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A stock will have a loss of 12.5 percent in a recession, a return of 11.2...

A stock will have a loss of 12.5 percent in a recession, a return of 11.2 percent in a normal economy, and a return of 25.9 percent in a boom. There is 22 percent probability of a recession, 47 percent probability of normal economy, and 31 percent probability of boom. What is the standard deviation of the stock's returns?

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Answer #1

Standard deviation measures the risk of a security. Here we have various economic conditions and varying return. Therefore, inorder to calculate the standard deviation of stock we assign different probabilities to returns. i.e.,

Standard deviation means variance from it return. Hence to calculate standard deviation we first of measure return of the stock in different periods. i.e.,

returns = .22 * (-12.5%) + .47 *(11.20%) + .31 *(25.90%)

= (-.0275) + .05264 + .08029

= .10543 viz = 10.54%

variance = .22 (-12.5 -10.54)^2 + .47 (11.20 - 10.54)^2 + .31 (25.90 - 10.54)^2

= 116.79 + .2047 + 73.14

= root of 190.134

= 13.79%

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