In my previous blog, I showed how different the world of investment return and risk when viewed through the prism of partial moments. Your personal target determines the performance of capital markets and the efficient frontier from which you select desirable portfolios.
Services that offer performance evaluation services on traditional investment funds such as mutual funds have traditionally focused on distilling reported performance history into statistical measures such as average return, the volatility or standard deviation of historical returns, systematic risk or market beta, and, in the case of U.S. equity funds, style analysis derived from exposures to multiple common factors such as market, size, book to market and momentum. It is difficult to see the extent that a manager’s performance is dominated by upside or downside reward and risk.
We begin with two simple examples of evaluating a manager’s performance relative to a zero target level. The manager selected is a Multi-Cap Core Fund manager with reported returns starting in January 1972. Specifically, we examine the realized returns for the 24 month period ending March 2011. Table 1 shows the standard and partial moments for the nominal returns. The average monthly return was 2.5621% with a realized volatility of 4.6678%. The columns labeled LPM 0, LPM 1 and LPM 2 correspond to downside probability, downside loss and downside volatility. The columns labeled UPM 0, UPM 1 and UPM 2 are associated with upside probability, upside reward and upside volatility On the basis of nominal returns, the investor would be pleased to see that the upside probability of 0.7917 overwhelms the downside probability of 0.2083 and that the upside reward of exceeds the downside loss by a factor of three. There is also more upside volatility than downside volatility.
A different picture emerges when you look at the active returns of the manager relative to its benchmark. I have taken the Russell 3000 to be the benchmark for the manager and Table 2. The active fund on the basis of average return performed like the benchmark. Looking at upside and downside volatility, the active reward or loss is about the same that you would get by flipping a fair coin with similar amounts and rewards. I suspect that, given this information, the prospective investor might be a bit concerned about consistency of active returns from this manager.
Table 1 Nominal Return Moments Click to enlarge
Table 2 Active Return Moments Click to enlarge
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