tex">\sigma_b = 20\%, \gamma = 1.5</script>, we only want to mission hedge if <script type="math/tex">r \ge 0.88</script>, which is probably unattainable.</p>
<h2 id="results-with-a-legacy-investment">Results with a legacy investment</h2>
<p>One common scenario: You have a lot of money in some position. It’s <a href="https://mdickens.me/2020/10/18/risk_of_concentrating/">not well-diversified</a>, but you still hold it for historical reasons. Maybe you don’t want to sell all of your legacy asset right away, but you can sell a little bit and invest the proceeds in something else. Should you prioritize mission hedging, or is it better to invest in the mean-variance optimal asset?</p>
<p>Under this model, you should prefer the MVO asset, even given parameters that heavily lean toward mission hedging.<sup id="fnref:10"><a href="#fn:10" class="footnote">9</a></sup> Even if we already invest half our portfolio in the MVO asset (and the other half in the legacy asset), it’s still (slightly) better on the margin to move money into MVO.<sup id="fnref:11"><a href="#fn:11" class="footnote">10</a></sup></p>
<p>This is a much stronger result than what we got from the unconstrained model—the input parameters don’t change the outcome except at the extreme high end.</p>
<h1 id="how-accurate-is-this-model">How accurate is this model?</h1>
<p>Getting results out of a model always requires making a lot of assumptions. And every time you make an assumption, that’s another opportunity for the model to diverge from reality.</p>
<p>My mission hedging framework includes a lot of parameters, which are easy to modify. It also builds in some less-easily-fixable properties, including:</p>
<ol>
<li>This model treats investment returns as lognormal. In reality, investments are more likely to show big declines than a lognormal distribution would suggest. A more accurate model would invest more conservatively, but it’s not clear how this would affect mission hedging. Intuitively, I’d expect an improved model to relatively favor whichever asset has a smaller left skew.</li>
<li>This model uses a particular class of utility functions. These utility functions have certain nice features, for example, the optimal asset allocation doesn’t depend on your time horizon or on how much money you start with. A philanthropist’s real-life utility function probably doesn’t look like the one I used, but real-life utility functions are notoriously difficult to ascertain. (We could perhaps improve the utility function by further investigating how our ability to do good varies with the target we’re trying to hedge.)</li>
<li>This model treats leverage, short positions, and trading as free. But even for investors who can use leverage and shorts, they have to pay some extra cost for those.</li>
<li>This model ignores the direct effects of investing. Buying stock in a company might cause the company to become more successful. And philanthropists might want to prioritize impact investing over mission hedging or profit maximization.</li>
</ol>
<p>The most robust output of this model is the result with a legacy investment: if you currently hold most of your money in a legacy investment, then it’s better on the margin to shift toward the mean-variance optimal portfolio than to shift toward mission hedging. This result held true regardless of how I changed the model parameters (within reason). However, this result still depends on the choice of utility function, and it’s possible to construct a utility function where it’s better on the margin to put funds toward mission hedging.</p>
<p>For an unconstrained portfolio, it’s unclear how much to mission hedge. This model can produce a wide range of numbers depending on input parameters. The choice of risk aversion has a fairly small impact, choice of correlation has a moderate impact, and the standard deviation of the mission target matters a lot.<sup id="fnref:22"><a href="#fn:22" class="footnote">11</a></sup> This suggests that, if we want to know more about what to do, we should prioritize figuring out the mission target’s volatility.</p>
<h1 id="future-work">Future work</h1>
<p>Six ideas for projects that could help philanthropists decide how to mission hedge:</p>
<p><strong>1. What changes would make mission hedging worthwhile on the margin?</strong></p>
<p>The strongest conclusion of my model is that, on the margin, mission hedging is worse than improving the risk-adjusted return of an investment portfolio. This result held across a range of input parameters. What assumptions could break this result? Are those changes reasonable?</p>
<p>If no such changes exist, we can conclude that mission hedging isn’t worth doing in practice.</p>
<p><strong>2. Mission hedging vs. impact investing.</strong></p>
<p>Many philanthropists want to directly do good with their investments. But impact investing often has the exact opposite prescriptions as mission hedging. Does divestment do enough good to damper—or even negate—the benefits of mission hedging? Should we over-weight investments in bad things, or under-weight them? How do we decide?</p>
<p>Jonathan Harris, founder of the <a href="https://total-portfolio.org/">Total Portfolio Project</a>, has <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3939991">done some relevant work</a><sup id="fnref:20"><a href="#fn:20" class="footnote">12</a></sup> on this.</p>
<p><strong>3. Find the specific assets that provide the strongest mission correlation.</strong></p>
<p>What can we invest in to mission hedge various causes? Which ones will work best? Or, in cases where <a href="https://forum.effectivealtruism.org/posts/YApaCr98Q7wSYcaoB/mission-correlation-more-than-just-hedging">mission leverage</a> makes more sense than mission hedging, which assets provide the most effective mission leverage? And how can we tell?</p>
<p>For some causes, like climate change (and maybe farm animal welfare), plenty of data exists, and it’s just a matter of putting it together. For others, there’s not much existing data, so we’d have to get more creative.</p>
<p><strong>4. Optimization over real-world historical data.</strong></p>
<p>Pick some mission target, then get historical data on the growth rate/volatility of that target and find an investment asset that hedged it well. What would the historically optimal portfolio allocation have been?</p>
<p>Using real-world data alleviates certain concerns with using a model. The model assumes asset prices follow lognormal distributions and maintain consistent correlations over time, but those things aren’t true. Optimizing over historical data would show us how asset prices really behave (or, at least, how they used to behave).</p>
<p>Getting this data shouldn’t be too hard to do for some causes. For climate change, we could look at historical annual CO2 emissions, market returns, and returns for some plausibly good hedges like oil company stocks or oil futures.</p>
<p><strong>5. Shape of the utility function.</strong></p>
<p>Does the marginal utility of wealth really increase linearly with the mission target? Maybe it increases with some power function of the mission target, or maybe the relationship is more complicated. What if the mission target is a <em>good</em> thing (see <a href="https://forum.effectivealtruism.org/posts/5hjcGjsmkD4RPmyRF/mission-correlated-investing-examples-of-mission-hedging-and#Mission_leveraging">here</a> for examples)?</p>
<p>My current thinking on this subject is pretty primitive, so I expect there’s room to come up with something a lot better.</p>
<p><strong>6. Alternative approaches for evaluating mission-correlated investing.</strong></p>
<p>Could we look at the value of mission-correlated investing in an entirely different way? What other methods might we use to decide how much of our portfolio (if any) to dedicate to it? Could we decide on a percentage allocation using a qualitative, rather than quantitative, approach?</p>
<h1 id="acknowledgments">Acknowledgments</h1>
<p>Thank you to Jonathan Harris for providing feedback on drafts of this essay.</p>
<h1 id="appendices">Appendices</h1>
<h2 id="appendix-a-mission-leveraging">Appendix A: Mission leveraging</h2>
<p>Mission leveraging is the opposite of mission hedging. With mission hedging, we invest in a way that gives us more money when the world gets worse. With mission leveraging, we get more money when the world gets <em>better</em>, doubling down on our mission instead of hedging it.</p>
<p>I won’t discuss when to hedge vs. leverage in full generality. (See <a href="https://forum.effectivealtruism.org/posts/5hjcGjsmkD4RPmyRF/mission-correlated-investing-examples-of-mission-hedging-and">here</a> for a discussion plus some real-world examples.) But when should we hedge vs. leverage when we’re working with the <a href="#the-utility-function">class of utility functions</a> discussed in this essay?</p>
<p>With any utility function that matches my stated assumptions, we always prefer to mission hedge. But there are similar utility functions under which we’d prefer to leverage.</p>
<p>We can take a utility function with the same form as before:</p>
<p>\begin{align}
U(W, b) = b \displaystyle\frac{W^{1 - \gamma}}{1 - \gamma}
\end{align}</p>
<p>But instead of <script type="math/tex">\gamma > 1</script>, let <script type="math/tex">% <![CDATA[
\gamma < 1 %]]></script>. This changes two of the six stated assumptions:</p>
<ol>
<li>Utility is now bounded below by 0, and has no upper bound.</li>
<li><script type="math/tex">b</script> is now a good thing: utility is positive instead of negative, which means a larger <script type="math/tex">b</script> increases utility rather than decreasing it.</li>
</ol>
<p>Because <script type="math/tex">b</script> is now a good thing, by investing in an asset that’s correlated with <script type="math/tex">b</script>, we are leveraging rather than hedging.</p>
<p>If we want <script type="math/tex">b</script> to be a bad thing, we can write the utility function as <script type="math/tex">\displaystyle\frac{1}{b} \frac{W^{1 - \gamma}}{1 - \gamma}</script>. The <a href="#general-solution">solution</a> with this new utility function becomes:</p>
<p>\begin{align}
\omega_h = -\displaystyle\frac{\sigma_{bh}}{\sigma_h^2 \gamma}
\end{align}</p>
<p>So now, rather than buying the hedge asset, we want to short it. And the higher its covariance with <script type="math/tex">b</script>, the larger our short position should be. In other words, we want to mission leverage.</p>
<p>In broad terms, when utility of wealth grows quickly (<script type="math/tex">% <![CDATA[
\gamma < 1 %]]></script>), we should leverage. And when utility of wealth grows slowly (<script type="math/tex">\gamma > 1</script>), we should hedge.</p>
<p>The exact conditions are:</p>
<ol>
<li>When <script type="math/tex">\frac{dU}{db}</script> is negative, <script type="math/tex">b</script> is a bad thing. When it’s positive, <script type="math/tex">b</script> is a good thing.</li>
<li>When <script type="math/tex">\frac{d^2U}{db dW}</script> has the same sign as <script type="math/tex">\frac{dU}{db}</script>, we want to leverage. When it has an opposite sign, we want to hedge.</li>
</ol>
<h2 id="appendix-b-why-use-this-approach">Appendix B: Why use this approach?</h2>
<p>The model I use in this post is an extension of Harry Markowitz’s <a href="https://en.wikipedia.org/wiki/Modern_portfolio_theory">mean-variance optimization model</a> (see <a href="https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1540-6261.1952.tb01525.x">Markowitz (1952)</a><sup id="fnref:23"><a href="#fn:23" class="footnote">13</a></sup>). Markowitz won a Nobel Prize for this model, and it has been explored extensively in academic finance. At the same time, few investing practitioners use it.</p>
<p>Mean-variance optimization finds the portfolio with the best risk-adjusted return (a.k.a. <a href="https://www.investopedia.com/terms/s/sharperatio.asp">Sharpe ratio</a>) when given a set of assets with known means, standard deviations, and correlations with each other. This approach has some serious downsides:</p>
<ol>
<li>If you feed the model historical data for return/volatility/correlation, the model only tells you what portfolio would have been optimal historically. As William Bernstein put it: “If you can predict the optimizer inputs well enough to come close to the future [optimal portfolio], then you don’t need an optimizer in the first place.”<sup id="fnref:16"><a href="#fn:16" class="footnote">14</a></sup></li>
<li>The Sharpe-ratio-maximizing portfolio is only optimal if standard deviation fully captures what people mean by “risk” (spoiler: it doesn’t).</li>
<li>Often, the resulting portfolio requires using so much leverage that it’s impossible to invest in in practice.</li>
</ol>
<p>Most practitioners prefer other portfolio construction approaches. A simple equal-weight strategy—where you divide your money evenly across every asset class—works pretty well.<sup id="fnref:17"><a href="#fn:17" class="footnote">15</a></sup><sup id="fnref:18"><a href="#fn:18" class="footnote">16</a></sup> However, a few firms (such as <a href="https://rhsfinancial.com/services/investing/">RHS Financial</a>) explicitly use portfolio optimization, but instead of naively inputting historical data, they take a sophisticated approach to generate more reasonable model results.</p>
<p>So mean-variance optimization doesn’t produce good results (at least if applied naively). Why, then, am I extending this model to mission-correlated investing?</p>
<p>One reason is that it’s a good starting point—this model is well-understood, and so a simple extension of it is easy to reason about.</p>
<p>A second reason is that, just as recent research has found more practical variations on the mean-variance approach, so too might we find a modification of my model that fixes the biggest issues. (It might be as simple as taking a published extension to the Markowitz model and incorporating mission-correlated investing.)</p>
<p>But most importantly, it’s because I don’t see how a non-quantitative approach could work. With ordinary investing, you can simply invest in an equal-weighted portfolio and you won’t go too wrong. Or you can use popular rules of thumb like 60% stocks, 40% bonds. But there’s no fallback approach for allocating to mission-correlated investing. Equal-weighting would tell us to put 50% in mission hedging/leveraging, which seems excessive. And we don’t have any convenient rules of thumb, either. Without any strong guiding heuristics, I believe the best approach is to make a bunch of reasonable(ish) assumptions and use those to explicitly calculate the portfolio that maximizes expected utility.</p>
<h2 id="appendix-c-proof-of-analytic-solution">Appendix C: Proof of analytic solution</h2>
<p><em>Thanks to Gordon Irlam’s <a href="https://www.gordoni.com/lifetime_portfolio_selection.pdf">Lifetime Portfolio Selection: A Simple Derivation</a>, which provides a simple proof of the asset allocation result from <a href="http://lifecycleinvesting.net/Resources/merton%20lifetime%20portfolio%20selection%201969.pdf">Merton (1969)</a><sup id="fnref:15"><a href="#fn:15" class="footnote">17</a></sup>, and which I found indispensable in proving the result in this section.<sup id="fnref:12"><a href="#fn:12" class="footnote">18</a></sup></em></p>
<p>Recall that we defined</p>
<p>\begin{align}
U(W, b) = b \displaystyle\frac{W^{1 - \gamma}}{1 - \gamma}
\end{align}</p>
<p>For this proof, let’s generalize this to</p>
<p>\begin{align}
U(W, b) = b^\lambda \displaystyle\frac{W^{1 - \gamma}}{1 - \gamma}
\end{align}</p>
<p>where <script type="math/tex">\lambda</script> determines the rate at which it becomes easier to affect the mission target as the mission target grows.</p>
<p>Wealth is determined by the proportional allocation to the MVO asset and to the hedge asset and the returns of each. Each variable follows a lognormal distribution.</p>
<p>A single-variable lognormal distribution is given by <script type="math/tex">e^{\mu + \sigma N(0,1)}</script> where <script type="math/tex">N(0,1)</script> is a standard normal distribution (with mean 0 and standard deviation 1).</p>
<p><script type="math/tex">b</script> is a lognormal distribution given by <script type="math/tex">\exp(\mu_b + \sigma_b N(0,1))</script>.</p>
<p>Our objective is to maximize expected utility with respect to allocations <script type="math/tex">\omega_m</script> and <script type="math/tex">\omega_h</script>:</p>
<p>\begin{align}
\arg \max\limits_{\omega_m, \omega_h} E\left[b^\lambda \displaystyle\frac{W^{1 - \gamma}}{1 - \gamma}\right]
\end{align}</p>
<p>Expanding <script type="math/tex">b</script> and <script type="math/tex">W</script>, we get</p>
<p>\begin{align}
\arg \max\limits_{\omega_m, \omega_h} E\left[\exp(\lambda \mu_b + \lambda \sigma_b N_b(0,1)) (\exp(\omega_m \mu_m + \omega_m \sigma_m N_m(0,1) + \omega_h \mu_h + \omega_h \sigma_h N_h(0,1)))^{1 - \gamma}\right]
\end{align}</p>
<p>where <script type="math/tex">N_m(0,1), N_h(0,1), N_b(0,1)</script> are all standard normal distributions.</p>
<p>(ignoring the <script type="math/tex">1 - \gamma</script> in the denominator, because scaling by a constant does not change the argmax)</p>
<p>When taking an expected value, we can separate out any independent variables—<script type="math/tex">E[X Y] = E[X] E[Y]</script>. By assumption, <script type="math/tex">m</script> is independent of both <script type="math/tex">b</script> and <script type="math/tex">h</script>. So we can separate this into two maximization problems:</p>
<p>\begin{align}
\arg \max\limits_{\omega_m} E\left[\exp(\omega_m \mu_m + \omega_m \sigma_m N_m(0,1)) \right]
\end{align}</p>
<p>\begin{align}
\arg \max\limits_{\omega_h} E\left[\exp(\lambda \mu_b + \omega_h \mu_h (1 - \gamma) + \lambda \sigma_b N_b(0,1) + \omega_h \sigma_h (1 - \gamma) N_h(0,1)) \right]
\end{align}</p>
<p>The first problem is simply the traditional portfolio optimization problem, which has the solution</p>
<p>\begin{align}
\omega_m = \displaystyle\frac{\mu_m + \frac{1}{2} \sigma_m^2}{\sigma_m^2 \gamma}
\end{align}</p>
<p>If we let <script type="math/tex">\alpha = \mu_m + \frac{1}{2} \sigma_m^2</script>, we can write this as <script type="math/tex">\displaystyle\frac{\alpha_m}{\sigma_m^2 \gamma}</script>. This is convenient in some cases because <script type="math/tex">e^\alpha</script> is the arithmetic mean of a lognormal distribution.</p>
<p>The second maximization problem does not have a pre-existing solution (to my knowledge), so let’s solve it.</p>
<p>If <script type="math/tex">N_b(0,1)</script> and <script type="math/tex">N_h(0,1)</script> have correlation <script type="math/tex">\rho</script>, then the part inside the exponent is a sum of dependent normally distributed random variables. The mean of the sum is simply the sum of the means. The standard deviation of the sum equals</p>
<p>\begin{align}
\sigma_{b + h} = \sqrt{\sigma_b^2 + (\omega_h \sigma_h)^2 + 2 \rho \sigma_b (\omega_h \sigma_h)}
\end{align}</p>
<p>Note that <script type="math/tex">\rho \sigma_b \sigma_h</script> is the covariance between <script type="math/tex">b</script> and <script type="math/tex">h</script>, so we can replace this with <script type="math/tex">\sigma_{bh}</script>.</p>
<p>The expected value of a lognormal distribution parameterized by <script type="math/tex">\mu</script> and <script type="math/tex">\sigma</script> is <script type="math/tex">e^{\mu + \sigma^2/2}</script>. Maximizing this quantity is equivalent to maximizing its logarithm, so we want to find</p>
