### Forecasting Factor and Smart Beta Returns (Hint: History Is Worse than Useless)

**Key Points**

- Using past performance to forecast future performance is likely to disappoint. We find that a factor’s most recent five-year performance is negatively correlated with its subsequent five-year performance.
- By significantly extending the period of past performance used to forecast future performance, we can improve predictive ability, but the forecasts are still negatively correlated with subsequent performance: the forecast is still essentially useless!
- Using relative valuations, we forecast the five-year expected alphas for a broad universe of smart beta strategies as a tool for managing expectations about current portfolios and constructing new portfolios positioned for future outperformance. These forecasts will be updated regularly and available on our website.

In a series of articles we published in 2016,^{1} we show that relative valuations predict subsequent returns for both factors and smart beta strategies in exactly the same way price matters in stock selection and asset allocation. To many, one surprising revelation in that series is that a number of “smart beta” strategies are expensive today relative to their historical valuations. The fact they are expensive has two uncomfortable implications. The first is that the past success of a smart beta strategy—often only a simulated past performance—is partly a consequence of “revaluation alpha” arising because many of these strategies enjoy a tailwind as they become more expensive. We, as investors, extrapolate that part of the historical alpha at our peril. The second implication is that any mean reversion toward the smart beta strategy’s historical normal relative valuation could transform lofty historical alpha into negative future alpha. As with asset allocation and stock selection, relative valuations can predict the long-term future returns of strategies and factors—not precisely, nor with any meaningful short-term timing efficacy, but well enough to add material value. These findings are robust to variations in valuation metrics, geographies, and time periods used for estimation.

Two assumptions widely supported in the finance literature form the basis for how most investors forecast factor alpha and smart beta strategy alpha. We believe both, although strongly entrenched in investors’ thinking, are wrong. The two assumptions we take issue with are that past performance of factor tilts and smart beta strategies is the best estimate of their future performance, and that factors and smart beta strategies have constant risk premia (value-add) over time.

Common sense tells us that current yield begets future return. Nowhere is this more intuitive than in the bond market. Investors fully understand that the average 30-year past return of long bonds, currently north of 7%, tells us nothing about the future return of long bonds. The current yield, around 3%, is far more predictive. In the equity market, at least since the 1980s, we know that the cyclically adjusted price-to-earnings (CAPE) ratio, as demonstrated by Robert Shiller, and the dividend yield are both good predictors of long-term subsequent returns.

If relative valuation, and the implication it has for mean reversion, is useful for stock selection and for asset allocation, why would it not matter in choosing factor tilts and equity strategies? The widespread promotion by the quant community of products based on past performance—often backtests and simulations—has contributed, and still does contribute, to investors’ costly bad habit of performance chasing. The innocent-looking assumption of “past is prologue” conveniently encourages investors and asset managers to pick strategies with high past performance and to presume the past alpha will persist in the future.

In our 2016 smart beta series we offer evidence that relative valuations are important in the world of factors and smart beta strategies. We show that variations in valuation levels predict subsequent returns and that this relationship is robust across geographies, strategies, forecast periods, and our choice of valuation metrics. Our research tells us that investors who (too often) select strategies based on wonderful past performance are likely to have disappointing performance going forward. For many, mean reversion toward historical valuation norms dashes their hopes of achieving the returns of the recent past.

These conclusions are, of course, just qualitative. To make them practical, we need to quantify the effects we observe. In this article we do precisely that. We measure the richness of selected factors based on their relative valuations versus their respective historical norms and calculate their implied alphas. We also call attention to the real-world “haircuts” on the implied alphas—implementation shortfall, trading costs, and manager fees—which don’t show up in paper portfolios and simulations.

**Why Valuations Matter**

We can easily see the link between valuation and subsequent performance on a scatterplot created using these two variables. The two scatterplots in Figure 1 are from Arnott, Beck, and Kalesnik (2016a) and are examples of the historical distributions of valuation ratios and subsequent five-year returns for a long–short factor, the classic Fama–French definition of value, and for a smart beta strategy (the low volatility index), as of March 31, 2016. In June 2016, we identified the former as the cheapest factor, relative to its history, and the latter as the most expensive strategy, relative to its history.

