Investments, tenth edition

Portfolio

Estimate

P

Q

Alpha (a)

1.77 (1.63)

–2.29 (5.28)

Beta (b)

0.70 (0.69)

1.10 (1.40)

Timing (c)

0.00

0.10

R-SQR

0.91 (0.91)

0.98 (0.64)

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bod61671_ch24_835-881.indd   856

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  C H A P T E R  

2 4

  Portfolio Performance Evaluation

857

of portfolios  P  and  Q  remains unclear in the sense that the value of the timing success and 

selectivity failure of  Q  compared with  P  has yet to be evaluated. The important point for 

performance evaluation, however, is that expanded regressions can capture many of the 

effects of portfolio composition change that would confound the more conventional mean-

variance measures.  

   The Potential Value of Market Timing 

 Suppose we define perfect market timing as the ability to tell (with certainty) at the begin-

ning of each year whether the S&P 500 portfolio will outperform the strategy of rolling 

over 1-month T-bills throughout the year. Accordingly, at the beginning of each year, the 

market timer shifts all funds into either cash equivalents (T-bills) or equities (the all U.S. 

stock portfolio), whichever is predicted to do better. Beginning with $1 on January 1, 1927, 

how would the perfect timer end an 86-year experiment on December 31, 2012, in com-

parison with investors who kept their funds in either equity or T-bills for the entire period? 

  Table 24.4 , columns 1–3, presents summary statistics for each of the three passive strat-

egies, computed from the historical annual returns of bills and equities. From the returns 

on stocks and bills, we calculate wealth indexes of the all-bills and all-equity investments 

and show terminal values for these investors at the end of 2012. The return for the perfect 

timer in each year is the  maximum  of the return on stocks and the return on bills.  

 The first row in  Table 24.4  tells all. The terminal value of investing $1 in bills over the 

86 years (1927–2012) is $20, while the terminal value of the same initial investment in 

equities is about $2,652. We saw a similar pattern for a 25-year investment in Chapter 5; 

the much larger terminal values (and difference between them) when extending the hori-

zon from 25 to 86 years is just another manifestation of the power of compounding. We 

argued in Chapter 5 that as impressive as the difference in terminal values is, it is best 

interpreted as no more than fair compensation for the risk borne by equity investors. 

Notice that the standard deviation of the all-equity investor was a hefty 20.39%. This is 

also why the geometric average of stocks for the period is “only” 9.60%, compared with 

the arithmetic average of 11.63%. (The difference between the two averages increases 

with volatility.)