<p>\begin{align}
\arg \max\limits_{\omega_h} \left[ \lambda \mu_b + \omega_h \mu_h (1 - \gamma) + \frac{1}{2} \lambda^2 \sigma_b^2 + \frac{1}{2} \omega_h^2 \sigma_h^2 (1 - \gamma)^2 + \omega_h \sigma_{bh} (1 - \gamma) \right]
\end{align}</p>
<p>At this point, it is convenient to replace <script type="math/tex">\mu</script> with <script type="math/tex">\alpha - \sigma^2/2</script> (recall that <script type="math/tex">\alpha</script> is the log of the arithmetic mean). In an efficient market, an uncorrelated asset such as a mission hedge has <script type="math/tex">\alpha = 0</script>, which allows us to ignore the <script type="math/tex">\alpha_h</script> term if we want to.</p>
<p>Setting the derivative to 0,</p>
<p>\begin{align}
\displaystyle\frac{dE(U)}{d\omega_h} = \alpha_h (1 - \gamma) - \omega_h \sigma_h^2(1 - \gamma) + \omega_h \sigma_h^2 (1 - \gamma)^2 + \lambda \sigma_{bh} (1 - \gamma) = 0
\end{align}</p>
<p>Solving for <script type="math/tex">\omega_h</script> and simplifying gives</p>
<p>\begin{align}
\omega_h = \displaystyle\frac{\lambda \sigma_{bh} + \alpha_h}{\sigma_h^2 \gamma}
\end{align}</p>
<p>And naturally, for <script type="math/tex">\lambda = 1, \alpha_h = 0</script>, this further simplifies to</p>
<p>\begin{align}
\omega_h = \displaystyle\frac{\sigma_{bh}}{\sigma_h^2 \gamma}
\end{align}</p>
<p>Jonathan Harris wrote an alternative proof <a href="https://link.total-portfolio.org/MCpremia">here</a>, starting from the model he developed in <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3934090">A Framework for Investing in Altruism</a>—which is more general than my model—and plugging in some numbers. His model provides an approximation, not an exact general solution, but the solution happens to be exact in this case.</p>
<h2 id="appendix-d-tables-of-optimization-results">Appendix D: Tables of optimization results</h2>
<p>Results for <script type="math/tex">\sigma_b = 3\%</script></p>
<table>
<thead>
<tr>
<th><script type="math/tex">\rho</script></th>
<th><script type="math/tex">\gamma</script></th>
<th>market</th>
<th>hedge</th>
<th>ratio</th>
</tr>
</thead>
<tbody>
<tr>
<td>0.25</td>
<td>1.1</td>
<td>2.245</td>
<td>0.038</td>
<td>1.7%</td>
</tr>
<tr>
<td> </td>
<td>1.5</td>
<td>1.646</td>
<td>0.028</td>
<td>1.7%</td>
</tr>
<tr>
<td> </td>
<td>2.0</td>
<td>1.235</td>
<td>0.021</td>
<td>1.7%</td>
</tr>
<tr>
<td>0.5</td>
<td>1.1</td>
<td>2.245</td>
<td>0.076</td>
<td>3.3%</td>
</tr>
<tr>
<td> </td>
<td>1.5</td>
<td>1.646</td>
<td>0.056</td>
<td>3.3%</td>
</tr>
<tr>
<td> </td>
<td>2.0</td>
<td>1.235</td>
<td>0.042</td>
<td>3.3%</td>
</tr>
<tr>
<td>0.9</td>
<td>1.1</td>
<td>2.245</td>
<td>0.136</td>
<td>5.7%</td>
</tr>
<tr>
<td> </td>
<td>1.5</td>
<td>1.646</td>
<td>0.100</td>
<td>5.7%</td>
</tr>
<tr>
<td> </td>
<td>2.0</td>
<td>1.235</td>
<td>0.075</td>
<td>5.7%</td>
</tr>
</tbody>
</table>
<p>Results for <script type="math/tex">\sigma_b = 20\%, \gamma = 1.5</script> (note: optimal absolute market allocation for a given <script type="math/tex">\gamma is the same as for</script>\sigma_b = 3\%$$)</p>
<table>
<thead>
<tr>
<th><script type="math/tex">\rho</script></th>
<th>market</th>
<th>hedge</th>
<th>ratio</th>
</tr>
</thead>
<tbody>
<tr>
<td>0.25</td>
<td>1.646</td>
<td>0.185</td>
<td>10.1%</td>
</tr>
<tr>
<td>0.5</td>
<td>1.646</td>
<td>0.370</td>
<td>18.4%</td>
</tr>
<tr>
<td>0.9</td>
<td>1.646</td>
<td>0.667</td>
<td>28.8%</td>
</tr>
</tbody>
</table>
<p>Results for <script type="math/tex">\sigma_b = 30\%, \gamma = 1.5</script></p>
<table>
<thead>
<tr>
<th><script type="math/tex">\rho</script></th>
<th>market</th>
<th>hedge</th>
<th>ratio</th>
</tr>
</thead>
<tbody>
<tr>
<td>0.25</td>
<td>1.646</td>
<td>0.278</td>
<td>14.4%</td>
</tr>
<tr>
<td>0.5</td>
<td>1.646</td>
<td>0.556</td>
<td>25.2%</td>
</tr>
<tr>
<td>0.9</td>
<td>1.646</td>
<td>1.000</td>
<td>37.8%</td>
</tr>
</tbody>
</table>
<p>Results for <script type="math/tex">\sigma_b = 20\%</script>, no leverage allowed (<script type="math/tex">\omega_m + \omega_h = 1</script>), computed by numeric approximation:</p>
<table>
<thead>
<tr>
<th><script type="math/tex">\rho</script></th>
<th><script type="math/tex">\gamma</script></th>
<th>market</th>
<th>hedge</th>
</tr>
</thead>
<tbody>
<tr>
<td>0.25</td>
<td>1.1</td>
<td>1.497</td>
<td>-0.497</td>
</tr>
<tr>
<td> </td>
<td>1.5</td>
<td>1.230</td>
<td>-0.230</td>
</tr>
<tr>
<td> </td>
<td>2</td>
<td>1.048</td>
<td>-0.048</td>
</tr>
<tr>
<td>0.5</td>
<td>1.1</td>
<td>1.370</td>
<td>-0.370</td>
</tr>
<tr>
<td> </td>
<td>1.5</td>
<td>1.138</td>
<td>-0.138</td>
</tr>
<tr>
<td> </td>
<td>2</td>
<td>0.978</td>
<td>0.022</td>
</tr>
<tr>
<td>0.9</td>
<td>1.1</td>
<td>1.177</td>
<td>-0.177</td>
</tr>
<tr>
<td> </td>
<td>1.5</td>
<td>0.992</td>
<td>0.008</td>
</tr>
<tr>
<td> </td>
<td>2</td>
<td>0.869</td>
<td>0.131</td>
</tr>
</tbody>
</table>
<h2 id="appendix-e-numeric-approximation-of-the-optimal-solution">Appendix E: Numeric approximation of the optimal solution</h2>
<p>It is possible to numerically approximate the optimal allocation for any utility function. In this section, I describe how I did this.</p>
<p><em>Epistemic status: Before I started working on this problem, I didn’t understand most of the required math, and I picked it up as I went along. So there’s a reasonable chance that I’m making some mistakes.</em></p>
<p>We want to find the utility-maximizing asset allocation, where:</p>
<ol>
<li>Utility is a two-dimensional function of wealth and the mission target.</li>
<li>There are three lognormally-distributed random variables: price of the MVO asset <script type="math/tex">m</script>, price of the hedge asset <script type="math/tex">h</script>, and quantity of the mission target <script type="math/tex">b</script>.</li>
</ol>
<p>The three variables are parameterized by a length-3 mean vector <script type="math/tex">\mu</script> and a covariance matrix <script type="math/tex">\Sigma</script>, which together describe a three-dimensional multivariate normal distribution. The random variables we care about—<script type="math/tex">m, h, b</script>—are defined as the exponentials of three normally-distributed random variables <script type="math/tex">x_1, x_2, x_3</script>, which together form a vector <script type="math/tex">x</script>. That is, <script type="math/tex">m = e^{x_1}, h = e^{x_2}, b = e^{x_3}</script>.</p>
<p>The probability density function for a three-variable <a href="https://en.wikipedia.org/wiki/Multivariate_normal_distribution">multivariate normal distribution</a> is</p>
<p>\begin{align}
f(x) = \displaystyle\frac{\exp(-\frac{1}{2}(x - \mu)^T \Sigma^{-1} (x - \mu))}{\sqrt{(2\pi)^3 \det(\Sigma)}}
\end{align}</p>
<p>where <script type="math/tex">\Sigma^{-1}</script> is the inverse of the covariance matrix <script type="math/tex">\Sigma</script> and <script type="math/tex">\det(\Sigma)</script> is its <a href="https://en.wikipedia.org/wiki/Determinant">determinant</a>.</p>
<p>Transforming this normal density function into lognormal space according to the <a href="https://www.cs.ubc.ca/~murphyk/Teaching/Stat406-Spring08/homework/changeOfVariablesHandout.pdf">multivariate change of variables formula</a>, letting <script type="math/tex">y = [m, h, b] = \exp(x)</script>, we have</p>
<p>\begin{align}
f(y) = \displaystyle\frac{\exp(-\frac{1}{2}(\log(y) - \mu)^T \Sigma^{-1} (\log(y) - \mu))}{m h b \sqrt{(2 \pi)^3 \det{\Sigma}}}
\end{align}</p>
<p>where <script type="math/tex">\frac{1}{m h b}</script> is the determinant of the Jacobian matrix of <script type="math/tex">y</script>. (<a href="https://math.stackexchange.com/questions/267267/intuitive-proof-of-multivariable-changing-of-variables-formula-jacobian-withou">This Stack Exchange post</a> gives an intuitive explanation of why the change-of-variables formula works this way.)</p>
<p>Let <script type="math/tex">\omega_m, \omega_h</script> be the asset proportions in the MVO asset and the hedge asset, respectively (recall that these can sum to greater or less than 1, and they can be negative). Wealth is then calculated as <script type="math/tex">w = \exp(\omega_m m + \omega_h h)</script>. The mission target <script type="math/tex">b</script> is simply the third value of the random vector <script type="math/tex">y</script>.</p>
<p>Expected utility is given by</p>
<p>\begin{align}
E[U(W, b)] = \int_{-\infty}^\infty U(W, b) f(y) dy
\end{align}</p>
<p>Our goal is to maximize this function.</p>
<p>To solve this problem, I wrote a program to compute expected utility using numerical integration and then perform gradient descent to find the optimal asset proportions.</p>
<p>My numerical integration uses Richardson’s extrapolation formula<sup id="fnref:4"><a href="#fn:4" class="footnote">19</a></sup> with 12 and 24 trapezoids per dimension (up to 24<sup>3</sup> = 13,824 four-dimensional trapezoids per integral). According to my tests, this method is accurate to within 0.02% (e.g., if the true optimal allocation is 10%, this method will give an answer between 9.998% and 10.002%).</p>
<p>I define the trapezoid bounds by first generating evenly-spaced 3D bases for a three-variable i.i.d. standard normal distribution. Then I transform the bounds of these squares according to <script type="math/tex">g(x) = e^{\mu + \sigma x}</script>, where <script type="math/tex">\sigma</script> is the vector of standard deviations for the three variables in <script type="math/tex">x</script>. Then I use these new bounds given by <script type="math/tex">g(x)</script> as the base of each trapezoid. This transformation function assumes the three variables are independent, which they’re not, but I found that this method was accurate enough.</p>
<p>My source code is available <a href="https://github.com/michaeldickens/public-scripts/blob/master/MissionHedging.hs">here</a>.</p>
<h1 id="notes">Notes</h1>
<div class="footnotes">
<ol>
<li id="fn:3">
<p>Brigitte Roth Tran (2019). <a href="https://pubs.aeaweb.org/doi/pdfplus/10.1257/aeri.20180347">Divest, Disregard, or Double Down? Philanthropic Endowment in Objectionable Firms.</a> <a href="#fnref:3" class="reversefootnote">↩</a></p>
</li>
<li id="fn:8">
<p>An allocation of (say) 20% on a risk-adjusted basis means that 20% of the risk of my portfolio comes from mission hedging investments, which is not the same as a 20% allocation. For example, if my normal investments have a 15% standard deviation and my mission hedging investments have a 30% standard deviation, then I should allocate 11% to mission hedging, because 11% * 30% / (11% * 30% + 89% * 15%) = 20%. <a href="#fnref:8" class="reversefootnote">↩</a></p>
</li>
<li id="fn:14">
<p>Technically, “mean-variance optimal” means that if you apply leverage or mix in cash, this portfolio maximizes the arithmetic mean return for any given variance, or (equivalently) minimizes variance for any given mean return. In realistic conditions, you might not want to invest in the MVO portfolio (e.g., because you don’t want to use leverage), so I’m generalizing the term “MVO” to refer to the optimal portfolio from a self-interested standpoint, even if it’s not technically mean-variance optimal. <a href="#fnref:14" class="reversefootnote">↩</a></p>
</li>
<li id="fn:1">
<p>If <script type="math/tex">f(b) = 1</script>, this is equivalent to a standard CRRA utility function (plus a constant). <a href="#fnref:1" class="reversefootnote">↩</a></p>
</li>
<li id="fn:21">
<p>I spoke to an expert in carbon capture, who suggested that the cost of removing CO2 from the atmosphere scales roughly with the square root of atmospheric concentration. As shown by the formula in <a href="#appendix-c-proof-of-analytic-solution">Appendix C</a>, using a square root function instead of a linear function would halve the optimal allocation to mission hedging. But this expert also suggested that higher atmospheric CO2 would drive innovation on carbon removal, bringing the cost down, possibly resulting in a super-linear cost-effectiveness function. For simplicity, I will stick with a linear function for this essay. <a href="#fnref:21" class="reversefootnote">↩</a></p>
</li>
<li id="fn:9">
<p><script type="math/tex">U(W, b)</script> is defined as a CRRA utility function of <script type="math/tex">W</script> scaled linearly by <script type="math/tex">b</script>, and CRRA utility functions are invariant with scale. Changing <script type="math/tex">\alpha_b</script> changes the scaling, but that doesn’t change the optimal allocation. <a href="#fnref:9" class="reversefootnote">↩</a></p>
</li>
<li id="fn:6">
<p>Using <a href="https://datatopics.worldbank.org/world-development-indicators/themes/environment.html">World Bank data</a>, I estimated that CO2 emissions growth has an annual volatility of 3%. <a href="#fnref:6" class="reversefootnote">↩</a></p>
</li>
<li id="fn:7">
<p>I estimated the volatility of AI progress using the Electronic Frontier Foundation’s <a href="https://www.eff.org/ai/metrics">AI Progress Measurement</a> database, which aggregates ML model scores across a variety of benchmarks. I found a standard deviation of growth rate of about 15%. Let’s bump this up to 20% to increase the width of the parameter range. <a href="#fnref:7" class="reversefootnote">↩</a></p>
</li>
<li id="fn:10">
<p><script type="math/tex">\sigma_b=20\%, r=0.9, \gamma=2</script> gives</p>
<script type="math/tex; mode=display">\nabla E[U(\text{MVO}, \text{legacy}, \text{hedge})]_{[0, 1, 0]} = [5.43, -19.9, 3.60]</script>
<p>The gradient is largest in the direction of MVO, which means we maximize expected utility by moving in that direction. <a href="#fnref:10" class="reversefootnote">↩</a></p>
</li>
<li id="fn:11">
<p><script type="math/tex">\sigma_b=20\%, r=0.9, \gamma=2</script> gives</p>
<script type="math/tex; mode=display">\nabla E[U(\text{MVO}, \text{legacy}, \text{hedge})]_{0.5, 0.5, 0} = [3.35, -6.67, 3.33]</script>
<p><a href="#fnref:11" class="reversefootnote">↩</a></p>
</li>
<li id="fn:22">
<p>Technically, optimal allocation varies linearly with both correlation and standard deviation of the mission target. But I have greater uncertainty about the standard deviation, and it can cover a wider range of plausible values. <a href="#fnref:22" class="reversefootnote">↩</a></p>
</li>
<li id="fn:20">
<p>Jonathan Harris (2021). <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3939991">Investing for Impact in General Equilibrium.</a> Working paper. <a href="#fnref:20" class="reversefootnote">↩</a></p>
</li>
<li id="fn:23">
<p>Harry Markowitz (1952). <a href="https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1540-6261.1952.tb01525.x">Portfolio Selection.</a> <a href="#fnref:23" class="reversefootnote">↩</a></p>
</li>
<li id="fn:16">
<p>William Bernstein (1998). The Intelligent Asset Allocator. Kindle location 1082. <a href="#fnref:16" class="reversefootnote">↩</a></p>
</li>
<li id="fn:17">
<p>Victor DeMiguel, Lorenzo Garlappi & Raman Uppal (2007). <a href="http://faculty.london.edu/avmiguel/DeMiguel-Garlappi-Uppal-RFS.pdf">Optimal Versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy?</a> <a href="#fnref:17" class="reversefootnote">↩</a></p>
</li>
<li id="fn:18">
<p>Georg Ch. Pflug, Alois Pichler & David Wozabal (2011). <a href="https://www.tu-chemnitz.de/mathematik/fima/public/publications/JBF.pdf">The 1/N investment strategy is optimal under high model ambiguity.</a> <a href="#fnref:18" class="reversefootnote">↩</a></p>
</li>
<li id="fn:15">
<p>Robert Merton (1969). <a href="http://lifecycleinvesting.net/Resources/merton%20lifetime%20portfolio%20selection%201969.pdf">Lifetime Portfolio Selection Under Uncertainty: The Continuous-Time Case.</a> <a href="#fnref:15" class="reversefootnote">↩</a></p>
</li>
<li id="fn:12">
<p>I didn’t actually find the analytic solution by proving it. I originally wrote a program to numerically compute the optimal allocation. After messing with this program for a while, I discovered that the outputs appeared to change in predictable ways with the inputs, and I wrote down what I believed to be an analytic solution. Then, already having some confidence in the answer, I attempted to prove it. This provided some useful guidance—my original proof contained some mistakes, which I noticed because the result of my proof did not match the formula that I knew empirically to be correct. <a href="#fnref:12" class="reversefootnote">↩</a></p>
</li>
<li id="fn:4">
<p><a href="https://mathforcollege.com/nm/mws/gen/07int/mws_gen_int_txt_romberg.pdf">This site</a> has a good explanation of how it works. In short, if <script type="math/tex">F_n(x)</script> is the numeric integral of a function <script type="math/tex">f(x)</script> using <script type="math/tex">n</script> trapezoids per dimension, then the Richardson estimate is <script type="math/tex">F_n(x) + \frac{1}{3} (F_{2n}(x) - F_n(x))</script>. <a href="#fnref:4" class="reversefootnote">↩</a></p>
</li>
</ol>
</div>
Mon, 04 Apr 2022 00:00:00 -0500
http://mdickens.me/2022/04/04/model_of_mission-correlated_investing/
http://mdickens.me/2022/04/04/model_of_mission-correlated_investing/How I Estimate Future Investment Returns<p>To make informed investing decisions, I want to estimate the future expected return of my portfolio. Markets are unpredictable, and future returns will likely significantly deviate from estimates—AQR <a href="https://www.aqr.com/Insights/Research/Alternative-Thinking/2022-Capital-Market-Assumptions-for-Major-Asset-Classes">believes</a> there’s a 50% chance that 10-year realized equity returns will differ from their predictions by more than 3% per year. Still, it’s helpful to come up with a median guess.</p>
<p>In this post, I explain the projections that I use for my own financial planning.</p>
<!-- more -->
<h2 id="market-returns">Market returns</h2>
<p>For market returns, I look at three institutional forecasts:</p>
<ol>
<li><a href="https://www.aqr.com/Insights/Research/Alternative-Thinking/2022-Capital-Market-Assumptions-for-Major-Asset-Classes">AQR</a></li>
<li><a href="https://interactive.researchaffiliates.com/asset-allocation">Research Affiliates (RAFI)</a></li>
<li><a href="https://advisors.vanguard.com/insights/article/marketperspectivesdecember2021">Vanguard</a></li>
</ol>
<p>They each use somewhat different methodology:</p>
<ol>
<li>AQR uses the <a href="https://en.wikipedia.org/wiki/Dividend_discount_model">dividend discount model</a>, the most standard method of estimating future returns.</li>
<li>RAFI uses the discounted dividend model, but also assumes that valuations tend to revert to the mean (like the <a href="https://awealthofcommonsense.com/2016/09/the-john-bogle-expected-return-formula/">Bogle expected return formula</a>).</li>
<li>Vanguard uses a <a href="https://www.vanguard.ca/documents/vanguard-global-capital-markets-model.pdf">complicated model</a> that incorporates lots of economic factors.</li>
</ol>
<p>(If I’d had to guess in advance which of these three firms uses the most complicated model, I definitely wouldn’t have guessed Vanguard.)</p>
<p>Historical evidence suggests that valuations tend to mean revert, but not reliably. My best-guess estimate would incorporate partial but not complete mean reversion, so I believe it makes sense to take an average of AQR’s and RAFI’s return estimates. I don’t really understand how Vanguard came up with its estimates, but it tends to give numbers in between AQR’s and RAFI’s.</p>
<p>A table of estimates for the 10-year real geometric returns of various asset classes:</p>
