Asset Allocator

ASSET ALLOCATION: MANAGEMENT STYLE AND PERFORMANCE MEASUREMENT

An Asset class factor model can help make order out of chaos

William F. Sharpe^*

^{Excerpts from the Journal of Portfolio Management, Winter 1992, pp. 7-19.}

It is widely agreed that asset allocation accounts for a large part of the variability in the return on a typical investor's portfolio. This is especially true if the overall portfolio is invested in multiple funds, each including a number of securities.

Asset allocation is generally defined as the allocation of an investor's portfolio among a number of "major" asset classes. Clearly such a generalization cannot be made operational without defining such classes.

Once a set of asset classes has been defined, it is important to determine the exposures of each component of an investor's overall portfolio to movements in their returns. Such information can be aggregated to determine the investor's overall effective asset mix. If it does not conform to the desired mix, appropriate alterations can then be made.

Once a procedure for measuring exposures to variations in returns of major asset classes is in place, it is possible to determine how effectively individual fund managers have performed their functions and the extent (if any) to which value has been added through active management. Finally, the effectiveness of the investor's overall asset allocation can be compared with that of one or more benchmark asset mixes.

An effective way to accomplish all these tasks is to use an asset class factor model. After describing the characteristics of such a model, we illustrate applications of a model with twelve asset classes to analyze the performance of a set of open-end mutual funds between 1985 and 1989.

ASSET CLASS FACTOR MODELS

EVALUATING ASSET CLASS FACTOR MODELS

A TWELVE ASSET CLASS MODEL

Figure 2 provides relevant evidence: The variability in returns across the four asset classes from year-to-year is far greater than would be encountered if groups with similar numbers of securities had been formed randomly. Fund exposures across these dimensions vary greatly. As a result, much of the variation in fund returns in any given period can be attributed to the combined effects of their exposures to these asset classes and the realized returns on those classes.

DETERMINING FUND EXPOSURES

Figures 5 and 6 show the results obtained when the same type of analysis was applied to the returns of Fidelity Magellan Fund -- a highly popular open-end common stock fund. As Figure 5 shows, its style differed considerably from that of Trustees' Commingled U.S. Fund, with emphasis on growth rather than value stocks and exposure to medium-capitalization stocks in addition to smaller ones.

The pie chart in Figure 5 shows that the fund is considerably more diversified (and/or engaged in less rotation) than Trustees' Commingled U.S. Fund. During the period covered, over 97.3% of the monthly variation in Magellan returns could be attributed to the concurrent return on a passive portfolio with the style shown in the bar chart in Figure 5.

Figure 6 suggests that the Magellan Fund progressively increased its emphasis on large growth stocks and decreased its exposure to small capitalization stocks during the 1980s. This is not surprising, as the fund grew to approximately $14 billion by the end of the period, making substantial investment in very small stocks increasingly difficult.

MUTUAL FUND TYPES

Figures 3 through 6 show results for two particular mutual funds. Here we provide a more representative view of the efficacy of the procedure, with style analysis performed for each of 395 funds using returns from January 1985 through December 1989. Averages are taken for both the styles and R-squared values of all funds classified as being of the same "type" by Jaye C. Jarrett & Company, Inc., the providers of the data used for this study. In all, seven such types are represented. The results are shown in Figures 7 through 13.

Each figure should be interpreted as representative of the style (bar chart) and variance due to style (pie chart) of a "typical" fund of the type. A portfolio invested in all the funds of a particular type would typically have a much higher R-squared (percent of variance attributable to style) than is shown in the figure in question. Moreover, there is typically considerable variation in both style and R-squared values among the funds within each type group. Given these caveats, the analyses provide useful illustrations of some of the features of the style analysis method.

Utility Stock Fund

Figure 7 shows the results for a typical utility stock fund. Such funds (atypically) concentrate their holdings in one industry. As a result, style accounts for an unusally small part (although still 59.3%) of the variance in return. Although such funds hold common stocks, their returns behave more like a passive portfolio invested in both stocks and bonds. That is, utility revenues are "sticky" because to the regulatory process, causing shares of such companies to have features that are both stock-like and bond-like.

The utility fundexample emphasizes the fact that style analysis provides measures that reflect how returns act, rather than a simplistic concept of what the portfolios include. Note, finally, all equity exposure is to value stocks, relflecting the high dividend yields typical of utility shares.

Growth Equity Fund

Figure 8 portrays a typical growth equity fund. Here the most prominent exposure is, as expected, to growth stocks, although the typical fund of this type also responds to movements in the returns of other asset classes. Note the exposure to Bills, which probably results from the actual cash holdings that many such funds maintin to meet liquidity needs.

Overall, the results illustrate the fact that few funds are "pure" in the sense of responding only to movements in returns of one asset class. The style analysis procedure can detect some of the subtleties that exist in practice, instead of classifying each fund by a single (pure) style. Finally, note that almost 90% of the monthly variation in return of the typical growth equity fund can be attributed to its style -- a result typical of common stock funds.

Growth and Income Equity Fund

Figure 9 shows the characteristics of a typical growth and income equity fund. Here too, style accounts for approximately 90% of the monthly variation in returns. The effects of a liquidity reserve are probably at least partly responsible for the exposure to Bills, although choices of stocks with lower beta values than those in the asset class indexes could also play a role.

