Investments, tenth edition

  Strategy  

  Bills  

  Equities  

  Perfect Timer  

  Imperfect Timer   *   

  Terminal Value  

 20  

2,652  

352,796  

8,859 

  Arithmetic Average  

 3.59  

11.63  

16.75  

11.98 

  Standard Deviation  

 3.12  

20.39  

13.49  

14.36 

  Geometric Average  

 3.54  

9.60  

16.01  

11.09 

  LPSD (relative to bills)  

 0  

21.18  

0  

17.15 

  Minimum  

†

  

  2 0.04  

 2 44.00  

 2 0.02  

 2 27.09 

  Maximum  

 14.72  

57.42  

57.42  

57.42 

  Skew  

 0.99 

  2 0.42 

 0.72  

0.71 

  Kurtosis  

 0.98  

0.02 

  2 0.13 

 1.50 

 Table 24.4 

 Performance of bills, equities, and (annual) timers—perfect and imperfect 

 *The imperfect timer has  P  

1

  5 .7, and  P 

2

  5  .7. Therefore,  P 

1 

 1   P 

2

  2  1  5  .4. 

 

†

A negative rate on “bills” was observed in 1940. The Treasury security used in the data series in these early years was actually not a 

T-bill but a T-bond with 30 days to maturity. 

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P A R T   V I I

  Applied Portfolio Management

 Now observe that the terminal value of the perfect timer is about $353,000, a 133-fold 

increase over the already large terminal value of the all-equity strategy! In fact, this result 

is even better than it looks, because the return to the market timer is truly risk-free. This 

is the classic case where a large standard deviation (13.49%) has nothing to do with risk. 

Because the timer never delivers a return below the risk-free rate, the standard deviation is 

a measure of  good  surprises only. The positive skew of the distribution (compared with the 

negative skew of equities) is a manifestation of the fact that the extreme values are all 

positive. Another indication of this stellar performance is the minimum and maximum 

returns—the minimum return equals the minimum return on bills (in 1940) and the maxi-

mum return is that of equities (in 1933)—so that all negative returns on equities (as low as 

244% in 1931) were avoided by the timer. Finally, the best indication of the performance 

of the timer is a lower partial standard deviation, LPSD.  

22

   The LPSD of the all-equity port-

folio is only slightly greater than the conventional standard deviation, but it is necessarily 

zero for the perfect timer.  

 If we interpret the terminal value of the all-equity portfolio in excess of the value of the 

T-bill portfolio entirely as a risk premium commensurate with investment risk, we must 

conclude that the risk-adjusted equivalent value of the all-equity terminal value is the same 

as that of the T-bill portfolio, $20.  

23

   In contrast, the perfect timer’s portfolio has no risk, 

and so receives no discount for risk. Hence, it is fair to say that the forecasting ability of the 

perfect timer converts a $20 final value to a value of $352,796.