<table>
<thead>
<tr>
<th>Asset Class</th>
<th>AQR</th>
<th>RAFI</th>
<th>Vanguard</th>
</tr>
</thead>
<tbody>
<tr>
<td>US equities</td>
<td>3.6%</td>
<td>-0.7%</td>
<td>1.3%</td>
</tr>
<tr>
<td>developed ex-US equities</td>
<td>4.3%</td>
<td>4.4%</td>
<td>4.2%</td>
</tr>
<tr>
<td>emerging equities</td>
<td>5.3%</td>
<td>7.4%</td>
<td>3.2%</td>
</tr>
<tr>
<td>US 10-year Treasuries</td>
<td>-0.8%</td>
<td>0.9%</td>
<td>-0.3%</td>
</tr>
<tr>
<td>commodities</td>
<td>-1.5%</td>
<td>1.4%</td>
<td>N/A</td>
</tr>
</tbody>
</table>
<p>Estimated standard deviations:</p>
<table>
<thead>
<tr>
<th>Asset Class</th>
<th>RAFI</th>
<th>Vanguard</th>
</tr>
</thead>
<tbody>
<tr>
<td>US equities</td>
<td>15.2%</td>
<td>16.7%</td>
</tr>
<tr>
<td>developed ex-US equities</td>
<td>17.2%</td>
<td>18.4%</td>
</tr>
<tr>
<td>emerging equities</td>
<td>20.9%</td>
<td>26.8%</td>
</tr>
<tr>
<td>US 10-year Treasuries</td>
<td>3.3%</td>
<td>4.7%</td>
</tr>
<tr>
<td>commodities</td>
<td>16.3%</td>
<td>N/A</td>
</tr>
</tbody>
</table>
<p>Taking an approximate average of these, I assume a 2% real return for US equities, 4% for developed ex-US, and 5% for emerging markets.</p>
<p>I would also like to know the expected return of the global market portfolio.</p>
<ul>
<li>Vanguard does not provide any such estimate.</li>
<li>RAFI forecasts the global market portfolio to have a 1.5% real return with a 9.2% standard deviation.</li>
<li>AQR forecasts global 60/40 to earn a 2.0% real return (no standard deviation given), and believes that this return can be increased to 3.0% at the same level of risk by adding a little leverage, increasing the weight to bonds and low-volatility equities, and mixing in commodities.</li>
</ul>
<p>We could also look at historical performance. Meb Faber’s <a href="https://www.amazon.com/Global-Asset-Allocation-Survey-Strategies-ebook/dp/B00TYY3F3C">Global Asset Allocation</a> found that from 1973 to 2013, the global market portfolio earned a real return of 5.4% with an 8.8% standard deviation.</p>
<p>I approximated the global market portfolio using data from <a href="https://academic.oup.com/qje/article/134/3/1225/5435538">The Rate of Return on Everything, 1870–2015</a><sup id="fnref:1"><a href="#fn:1" class="footnote">1</a></sup>. I found that from 1950 to 2015 (the time range over which every country has annual data), global 60/40<sup id="fnref:2"><a href="#fn:2" class="footnote">2</a></sup> had a nominal return of 10.3% with a standard deviation of 14.5%.</p>
<p>Putting all these together, my best-guess forecast is a 3% real return with a 9% standard deviation.</p>
<h2 id="factor-premia">Factor premia</h2>
<p>I make investments in certain factors that historically predicted asset returns, including value, momentum, and trendfollowing.</p>
<p><a href="https://www.aqr.com/Insights/Research/Alternative-Thinking/2022-Capital-Market-Assumptions-for-Major-Asset-Classes">AQR</a> and <a href="https://interactive.researchaffiliates.com/smart-beta">RAFI</a> provide projected returns for some factors. (See also <a href="https://www.researchaffiliates.com/content/dam/ra/documents/smart-beta-methodologies.pdf">RAFI methodology</a>.)</p>
<ul>
<li>AQR projects a 0.5% excess return over the benchmark for a market portfolio with a single factor tilt, and 1% excess return for a portfolio with multiple factor tilts.</li>
<li>AQR projects a Sharpe ratio of 0.7–0.8 for a long/short multi-factor portfolio.</li>
<li>RAFI projects a 4–5% excess return for a long-only value strategy and a 1.5–2% excess return for a long-only momentum strategy.</li>
<li>Vanguard projects a 1% excess return for a long-only value strategy, but doesn’t offer any other factor projections.</li>
</ul>
<p>AQR numbers are net of fees and transaction costs. RAFI estimates are net of transaction costs, but don’t account for fees.</p>
<p>None of them provide as much detail as I’d like on how they came up with these numbers. I do think RAFI overestimates value and underestimates momentum because they believe value looks unusually undervalued right now and momentum looks unusually overvalued. But predicting factor performance based on valuation probably doesn’t work as well as they think it does. (For more on factor timing, see <a href="https://www.aqr.com/Insights/Research/Journal-Article/Contrarian-Factor-Timing-is-Deceptively-Difficult">Contrarian Factor Timing Is Deceptively Difficult</a><sup id="fnref:3"><a href="#fn:3" class="footnote">3</a></sup> from AQR.)</p>
<p>And anyway, the way I invest doesn’t match how AQR and RAFI came up with their estimates. I invest in <a href="https://mdickens.me/2021/02/08/concentrated_stock_selection/">concentrated</a>, equal-weighted factor portfolios, which should earn higher returns than the sorts of portfolios AQR and RAFI looked at. Historically, concentrated strategies had 3–4x larger premia than weakly-tilted portfolios. On the other hand, I believe their estimates (especially RAFI’s) are too optimistic. AQR estimates future factor premia by dividing historical premia in half, which I believe is appropriately conservative, but I’m concerned that they underestimate the costs and tail risk of a leveraged long/short portfolio.</p>
<p>I came up with my own projections for concentrated factor returns by following these steps:</p>
<ol>
<li>Run a backtest to find the historical factor premium for a comparable portfolio to the one I invest in.</li>
<li>Subtract fees and expected transaction costs.</li>
<li>Divide the result by two, on the assumption that factors will only work half as well in the future.</li>
</ol>
<p>Why divide historical factor returns in half?</p>
<ul>
<li>We have good reason to expect factors to <a href="https://mdickens.me/2020/11/23/uncorrelated_investing/#will-these-factors-continue-to-work">continue to work</a>.</li>
<li>But they might work less well in the future, simply because investment strategies tend to get worse over time.</li>
<li>To keep it simple, just cut expected returns in half.</li>
</ul>
<p>I get factor exposure through <a href="https://alphaarchitect.com/focusedfactors/">the Alpha Architect ETFs</a>, which I believe are the best on the market for investors like me. They provide backtests of their methodology to 1973. I did my own backtests to 1926 using the <a href="https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html">Ken French Data Library</a>, approximating the methodology as closely as I could, and got similar but slightly worse results (which I believe is explained by a weaker methodology, see footnote<sup id="fnref:10"><a href="#fn:10" class="footnote">4</a></sup>). According to these backtests, concentrated value and momentum indexes each had an 8% premium before costs. With a 0.5% management fee, and conservatively assuming 1.5% transaction costs,<sup id="fnref:4"><a href="#fn:4" class="footnote">5</a></sup> that gives a 6% premium. Then divide this in half to get a 3% expected future premium.</p>
<p>I use equity trendfollowing to reduce market exposure during downtrends, like what the <a href="https://www.etf.com/VMOT">VMOT</a> ETF does. Historical evidence suggests that this does not affect expected return, but it reduces equity volatility from ~16% to ~13%. (This understates the value of trendfollowing because trendfollowing tends to change an investment’s skewness from negative to positive.) See <a href="https://papers.ssrn.com/sol3/Papers.cfm?abstract_id=962461">Faber (2013)</a><sup id="fnref:7"><a href="#fn:7" class="footnote">6</a></sup> for a review of trendfollowing across asset classes. I also performed my own backtests over 80+ years of equity, bond, and commodity data from various sources and got similar results.</p>
<p>In addition, I invest in long/short trendfollowing over commodities and fixed income, similar to what <a href="https://www.etf.com/KMLM">KMLM</a> does. (I don’t invest in KMLM; I have an <a href="https://en.wikipedia.org/wiki/Separately_managed_account">SMA</a> with Alpha Architect where they directly run managed futures, which is more tax- and leverage-efficient.<sup id="fnref:8"><a href="#fn:8" class="footnote">7</a></sup> But if I weren’t doing that, I’d invest in KMLM.) The best data on long/short trendfollowing performance comes from <a href="https://www.trendfollowing.com/whitepaper/Century_Evidence_Trend_Following.pdf">Hurst et al. (2014)</a><sup id="fnref:9"><a href="#fn:9" class="footnote">8</a></sup>, which found a 100-year historical return of 11.2% net of 2-and-20 fees with a 9.7% standard deviation. I’m reluctant to take even half this return as a future expectation because it just seems implausibly high—I expect trendfollowing to work, but not that well.<sup id="fnref:13"><a href="#fn:13" class="footnote">9</a></sup> In my projections, I assume an aggressive long/short trendfollowing strategy will earn 4% real with a 15% standard deviation, but that’s not based on anything concrete.</p>
<p>For volatility projections, there’s no strong reason to expect volatility to change over time—it might go up or down, but neither direction looks more likely than the other. So I’ll simply assume that historical volatility continues.</p>
<p>In summary, I expect <a href="https://www.etf.com/VMOT">VMOT</a> to earn a 6% real return with a 13% standard deviation, for a Sharpe ratio of 0.6.<sup id="fnref:12"><a href="#fn:12" class="footnote">10</a></sup> I expect VMOT + bond/commodity trendfollowing to do somewhat better than this—maybe 5% real with 11% standard deviation.<sup id="fnref:11"><a href="#fn:11" class="footnote">11</a></sup> Remember that, even if this projection is exactly correct ex-ante (which it isn’t), the true number will probably be significantly higher or lower.</p>
<h1 id="notes">Notes</h1>
<div class="footnotes">
<ol>
<li id="fn:1">
<p>Òscar Jordà, Katharina Knoll, Dmitry Kuvshinov, Moritz Schularick & Alan M Taylor (2019). <a href="https://academic.oup.com/qje/article/134/3/1225/5435538">The Rate of Return on Everything, 1870–2015</a> <a href="#fnref:1" class="reversefootnote">↩</a></p>
</li>
<li id="fn:2">
<p>60/40 is supposed to be market cap weighted, but I weighted by GDP instead because the data set doesn’t include market cap. <a href="#fnref:2" class="reversefootnote">↩</a></p>
</li>
<li id="fn:3">
<p>Cliff Asness, Swati Chandra, Antti Ilmanen & Ronen Israel (2017). <a href="https://www.aqr.com/Insights/Research/Journal-Article/Contrarian-Factor-Timing-is-Deceptively-Difficult">Contrarian Factor Timing Is Deceptively Difficult.</a> <a href="#fnref:3" class="reversefootnote">↩</a></p>
</li>
<li id="fn:10">
<p>The Alpha Architect value and momentum ETFs mainly focus on the value and momentum factors (as the names suggest), but they also tilt toward the quality and low-volatility factors, which also show robust predictive power, although not as much as value or momentum. Those additional tilts should increase the excess risk-adjusted return. But the Ken French Data Library does not have the data I’d need to test those tilts. <a href="#fnref:10" class="reversefootnote">↩</a></p>
</li>
<li id="fn:4">
<p>This is comparable to AQR’s estimated transaction costs based on their own live training data,<sup id="fnref:5"><a href="#fn:5" class="footnote">12</a></sup> but (1) AQR (during the sample period) managed about 100x more money than Alpha Architect does and (2) AQR’s strategies rebalanced monthly, and the Alpha Architect funds only rebalance every 3–6 months.</p>
<p>AQR found a realized cost of 0.20% per individual trade. At a typical turnover of 50% per 6 months for value or 50% per 3 months for momentum, that implies an annual trading cost of 0.40% for value and 0.80% for momentum. A significantly smaller firm could probably achieve lower trading costs. <a href="#fnref:4" class="reversefootnote">↩</a></p>
</li>
<li id="fn:7">
<p>Meb Faber (2013). <a href="https://papers.ssrn.com/sol3/Papers.cfm?abstract_id=962461">A Quantitative Approach to Tactical Asset Allocation.</a> <a href="#fnref:7" class="reversefootnote">↩</a></p>
</li>
<li id="fn:8">
<p>You can get something like 10:1 leverage for cheap by buying futures collateralized by your equity holdings (although I don’t have anywhere close to 10:1 leverage). To leverage an ETF, you have to use margin, which is a bit more expensive, and also wasteful because managed futures ETFs hold a lot of cash on their balance sheets, so you’re mostly just paying to get leverage on cash. <a href="#fnref:8" class="reversefootnote">↩</a></p>
</li>
<li id="fn:9">
<p>Brian Hurst, Yao Hua Ooi & Lasse H. Pedersen (2014). <a href="https://www.trendfollowing.com/whitepaper/Century_Evidence_Trend_Following.pdf">A Century of Evidence on Trend-Following Investing.</a> <a href="#fnref:9" class="reversefootnote">↩</a></p>
</li>
<li id="fn:13">
<p>I compared AQR’s <a href="https://www.aqr.com/Insights/Datasets/Time-Series-Momentum-Factors-Monthly">trendfollowing index</a> to the performance of one of AQR’s actual trendfollowing funds, <a href="https://funds.aqr.com/funds/alternatives/aqr-managed-futures-strategy-fund/aqmix">AQMIX</a>. The index performed better by about 3 percentage points per year from 2010 to 2019. I’m not sure why—the performance difference varies a lot from year to year, which suggests that it’s not (entirely) due to transaction costs (or else we’d see consistent underperformance by a ~fixed amount). <a href="#fnref:13" class="reversefootnote">↩</a></p>
</li>
<li id="fn:12">
<p>The Sharpe ratio is the return in excess of cash divided by standard deviation. Right now, the risk-free rate is lower than inflation, so the excess return is greater than the real return by 1 to 2 percentage points. <a href="#fnref:12" class="reversefootnote">↩</a></p>
</li>
<li id="fn:11">
<p>A backtest of this strategy, using Ken French factor data and AQR trendfollowing data, found a real return of 10% with an 11% standard deviation net of estimated fees and trading costs. <a href="#fnref:11" class="reversefootnote">↩</a></p>
</li>
<li id="fn:5">
<p>Andrea Frazzini, Ronen Israel & Tobias J. Moskowitz (2014). <a href="https://www.aqr.com/Insights/Research/Working-Paper/Trading-Costs-of-Asset-Pricing-Anomalies">Trading Costs of Asset Pricing Anomalies.</a> <a href="#fnref:5" class="reversefootnote">↩</a></p>
</li>
</ol>
</div>
Fri, 01 Apr 2022 00:00:00 -0500
http://mdickens.me/2022/04/01/how_I_estimate_future_investment_returns/
http://mdickens.me/2022/04/01/how_I_estimate_future_investment_returns/Can Good Writing Be Taught?<p><em>Epistemic status: Highly speculative; unburdened by any meaningful supporting evidence.</em></p>
<p>I’ve written something like 200 essays for school. Writing those essays did not teach me how to write. Writing for fun taught me how to write.</p>
<p>When I was in high school, I used to complain that the essays I was required to write were both boring and unhelpful, and I’d learn more by writing essays about whatever I wanted. But if my teachers had let students write whatever they wanted, I don’t think most of them would have gotten very far. I don’t think I would have gotten very far, either. There’s a big difference between</p>
<blockquote>
<p>me: I have an idea! I will write about it!</p>
</blockquote>
<p>versus</p>
<blockquote>
<p>teacher: Please have an idea and write about it.</p>
<p>me: What should I write about? I dunno, I guess I could write about X, I can probably force myself to come up with something to say about it.</p>
</blockquote>
<p>Instead of writing something detached from ordinary life, like literary analysis, should high schoolers be taught to write something relevant, like emails?</p>
<p>In fact, I <em>was</em> taught how to write emails in high school (although that was only a small % of what we did), and the teaching was counterproductive. The way my teachers taught me to write emails was significantly wrong, and probably would have hindered my career if I had listened. (As a basic example, they said to always start an email with “Dear [name]”. Nobody starts emails that way in real life.) All the people with jobs who write emails somehow managed to un-learn the anti-lessons that they were taught.</p>
<p>But even if my teachers had taught me how to write emails correctly, it wouldn’t have mattered. If I have to slog through a purposeless assignment that I don’t care about, anything I learn from it doesn’t stick. I only learn from doing things if I’m doing them for a reason.</p>
<p>In conclusion, it’s impossible to force someone to learn good writing. They have to want to write.</p>
Tue, 22 Mar 2022 00:00:00 -0500
http://mdickens.me/2022/03/22/can_good_writing_be_taught/
http://mdickens.me/2022/03/22/can_good_writing_be_taught/Existential Risk Reduction Is Naive (And That's a Good Thing)<p>I see many people criticize existential risk reduction as naive or arrogant. “What, you think you can save the world?”</p>
<p>I’m not going to dispute this. Yes, it’s naive and arrogant, and that’s a good thing.</p>
<p>There are countless movies about saving the world. Lots of people fantasize about saving the world (or, at least, my friends and I did when we were kids, and I still do). Ask any five-year-old child, and they can tell you that saving the world is awesome. But it takes a particularly <a href="https://www.lesswrong.com/posts/9kcTNWopvXFncXgPy/intellectual-hipsters-and-meta-contrarianism">subtle and clever mind</a> to understand that actually, trying to save the world is a silly waste of time.</p>
<p>But actually, the five-year old was correct all along. Saving the world is, in fact, awesome! We should do it!</p>
<p>The mature, adult response is that you can’t save the world, and you should be content with contributing to society in your own small way. I could make some clever argument about scope sensitivity or universalist morality or something, but I don’t need to. You already know that saving the world is awesome. Everybody knows it, they’ve just forgotten.</p>
<p>Climate change is the only mainstream cause that at least has a plausible case for saving the world. And indeed some climate change activists think in those terms. Even though I believe it’s unlikely that mitigating climate change can save the world, it’s still admirable to try. I would like to see more people try. Ask yourself: What could destroy the world, and how do we stop that from happening?</p>
Fri, 18 Mar 2022 00:00:00 -0500
http://mdickens.me/2022/03/18/x-risk_is_naive/
http://mdickens.me/2022/03/18/x-risk_is_naive/Altruistic Investors Care About Other Altruists' Portfolios<p><em><a href="https://mdickens.me/confidence_tags/">Confidence</a>: Highly likely.</em></p>
<p>In some sense, altruists and traditional investors have the same investing goals—they want to own the portfolio with the best balance of return and risk. But self-interested people only care about their own portfolios. If you’re a philanthropist, you also care about other (value-aligned) philanthropists’ portfolios.</p>
<p>When the market goes up, you have more money, and you can donate more to charity. But other altruists also have more money, and they can donate more to charity, so your money isn’t as valuable. Conversely, when markets go down, you have less money to donate at the exact time when charities need funding the most.</p>
<p>That means you should not (necessarily) invest your money in the best overall portfolio. Instead, you should use your investments to move the pool of altruistic money in the direction of optimal.</p>
<p>An illustration:</p>