**Comparing Alpha-Forecasting Models**

Many investors expect the alpha of a strategy to be its historical alpha, so much so that this assumption itself is an example of an alpha-forecasting model. Arguably, the cornerstone of any investment process is an estimate of forward-looking return. We argue that a good alpha-forecasting model, whether for a strategy or a factor tilt, should have three key attributes:

1. Forecasts should correlate with subsequent alphas.

2. Forecasts should be paired with a measure of the likely accuracy of the forecast. A standard statistical way to measure the accuracy of a forecast is mean squared error, a measure of how reality has differed from past forecasts.

3. Forecasts should provide realistic estimates of expected returns.

These criteria provide useful metrics for us to compare different alpha-forecasting models. We select six models for comparison. One model assumes an efficient market: no factors or strategies have any alpha. Two of the models use only past performance and ignore valuations, and four of the models are based on valuation levels relative to historical norms.

**Model 0**. Zero factor alpha. In an early version of the efficient market hypothesis—the capital asset pricing model, or CAPM—researchers argued that an asset’s return was solely determined by its exposure to the market risk factor. Similarly, Model 0 assumes the risk-adjusted alpha of a factor tilt or smart beta strategy is approximately zero. We measure the mean squared error relative to an expected alpha of zero.

**Model 1**. Recent past return (most recent five years). This model uses the most recent five-year performance of a factor or strategy to forecast its future return. Because our research tells us that investors who select strategies based on wonderful past performance are likely buying stocks with high valuations, we expect this model will favor the strategies that are currently expensive and have low future expected returns.

**Model 2**. Long-term historical past return (inception to date). Long-term historical factor returns are perhaps the most widely accepted way to estimate factor premiums (expected returns), both in the literature and in the practitioner community. Doing so requires that we extrapolate historical alpha to make the forecast: what has worked in the past is deemed likely to work in the future. Averaging performance over a very long period of time should theoretically mitigate vulnerability to end-point richness.^{2} By using multiple decades of history (versus a short five-year span as Model 1 does), we would expect this model to perform relatively well in differentiating well-performing factors from less-well-performing ones.

**Model 3**. Valuation dependent (overfit to data). This model is a simple and intuitive valuation-dependent model, as illustrated by the log-linear line of best fit in Figure 1.^{3} At each point in time, we calibrate the model only to the historically observed data available at that time; no look-ahead information is in the model calibration. This model encourages us to buy what’s become cheap (performed badly in the past), rather than chasing what’s become newly expensive (has performed exceptionally well).

**Model 4**. Valuation dependent (shrunk parameters). A model calibrated using past results may be overfitted, and as a result provide exaggerated forecasts that are either too good or too bad to be true. Parameter shrinkage is a common way to reduce model overfitting to rein in extreme forecasts. (Appendix A provides more information on how we modify the parameters estimated in Model 4 to less extreme values.)

Valuation-dependent Models 3–6 all have positive correlations between their forecasts and subsequent returns, and all beat Model 0 in this regard; the correlation is undefined for Model 0 because its forecasts are always constant. Models 4–6 beat Model 0 in forecast accuracy, with all having a lower MSE than Model 0.

The volatilities of the factor portfolios are a measure of the volatility of a long–short portfolio; in other words, these volatilities measure the volatility of the return difference between the long and the short portfolios. Take, for example, the low beta factor in the United States, which has a volatility second only to the momentum factor. Does this mean that low beta stocks have high volatility? No. The factor portfolio that goes long in low beta stocks and short in high beta stocks carries with it a substantial negative net beta, which contributes to the volatility of the factor.^{7}

The volatility of the low beta factor in this long–short framework therefore suggests that a long-only low beta investor should expect large tracking error with respect to the market, even if the portfolio is much less risky than the market. Momentum also typically leads to high tracking error, while the investment factor leads to low tracking error. Viewing projected alpha and relative risk together gives us an insight into the likely information ratios currently available in these factors.

