A stock will have a loss of 13.6 percent in a recession, a return of 12.3 percent in a normal economy, and a return of 27 percent in a boom. There is 33 percent probability of a recession, 36 percent probability of normal economy, and 31 percent probability of boom. What is the standard deviation of the stock's returns?

Standard deviation =21.34

Explanation:

Standard deviation is measure of the total risks of an investment. It measures the volatility in return of an investment as a result of both systematic and non-systematic risks. Non-systematic risk includes risk that are unique to a company like poor management, legal suit against the company .

Standard deviation is the sum of the squared deviation of the individual return from the mean return under different scenarios

Expected return (r) = (13.6% × 0.33 ) +  (12.3% × 0.36)  + (27%× 0.31)=17.3%

Outcome           R       (R- r )^2           P×(R- r )^2

Recession        13.6       13.6                 4.5

Normal         12.3         24.9                  8.9

Boom           27%        94.4                   29.3

Total                                                   42.7

Standard deviation = √42.7 = 21.34

Standard deviation =21.34

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