<p>Alice and Bob both donate to the Against Malaria Foundation (AMF). (For simplicity, let’s say they’re the only two donors.) AMF has diminishing marginal utility of money—once it distributes malaria nets in all the best places, the next round of nets won’t save quite as many lives. So Alice and Bob prefer to invest in a way that will earn good returns but without too much risk. Ideally, they’d both hold something like the total world stock market.</p>
<p>Bob lives in the United States, and he invests all his money in US stocks. Alice could simply buy the global stock portfolio, which is roughly 50% US stocks and 50% international stocks. But that would put their aggregate portfolio at 75% US stocks, 25% international stocks (assuming Alice and Bob have the same amount of money). So AMF is being funded by an investment portfolio that’s overweighted toward US stocks, which adds risk without any reward to compensate.</p>
<p>Alice can fix this by investing her entire portfolio in non-US stocks. Now the aggregate portfolio of AMF donors is 50% US stocks, 50% international stocks, just as it should be. It wouldn’t make sense for someone to hold 0% US stocks in their personal retirement portfolio, but this strategy works for Alice because she’s a philanthropist.</p>
<p>(Of course, Alice could also talk to Bob and persuade him to diversify his investments, which might be an even better idea!)</p>
<p>Now, I’m not trying to say that the global stock market is the best investment, or that Alice did the exact right thing in this scenario. This is just an illustration of a broader point: for an individual altruistic donor, the best investment portfolio <em>on the margin</em> might not be the same thing as the best <em>overall</em> portfolio. And altruists should pick the portfolio that’s best on the margin.</p>
<p><em>(I wrote this post to provide an easy reference for this concept. The concept is not original to me—I originally heard it from Paul Christiano’s <a href="https://rationalaltruist.com/2013/02/28/risk-aversion-and-investment-for-altruists/">Risk aversion and investment (for altruists)</a>.)</em></p>
Fri, 18 Mar 2022 00:00:00 -0500
http://mdickens.me/2022/03/18/altruistic_investors_care_about_aggregate_altruistic_portfolio/
http://mdickens.me/2022/03/18/altruistic_investors_care_about_aggregate_altruistic_portfolio/Should Earners-to-Give Work at Startups Instead of Big Companies?<h2 id="summary">Summary</h2>
<p><em><a href="/confidence_tags">Confidence</a>: Somewhat likely.</em></p>
<p><em>Cross-posted to the <a href="https://forum.effectivealtruism.org/posts/kGbHxYhfqttQZx2QD/should-earners-to-give-work-at-startups-instead-of-big">Effective Altruism Forum</a>.</em></p>
<p>Effective altruist earners-to-give might be able to donate more money if, instead of working at big companies for high salaries, they work at startups and get paid in equity. Startups are riskier than big companies, but EAs care less about risk than most people.</p>
<p>Working at a startup is easier than starting one. It doesn’t pay as well, but based on my research, it looks like EA startup employees can earn more than big company employees in expectation.</p>
<p>Does the optimal EA investment portfolio include a significant allocation to startups? To answer that question, I estimated the expected return and risk of startups by adding up the <a href="#what-factors-determine-the-expected-return-of-startups">following considerations</a>:</p>
<ol>
<li>Find a baseline of startup performance by looking at historical data on VC firm returns.</li>
<li>VC performance is somewhat persistent. EAs can beat the average by working at startups that the top VC firms invest in.</li>
<li>Startup employees get worse equity terms than VCs, but they also don’t have to pay management fees, and they get <a href="https://www.benkuhn.net/optopt/">meta-options</a>. Overall, employees come out looking better than VCs.</li>
<li>Current market conditions suggest that future performance will be worse than past performance.</li>
<li>Startups are much riskier than publicly-traded stocks, and the startup market is moderately correlated with stocks (r=0.7).</li>
</ol>
<p>All things considered, my best guess is that more earners-to-give should consider working at startups.</p>
<!-- more -->
<h2 id="contents">Contents</h2>
<ul id="markdown-toc">
<li><a href="#summary" id="markdown-toc-summary">Summary</a></li>
<li><a href="#contents" id="markdown-toc-contents">Contents</a></li>
<li><a href="#framing-the-problem" id="markdown-toc-framing-the-problem">Framing the problem</a></li>
<li><a href="#the-right-question" id="markdown-toc-the-right-question">The right question</a></li>
<li><a href="#modeling-the-solution" id="markdown-toc-modeling-the-solution">Modeling the solution</a></li>
<li><a href="#what-factors-determine-the-expected-return-of-startups" id="markdown-toc-what-factors-determine-the-expected-return-of-startups">What factors determine the expected return of startups?</a> <ul>
<li><a href="#returns-for-vc-firms" id="markdown-toc-returns-for-vc-firms">Returns for VC firms</a></li>
<li><a href="#returns-for-employees" id="markdown-toc-returns-for-employees">Returns for employees</a></li>
<li><a href="#forecasting-future-returns" id="markdown-toc-forecasting-future-returns">Forecasting future returns</a></li>
<li><a href="#giving-now-vs-later" id="markdown-toc-giving-now-vs-later">Giving now vs. later</a></li>
</ul>
</li>
<li><a href="#putting-together-the-expected-return" id="markdown-toc-putting-together-the-expected-return">Putting together the expected return</a></li>
<li><a href="#risk-and-correlation-of-startups" id="markdown-toc-risk-and-correlation-of-startups">Risk and correlation of startups</a></li>
<li><a href="#leverage" id="markdown-toc-leverage">Leverage</a></li>
<li><a href="#startups-vs-public-equities" id="markdown-toc-startups-vs-public-equities">Startups vs. public equities</a></li>
<li><a href="#startups-vs-an-optimized-public-investment-portfolio" id="markdown-toc-startups-vs-an-optimized-public-investment-portfolio">Startups vs. an optimized public investment portfolio</a></li>
<li><a href="#alternative-predictionless-approach" id="markdown-toc-alternative-predictionless-approach">Alternative: Predictionless approach</a></li>
<li><a href="#alternative-models-are-bad-what-if-we-dont-use-a-model" id="markdown-toc-alternative-models-are-bad-what-if-we-dont-use-a-model">Alternative: Models are bad. What if we don’t use a model?</a></li>
<li><a href="#practical-details" id="markdown-toc-practical-details">Practical details</a></li>
<li><a href="#conclusion" id="markdown-toc-conclusion">Conclusion</a></li>
<li><a href="#areas-for-further-research" id="markdown-toc-areas-for-further-research">Areas for further research</a></li>
<li><a href="#acknowledgements" id="markdown-toc-acknowledgements">Acknowledgements</a></li>
<li><a href="#appendix-a-startups-for-founders-and-investors" id="markdown-toc-appendix-a-startups-for-founders-and-investors">Appendix A: Startups for founders and investors</a></li>
<li><a href="#appendix-b-some-important-tangents" id="markdown-toc-appendix-b-some-important-tangents">Appendix B: Some important tangents</a></li>
<li><a href="#notes" id="markdown-toc-notes">Notes</a></li>
</ul>
<h1 id="framing-the-problem">Framing the problem</h1>
<p>Suppose you’re an effective altruist and you want to donate as much money as possible. Perhaps you’ve heard the arguments that <a href="https://80000hours.org/2012/01/salary-or-startup-how-do-gooders-can-gain-more-from-risky-careers/">EAs should start startups</a>. Starting a startup is a lot of work and requires special skills, so you’d rather not. Maybe you’d like to invest in venture capital, but the really good VC firms won’t accept your money. However, you wouldn’t mind <em>working</em> at a startup. You could also work at a big company that pays a high salary. Which should you choose?</p>
<p>This is how I would think about the problem:</p>
<p>Say a startup offers you an equity package that’s worth $X per year at the current valuation. At the same time, a big company offers you a salary that’s $X higher than your salary would be at the startup. Both compensation packages have the same face value.</p>
<p>If you work at the startup, you get <code>$X</code> per year of equity. Some number of years later, the startup might go public or get acquired, at which point you can sell your equity for <code>$Y</code>. Over that time, your equity earned a return of <code>Y/X</code>.</p>
<p>If you work at the big company, you could invest your extra <code>$X</code> salary in the stock market. Will that investment earn a higher or lower return than the startup equity? Whichever you expect to earn a higher return is the one you should pick. (Well, that’s not really true. Read the next section to find out why not.)</p>
<h1 id="the-right-question">The right question</h1>
<p>Which do we expect to earn a higher return, startups or the public stock market?</p>
<p>We don’t have good data on the historical performance of startup employees. We do have data on VC returns, so we can use that.</p>
<p>“Have VCs historically outperformed the public market?” is the wrong question, because some VCs consistently outperform the average.</p>
<p>“Have top VCs historically outperformed the public market?” is the wrong question, because future expected performance probably isn’t the same as past performance.</p>
<p>“Can we expect top VCs to outperform the public market?” is the wrong question, because startup employees don’t earn the same returns as VCs. Employee equity has a worse liquidation preference than VC equity, but investors in VC firms have to pay fund fees, which employees don’t. And employees have the <a href="https://www.benkuhn.net/optopt/">meta-option</a> to keep vesting when their company does well, or to quit when it does poorly. We can use these considerations to estimate the value of employee equity compared to VC equity.</p>
<p>“Can we expect startup employees to outperform the public market?” is the wrong question, because we need to consider <a href="https://mdickens.me/2020/01/06/how_much_leverage_should_altruists_use/">leverage</a>. Investors in public markets can use leverage to increase their risk and expected return, but startup employees can’t.</p>
<p>“Can we expect startup employees to outperform the leveraged public market?” is the wrong question, because an effective altruist’s goal isn’t to maximize their own portfolio return, it’s to maximize the expected utility of the overall EA portfolio. If no other EAs work at the startup where you choose to work, then you’re adding better diversification than if you invest in the public market.</p>
<p>“Do startup employees contribute more expected utility to the EA portfolio than if they invested in the leveraged public market?” is the wrong question, because if they did work at a big company and invest their salary, they might be able to invest in something better than the broad market. For example, I have <a href="https://mdickens.me/2020/12/14/asset_allocation_for_altruists_with_constraints/">previously discussed</a> investing in concentrated value/momentum/trend portfolios, and I made a rough attempt to calculate the expected utility of doing so. For us to prefer to become startup employees, startups would have to look better than the best possible public investment (whether that’s value/momentum/trend or something else).</p>
<p>“Do startup employees contribute more expected utility to the EA portfolio than if they invested in the optimal set of public investments?” is more or less the right question.</p>
<h1 id="modeling-the-solution">Modeling the solution</h1>
<p>Do startup employees contribute more expected utility to the EA portfolio than if they invested in the optimal set of public investments?</p>
<p>The answer to this depends on two things:</p>
<ol>
<li>How do we model the answer?</li>
<li>What values should we use for the model inputs?</li>
</ol>
<p>#2 is hard. #1 is sort of hard, but luckily, it’s already a solved problem. I described an applicable model in <a href="https://mdickens.me/2020/12/14/asset_allocation_for_altruists_with_constraints/">Asset Allocation and Leverage for Altruists with Constraints</a>. In short, we set up a mean-variance optimization problem where we assume 99% of the capital is controlled by other people, and we can decide how to allocate the remaining 1%. Suppose we can allocate between three investment choices:</p>
<ol>
<li>A typical investment portfolio, such as a stock market index fund</li>
<li>The optimal (ex ante) public investment portfolio</li>
<li>Startups</li>
</ol>
<p>The simplest method is to assume we should put all our money into just one choice. What is the overall expected utility if we put our money into choice 1, choice 2, or choice 3?</p>
<p>If we tell our model the expected returns, standard deviations, correlations between these three portfolios, and a utility function, then the model will spit out the expected utility of each choice.</p>
<p>Let’s say the average EA investment portfolio equals the global equity market, which is at least sort of correct. What’s the expected return and standard deviation of global equities?</p>
<p>We have no idea how equities will perform in the short run. But in the long run, the market’s return is <a href="https://awealthofcommonsense.com/2016/09/the-john-bogle-expected-return-formula/">somewhat predictable</a>. And over long time horizons, volatility stays pretty consistent, so we can simply assume the future standard deviation of global equities equals the historical standard deviation.</p>
<p>Similarly, we can approximate the future standard deviation of startups, and their correlation with global equities, by taking the historical standard deviation and correlation and assuming they will stay the same.</p>
<p>The most difficult input variable is the expected return of startups.</p>
<h1 id="what-factors-determine-the-expected-return-of-startups">What factors determine the expected return of startups?</h1>
<p>How to estimate the expected return of startups for employees:</p>
<ol>
<li>Start with some index of VC returns, such as the <a href="https://www.cambridgeassociates.com/cmb_benchmark_labels/us-venture-capital/">Cambridge Associates Venture Capital Index</a>.</li>
<li>These indexes usually provide returns net of fees. VC investors have to pay fees, but startup employees don’t. Add <a href="https://www.investopedia.com/terms/t/two_and_twenty.asp">2-and-20 fees</a> back in to get the gross return.</li>
<li>Unlike with public market investors, VC firms that beat the market in the past tend to continue to beat the market. Employees can choose to work at startups with funding from top VCs. Add a premium to the expected return to account for this.</li>
<li>Maybe EAs can pick startups better than top VC firms. Possibly add a premium.</li>
<li>Employees get worse equity terms than VCs, so subtract some discount to account for tihs.</li>
<li>Startup employees get <a href="https://www.benkuhn.net/optopt/">meta-options</a>, which VCs don’t get. Add an appropriate premium.</li>
<li>Use the current market environment to forecast how future returns will look compared to past returns. (This is the sketchiest step, so we might skip this and just assume future returns equal historical returns. But I think we don’t want to skip this because we don’t even really know what historical returns were—more on that later.)</li>
<li>Giving now might be better than giving later. If so, that means we shouldn’t compare startups to public investments because public investments aren’t the best thing to do with money. Instead, we should compare startup equity to money donated now.</li>
</ol>
<p>In the next four subsections, let’s break down each of these steps.</p>
<ul>
<li><a href="#returns-for-vc-firms">Returns for VC firms</a> covers steps 1–3;</li>
<li><a href="#returns-for-eas">Returns for EAs</a> covers steps 4–6;</li>
<li><a href="#forecasting-future-returns">Forecasting future returns</a> covers step 7; and</li>
<li><a href="#giving-now-vs-later">Giving now vs. later</a> covers step 8.</li>
</ul>
<h3 id="returns-for-vc-firms">Returns for VC firms</h3>
<p>I used <a href="https://www.cambridgeassociates.com/wp-content/uploads/2020/07/WEB-2020-Q1-USVC-Benchmark-Book.pdf">Cambridge Associates’ Venture Capital Index</a> 2020 report to find the aggregate historical return of VC firms from 1995 to 2018<sup id="fnref:3"><a href="#fn:3" class="footnote">1</a></sup>. According to this data set, VCs had a geometric mean return of 13.1% with a standard deviation of 18.9%. That’s a good starting point.</p>
<p>As the saying goes, a person with one clock always knows what time it is. Someone with two clocks is never quite sure. Cambridge Associates’ <a href="https://www.cambridgeassociates.com/wp-content/uploads/2018/05/WEB-2017-Q4-USVC-Benchmark-Book.pdf">2017 report</a> has data from 1988 to 2016, which gives a geometric mean return of 14.9% and a standard deviation of 17.2%.<sup id="fnref:12"><a href="#fn:12" class="footnote">2</a></sup></p>
<p>According to these data sets, VC experienced several regimes:</p>
<ul>
<li>Strong performance 1988–2000, and especially 1998–2000 at the peak of the tech bubble.</li>
<li>Very bad returns 2001–2003.</li>
<li>Mediocre returns 2004–2013, with a mix of good years and bad years.</li>
<li>Strong returns 2014–2020.</li>
</ul>
<p>The “historical performance of VC” substantially changes depending on which time period you look at. And we don’t know what sort of regime will come next.</p>
<p>Another problem: Other VC return databases give entirely different numbers. For example, I could have used the VentureXpert database, which some (e.g., <a href="http://www.vernimmen.com/ftp/KOCH_S_Research_paper.pdf">Koch (2014)</a><sup id="fnref:1"><a href="#fn:1" class="footnote">3</a></sup>) claim is more accurate. (I used Cambridge Associates purely out of convenience.) Cambridge Associates tends to give higher VC returns than other databases (by a couple percentage points).<sup id="fnref:2"><a href="#fn:2" class="footnote">4</a></sup></p>
<p>I will use the 2020 Cambridge Associates report as a starting point. Just be aware that the startup market will likely behave very differently in the future.</p>
<p>Now let’s convert net returns to gross returns. If we assume VCs usually charge 2-and-20 fees, this step is pretty easy. Using the Cambridge Associates 1995–2018 data, we find a gross historical return of 18.1% with a 23.5% standard deviation.</p>
<p>Some people (especially VCs) like to talk about how the “top quartile” of VC firms persistently beat the market. This is true, but potentially misleading. VC firms who beat the market in year N are more likely than chance to beat the market in year N+1. But top-quartile firms are by no means guaranteed to stay in the top quartile.</p>
<p>How strongly do top-VC returns persist? Data from <a href="https://bfi.uchicago.edu/wp-content/uploads/2020/11/BFI_WP_2020167.pdf">Harris et al. (2020)</a><sup id="fnref:5"><a href="#fn:5" class="footnote">5</a></sup> (1984–2014) is presented in the table below<sup id="fnref:9"><a href="#fn:9" class="footnote">6</a></sup>.</p>
<p>The table uses these terms:</p>
<ul>
<li>IRR = internal rate of return, or the annual return achieved by investors.</li>
