Investments, tenth edition

 Figure 24.5 

Portfolio returns. Returns in last four quarters 

are more variable than in the first four.  

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  C H A P T E R  

2 4

  Portfolio Performance Evaluation 

855

    24.4 

Market Timing 

  In its pure form, market timing involves shifting funds between a market-index portfolio 

and a safe asset, depending on whether the market index is expected to outperform the safe 

asset. In practice, most managers do not shift fully between T-bills and the market. How 

can we account for partial shifts into the market when it is expected to perform well? 

 To simplify, suppose that an investor holds only the market-index portfolio and T-bills. 

If the weight of the market were constant, say, .6, then portfolio beta would also be con-

stant, and the SCL would plot as a straight line with slope .6, as in  Figure 24.6, panel A . 

If, however, the investor could correctly time the market and shift funds into it in periods 

when the market does well, the SCL would plot as in  Figure 24.6, panel B . If bull and bear 

markets can be predicted, the investor will shift more into the market when the market 

is about to go up. The portfolio beta and the slope of the SCL will be higher when  r  

 M 

   is 

higher, resulting in the curved line that appears in  Figure 24.6, panel B .  

 Treynor and Mazuy were the first to propose estimating such a line by adding a squared 

term to the usual linear index model:  

19

   

   r

P

2 r

f

5 a 1 b(r

M

2 r

f

)

1 c(r

M

2 r

f

)

2

1 e

P

  

 where   r  

 P 

  is the portfolio return, and  a,    b,  and  c  are estimated by regression analysis. 

If  c  turns out to be positive, we have evidence of timing ability, because this last term will 

make the characteristic line steeper as  r  

 M 

   2   r  

 f 

  is larger. Treynor and Mazuy estimated this 

equation for a number of mutual funds, but found little evidence of timing ability. 

 

A similar but simpler methodology was proposed by Henriksson and Merton. 

 

20

   

These authors suggested that the beta of the portfolio take only two values: a large value 

if the market is expected to do well and a small value otherwise. Under this scheme 

the portfolio characteristic line appears as  Figure 24.6, panel C . Such a line appears in 

regression form as

   r

P

2 r

f

5 a 1 b(r

M

2 r

f

)

1 c(r

M

2 r

f

)D

1 e

P

  

 where   D  is a dummy variable that equals 1 for  r  

 M 

  .  r  

 f 

  and zero otherwise. Hence the beta 

of the portfolio is  b  in bear markets and  b   1   c  in bull markets. Again, a positive value of  c  

implies market timing ability. 

 Henriksson  

21

   estimated this equation for 116 mutual funds. He found that the average 

value of  c  for the funds was  negative,  and equal to 2.07. In sum, the results showed little 

evidence of market timing ability. Perhaps this should be expected; given the tremendous 

values to be reaped by a successful market timer, it would be surprising in nearly efficient 

markets to uncover clear-cut evidence of such skills. 

 To illustrate a test for market timing, return to  Table 24.2 . Regressing the excess returns 

of portfolios  P  and  Q  on the excess returns of  M  and the square of these returns,

    r

P

2 r

f

5 a

P

1 b

P 

(r

M

2 r

f

)

1 c

P 

(r

M

2 r

f

)

2

1 e

P

 r

Q

2 r

f

5 a

Q

1 b

Q 

(r

M

2 r

f

)

1 c

Q 

(r

M

2 r

f

)

2

1 e

Q

  

  

19

 Jack L. Treynor and Kay Mazuy, “Can Mutual Funds Outguess the Market?”  Harvard Business Review   43 

(July–August 1966). 

  

20

 Roy D. Henriksson and R. C. Merton, “On Market Timing and Investment Performance. II. Statistical Proce-

dures for Evaluating Forecast Skills,”  Journal of Business  54 (October 1981). 

  

21

 Roy D. Henriksson, “Market Timing and Mutual Fund Performance: An Empirical Investigation,”  Journal of 

Business  57 (January 1984). 

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856

P A R T   V I I

  Applied Portfolio Management

 we derive the following statistics: