Investments, tenth edition

  Valuing Market Timing as a Call Option 

 The key to valuing market timing ability is to recognize that perfect foresight is equivalent 

to holding a call option on the equity portfolio. The perfect timer invests 100% in either 

the safe asset or the equity portfolio, whichever will provide the higher return. The rate of 

return is  at least  the risk-free rate. This is shown in  Figure 24.7 .  

 To see the value of information as an option, suppose that the market index currently 

is at  S  

0

  and that a call option on the index has an exercise price of  X   5   S  

0

 (1  1   r  

 f 

 ). If the 

market outperforms bills over the coming period,  S  

 T 

  will exceed  X,  whereas it will be less 

than  X  otherwise. Now look at the payoff to a portfolio consisting of this option and  S  

0

  

dollars invested in bills:  

  

22

 The conventional LPSD is based on the average squared deviation below the mean. Because the threshold 

performance in this application is the risk-free rate, we modify the LPSD for this discussion by taking squared 

deviations from that rate and the observations are conditional on being below that threshold. It ignores the num-

ber of such events. 

  

23

 It may seem hard to attribute such a big difference in final outcome solely to risk aversion. But think of it 

this way: the final value of the equity position is 133 times that of the bills position ($2,652 versus $20). Over 

86 years, this implies a reasonable annualized risk premium of 5.85%: 133 

1/86

   5  1.0585. 

  

24

 The analogy between market timing and call options, and the valuation formulas that follow from it, were devel-

oped in Robert C. Merton, “On Market Timing and Investment Performance: An Equilibrium Theory of Value for 

Market Forecasts,”  Journal of Business,  July 1981.