<li>PME = public market equivalent, or the total return of VCs relative to the S&P 500 (see <a href="http://web.mit.edu/aschoar/www/KaplanSchoar2005.pdf">Kaplan & Schoar (2005)</a><sup id="fnref:7"><a href="#fn:7" class="footnote">7</a></sup>). For example, if a VC fund earns a total return of 60% and the S&P earns 50% in the same period, then the PME is 60% / 50% = 1.2.</li>
</ul>
<table>
<thead>
<tr>
<th> </th>
<th>IRR</th>
<th>PME</th>
</tr>
</thead>
<tbody>
<tr>
<td>Average VC</td>
<td>14.8%</td>
<td>1.22</td>
</tr>
<tr>
<td>Top-quartile VC, backward-looking</td>
<td>45.3%</td>
<td>2.60</td>
</tr>
<tr>
<td>Top-quartile VC, forward-looking</td>
<td>26.3%</td>
<td>1.70</td>
</tr>
</tbody>
</table>
<p>Results for VC firms 2001–2014:</p>
<table>
<thead>
<tr>
<th> </th>
<th>IRR</th>
<th>PME</th>
</tr>
</thead>
<tbody>
<tr>
<td>Average VC</td>
<td>10.4%</td>
<td>(+)</td>
</tr>
<tr>
<td>Top-quartile VC, backward-looking</td>
<td>30.0%</td>
<td>2.11</td>
</tr>
<tr>
<td>Top-quartile VC, forward-looking</td>
<td>14.7%</td>
<td>1.20</td>
</tr>
</tbody>
</table>
<p>(+) This figure is not provided by Harris et al.</p>
<p>In the full sample (1984–2014), top-quartile VCs retained about half of their outperformance out of sample, although they lost most of their relative outperformance (compared to the S&P 500). In the post-2001 sample, they lost most of their outperformance both in relative and absolute terms, but still showed nonzero persistence.</p>
<p>Harris et al. also did a regression analysis, and found that across all VC firms, one third of PME outperformance persisted.</p>
<p>(Note: Harris et al. used data from <a href="https://www.burgiss.com/">Burgiss</a>, yet another source for VC returns.)</p>
<h3 id="returns-for-employees">Returns for employees</h3>
<p>Almost all startups give preferred shares to VCs and common shares to employees. Normally, preferred shares get a 1x <a href="https://www.investopedia.com/terms/l/liquidation-preference.asp">liquidation preference</a>. That means if the company exits, VCs are guaranteed to get back at least the money they put in before employees get anything. This makes employee equity worth less than it appears.</p>
<p>Example:</p>
<ul>
<li>A startup raises funding at a $100 million valuation. VCs have $20 million of preferred shares; founders and employees have $80 million of common shares.</li>
<li>Later, the startup is acquired for $50 million.</li>
<li>VCs get back their $20 million. That leaves just $30 million to split among the common shareholders. The valuation went down by 50%, but employees lost 62.5% of their equity value.</li>
</ul>
<p>This is basically standard practice. Some startups also give special advantages to VCs. There are lots of ways they can do this, such as:</p>
<ol>
<li>a liquidation preference that’s higher than 1x (e.g., a 2x preference guarantees that VCs get to double their money before employees get anything)</li>
<li>a <a href="https://www.investopedia.com/terms/f/fullratchet.asp">ratchet</a>, which gives VCs protection against dilution at the expense of employees</li>
</ol>
<p>These sorts of conditions are really bad for startup employees. You might just want to avoid any startup that offers terms like these. (If you work at a startup with no sketchy terms, and they raise a new round of funding that introduces sketchy terms, that alone might be enough reason to start looking for a new job.) For more on what to watch out for, read Ben Kuhn’s <a href="https://www.benkuhn.net/terms/">How bad are fundraising terms?</a></p>
<p>Even without any bad terms, employee stock options introduce some other problems:</p>
<ul>
<li>If you don’t exercise your options, they could expire before the company exits.</li>
<li>If you don’t exercise your options and they go up in value, you might have to pay income tax or <a href="https://www.investopedia.com/terms/a/alternativeminimumtax.asp">alternative minimum tax</a> instead of capital gains tax.</li>
</ul>
<p>You can avoid these problems by exercising your options as soon as they vest, or even <a href="https://www.investopedia.com/terms/e/earlyexercise.asp">early exercising</a> if you can. But even if you do exercise, you might end up paying higher taxes when the startup exits because you’ll get pushed into a higher tax bracket. You can (at least partially<sup id="fnref:24"><a href="#fn:24" class="footnote">8</a></sup>) mitigate this by donating the stock instead of selling it.</p>
<p>(A lot of people can’t afford to exercise their employee stock options. Perhaps an EA org could make grants or loans to help EAs exercise their options. That would be difficult to set up and they’d have to carefully vet grant recipients, but maybe it could work.)</p>
<p>According to my rough estimate, a 1x liquidation preference reduces the expected value of common shares by about 10%<sup id="fnref:22"><a href="#fn:22" class="footnote">9</a></sup>. That equates to around 1–2% per year, depending on how long the company takes to exit. Let’s assume a 3% annual discount due to liquidation preference plus tax disadvantage.</p>
<p>Many startups pay below-market compensation by claiming that their equity is underpriced. Don’t buy it. The whole point of working at a startup is that your equity will earn (in expectation) above-market returns. If your employer adjusts for this by giving you less equity, that ruins the (monetary) advantage of working at a startup.</p>
<p>This essay is not about employee equity terms, but it’s an important topic for anyone considering working at a startup. For an in-depth guide, see <a href="https://github.com/jlevy/og-equity-compensation">The Open Guide to Equity Compensation</a> by Joshua Levy et al. For something shorter, I recommend Ben Kuhn’s <a href="https://www.benkuhn.net/offer/">checklist for stock option offers</a>.</p>
<p><a href="https://www.benkuhn.net/optopt/">Startup options are better than they look</a> because employees get “meta-options”: your compensation package gives you the option to vest stock options at the current price for the next four years. If the company does well, you can “exercise” your meta-options by continuing to work there. If it doesn’t do well, you can quit. Neither startup founders nor startup investors can do this.</p>
<p>I piggybacked on <a href="https://github.com/benkuhn/option-val">Ben Kuhn’s meta-option model</a> (my code <a href="https://github.com/michaeldickens/option-val/tree/apr">here</a>) and found that meta-options are worth an extra 16 percentage points of return (!!). I just did a quick calculation and didn’t perform a sensitivity analysis or anything, so this number could be way off, but let’s go with it for now. If correct, this number is so large that working at a startup looks more profitable than starting a startup, unless you believe you’d make for an unusually good entrepreneur.</p>
<p>It’s worth mentioning that you could work at a big company that offers equity compensation, which also behaves like a meta-option—albeit a much less valuable one, because big company stock is not as volatile. Using similar methodology, I found that meta-options at a big company are worth 5 percentage points. That means startup meta-options provide an extra 11 percentage points of value (16% – 5%).</p>
<p>As far as I know, Ben Kuhn invented the concept of meta-options, and no one has ever rigorously analyzed them. My own modification of his program could contain bugs or logical flaws. The value of meta-options <em>could</em> be large enough to dominate every other factor, or they could be worth nothing. This subject strongly warrants a deeper investigation.</p>
<p><div align="center">–––––</div></p>
<p>If we can get around the practical concerns, EAs can easily match the returns of top VC firms by getting jobs at their portfolio companies. Can EAs do even better? Can we outperform VCs at picking winning startups?</p>
<p>Let me say up front that I don’t believe EAs in general can outperform top-quartile VC firms. But when I say I don’t believe it, what I really mean is I assign it less than a 50% probability. So it might still be worth trying.</p>
<p>(To be more precise, I would give an 80% probability that at least a handful of EAs could pick winning startups better than top VCs, but I don’t know how to identify those people in advance.<sup id="fnref:23"><a href="#fn:23" class="footnote">10</a></sup> I’d estimate a 30% chance that, if a group of EAs decide to go work at startups and make a conscious effort to pick winning startups, then they will do better than top-quartile VCs.)</p>
<p>EAs as a group are really smart. But professional investors are also really smart, and the overwhelming majority of them still fail to beat the market. Maybe EAs are smarter? Maybe EAs are more rational or clear-thinking in some way that most professional investors aren’t? I don’t know.</p>
<p>It’s possible that EAs could do a better job than VCs of identifying the best startups. On the other hand, EAs might also do a better job of identifying the best <em>public</em> investments. On the <em>other</em> other hand, startups are hard to invest in, so it might be easier to find underappreciated opportunities. If EAs have an edge in public markets, they probably have an even bigger edge in startups.</p>
<p>I don’t have strong evidence on this either way, so I’m leaning on my prior that almost nobody can beat the market. We do have at least <em>some</em> evidence, but I’m not sure how to interpret it.</p>
<p>The evidence we do have:</p>
<ol>
<li>Over the past few years, EA investors <a href="https://forum.effectivealtruism.org/posts/zA6AnNnYBwuokF8kB/is-effective-altruism-growing-an-update-on-the-stock-of">have beaten the market</a>. This is mostly driven by a single company (FTX), so I don’t know how much we can infer from this.</li>
<li>One person reviewed a few months’ worth of EAs’ proposed investing ideas and found that they had beaten the market over those few months. (I don’t want to go into specifics because this review was not shared publicly, but that’s the gist of it.)</li>
</ol>
<p>In the rest of this essay, I will assume EAs can’t beat top-quartile VCs—not because I am confident that this is true, but because I don’t know how to evaluate the evidence. It could be a good idea to look into this in more depth.</p>
<h3 id="forecasting-future-returns">Forecasting future returns</h3>
<p>As discussed <a href="#historical-returns">above</a>, startup returns tend to vary a lot over time, so past performance does a poor job of predicting future performance. But we can’t choose between two investments (in this case, public investments vs. startups) unless we believe something about how they will perform. So what should we believe?</p>
<ul>
<li>Public US equity and bond markets have unusually low return expectations right now, thanks to high valuations/low yields. When stocks and bonds look bad, money flows into alternatives, including VC. Therefore, it’s reasonable to expect VC to have worse future returns as well.</li>
<li>For the past few years, VCs have been investing much more money than the historical average (<a href="https://www.statista.com/statistics/277501/venture-capital-amount-invested-in-the-united-states-since-1995/">Statista</a>, 2021). Crowdedness suggests low future returns. The only other time we saw similar crowdedness was in the year 2000, which was the beginning of a major losing streak for VC.</li>
<li>Private equity (that is, leveraged buyouts, not VC) has gotten more expensive over the last decade or so (<a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2639647">Chingono & Rasmussen, 2015</a><sup id="fnref:8"><a href="#fn:8" class="footnote">11</a></sup>), which predicts muted future performance. And Harris et al.<sup id="fnref:5:1"><a href="#fn:5" class="footnote">5</a></sup> found that, while top VC firms’ persistence persisted in their whole sample, top private equity firms’ returns stopped persisting after 2001. It’s not clear why private equity’s persistence didn’t persist, but whatever the reason, the same thing might happen to VCs.</li>
</ul>
<p>The outlook for VCs looks worse than usual. The question is, how much worse? Should we expect future returns to be 1 percentage point lower per year? Or 20 percentage points?</p>
<p>Well, how much worse to US equities and bonds look? We can reliably predict bonds’ long-term returns using the yield. 5-year bonds currently yield around 1%, compared to a 1984–2014 average nominal return of 8% (<a href="http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html">Damodaran, 2021</a>).</p>
<p>Stock returns are harder to predict. In the short term, they’re almost impossible to predict, but we can estimate their return over 10+ year periods with reasonable accuracy. Under a more <a href="https://www.investopedia.com/terms/e/efficientmarkethypothesis.asp">EMH</a>-y model that assumes no change in market valuation (e.g., <a href="https://www.aqr.com/Insights/Research/Alternative-Thinking/2021-Capital-Markets-Assumptions-for-Major-Asset-Classes">AQR, 2021</a>), forward-looking US equity return expectations look around 5 percentage points worse than they did from 1984 to 2014 (4% vs. 9% after inflation). According to a model that assumes valuations will revert to their historical average (such as <a href="https://interactive.researchaffiliates.com/asset-allocation#!/?currency=USD&model=ER&scale=LINEAR&terms=REAL">Research Affiliates, 2021</a>), returns look 10 percentage points worse (-1% vs. 9%). The truth is probably somewhere in the middle.</p>
<p>In theory, all asset classes should have the same risk-adjusted return. Startups are riskier than stocks or bonds. So if return expectations for stocks/bonds go down by some amount, expectations for startups should go down by more than that. But we don’t know if this holds in practice, and we don’t even know exactly how risky startups are. If bonds look 7% worse, and stocks look between 5% and 10% worse, then maybe we could assume VC will perform 7% to 10% worse in expectation.</p>
<p>As for top-quartile VCs: according to Harris et al., over the full historical sample, they outperformed average VCs by a full 11 percentage points. In the post-2000 era, they only outperformed by 4 percentage points, and had a public-market equivalent performance of 1.2 (which means they only weakly outperformed the S&P 500). It seems fair to assume that the future for VCs will look more like 2001–2014 than like 1984–2000, as the pre-2000 VC market was probably less efficient. We could simply assume top VCs will perform 4 percentage points better than average VCs going forward. But it’s also possible that the gap between average and top VCs will continue to narrow.</p>
<h3 id="giving-now-vs-later">Giving now vs. later</h3>
<p>Working at a startup is comparable to working for a salary and investing it. But if giving now beats giving later, then you wouldn’t want to invest your salary. Instead, you’d want to donate it right away. This makes working at a startup look worse because you can’t donate your equity until it becomes liquid.</p>
<p>This possibility makes the comparison more difficult, so I will mostly ignore it. It’s not as simple as applying a fixed discount rate to the value of your startup equity. Just be aware that my methodology for comparing startups vs. big companies only works if giving later is at least as good as giving now, at least for the next few years.</p>
<h1 id="putting-together-the-expected-return">Putting together the expected return</h1>
<p>If we combine all the numbers I came up with in the previous section, we get:</p>
<ol>
<li>13% after-fees historical return to VC firms, or 10% after inflation.</li>
<li>15% real historical return before fees.</li>
<li>Add 4% for the persistence of top-quartile VCs, giving 19%.</li>
<li>Add 0% for EAs’ extra outperformance. Still 19%.</li>
<li>Subtract 3% for employee equity terms, giving 16%.</li>
<li>Add 11% for meta-options, giving 27%.</li>
<li>Subtract 9% for the relatively poor market outlook, giving 18%.</li>
<li>Ignore giving now vs. later. Still 18%.</li>
</ol>
<p>Thus, I predict a 18% real return for startup employees who try to maximize their earnings (by working at startups with funding from top VCs, getting good equity terms, and exercising their meta-options when necessary).</p>
<p>How big are the error bars on each of these numbers? In order:</p>
<ol>
<li>Historical return depends a lot on what time period you look at. <strong>Wide error bars.</strong></li>
<li>Calculating before-fees return just requires knowing fees, which are usually 2-and-20. Narrow error bars.</li>
<li>It wouldn’t be too surprising it top-quartile VCs had as much as 11% extra return or as little as 0%. <strong>Wide error bars.</strong></li>
<li>Even if we have good reason to expect EAs to do better at picking startups than top-quartile VCs, it seems unlikely that they could perform <em>much</em> better. Narrow error bars.</li>
<li>Liquidation preference matters relatively little. Narrow error bars.</li>
<li>The concept of meta-options is complicated and has received hardly any attention. My best-guess estimate for their value is very large, but I could be way off. <strong>Extremely wide error bars.</strong></li>
<li>Future performance is really hard to predict, even over long time horizons. <strong>Wide error bars.</strong></li>
</ol>
<p>By my estimate, startup employees’ expected returns could optimistically be as high as 52% (!); or they could be as low as -2%.<sup id="fnref:10"><a href="#fn:10" class="footnote">12</a></sup> (Remember, these are <em>expected</em> returns. <em>Realized</em> returns could fluctuate by much more than this. Startups in aggregate could easily realize a 100% return next year, and I wouldn’t find that surprising, but I would be crazy to <em>expect</em> it to happen.)</p>
<h1 id="risk-and-correlation-of-startups">Risk and correlation of startups</h1>
<p>Expected return alone isn’t what we care about. We really want to know <em>risk-adjusted return</em>.</p>
<p>And we don’t just care about the risk-adjusted return of startups in isolation. We want to know how they fit into a broader EA investment portfolio.</p>
<p>There are two equivalent ways of looking at this:</p>
<ol>
<li>Find the risk of startups, and their correlation to the aggregate EA investment portfolio. Then we can calculate whether EAs on the margin should work at startups instead of big companies.</li>
<li>Find the <a href="https://www.investopedia.com/terms/a/alpha.asp">alpha</a> of startups relative to the EA portfolio. If alpha > 0, that means at least some EAs should work at startups.</li>
</ol>
<p>I will focus on the first because I find it more intuitive. I also calculated the second and got similar results (not presented in this essay).</p>
<p>I’m looking at the risk and correlation of the startup industry, rather than the average risk/correlation of a single startup. We can think of it as a collective decision by many EAs to work at a diversified group of startups, rather than the decision of a single person.</p>
<p>As with expected return, we have no way to know the future risk of startups, or their correlation to the EA portfolio. But with risk and correlation, we get to make some simplifying assumptions.</p>
<p>We can’t learn much about the future return of an asset class by looking at its past return. Markets are reasonably efficient, so if an asset class performs well, more money floods in and performance reverts to the mean. But the efficient market hypothesis doesn’t say <em>risk</em> mean-reverts. Studies show that, at least for public equities, historical volatility is a pretty good predictor of future volatility (e.g., <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3074529">Dreyer & Hubrich, 2017</a><sup id="fnref:25"><a href="#fn:25" class="footnote">13</a></sup>).</p>
