Investments, tenth edition

  Hedge Fund Performance 

and Changing Factor Loadings 

 In Chapter 24, we pointed out that an impor-

tant assumption underlying conventional 

performance evaluation is that the portfolio 

manager maintains a stable risk profile over 

time. But hedge funds are designed to be 

opportunistic and have considerable flexibil-

ity to change that profile. This too can make 

performance evaluation tricky. If risk is not 

constant, then estimated alphas will be biased 

if we use a standard, linear index model. And 

if the risk profile changes in systematic man-

ner with the expected return on the market, 

performance evaluation is even more difficult. 

 To see why, look at  Figure  26.4 , which 

illustrates the characteristic line of a per-

fect market timer (see Chapter 24, Section 

24.4) who engages in no security selection 

but moves funds from T-bills into the market 

portfolio only when the market will outper-

form bills. The characteristic line is non-

linear, with a slope of 0 when the market’s 

excess return is negative, and a slope of 1 

when it is positive. But a naïve attempt to 

estimate a regression equation from this pat-

tern would result in a fitted line with a slope 

between 0 and 1, and a positive alpha. Nei-

ther statistic accurately describes the fund. 

  As we noted in Chapter 24, and as is evi-

dent from  Figure 26.4 , an ability to conduct 

perfect market timing is much like obtaining 

a call option on the underlying portfolio with-

out having to pay for it. Similar nonlinearities 

would arise if the fund actually buys or writes 

options.  Figure  26.5 , panel A illustrates the 

case of a fund that holds a stock portfolio and 

writes put options on it, and panel B illustrates 

the case of a fund that holds a stock portfo-

lio and writes call options. In both cases, the 

characteristic line is steeper when portfolio 

returns are poor—in other words, the fund 

has greater sensitivity to the market when it is 

falling than when it is rising. This is the oppo-

site profile that would arise from timing abil-

ity, which is much like acquiring rather than 

writing options, and therefore would give the 

fund greater sensitivity to market advances.  

14

  

   

Return to Perfect Market Timer

Fitted Regression Line

Portfolio Return

Market Return

r

f

 Figure 26.4 

Characteristic line of a perfect market timer. 

The true characteristic line is kinked, with a shape like that 

of a call option. Fitting a straight line to the relationship 

will result in misestimated slope and intercept.  

Stock Alone

Stock Alone