A key part of informed decision-making on asset allocation is estimating future risk premia and using those projections to influence weights in the portfolio. The question, of course, is how to estimate premia? There are no easy answers for the simple reason that forecasting the future is complicated. A good way to start, however, is by managing expectations via history. There are many possibilities on this front, including one that’s often overlooked: profiling the distribution of historical premia for a preliminary dose of perspective.
As a basic illustration, let’s review how three sets of risk premia stack up: the small-cap equity premium (relative to large caps), the broad equity premium (relative to bonds), and the value equity premium (relative to growth stocks). To calculate the data we’ll use ETFs as proxies.
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A key variable is choosing a time period to analyze. Ideally the time window matches the investment horizon for the portfolio. Building a strategy for an investor with an x-year horizon would focus on historical risk premia on a rolling x-year basis. In this toy example, we’ll use rolling 1-year periods (based on returns for Apr. 30, 2008 through Jan. 30, 2020) to illustrate the concept, using the following definitions for premia:
Small-cap premium: iShares Russell 2000 (IWM) – iShares Russell 1000 ETF (IWB)
Equity premium: iShares Russell 1000 ETF (IWB) – Vanguard Total Bond Market (BND)
Value equity premium: iShares S&P 500 Value (IVE) — iShares S&P 500 Growth (IVW)
The first chart shows the small-cap premium has posted results that are roughly normally distributed. Note, too, that the range of premia varies widely for a one-year window. Since 2008, premia has been as low as -16.8% and as high as +23.0%. The current reading is -12.1%–an unusually weak but not unexpected result. The historical distribution for this premium suggests that better days are likely for the one-year performance.
The next chart profiles the distribution for the equity premium (relative to bonds). In this case, the distribution is conspicuously non-normal. Note, for instance, the outsized cases of negative premia (as shown by the fat left tail)—a reminder that stocks can trail bonds by a large degree and the instances of this subpar performance can occur far more frequently than a normal distribution implies. The good news is that positive premia occurs with even more frequency relative to what you’d expect from a normal distribution. For the moment, the current premium is a solid 14.4%.
The value equity premium is shown in the final example. In this case, negative premia have an outsized influence on the historical distribution since 2008. Perhaps it’s no surprise, then, that the current value premium is -7.3%.
A complete research effort on risk premia requires deeper study beyond looking backward, of course – estimating expecting premia, for instance. But before diving into forecasting, it’s useful to review the road that led us to the current state of risk premia—a task well-suited to distribution charts for summarizing history.
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