<p>Three different data sets all give similar(ish) numbers for startups’ standard deviations:</p>
<table>
<thead>
<tr>
<th>Data Set (Gross)</th>
<th>Standard Deviation</th>
</tr>
</thead>
<tbody>
<tr>
<td>Cambridge Associates, 1988–2016</td>
<td>21.4%</td>
</tr>
<tr>
<td>Cambridge Associates, 1995–2018</td>
<td>23.5%</td>
</tr>
<tr>
<td>Harris et al., 1984–2014</td>
<td>28.5%</td>
</tr>
</tbody>
</table>
<p>Note that, according to Cambridge Associates, top-quartile VCs have higher standard deviations than average VCs (25% or 28%, depending on which time horizon you use). So if we only work at top startups, we should bump these numbers up by a few percentage points. Also, startups don’t have public prices the same way stocks do, and VCs have some leeway to value their portfolios however you want. I expect that they tilt their portfolios toward low volatility to make themselves look better, so the “true” volatility is probably higher.</p>
<p><a href="http://sandhillecon.com/pdf/MeasuringRiskForVentureAndBuyouts.pdf">Woodward (2009)</a><sup id="fnref:13"><a href="#fn:13" class="footnote">14</a></sup> argues that, because startup valuations tend to lag the market, a naive regression doesn’t show the true relationship between startups and public equities. The paper finds that startups have a stock market <a href="https://www.investopedia.com/terms/b/beta.asp">beta</a> of a little over 2, which corresponds to a standard deviation of about 35%.</p>
<p>For correlation, as with standard deviation, we can assume the future looks the same as the past. Historical correlation between startups and public equities was around r=0.7. (My own analysis found a correlation of 0.6, and <a href="http://sandhillecon.com/pdf/MeasuringRiskForVentureAndBuyouts.pdf">Woodward (2009)</a><sup id="fnref:13:1"><a href="#fn:13" class="footnote">14</a></sup> found a correlation of around 0.7–0.8 using more limited data but better methodology. Woodward’s analysis suggests that the naive approach underestimates the true correlation. So let’s use 0.7.)</p>
<h1 id="leverage">Leverage</h1>
<p>Many EA investors probably want to use <a href="https://mdickens.me/2020/01/06/how_much_leverage_should_altruists_use/">leverage</a>. But startup employees can’t leverage their equity: they get however much they get based on their employment contract, and there’s no way to borrow money to get more equity.<sup id="fnref:15"><a href="#fn:15" class="footnote">15</a></sup> Instead of comparing startup equity to a public investment portfolio, we should compare startup equity to an <em>optimally leveraged</em> public investment portfolio (taking into account that leverage typically costs more than theoretical models assume).</p>
<h1 id="startups-vs-public-equities">Startups vs. public equities</h1>
<p>Now that we’ve discussed the main considerations, we can return to the original question: is it better for earners-to-give to work at high-paying companies and invest their salaries in the market, or to work at startups and “invest” in startup equity?</p>
<p>Some additional assumptions:</p>
<ol>
<li>Our goal is to maximize the <a href="https://www.effisols.com/basics/rebal.pdf">geometric return</a> of the overall EA investment portfolio. (This is consistent with logarithmic utility of money.)</li>
<li>We can only invest in two things: public equities or startups.</li>
<li>We control 1% of the EA portfolio. We can’t affect the other 99%.</li>
<li>EAs currently invest all their money in public equities, and none in startups. (The latter is obviously false, but it’s also sort of true: on the margin, earners-to-give can consider working for startups that don’t already have any EAs working for them. That set of startups has 0% EA investment.)</li>
<li>If we buy public investments, we can use up to 2:1 leverage.<sup id="fnref:17"><a href="#fn:17" class="footnote">16</a></sup></li>
<li>Public equities earn an expected real return of 3% with a standard deviation of 16%.<sup id="fnref:14"><a href="#fn:14" class="footnote">17</a></sup></li>
</ol>
<p>Recall from above that we’re giving startup equity an 18% expected real return, a 35% standard deviation, and a 0.7 correlation to public equities.</p>
<p>Our two choices:</p>
<ol>
<li>Work at a big company. Invest our salary in public equities with 2:1 leverage.</li>
<li>Work at a startup.</li>
</ol>
<p>Given all the stated assumptions, working at a startup is more than four times better than working at a big company (37 expected utility vs. 200 expected utility, according to a scaled logarithmic utility function<sup id="fnref:16"><a href="#fn:16" class="footnote">18</a></sup>).</p>
<p>Suppose we hold everything else constant but reduce the expected real return of startups. The return needs to be as low as 1% before the startup looks like the worse choice. (Notice that that’s lower than the 3% expected return of the public stock market, even before accounting for leverage. Startups with a 2% expected return are still (barely) preferable to public equities with a 3% return because we’re assuming startups have a lower correlation to the EA portfolio.) So even under a much more pessimistic projection for startup returns, they still look preferable to big companies.</p>
<h1 id="startups-vs-an-optimized-public-investment-portfolio">Startups vs. an optimized public investment portfolio</h1>
<p>Buying an index of public equities might not be the best way to invest one’s big-company salary. I personally prefer to invest in <a href="https://mdickens.me/2020/11/23/uncorrelated_investing/#factor-investing">concentrated value, momentum, and trend strategies</a>. Some EAs believe cryptocurrency or AI stocks will beat the market. The specifics don’t matter too much. What matters is that if you believe some other investment has substantially better expected performance than a broad index fund, then you should use that other investment as your benchmark instead. And startups need to look better than that benchmark.</p>
<p>My best guess is that a concentrated value/momentum/trend portfolio will earn an expected real return of 6% with a standard deviation of 11%. (Of course, as with my estimates for startup returns, these numbers are not remotely robust.) If we also use 2:1 leverage, then value/momentum trend still looks somewhat worse than startups, although not by a as big of a margin (126 expected utility points vs. 200). If startups returned 10% instead of 18%, then value/momentum/trend would be the better choice.</p>
<h1 id="alternative-predictionless-approach">Alternative: Predictionless approach</h1>
<p>Alternatively, take the same basic model as above, but don’t try to predict the future. Instead, assume asset classes will perform exactly as well in the future as they performed in the past. As I discussed above, this approach has issues—performance fluctuates a lot over time, so past performance doesn’t tell us what will happen in the future. But there’s also something appealing about this method. Trying to predict future performance leaves lots of room for you to bias the outcome toward what you (perhaps subconsciously) want. It’s harder to introduce bias if you just use past performance.<sup id="fnref:11"><a href="#fn:11" class="footnote">19</a></sup></p>
<p>For the predictionless approach, I estimated the expected return to employee equity as:</p>
<ol>
<li>13% after-fees historical return to VC firms, or 10% after inflation</li>
<li>15% real historical return before fees</li>
<li>Subtract 2% for employee liquidation preference, giving 13%</li>
<li>Add 11% for meta-options, giving 24%</li>
<li>Add 4% for the persistence of top-quartile VCs, giving 28%</li>
</ol>
<p>For public equities and for my value/momentum/trend portfolio, instead of making projections, I used the (estimated) historical return after inflation from 1995 to 2018:<sup id="fnref:19"><a href="#fn:19" class="footnote">20</a></sup></p>
<table>
<thead>
<tr>
<th> </th>
<th>Return</th>
<th>Std Dev</th>
</tr>
</thead>
<tbody>
<tr>
<td>Public Equities</td>
<td>9%</td>
<td>19%</td>
</tr>
<tr>
<td>Val/Mom/Trend</td>
<td>15%</td>
<td>12%</td>
</tr>
</tbody>
</table>
<p>The three choices have the following expected utilities:</p>
<ol>
<li>Public equities: 142 utility</li>
<li>Val/Mom/Trend: 288 utility</li>
<li>Startups: 279 utility</li>
</ol>
<p>Startups look preferable to public equities, but slightly worse than value/momentum/trend.</p>
<h1 id="alternative-models-are-bad-what-if-we-dont-use-a-model">Alternative: Models are bad. What if we don’t use a model?</h1>
<p>I love using quantitative models like the one in this essay. I think more people should use them. But most models are bad, including mine. They depend on lots of assumptions, and you can change the model output by making small changes to the assumptions.</p>
<p>How could we reason through this decision <em>without</em> using an explicit model? Let’s review some arguments, both pro- and anti-startup.</p>
<p><strong>Argument from risk preferences:</strong> Most startup employees don’t want to donate all their equity. That makes them much more risk-averse than EAs who work at startups. If they’re acting rationally, we should expect them to demand higher equity to compensate for the risk. Therefore, startup equity should look particularly compelling to EAs.</p>
<p><strong>Argument from inefficiency:</strong> The market for startups is illiquid and has high barriers to entry. We might reasonably expect it to be less efficient than public markets, which means we have a better chance of identifying startups that will outperform.</p>
<p><strong>Argument from investability:</strong> The most reputable VC firms usually don’t accept new investors. Even if they can beat the market, you can’t invest with them, so it doesn’t matter. But there’s nothing stopping you from getting jobs at top VCs’ portfolio companies.</p>
<p><strong>Argument from overpopularity of startups:</strong></p>
<ul>
<li>A lot of people want to work at startups because startups are cool, and they’re willing to accept below-market compensation.</li>
<li>Total VC investment dollars have <a href="https://www.toptal.com/finance/venture-capital-consultants/state-of-venture-capital-industry-2019">increased a lot</a> over the past few years, even though the number of startups hasn’t changed much. So the startup market might be overinflated.</li>
</ul>
<p><strong>Argument from underappreciated risk:</strong> In my experience, almost nobody understands how risky individual startups are. Even medium-sized companies are about <a href="https://mdickens.me/2020/10/18/risk_of_concentrating/">3x as risky</a> as the S&P 500. I don’t have sufficiently granular data on startups, but startup-sized public companies are about 5–6x as volatile as the S&P 500, and my guess is startups are even worse. When I see people discussing the value of startup equity, they almost never properly account for this.</p>
<p><strong>Argument from diversification:</strong> If you get a job at a startup where no other EAs work, you’re adding an entirely new investment to the EA portfolio. That could be a good thing even if that particular investment has a worse expected value than the market. On the other hand, there are <a href="https://mdickens.me/2020/11/23/uncorrelated_investing/">other ways of diversifying</a> that might be better.</p>
<p>These qualitative arguments don’t obviously lean one way or the other. My intuition from my time working at startups and knowing lots of startup employees is that most people overvalue startups and underestimate risk, which means they probably push down the market rate for equity compensation. But even if most startup employees don’t behave consistently with their personal risk appetite, they still might behave more risk-aversely than EAs ought to.</p>
<h1 id="practical-details">Practical details</h1>
<p>If more EAs want to work at startups, there are some ways that people or organizations could support this effort, such as:</p>
<ul>
<li>Maintain a list of startups with funding from top VCs, or startups that look particularly promising for whatever reason.</li>
<li>Coordinate to identify companies that don’t already have EAs working at them, or that might provide the most diversification benefits to the EA portfolio.</li>
<li>Help EAs review employment contracts from prospective employers.</li>
<li>Make loans or grants to EAs to help them exercise stock options as soon as they vest.</li>
<li>Career support/recruiting services for EAs who want to work at startups.</li>
<li>Support for EAs whose startups fail. Maybe even offer some kind of insurance to reduce risk, e.g., if you go work for a startup and it fails, we will pay you to compensate for the earnings you could have had.</li>
<li>Help people negotiate for better equity terms.</li>
</ul>
<p>Some of these ideas are logistically difficult, maybe even impossible. I’m not sure the best way to provide support for earners-to-give who choose to work at startups, but it’s something to consider. I believe it would be valuable if an organization existed that helped EAs with these practical details.</p>
<h1 id="conclusion">Conclusion</h1>
<p>Assuming my model is approximately correct, what type of person might want to work at a startup?</p>
<ul>
<li>Someone who wants to earn to give.</li>
<li>Someone who doesn’t have the right skills or temperament to start a startup, but still might want to work at one.</li>
<li>Someone with special insight into a field who thinks they can identify the most promising companies.</li>
<li>Perhaps someone who can’t invest with leverage, or who doesn’t want to use leverage, but who is comfortable with the risk of startup equity.</li>
</ul>
<p>Who might not want to work at a startup?</p>
<ul>
<li>Someone who’s not comfortable with the risk (equity risk or career risk or both).</li>
<li>Someone who believes they can see particularly good investment opportunities /outside/ of startups, and wants to earn a high salary so they can invest in those other opportunities.</li>
<li>Someone who thinks donating now is significantly better than donating a few years from now, and therefore doesn’t want to wait for startup equity to vest.</li>
</ul>
<p>My analysis suggests that working at a startup has good expected value <strong>under ideal conditions</strong>. If you get a job offer from a startup, remember to pay attention to the <a href="https://www.benkuhn.net/offer/">specifics of the offer</a>:</p>
<ol>
<li>Is your total compensation competitive with what you’d get at a big company? (Taking startup equity at face value)</li>
<li>Does your equity contract include any sketchy terms?</li>
<li>etc. (Too many specifics to list all of them)</li>
</ol>
<h1 id="areas-for-further-research">Areas for further research</h1>
<p>Many subjects warrant a deeper investigation:</p>
<ul>
<li>Historical VC returns</li>
<li>Historical returns earned by startup employees</li>
<li>How employee equity terms affect the value of equity</li>
<li>Value of meta-options</li>
<li>How most startup employees decide where to work—most importantly, how sensitive are they to the value of equity?</li>
<li>Why EAs might or might not expect to beat the market</li>
<li>How Woodward (2009)<sup id="fnref:13:2"><a href="#fn:13" class="footnote">14</a></sup>’s analysis looks if you update it to include more recent data</li>
<li>Relevance of giving now vs. later</li>
<li>Career capital from working at startups. Does working at a startup train you to start a startup or a nonprofit?</li>
<li>Other considerations worth including</li>
</ul>
<h1 id="acknowledgements">Acknowledgements</h1>
<p>Thanks to Linchuan Zhang for commissioning this research project and providing support. Thanks to Charles Dillon for feedback.</p>
<h1 id="appendix-a-startups-for-founders-and-investors">Appendix A: Startups for founders and investors</h1>
<p>This essay has looked at startups from the perspective of employees. How do startups look for other types of people?</p>
<p><strong>Founders:</strong> Similar to employees in many ways. The upside is you get a lot more equity. (<a href="https://web.stanford.edu/~rehall/Hall-Woodward%20on%20entrepreneurship.pdf">Hall & Woodward (2012)</a><sup id="fnref:21"><a href="#fn:21" class="footnote">21</a></sup> found that VC-backed startup founders on average made much more money than salaried employees.) The downside is you have to actually start a startup, which is much harder and may require an entirely different skillset.</p>
<p>Other people have written about whether EAs should start startups:</p>
<ul>
<li>Applied Divinity Studies, <a href="https://applieddivinitystudies.com/billionaire/">Life Advice: Become a Billionaire</a></li>
<li>Mathieu Putz, <a href="https://forum.effectivealtruism.org/posts/m35ZkrW8QFrKfAueT/an-update-in-favor-of-trying-to-make-tens-of-billions-of">An update in favor of trying to make tens of billions of dollars</a></li>
<li>Carl Shulman, <a href="https://80000hours.org/2012/01/salary-or-startup-how-do-gooders-can-gain-more-from-risky-careers/">Salary or startup? How do-gooders can gain more from risky careers</a></li>
<li>Brian Tomasik, <a href="https://reducing-suffering.org/calculator-expected-utility-founding-startup/">Calculator for Expected Utility of Founding a Startup</a></li>
</ul>
<p><strong>VC limited partners:</strong> If you give your money to a VC firm to invest, this is probably worse than being a startup employee (although it does have the advantage that you don’t need to get a new job). You have to pay VC fees and you don’t get meta-options. You do get a better liquidation preference, but that’s usually not worth as much. For a more detailed discussion on investing in VC, see <a href="https://gigaom2.files.wordpress.com/2012/05/vc-enemy-is-us-report.pdf">Mulcahy et al. (2012)</a><sup id="fnref:20"><a href="#fn:20" class="footnote">22</a></sup>.</p>
<p><strong>Angel investors:</strong> If you become an angel investor, you don’t have to pay VC fund fees, but you do have to evaluate startups on your own.</p>
<h1 id="appendix-b-some-important-tangents">Appendix B: Some important tangents</h1>
<p>The points below are all important, but they distract from the thesis of this essay, so I’m not commenting on them in detail.</p>
<ol>
<li>Within the context of my model, some big companies’ compensation packages behave more like startups’. Companies such as Facebook and Google offer equity to employees. Unlike with startups, you can sell the equity as soon as you get it. But you usually have to wait a year, and a big company’s equity grant still behaves like a meta-option.</li>
<li>There are many non-monetary pros and cons to working at a startup. For instance, see <a href="https://danluu.com/startup-tradeoffs/">Big companies vs. startups</a> and <a href="https://forum.effectivealtruism.org/posts/ejaC35E5qyKEkAWn2/early-career-ea-s-should-consider-joining-fast-growing">Early career EA’s should consider joining fast-growing startups in emerging technologies</a>.</li>