Note the almost perfect balance between value and growth Stocks, relecting an "SP500-like" stance with respect to large-capitalization stocks. The exposures to small and medium stocks may reflect actual investment in such stocks and/or a preference for equal weighting rather than capitalization weighting within the large stock sector. In an important sense, the source of a set of exposures may not even need to be identified, as long as the exposures are representative of likely future results.

Small Stock Fund

Figure 10 indicates that small stock funds do indeed buy small stocks (as defined by the asset class used for this study). However, they also appear to buy somewhat larger ones. Moreover, there tends to be an emphasis on growth rather than value. This may reflect the actual purchase of large-capitalization growth stocks by some funds. It may also indicate a preference for medium-capitalization stocks with growth characteristics. As Figure 1 suggests, a point lying to the right of the point rerpresentin the medium stock index can be represented by a combination of the large growth stock index, the small stock index and the medium stock index.

As before, the goal is to represent the behavior of the fund, not its precise composition. Finally, note that the R-squared value is slightly lower (87.6%) than for the other diversified funds -- perhaps reflecting the lower liquidity of this sector of the equity market.

Balanced Fund

Figure 11 shows that balanced funds are precisely that. While any single fund may diverge substantially from the style shown in the figure, collectively balanced funds provide results similar to those obtained by holding all U.S. asset classes and small amounts of foreign ones. As with other diversified funds, style accounts for roughly 90% of the monthly variation in the returns for the typical fund of this type.

High-Quality Bond Fund

Figure 12 shows that the method works well for bond funds as well as for stock and balanced ones. The typical high-quality bond fund provides exposure to corporate bonds, government bonds and mortgage-related securities, with style accounting for slightly over 88% of monthly variance in return. In any given case, a mix of, e.g., intermediate government bonds and corporate bonds might reflect actual holdings or the average quality of the corporate bond portfolio.

Thus a portfolio with a higher average quality than that reflected in the Corporate Bond Index typically acts more like a mixture of corporate bonds (defined by the index) and intermediate government bonds. Similarly, a portfolio of corporate bonds with a longer duration than that of the Corporate Bond index will "track" more closely with a mix of corporate bonds (defined by the index) and long-term Government bonds. As always behavior, not nomenclature, is relevant.

Convertible Bond Fund

Figure 13 shows a case where an asset class not explicitly represented in a model can be represented well by the classes that are included. As shown, 88.8% of the monthly variation in returns of a typical convertible bond fund can be attributed to the concurrent variation in the returns of a mix of stocks, bills, and bonds. This is not too surprising. A convertible bond has characteristics of both bonds and stocks.

Of course, as bond and stock markets diverge, the relative sensitivities of any given convertible bond to the two markets will change, giving such an instrument its distinctive non-linear characteristic. Interestingly, managers of convertible bond funds appear to have preferred habitats, causing them to buy and sell convertible bonds so as to maintain fairly consistent exposures to asset classes of the type utilized in this study.

Fund Type Summary

As these examples show, a remarkable amount of information can be revealed from an analysis of the returns provided by the manager of an investment fund. This is especially gratifying since in the final analysis return is the product the investor buys from such a manager.

THE INVESTOR'S EFFECTIVE ASSET MIX

PERFORMANCE MEASUREMENT

Figures 16 and 17 show the results of similar analyses for Fidelity Magellan Fund. As Figure 16 shows, the fund provided a positive but statistically insignificant outperformance when compared with the S&P500 over the period.

But Figure 17 shows that such a comparison masked Magellan's truly outstanding selection performance. During this period, the fund outperformed its style benchmarks by a cumulative amount of over 25%. Outperformance averaged 57 basis points per month with a standard deviation of 105 basis points. The t-statistic of 3.76 shows that such differences were highly significant statistically. Two aspects account for the large t-value: the relatively large average return difference and the relatively small variation in the difference from month to month.⁹

MUTUAL FUND PERFORMANCE

Fidelity Magellan's performance from 1985 through 1989 is far from typical. While only out-of-sample results can provide a definitive test of the collective performance of mutual funds, the average e_i values obtained as a by-products from fund style analyses can provide at least some evidence on the matter.

Figure 18 shows the distribution of the average tracking errors obtained from the style analyses of 636 stock, bond and balanced funds. Each value is the average e_i value obtained from a style analysis using returns for one fund covering the period from January 1985 through December 1989. Note that the distribution is roughly normal, with a mean of -0.074 (-7.4 basis points per month). This is roughly consistent with the hypothesis that the average mutual fund cannot "beat the market" before costs, because such funds constitute a large (and presumably representative) part of the market. Annualized, the mean underperformance is approximately 0.89% per year -- an amount that, if anything, may be slightly less than the non-transaction costs incurred by a typical mutual fund.

MEASURING AN INVESTOR'S PERFORMANCE

CONCLUSION

An asset class factor model can help make order out of the chaos that often attends the investment process. It can provide a consistent view of investment decisions investors make to economize on information flows and exploit comparative advantages. The style analysis procedure described in this article allows such a model to be implemented economically. At the very least it can serve as a valuable supplement to other methods designed to help investors achieve their goals in cost-effective ways.

REFERENCES