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 believes 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.

In this post, I explain the projections that I use for my own financial planning.

Market returns

For market returns, I look at three institutional forecasts:

  1. AQR
  2. Research Affiliates (RAFI)
  3. Vanguard

They each use somewhat different methodology:

  1. AQR uses the dividend discount model, the most standard method of estimating future returns.
  2. RAFI uses the discounted dividend model, but also assumes that valuations tend to revert to the mean (like the Bogle expected return formula).
  3. Vanguard uses a complicated model that incorporates lots of economic factors.

(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.)

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.

A table of estimates for the 10-year real geometric returns of various asset classes:

Asset Class AQR RAFI Vanguard
US equities 3.6% -0.7% 1.3%
developed ex-US equities 4.3% 4.4% 4.2%
emerging equities 5.3% 7.4% 3.2%
US 10-year Treasuries -0.8% 0.9% -0.3%
commodities -1.5% 1.4% N/A

Estimated standard deviations:

Asset Class RAFI Vanguard
US equities 15.2% 16.7%
developed ex-US equities 17.2% 18.4%
emerging equities 20.9% 26.8%
US 10-year Treasuries 3.3% 4.7%
commodities 16.3% N/A

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.

I would also like to know the expected return of the global market portfolio.

  • Vanguard does not provide any such estimate.
  • RAFI forecasts the global market portfolio to have a 1.5% real return with a 9.2% standard deviation.
  • 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.

We could also look at historical performance. Meb Faber’s Global Asset Allocation found that from 1973 to 2013, the global market portfolio earned a real return of 5.4% with an 8.8% standard deviation.

I approximated the global market portfolio using data from The Rate of Return on Everything, 1870–20151. I found that from 1950 to 2015 (the time range over which every country has annual data), global 60/402 had a nominal return of 10.3% with a standard deviation of 14.5%.

Putting all these together, my best-guess forecast is a 3% real return with a 9% standard deviation.

Factor premia

I make investments in certain factors that historically predicted asset returns, including value, momentum, and trendfollowing.

AQR and RAFI provide projected returns for some factors. (See also RAFI methodology.)

  • 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.
  • AQR projects a Sharpe ratio of 0.7–0.8 for a long/short multi-factor portfolio.
  • 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.
  • Vanguard projects a 1% excess return for a long-only value strategy, but doesn’t offer any other factor projections.

AQR numbers are net of fees and transaction costs. RAFI estimates are net of transaction costs, but don’t account for fees.

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 Contrarian Factor Timing Is Deceptively Difficult3 from AQR.)

And anyway, the way I invest doesn’t match how AQR and RAFI came up with their estimates. I invest in concentrated, 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.

I came up with my own projections for concentrated factor returns by following these steps:

  1. Run a backtest to find the historical factor premium for a comparable portfolio to the one I invest in.
  2. Subtract fees and expected transaction costs.
  3. Divide the result by two, on the assumption that factors will only work half as well in the future.

Why divide historical factor returns in half?

  • We have good reason to expect factors to continue to work.
  • But they might work less well in the future, simply because investment strategies tend to get worse over time.
  • To keep it simple, just cut expected returns in half.

I get factor exposure through the Alpha Architect ETFs, 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 Ken French Data Library, 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 footnote4). 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,5 that gives a 6% premium. Then divide this in half to get a 3% expected future premium.

I use equity trendfollowing to reduce market exposure during downtrends, like what the VMOT 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 Faber (2013)6 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.

In addition, I invest in long/short trendfollowing over commodities and fixed income, similar to what KMLM does. (I don’t invest in KMLM; I have an SMA with Alpha Architect where they directly run managed futures, which is more tax- and leverage-efficient.7 But if I weren’t doing that, I’d invest in KMLM.) The best data on long/short trendfollowing performance comes from Hurst et al. (2014)8, 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.9 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.

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.

In summary, I expect VMOT to earn a 6% real return with a 13% standard deviation, for a Sharpe ratio of 0.6.10 I expect VMOT + bond/commodity trendfollowing to do somewhat better than this—maybe 5% real with 11% standard deviation.11 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.

Notes

  1. Òscar Jordà, Katharina Knoll, Dmitry Kuvshinov, Moritz Schularick & Alan M Taylor (2019). The Rate of Return on Everything, 1870–2015 

  2. 60/40 is supposed to be market cap weighted, but I weighted by GDP instead because the data set doesn’t include market cap. 

  3. Cliff Asness, Swati Chandra, Antti Ilmanen & Ronen Israel (2017). Contrarian Factor Timing Is Deceptively Difficult. 

  4. 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. 

  5. This is comparable to AQR’s estimated transaction costs based on their own live training data,12 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.

    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. 

  6. Meb Faber (2013). A Quantitative Approach to Tactical Asset Allocation. 

  7. 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. 

  8. Brian Hurst, Yao Hua Ooi & Lasse H. Pedersen (2014). A Century of Evidence on Trend-Following Investing. 

  9. I compared AQR’s trendfollowing index to the performance of one of AQR’s actual trendfollowing funds, AQMIX. 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). 

  10. 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. 

  11. 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. 

  12. Andrea Frazzini, Ronen Israel & Tobias J. Moskowitz (2014). Trading Costs of Asset Pricing Anomalies.