<li>An unimportant point that I nonetheless want to address: Startup employees’ equity will get diluted by future fundraising rounds. This doesn’t matter because VCs will get diluted by the same amount, so it doesn’t make employee equity look worse relative to VC equity (unless the employment contract contains sketchy terms around who gets diluted, in which case maybe you shouldn’t work there). Normally, VCs have the option to invest more money in future rounds to negate their dilution, but this also doesn’t matter because it doesn’t change the return on their initial equity purchase.</li>
</ol>
<h1 id="notes">Notes</h1>
<div class="footnotes">
<ol>
<li id="fn:3">
<p>The report includes VC returns up to 2020, but it only includes detailed data up to 2018. So when I did my analysis, I used the 1995–2018 data. <a href="#fnref:3" class="reversefootnote">↩</a></p>
</li>
<li id="fn:12">
<p>Somewhat concerningly, these two data sets show different numbers even for years where they overlap. For example, the 1988–2016 data set quotes a 60.09% return for the year 1996, whereas the 1995–2018 data set claims a 63.46% return for the same year. This discrepancy is at least partially because the 1995–2018 series includes more VC firms, but I haven’t read the Cambridge Associates reports in enough detail to say if that’s the only reason. <a href="#fnref:12" class="reversefootnote">↩</a></p>
</li>
<li id="fn:1">
<p>Koch (2014). <a href="http://www.vernimmen.com/ftp/KOCH_S_Research_paper.pdf">The risk and return of venture capital.</a> <a href="#fnref:1" class="reversefootnote">↩</a></p>
</li>
<li id="fn:2">
<p>Woodward (2009). <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1458050">Measuring risk for venture capital and private equity portfolios.</a> <a href="#fnref:2" class="reversefootnote">↩</a></p>
</li>
<li id="fn:5">
<p>Harris, Jenkinson, Kaplan & Stucke (2020). <a href="https://bfi.uchicago.edu/wp-content/uploads/2020/11/BFI_WP_2020167.pdf">Has Persistence Persisted in Private Equity? Evidence from Buyout and Venture Capital Funds</a> <a href="#fnref:5" class="reversefootnote">↩</a> <a href="#fnref:5:1" class="reversefootnote">↩<sup>2</sup></a></p>
</li>
<li id="fn:9">
<p>Figures are copied or inferred from Harris et al. (2020), Table 1, Table 2, and Table 4. <a href="#fnref:9" class="reversefootnote">↩</a></p>
</li>
<li id="fn:7">
<p>Kaplan & Schoar (2005). <a href="http://web.mit.edu/aschoar/www/KaplanSchoar2005.pdf">Private Equity and Performance: Returns, Persistence, and Capital Flows.</a> <a href="#fnref:7" class="reversefootnote">↩</a></p>
</li>
<li id="fn:24">
<p>At least in the United States, if you donate stock to charity, you can only deduct up to 30% of your income. If you get lucky and make a bunch of money when your startup exits, your startup equity could account for something like 90% of your income. You can only deduct 30%, so you’re stuck paying taxes on the other 60%. <a href="#fnref:24" class="reversefootnote">↩</a></p>
</li>
<li id="fn:22">
<p>Very roughly, a startup has a 70% chance to be worth 0x, 20% chance of 0–1x, and 10% chance of >1x. Liquidation preference only matters in the 0–1x case, where common shares are worth about half as much as their face value.</p>
<p>If you don’t filter out sketchy terms, the appropriate discount is <a href="https://www.benkuhn.net/terms/">more like 36%</a>. <a href="#fnref:22" class="reversefootnote">↩</a></p>
</li>
<li id="fn:23">
<p>Actually, I know a few people who I believe could do a good job of identifying top startups if they took the time to conduct lots of interviews and due diligence. But they’re not going to do that because they’re busy doing other important EA-related activities. <a href="#fnref:23" class="reversefootnote">↩</a></p>
</li>
<li id="fn:8">
<p>Chingono & Rasmussen (2015). <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2639647">Leveraged Small Value Equities.</a> <a href="#fnref:8" class="reversefootnote">↩</a></p>
</li>
<li id="fn:10">
<p>For the optimistic estimate, I assumed: top-quartile VCs’ average out-of-sample return of 26% (or 23% real) fully persists; EAs perform 5% better than top VCs; and meta-options are worth 20% (which follows from optimistic assumptions about how meta-options behave).</p>
<p>For the pessimistic estimate, I assumed: public equity valuations fully mean revert, and startups perform even worse due to higher risk; top quartile VCs’ returns do not persist at all; and meta-options are worthless (probably because there’s some flaw with them that I haven’t thought of). <a href="#fnref:10" class="reversefootnote">↩</a></p>
</li>
<li id="fn:25">
<p>Dreyer & Hubrich (2017). <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3074529">Tail Risk Mitigation with Managed Volatility Strategies.</a> <a href="#fnref:25" class="reversefootnote">↩</a></p>
</li>
<li id="fn:13">
<p>Woodward (2009). <a href="http://sandhillecon.com/pdf/MeasuringRiskForVentureAndBuyouts.pdf">Measuring Risk for Venture Capital and Private Equity Portfolios.</a> <a href="#fnref:13" class="reversefootnote">↩</a> <a href="#fnref:13:1" class="reversefootnote">↩<sup>2</sup></a> <a href="#fnref:13:2" class="reversefootnote">↩<sup>3</sup></a></p>
</li>
<li id="fn:15">
<p>Technically, if you get employee stock options, your equity is leveraged. But the amount of leverage approaches zero as the stock price increases. And most stock options are only a little bit leveraged to begin with. For example, if your company stock was last valued at $4 and you get options with a $1 strike price, that’s only 1.33:1 leverage. If the stock price doubles to $8, now you only have 1.14:1 leverage. <a href="#fnref:15" class="reversefootnote">↩</a></p>
</li>
<li id="fn:17">
<p>In keeping with my <a href="https://mdickens.me/2020/01/06/how_much_leverage_should_altruists_use/#cost-of-leverage">previous work</a> on leverage, I assume that borrowers must pay 1% plus the risk-free rate. <a href="#fnref:17" class="reversefootnote">↩</a></p>
</li>
<li id="fn:14">
<p>This is the average of the projections by AQR and Research Affiliates as of October 2021. <a href="#fnref:14" class="reversefootnote">↩</a></p>
</li>
<li id="fn:16">
<p>The utility function takes the geometric mean return as the utility and multiplies by 100,000 to make the numbers more readable. As a baseline, it calculates the expected utility of the EA portfolio without your investment, and then subtracts that from the total expected utility of the EA portfolio including your investment. <a href="#fnref:16" class="reversefootnote">↩</a></p>
</li>
<li id="fn:11">
<p>Still not impossible, because you could pick the data set or the time series that most closely matches the outcome you want. <a href="#fnref:11" class="reversefootnote">↩</a></p>
</li>
<li id="fn:19">
<p>For public equities, I used the historical return of the total US stock market, assuming zero fees or trading costs. To find the historical return of Val/Mom/Trend, I created a hypothetical portfolio that invested 80% in Alpha Architect’s Value Momentum Trend Index and 20% in AQR’s Managed Futures Index, which roughly reflects how I actually invest my money. Both indexes subtract estimated fees and trading costs. The historical returns are hypothetical, not actual. I didn’t have data for 2018, so I calculated summary statistics over 1995–2017 instead. <a href="#fnref:19" class="reversefootnote">↩</a></p>
</li>
<li id="fn:21">
<p>Hall & Woodward (2012). <a href="https://web.stanford.edu/~rehall/Hall-Woodward%20on%20entrepreneurship.pdf">The Burden of the Nondiversifiable Risk of Entrepreneurship.</a> <a href="#fnref:21" class="reversefootnote">↩</a></p>
</li>
<li id="fn:20">
<p>Mulcahy, Weeks & Bradley (2012). <a href="https://gigaom2.files.wordpress.com/2012/05/vc-enemy-is-us-report.pdf">We Have Met the Enemy…and He Is Us: Lessons from Twenty Years of the Kauffman Foundation’s Investments in Venture Capital Funds and the Triumph of Hope over Experience.</a> <a href="#fnref:20" class="reversefootnote">↩</a></p>
</li>
</ol>
</div>
Fri, 12 Nov 2021 00:00:00 -0600
http://mdickens.me/2021/11/12/ea_work_at_startups/
http://mdickens.me/2021/11/12/ea_work_at_startups/Obvious Investing Facts<p><em>Last updated 2022-02-10.</em></p>
<p>Many investors, even professionals, are ignorant about obvious facts that they really should know. When I say a fact is “obvious”, what I mean is that you can easily observe it by looking at widely-available data using simple statistical tools.</p>
<p>A list of obvious but underappreciated facts:</p>
<p><strong>Fact 1. A single large-cap stock is about 2x as volatile as the total stock market.</strong> A small-cap stock is about 4x as volatile. It’s common knowledge that individual stocks are risky, but most people don’t know how to quantify the risk, and I believe they tend to underestimate it. I wrote <a href="https://mdickens.me/2020/10/18/risk_of_concentrating/">a whole essay</a> about this because I think it’s the most important underappreciated investing fact.</p>
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<p><strong>Fact 2. A basket of 50 randomly-chosen stocks isn’t much more volatile than the total stock market.</strong> This is kind of the opposite of fact 1. According to my backtest,<sup id="fnref:7"><a href="#fn:7" class="footnote">1</a></sup> the total US stock market had an annual standard deviation of 17.3%, whereas a randomly-chosen selection of 50 stocks had a standard deviation of 20.2%.<sup id="fnref:1"><a href="#fn:1" class="footnote">2</a></sup> That’s higher, but not by much.</p>
<p>Baskets of 30 stocks had standard deviations of 21.7%; 10 stocks had 25.5%; 5 stocks had 31.9%.</p>
<p>(For more on this, see Elton & Gruber (1977), <a href="http://pages.stern.nyu.edu/~eelton/papers/77-oct.pdf">Risk Reduction and Portfolio Size: An Analytic Solution.</a>)</p>
<p>My anecdote about this: When I was considering opening a donor-advised fund (DAF), I had phone calls with a few investment advisors who I thought might do a good job of managing it. I remember one advisor in particular who I liked at first because she said she was a fan of value and momentum investing. I asked her if she could invest my DAF in a concentrated portfolio of about 60 value stocks, like I describe in <a href="https://mdickens.me/2021/02/08/concentrated_stock_selection/">this essay</a>. She declined, saying that a 60 stock portfolio would be far riskier than the broad stock market, and without any extra expected return to compensate. This is obviously false if you simply look at the data. A randomly-chosen collection of 60 stocks is a little riskier than the broad market, but not much riskier. And it’s true that there’s no reason to take on risk if there’s no benefit, but if you’re specifically investing in value and momentum strategies, then historically, concentration risk also brought higher return, as I <a href="https://mdickens.me/2021/02/08/concentrated_stock_selection/">showed previously</a>.</p>
<p><strong>Fact 3. Stocks can underperform bonds for 30+ years at a time.</strong> Investment manager Meb Faber <a href="https://mebfaber.com/2020/02/18/expectations-investing/">wrote an article about this</a>, inspired by two amusing Twitter polls:</p>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr">What stretch of underperformance by stocks vs. bonds would you be willing to tolerate before selling your stock allocation?</p>— Meb Faber (@MebFaber) <a href="https://twitter.com/MebFaber/status/1225480365726261249?ref_src=twsrc%5Etfw">February 6, 2020</a></blockquote>
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<blockquote class="twitter-tweet"><p lang="en" dir="ltr">Would you be willing to invest in an asset that historically outperforms bonds by a few percentage points per year, but has, multiple times, generated zero outperformance for stretches lasting over 30 years?</p>— Meb Faber (@MebFaber) <a href="https://twitter.com/MebFaber/status/1225557434728620033?ref_src=twsrc%5Etfw">February 6, 2020</a></blockquote>
<p>53% of investors said they would not tolerate 10 years of stocks underperforming bonds. What did they do from 2000 to 2010, when US stocks performed worse than US bonds? (Bonds have beaten stocks many times, but 2000 to 2010 is such a recent decade that you’d think people would remember it.) Fully 76% of respondents said they wouldn’t tolerate 30 years of underperformance. So either they don’t invest in stocks at all (unlikely), or they don’t know that stocks have in fact underperformed bonds for 30 years on more than one occasion.</p>
<p><strong>Fact 4. Bonds are pretty risky after adjusting for inflation.</strong> US short-term T-bills—supposedly the safest investment around—have experienced a historical drawdown of –49% after inflation. On another fun Twitter poll by Meb Faber, <a href="https://mebfaber.com/2020/03/05/the-stay-rich-portfolio/">only 36% of respondents</a> guessed that the drawdown was worse than –45%. (Meb Faber’s Twitter is a great source of underappreciated investing facts.)</p>
<p><strong>Fact 5. The last 3–5 years of performance (of a fund or asset class) tell you almost nothing about future performance.</strong> For instance, see Hoffstein (2016), <a href="https://blog.thinknewfound.com/2016/04/3-year-track-records-meaningful/">Are 3-year track records meaningful?</a></p>
<p>And yet, <a href="https://blog.thinknewfound.com/2016/08/finding-7-5-returns/">89% of managers would replace an investment strategy that has underperformed for 3 years</a>. And when investment managers switch strategies after a period of poor performance, <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1523736">the new strategy tends to perform worse than the old one would have</a><sup id="fnref:10"><a href="#fn:10" class="footnote">3</a></sup>.</p>
<p><strong>Fact 6. Buybacks are financially equivalent to dividends.</strong> Many investors like dividends but dislike buybacks. But these are just two different ways of returning capital to shareholders. In an efficient market, if a company buys back 2% of its shares and then you sell 2% of your holdings, that’s exactly the same as if the company paid a 2% dividend. Conversely, if the company pays you a 2% dividend and you use that money to buy more shares, that’s exactly the same as if the company did a 2% buyback. These scenarios are slightly different for tax purposes, but in financial terms, they’re identical.</p>
<h2 id="sort-of-obvious-but-controversial-facts">Sort-of-obvious but controversial facts</h2>
<p>These facts in this section are less obviously true, either because they come from theoretical models that don’t necessarily hold in practice, or they rely on mixed empirical data. But I believe they’re still underappreciated, and it’s somewhat surprising just how underappreciated they are among investment professionals.</p>
<p><strong>Fact 6. Actively-managed mutual funds are just as risky as index funds.</strong> I don’t know if this is a common misconception among ordinary investors, but I frequently hear investment professionals claim that actively-managed funds are less risky than index funds, or that they perform better in market drawdowns. The evidence on this is mixed, but generally doesn’t look promising for the actively-managed funds (e.g., see <a href="https://www.vanguardcanada.ca/documents/7-myths.pdf">Vanguard (2018)</a>, specifically Myth #5).<sup id="fnref:3"><a href="#fn:3" class="footnote">4</a></sup></p>
<p>I could be wrong about this one, because the evidence isn’t great either way. But the mutual fund managers who confidently claim that they can reduce risk are definitely not standing on solid ground.</p>
<p>“It is difficult to get a man to understand something, when his salary depends on his not understanding it.” Most people know by now that active mutual funds don’t outperform index funds. So in an attempt to justify their existence, investment managers claim that they provide value by reducing risk. This is (probably) false, but it’s not as well-known that it’s false, so they think they can get away with it.</p>
<p><strong>Fact 7. If the efficient market hypothesis and <a href="https://www.investopedia.com/terms/c/capm.asp">CAPM</a> are strictly true, then the mean-variance-efficient portfolio is the global market portfolio.</strong><sup id="fnref:5"><a href="#fn:5" class="footnote">5</a></sup> Not the S&P 500. Not 60/40. Not global equities.</p>
<p>Maybe this fact isn’t exactly obvious—figuring it out required inventing new math. But it was proven over half a century ago, and the man who proved it went on to win a Nobel Prize in economics, in large part <a href="https://www.nobelprize.org/prizes/economic-sciences/1990/press-release/">thanks to precisely this result</a>. You’d think it would be more well-known by now.</p>
<p>A weaker version of this fact: if you want international exposure, buy a world stock market fund. Don’t buy a US market fund and then claim you’re getting international exposure because some US companies sell internationally. I’ve seen many investing professionals recommend the latter (including <a href="https://en.wikipedia.org/wiki/John_C._Bogle">Jack Bogle</a>). History shows that an international stock index is not perfectly correlated to a US index, so you can trivially get better diversification by buying internationally.</p>
<p><strong>Fact 8. In theory, the best way to increase expected return is by using leverage, not by increasing the ratio of stocks to bonds.</strong> This isn’t an empirical fact, but it easily follows from <a href="https://www.investopedia.com/terms/c/capm.asp">CAPM</a>, the standard theory of investment risk. CAPM makes some assumptions that don’t hold in practice. But under certain real-life conditions, it does indeed make sense to use leverage than rather than overweight risky assets. A few sophisticated investors, such as <a href="https://en.wikipedia.org/wiki/Bridgewater_Associates">Bridgewater Associates</a>, abide by this principle, but the vast majority of investors don’t.</p>
<p>(Bridgewater pioneered <a href="https://www.investopedia.com/terms/r/risk-parity.asp">risk parity</a> investing, where you allocate to each asset class such that each asset class exposes you to equal risk, and then add leverage. Risk parity is theoretically optimal when every asset class has the same <a href="https://www.investopedia.com/terms/s/sharperatio.asp">risk-adjusted return</a>.)</p>
<p><strong>Fact 9. Gold is not a great inflation hedge.</strong><sup id="fnref:6"><a href="#fn:6" class="footnote">6</a></sup> Many people claim that gold can hedge inflation, and there are reasonable theoretical reasons to expect it to. But gold is very volatile, and it frequently performs poorly even in times of high inflation. It might still make a good addition to a portfolio, but it doesn’t provide the straightforward inflation protection that a lot of people believe it does.</p>
<p><strong>Fact 10. Art has not outperformed the stock market.</strong> Art sellers like to claim that art is a great investment (e.g., <a href="https://robbreport.com/shelter/art-collectibles/investing-art-stock-2874901/">1</a>, <a href="https://www.forbes.com/sites/bardenprisant/2020/03/27/the-art-market-is-beating-the-stock-market/">2</a>), and they cite studies showing the returns to classic art. These results are <a href="https://www.gsb.stanford.edu/insights/research-art-good-investment">due to selection bias</a><sup id="fnref:4"><a href="#fn:4" class="footnote">7</a></sup><sup id="fnref:9"><a href="#fn:9" class="footnote">8</a></sup>. You can only measure an artwork’s change in value if it gets sold once and then sold again later. And art only tends to get re-sold when its value goes up, so your sample excludes most of the artwork that depreciated over time.</p>
