## Do you live in a meanvariance world

Assume that you had to pick between two investments. They have the same expected return of 15% and the same standard deviation of 25%; however, investment A offers a very small possibility that you could quadruple your money, while investment B's highest possible payoff is a 60% return. Would you a. be indifferent between the two investments, since they have the same expected return and standard deviation?

b. prefer investment A, because of the possibility of a high payoff?

c. prefer investment B, because it is safer?

Illustration 3.1: Calculation of standard deviation using historical returns: Disney

We collected the data on the returns we would have made on a monthly basis for every month from January 1999 to December 2003 on an investment in Disney stock. The monthly returns are graphed in figure 3.4:

Figure 3.4: Returns on Disney: 1999- 2003

Figure 3.4: Returns on Disney: 1999- 2003

Month e b P

The average monthly return on Disney over the 59 months was -0.07%. The standard deviation in monthly returns was 9.33% and the variance in returns was 86.96%.2 To convert monthly values to annualized ones: Annualized Standard Deviation = 9.33% *Vl2 = 32.31% Annualized Variance = 86.96% * 12 = 1043.55%

Without making comparisons to the standard deviations in stock returns of other companies, we cannot really draw any conclusions about the relative risk of Disney by just looking at its standard deviation.

optvar.xls is a dataset on the web that summarizes standard deviations and variances of stocks in various sectors in the United States.

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