**Smart beta strategies with negative forecasted alphas.** Like our findings regarding the low beta factor, we project that the low beta and low-volatility strategies will underperform their respective benchmarks across all regions. Even after some pretty disappointing results during the second half of 2016, these strategies still trade at premium valuations. This doesn’t mean that investors should avoid them! They will reduce portfolio volatility and are complementary to many other strategies.

We also project small-cap and equally weighted strategies to have negative returns over the next five years. After a sharp run-up in small versus large stocks during the second half of 2016, the size factor is now expensive relative to average historical valuations in all regions.

**Smart beta strategies with positive forecasted alphas.** On the other side of the spectrum, strategies with a value orientation, such as the Fundamental Index™, are projected to have high expected returns in most regions.^{11} Unlike low-volatility or small-cap strategies, value strategies produced only mediocre returns over the last decade, scaring many investors away even though the logic should be the opposite: poor past performance implies cheap valuations, positioning these strategies for healthy performance going forward.

Similarly, income-oriented strategies, such as High Dividend and RAFI™ Equity Income, are generally projected to have high expected returns across all regions. Momentum-oriented strategies in all regions—in stark contrast to a year ago—tend to have decent projected returns, gross of trading costs (which we discuss in the next section).

**Five-Year Forecasts**

We summarize the valuation ratios, historical returns, historical returns net of valuation changes, and expected returns along with estimation errors for the most popular factors and strategies in **Table 2. Panel A** shows the results for factors, and **Panel B** shows the results for smart beta strategies. All of these results reflect our method of calculating relative valuation and relative return forecasts, as described in the published methodology for each of these strategies. We caution against acting on these forecasts without considering the many factors and forecasts that our approach doesn’t capture. These forecasts have uncertainty that, in most cases, is larger than the alpha forecast.

Although large, these tables represent only a portion of the multitude of layers and dimensions that investors should consider when evaluating these strategies. We encourage investors and equity managers to use the tables as a reference point when making factor allocation decisions. As time passes, valuations change, and the expected returns in the table need to be updated to stay relevant. Strategies that seem vulnerable today may be attractively priced tomorrow, and vice versa. The good news is that we will be providing this information, regularly updated, for these and many more strategies and factors on a new interactive section of our website. We encourage readers to visit frequently and to liberally provide feedback.

**Putting It All Together**

In the brave new “smart beta” world, with the rapid proliferation of factor tilts and quant strategies, investors should be vigilant to the pitfalls of data mining and performance chasing. Our 2016 three-part series covers the topics we believe investors should consider before allocating to such strategies.

In our earlier research, we explained how smart beta can go horribly wrong if investors anchor performance expectations on recent returns. Expecting the past to be prologue sets up two dangerous traps. First, if past performance was fueled by rising valuations, that component of historical performance—revaluation alpha—is not likely to repeat in the future. Worse, we should expect this revaluation alpha to mean revert because strong recent performance frequently leads to poor subsequent performance, and vice versa.

We discussed that winning with smart beta begins by asking if the price is right. Valuations are as important in the performance of factors and smart beta strategies as they are in the performance of stocks, bonds, sectors, regions, asset classes, or any other investment-related category. Starting valuation ratios matter for factor performance regardless of region, regardless of time horizon, and regardless of the valuation metric being used.

We showed how valuations can be used to time smart beta strategies. We know factors can be a source of excess return for equity investors, but that potential excess return is easily wiped out (or worse!) when investors chase the latest hot factor. Investors fare better if we diversify across factors and strategies, with a preference for those that have recently underperformed and are now relatively cheap because of it.

In this article, we offer our estimation of expected returns going forward, based on the logic and the framework we develop in our prior three articles. We hope investors find our five-year forecasts useful in managing expectations about their existing portfolios, and perhaps also in creating winning combinations of strategies, positioned for future—not based on past—success.