<h2 id="obvious-facts-that-are-becoming-more-well-known">Obvious facts that are becoming more well-known</h2>
<p>20 or 30 years ago, most people didn’t know these facts. but fortunately, they’ve become more widely understood in recent years.</p>
<p><strong>Fact 9. High fees are really bad.</strong></p>
<p><strong>Fact 10. Actively-managed funds generally can’t outperform index funds.</strong></p>
<p>Many people know these facts, and the market for low-fee index funds is growing rapidly. Even so, about 2/3 of investment dollars still reside in expensive actively-managed mutual funds, so we have a long way to go.</p>
<h2 id="some-more-facts">Some more facts</h2>
<p>AQR has written three papers about investing facts and fictions. Most of AQR’s facts are obvious in the sense that you can easily verify them using empirical data. They’re somewhat less obvious than the facts above in that they’re about more specific types of investments, rather than the general behavior of markets.</p>
<p>Their three papers (PDF warning):</p>
<ol>
<li><a href="https://images.aqr.com/-/media/AQR/Documents/Journal-Articles/JPM-Fact-Fiction-and-Momentum-Investing.pdf">Fact, Fiction and Momentum Investing</a> (2014)</li>
<li><a href="https://images.aqr.com/-/media/AQR/Documents/Journal-Articles/JPM-Fact-Fiction-and-Value-Investing.pdf">Fact, Fiction and Value Investing</a> (2015)</li>
<li><a href="https://www.aqr.com/-/media/AQR/Documents/Whitepapers/Fact-Fiction-and-the-Size-Effect.pdf">Fact, Fiction and the Size Effect</a> (2018)</li>
</ol>
<h2 id="why-do-so-many-investment-professionals-not-know-these-obvious-facts">Why do so many investment professionals not know these obvious facts?</h2>
<p>I’m not sure. I can see two common themes:</p>
<ol>
<li>Investment professionals believe things because they can make more money by believing them, not because they’re true.</li>
<li>Investment professionals don’t look at empirical data, so regardless of how obvious an empirical fact might be, they will never notice it.</li>
</ol>
<p>One possible explanation is that when people think they know something, they don’t feel the need to look into it. For example, if you “know” that bonds are safe after adjusting for inflation, why would you look up their historical performance? Even so, that would mean financial professionals don’t make a habit of looking at simple data that’s relevant to their work, which seems bad. Or, like, you’d think this information would propagate. Somebody tweets about an obvious but little-known fact; their followers realize how wrong they were, and tell their colleagues about it; those colleagues tell their other colleagues; and pretty soon, everybody knows. (I must admit that I didn’t know bonds had experienced a –49% drawdown until I read Meb Faber’s tweet, so I’m also guilty of not looking at obvious data sometimes.)</p>
<p>(I do think professional credentials provide a positive signal, at least. In my experience, <a href="https://en.wikipedia.org/wiki/Chartered_Financial_Analyst">CFAs</a> are more likely to know these obvious facts.)</p>
<p>Maybe experts in most fields don’t know obvious facts. I don’t know much about most fields, so I can’t say. The two areas that I know a lot about are computer science and investing (and I know more about computer science because I studied it in college). In my experience, there aren’t a lot of obvious computer science misconceptions among programmers/computer scientists (unless I also believe all the common misconceptions).</p>
<p>Maybe investment advisors aren’t the right reference class for “experts”. Maybe the experts are the people publishing academic papers on investing.<sup id="fnref:8"><a href="#fn:8" class="footnote">9</a></sup> I’d guess that academics in finance know obvious facts more often than investment advisors do.</p>
<p>Sometimes, people don’t know important facts, but they behave correctly anyway. I frequently hear people touting advice such as, “pick an investment allocation and stick with it no matter what.” You might come up with this advice if you knew that stocks can underperform bonds for 30 years at a time, and that 3–5 years of historical performance tells you almost nothing about future performance. And many people follow this advice even without knowing those facts. If they end up doing the right thing, it doesn’t really matter if they know why they’re doing it. On the other hand, almost everyone behaves incorrectly in other ways—<a href="https://mdickens.me/2017/03/26/do_investors_put_too_much_stock_in_the_us/">overweighting their home country stock</a>, or <a href="https://mdickens.me/2020/10/18/risk_of_concentrating/">holding on to concentrated investments for too long</a>.</p>
<p>(This reminds me of <a href="https://slatestarcodex.com/2013/12/17/statistical-literacy-among-doctors-now-lower-than-chance/">Statistical Literacy Among Doctors Now Lower Than Chance</a>: doctors perform depressingly poorly on the Bayes mammogram problem, but when they get a positive test result in real life, they still do the correct thing—rather than jumping to conclusions, they order more tests.)</p>
<h1 id="notes">Notes</h1>
<div class="footnotes">
<ol>
<li id="fn:7">
<p>My analysis took about two hours, which is long enough that someone wouldn’t do it on a whim, but short enough that I still think it’s fair to describe the result as “obvious”. <a href="#fnref:7" class="reversefootnote">↩</a></p>
</li>
<li id="fn:1">
<p>My methodology:</p>
<ol>
<li>Each year from 1973 to 2013, choose 50 stocks uniformly at random.</li>
<li>Simulate a portfolio that buys the chosen stocks, weighted by market cap.</li>
<li>Calculate the standard deviation over the portfolio’s annual total return.</li>
<li>Repeat 100 times and take the arithmetic mean of all the standard deviations.</li>
</ol>
<p>The standard error was 0.17 percentage points. <a href="#fnref:1" class="reversefootnote">↩</a></p>
</li>
<li id="fn:10">
<p>Stewart, Neumann, Knittel & Heisler (2009). <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1523736">Absence of Value: An Analysis of Investment Allocation Decisions by Institutional Plan Sponsors.</a> <a href="#fnref:10" class="reversefootnote">↩</a></p>
</li>
<li id="fn:3">
<p>Ptak (2018), <a href="https://www.morningstar.com/articles/852864/will-active-stock-funds-save-your-bacon-in-a-downturn">Will Active Stock Funds Save Your Bacon in a Downturn?</a> found that actively-managed funds did tend to outperform in drawdowns, but not by enough (in the author’s opinion) to make up for their overall bad performance.</p>
<p>What I’d really like to see is how much <a href="https://www.investopedia.com/terms/a/alpha.asp">alpha</a> mutual funds have in up or down markets, but I haven’t found any research on that.</p>
<p>See also <a href="https://www.onedayinjuly.com/active-vs-passive-in-down-markets">financial advisor Josh Kruk’s take</a> on the matter. He did his own analysis and found that active funds did not outperform in down markets. <a href="#fnref:3" class="reversefootnote">↩</a></p>
</li>
<li id="fn:5">
<p>Sharpe (1964). <a href="https://onlinelibrary.wiley.com/doi/full/10.1111/j.1540-6261.1964.tb02865.x">Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk.</a> <a href="#fnref:5" class="reversefootnote">↩</a></p>
</li>
<li id="fn:6">
<p>Erb, Harvey & Viskanta (2020). <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3667789">Gold, the Golden Constant, COVID-19, ‘Massive Passives’ and Déjà Vu.</a> <a href="#fnref:6" class="reversefootnote">↩</a></p>
</li>
<li id="fn:4">
<p>Korteweg, Kräussl & Verwijmeren (2013). <a href="https://www.gsb.stanford.edu/faculty-research/working-papers/does-it-pay-invest-art-selection-corrected-returns-perspective">Does It Pay to Invest in Art? A Selection-Corrected Returns Perspective.</a> <a href="#fnref:4" class="reversefootnote">↩</a></p>
</li>
<li id="fn:9">
<p>Disclosure: The linked article did not convince me that classic art returns are due to selection bias. Rather, I was confident <em>a priori</em> that the apparent high returns came from selection bias, and this was the first empirical result I found that supported my prior hypothesis. <a href="#fnref:9" class="reversefootnote">↩</a></p>
</li>
<li id="fn:8">
<p>Successful day traders and quants are experts in some sense, but their work doesn’t actually have much in common with the way most people invest. <a href="#fnref:8" class="reversefootnote">↩</a></p>
</li>
</ol>
</div>
Fri, 29 Oct 2021 00:00:00 -0500
http://mdickens.me/2021/10/29/obvious_investing_facts/
http://mdickens.me/2021/10/29/obvious_investing_facts/Future Funding/Talent/Capacity Constraints Matter, Too<p><em>Last updated 2021-10-20.</em></p>
<p>People who talk about talent/funding/capacity constraints mostly talk about what’s the biggest constraint <em>right now</em>. But it also matters what the constraints will be later.</p>
<p>Right now, the EA community holds a lot of wealth—more wealth than it can productively spend in the next few years, at least on smaller cause areas such as AI safety, cause prioritization research, and wild animal welfare. Those newer fields need time to scale up so they can absorb more funding.</p>
<p>That doesn’t mean EAs should stop earning to give. Maybe most EAs could do more good <em>this year</em> with their direct efforts than with their donations. But perhaps 10 years from now, the smaller causes will have scaled up a lot, and they’ll be able to deploy much more money. Earners-to-give can invest their money for a while, and then deploy it once top causes develop enough spending capacity.</p>
<!-- more -->
<p>Even if top cause areas don’t currently have the capacity to spend more money, earning-to-give still looks valuable if three conditions all hold:</p>
<ol>
<li>The capacity:funding ratio will greatly increase in the future.</li>
<li>The money spent in high-capacity organizations will still produce a lot of utility per dollar.</li>
<li>The discount rate isn’t too much higher than the investment rate of return.</li>
</ol>
<p>In general, I believe it should be easier to grow capacity than to grow funding. By comparison, it’s not uncommon for startups to double the number of employees year over year. Charitable organizations usually can’t grow like startups, but they can at least get within the same ballpark.</p>
<p>Over the past few years, <a href="https://forum.effectivealtruism.org/posts/zA6AnNnYBwuokF8kB/is-effective-altruism-growing-an-update-on-the-stock-of">funding has grown faster than capacity</a>, not the other way around. So I could be wrong.</p>
<p>Once capacity grows, will orgs still be able to do a lot of good per dollar? They will use up the best giving opportunities first, so by the time capacity expands, the remaining opportunities won’t be as good. How much difference does that make? It depends on how much it costs to solve the world’s most important problems. If it cost a lot, we will still need lots of money. If it doesn’t cost much (relatively speaking), then future dollars will be worth much less than dollars today.</p>
<p>Is the discount rate high enough that we should care substantially less about future funding? I don’t think so. (What we actually care about is the discount rate minus the investment rate, because the investment rate determines how much money we will have in the future if we invest it now.) The altruistic discount rate minus the investment rate might be around 5% on the high end (it’s probably less than that, and it could be negative). I would be surprised if we couldn’t grow capacity <em>much</em> more quickly than 5% per year. So this factor is unlikely to be decisive.</p>
<p>My personal predictions on the three conditions:</p>
<ol>
<li>The capacity:funding ratio will indeed greatly increase in the future. <a href="/confidence_tags">Confidence</a>: Likely.</li>
<li>I don’t know how quickly the value of money will decrease over time. My best guess is that all current EA funds combined are not enough to solve the world’s biggest problems, so we will need as much additional funding as we can get. Confidence: Possible.</li>
<li>The discount rate is low enough that it doesn’t affect the outcome of this question. Confidence: Highly likely.</li>
</ol>
<p>Ultimately, this argument doesn’t tell us much about whether any particular person should go into direct work or earning to give. And even if earning to give looks valuable, it might still be true that, in general, more people should be doing direct work.</p>
<h2 id="appendix-some-related-but-distinct-arguments">Appendix: Some related but distinct arguments</h2>
<p><strong>The first argument:</strong></p>
<blockquote>
<ol>
<li>Altruists have a low discount rate.</li>
<li>[some other premises]</li>
<li>Therefore, they should give later rather than now.</li>
<li>Therefore, earning to give is good.</li>
</ol>
</blockquote>
<p>(Phil Trammell presents an argument like this <a href="https://forum.effectivealtruism.org/posts/amdReARfSvgf5PpKK/phil-trammell-philanthropy-timing-and-the-hinge-of-history">here</a>)</p>
<p>This is a related argument in the sense that it considers the value of marginal dollars now vs. later. But the argument I presented does not require altruists to have a low discount rate.</p>
<p><strong>The second argument:</strong></p>
<blockquote>
<ol>
<li>There is an optimal percentage of resources for the community to spend vs. invest in a given year.</li>
<li>The community may end up spending above this level in the future.</li>
<li>If that happens, having people switch to earning to save may be one of the best ways to deal with it.</li>
</ol>
</blockquote>
<p>(source: Ben Todd, <a href="https://forum.effectivealtruism.org/posts/J5aYvsiLoAC46DSuY/an-argument-for-keeping-open-the-option-of-earning-to-save">An argument for keeping open the option of earning to save</a>)</p>
<p>Like my argument, this argument also considers present vs. future constraints. But it’s talking about the tradeoff between spending and investing for people who are <em>already</em> earning to give, not about the choice to earn money vs. do direct work.</p>
Mon, 18 Oct 2021 00:00:00 -0500
http://mdickens.me/2021/10/18/future_talent_funding_constraints/
http://mdickens.me/2021/10/18/future_talent_funding_constraints/Low-Hanging (Monetary) Fruit for Wealthy EAs<p><em><a href="/confidence_tags">Confidence</a>: Likely.</em></p>
<p><em>Cross-posted to the <a href="https://forum.effectivealtruism.org/posts/2McPz3d3gr7gSoFFQ/low-hanging-monetary-fruit-for-wealthy-eas">Effective Altruism Forum</a>.</em></p>
<p>Ordinary wealthy people don’t care as much about getting more money because they already have a lot of it. So we should expect to be able to find overlooked methods for rich people to get richer.<sup id="fnref:2"><a href="#fn:2" class="footnote">1</a></sup> Wealthy effective altruists might value their billionth dollar nearly as much as their first dollar, so they should seek out these overlooked methods.</p>
<p>If someone got rich doing X (where X = starting a startup, excelling at a high-paying profession, etc.), their best way of making money on the margin might not be to do more X. It might be to do something entirely different.</p>
<p>Some examples:</p>
<p>Sam Bankman-Fried increased his net worth by $10,000,000,000 in four years by founding FTX. He earned most of those zeroes by doing the hard work of starting a company, and there’s no shortcut around that. But, importantly, he managed to retain most of his original stake in FTX. For most founders, by the time their company is worth $10 billion or more, they only own maybe 10% of it. If Sam had given away a normal amount of equity to VCs, he might have only gotten $2 billion from FTX instead of $10 billion. In some sense, 80% of the money he earned from FTX came purely from retaining equity.<sup id="fnref:4"><a href="#fn:4" class="footnote">2</a></sup></p>
<!-- more -->
<p>(Bill Gates might be another person who got richer than usual by retaining ownership.<sup id="fnref:3"><a href="#fn:3" class="footnote">3</a></sup>)</p>
<p>Warren Buffett is an investing genius. But if he had <em>only</em> been an investing genius, he would have made a lot less money. In addition to earning high investment returns, he borrowed money at below-market interest rates using <a href="https://www.shortform.com/blog/insurance-float-warren-buffett/">insurance float</a>. That let him compound his returns much faster than he otherwise would have.</p>
<p><a href="https://en.wikipedia.org/wiki/Long-Term_Capital_Management">Long-Term Capital Management</a> was an extremely successful hedge fund (at least until it blew up, but let’s not talk about that part). Much of its success didn’t come from its trading strategies, but from the fact that it negotiated unusually favorable deals with its banking partners.</p>
<p>A quasi-example: Instead of trying to make more money, try to (legally) pay less tax. This idea is not exactly overlooked, so it’s not a central example of what I’m talking about. But I <em>have</em> noticed that most “normal-level” rich people (with between $1 million and $10 million) don’t pay nearly enough attention to taxes. I know a lot of people who could save $10,000 to $100,000 per year with 20 hours of work or less.</p>
<p>In these examples, it’s not necessarily that the person (or company) came up with a trick that nobody else had thought of. Obviously every startup founder would love to retain as much of their stock as they can. But they usually have to choose between giving up equity and running out of funding, and they rightly choose to keep their company alive. My point isn’t that it’s easy. My point is that, <em>on the margin</em>, EA founders should probably pay more attention to retaining equity. Maybe a founder could do some extra work and find a way to keep 11% of their equity instead of 10%, without meaningfully reducing their startup’s chances of success. Getting that extra 1 percentage point of equity might be a lot easier than raising the company’s ultimate valuation by 10%.</p>
<p>Wealthy EAs care more about marginal dollars than ordinary wealthy people, and they can take advantage of that fact. They can look for (relatively) easy ways of getting money. I only spent about five minutes coming up with the examples I gave, so I’m sure there are plenty of other ideas.</p>
<h1 id="notes">Notes</h1>
<div class="footnotes">
<ol>
<li id="fn:2">
<p>For people with about average wealth, the best way to get more money is usually the obvious thing: get a higher salary. But there are still some neglected strategies. One that comes to mind is salary negotiation. <a href="#fnref:2" class="reversefootnote">↩</a></p>
</li>
<li id="fn:4">
<p>The mathy way to say this is that, on a logarithmic scale, most of his wealth came from doing the hard work. But on a linear scale, it mostly came from retaining equity. If most people have logarithmic utility of money but you have linear utility, that changes how you should behave. <a href="#fnref:4" class="reversefootnote">↩</a></p>
</li>
<li id="fn:3">
<p>Elon Musk did something sort of similar, where he got the Tesla board of directors to grant him highly leveraged call options. When Tesla stock went up, Elon Musk’s net worth went up by even more. <a href="#fnref:3" class="reversefootnote">↩</a></p>
</li>
</ol>
</div>
Sat, 16 Oct 2021 00:00:00 -0500
http://mdickens.me/2021/10/16/low_hanging_fruit_wealthy_eas/
http://mdickens.me/2021/10/16/low_hanging_fruit_wealthy_eas/