Investments, tenth edition

    Statistic  

  Actual  

  Normal Distribution  

  Large Stocks     Small Stocks     Large Stocks     Small Stocks  

 Maximum terminal loss (%) 

 95  

99  

82  

98 

 Probability of loss 

 .0095  

.0415  

.0064  

.0428 

 Probability of shortfall 

 .1044  

.1178  

.0603  

.1232 

  

24

  The Black Swan: The Impact of the Highly Improbable,  New York, Random House, 2010. 

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bod61671_ch05_117-167.indd   158

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  C H A P T E R  

5

  Risk, Return, and the Historical Record 

159

 What about risk for investors with 

other long-term horizons?  Figure 5.11  

compares 25-year to 10-year invest-

ments in large and small stocks. For 

an appropriate comparison we must 

supplement the 10-year investment 

with a 15-year investment in T-bills. 

To accomplish this comparison, we 

bootstrap 15-year samples from the 

history of T-bill rates and augment 

each sample with 10 annual rates 

drawn from the history of the risky 

investment. Panels A1 and A2 in 

 Figure  5.11  show the comparison for 

large stocks. The frequency distribu-

tions reveal a substantial difference in 

the risks of the terminal portfolio. This 

difference is clearly manifested in the 

portfolio performance statistics. The 

same picture arises in panels B1 and 

B2 for small stocks. Notice that even 

a 10-year investment in small stocks 

could lead to a terminal loss of 94%.  

  Figure  5.12   shows  trajectories  of 

wealth indexes for some of the pos-

sible outcomes of a 25-year invest-

ment in large stocks, compared with the wealth index of the average outcome of a T-bill 

portfolio. The outcomes of the stock portfolio in  Figure 5.12  range from the worst, through 

the bottom 1% and 5% of terminal value, and up to the mean and median terminal values. 

The bottom 5% still results in a significant shortfall relative to the T-bill portfolio. In sum, 

the analysis clearly rejects the notion that stocks become less risky in the long run.  

 Yet many practitioners hold on to the view that investment risk is less pertinent to long-

term investors. A typical demonstration shown in the nearby box relies on the fact that the 

standard deviation (or range of likely outcomes) of  annualized  returns is lower for longer-

term horizons. But the demonstration is silent on the range of  total   returns.