# LO 70.7: Describe techniques to measure the market timing ability of fund

LO 70.7: Describe techniques to measure the market timing ability of fund managers with a regression and with a call option model, and compute return due to market timing.
Measuring Market Timing with Regression
Extending basic return regression models offers a tool to assess superior market timing skills of a portfolio manager. A market timer will include high (low) beta stocks in her portfolio if she expects an up (down) market. If her forecasts are accurate, her portfolio will outperform the benchmark portfolio. Using a market timing regression model, we can empirically test whether there is evidence of superior market timing skills exhibited by the portfolio manager. The regression equation used for this test is as follows:
Rp – RF = a + Pp(Rm – RF) + Mp(RM – RF)D + ep
In this equation, D is a dummy variable that is assigned a value of 0 for down markets (i.e., when Rm Rp). Mp is the difference between the up market and down market betas and will be positive for a successful market timer. In a bear market, beta is simply equal to pp. In a bull market, beta is equal to pp + Mp. Empirical evidence of mutual fund return data suggests that Mp is actual negative for most funds. Thus, researchers have concluded that fund managers exhibit little, if any, ability to correctly time the market.
Measuring Market Timing with a Call Option Model
Consider an investor who has 100% perfect market forecasting ability and holds a portfolio allocated either 100% to Treasury bills or 100% to the S&P 500 equity market index, depending on the forecast performance of the S&P 500 versus the Treasury bill return. The investors portfolio will be:
100% invested in the S&P 500 if E(RM) > 100% invested in Treasury bills if E(RM) r f R F
If the market rises by less than the risk-free rate, the call option has no value, but the risk- free asset will still return Rp. Therefore, the down-market scenario return for the calls plus bills portfolio is:
Rp if Rm < Rp
In summary, the returns to the calls plus bills portfolio are identical to the 100% perfect foresight returns. Therefore, the value or appropriate fee for perfect foresight should equal the price of the call option on the market index.
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Topic 70 Cross Reference to GARP Assigned Reading – Bodie, Kane, and Marcus, Chapter 24
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