asset class should be dissimilar from other asset classes in the portfolio as well as combinations of the other asset classes.5 The addition of an asset class to a portfolio should raise its expected utility.
6 An asset class should not require selection skill to identify managers within the asset class.
7 An asset class should have capacity to absorb a meaningful fraction of a portfolio cost-effectively.
For illustrative purposes we begin by considering the following seven asset classes in our asset allocation analysis: domestic equities, foreign developed market equities, emerging market equities, Treasury bonds, US corporate bonds, commodities, and cash equivalents.6
Estimating Expected Returns
Before we estimate expected returns, we must decide which definition of expected return we have in mind. If we base our estimate of expected return on historical results, we might assume that the geometric average best represents the expected return. After all, it measures the rate of growth that occurred historically or what should happen prospectively with even odds of a better or worse result. However, it does not measure what we should expect to happen on average over many repetitions; the arithmetic average gives this value. But there is a more practical reason for choosing the arithmetic average instead of the geometric average as our estimate of expected return. The average of the geometric returns of the asset classes within a portfolio does not equal the geometric return of the portfolio, but the average of the arithmetic returns does indeed equal the portfolio's arithmetic return. Because we wish to express the portfolio's return as the weighted average of the returns of the component asset classes, we are forced to define expected return as the arithmetic average.7 Of course, we are not interested in the arithmetic average of past returns unless we believe that history will repeat itself precisely. We are interested in the arithmetic average of prospective returns.
To estimate expected returns, we start by assuming that markets are fairly priced; therefore, expected returns represent fair compensation for the degree of risk each asset class contributes to a broadly diversified market portfolio. These returns are called equilibrium returns, and we estimate them by first calculating the beta of each asset class with respect to a broad market portfolio. This calculation implicitly reflects the historical standard deviations and correlations of the assets. Next, we estimate the expected return for the market portfolio and the risk-free return. We calculate the equilibrium return of each asset class as the risk-free return plus the product of its beta and the excess return of the market portfolio. Moreover, we can easily adjust the expected return of each asset class to accord with our views about departures from fair value. Suppose we estimate the market's expected return to equal 7.5% and the risk-free return to equal 3.5%. Given these estimates, together with estimates of beta based on monthly returns from January 1976 through December 2015, we derive the equilibrium returns shown in Table 2.1.
TABLE 2.1 Expected Returns
| Asset Classes | Equilibrium Returns (%) | Views (%) | Confidence (%) | Expected Returns (%) |
|---|---|---|---|---|
| US Equities | 8.8 | 8.8 | ||
| Foreign Developed Market Equities | 9.5 | 9.5 | ||
| Emerging Market Equities | 11.4 | 11.4 | ||
| Treasury Bonds | 4.1 | 4.1 | ||
| US Corporate Bonds | 4.9 | 4.9 | ||
| Commodities | 5.4 | 7.0 | 50.0 | 6.2 |
| Cash Equivalents | 3.5 | 3.5 |
Assumes 3.5% risk-free return and 4.0% market risk premium.
This approach is straightforward to implement in practice, even with more nuanced assumptions. The current risk-free return is readily observable. There are a variety of methods for estimating the expected return of a diversified market portfolio. For example, we might adjust the historical risk premium to accord with current risk levels and add this adjusted risk premium to the current risk-free return. We may expect some asset classes to produce returns that differ from those that would occur if markets were in equilibrium and perfectly integrated, especially if they are not typically arbitraged against other asset classes. Suppose we expect commodities to return 7.0% and we assign as much confidence to this view as we do to the equilibrium return. We can blend the equilibrium estimate with our view to derive expected return. The final column of Table 2.1 shows the expected returns for each of the asset classes in our analysis.
Estimating Standard Deviations and Correlations
We also need to estimate the standard deviations of the asset classes as well as the correlations between each pair of asset classes. We estimate these values, shown in Table 2.2, from the monthly returns for the period beginning in January 1976 and ending in December 2015.
TABLE 2.2 Standard Deviations and Correlations
| Asset Classes | Standard Deviations (%) | Correlations | ||||||
|---|---|---|---|---|---|---|---|---|
| a | b | c | d | e | f | |||
| a | US Equities | 16.6 | ||||||
| b | Foreign Developed Market Equities | 18.6 | 0.66 | |||||
| c |
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