Consider the following probability distribution for stocks C and D: $10.307%−9%20.5011%14%30.20−16%26%\begin{array}{cccc}\text { State } & \text { Probability } & \text { Return on Stock C} & \text { Return on Stock D } \\1 & 0.30 & 7\% & -9\% \\2 & 0.50 & 11\% & 14\% \\3 & 0.20 & -16\% & 26\%\end{array}$

The standard deviations of stocks C and D are _ and _, respectively.

A) 7.62%; 11.24%
B) 11.24%; 7.62%
C) 10.35%; 12.93%
D) 12.93%; 10.35%

Question

Consider the following probability distribution for stocks C and D:

10.307%−9%20.5011%14%30.20−16%26%\begin{array}{cccc}\text { State } & \text { Probability } & \text { Return on Stock C} & \text { Return on Stock D } \\1 & 0.30 & 7\% & -9\% \\2 & 0.50 & 11\% & 14\% \\3 & 0.20 & -16\% & 26\%\end{array}

The standard deviations of stocks C and D are _____ and _____, respectively.

A) 7.62%; 11.24%
B) 11.24%; 7.62%
C) 10.35%; 12.93%
D) 12.93%; 10.35%

Brandon Schubmehl · Accepted Answer

Final Answer : C, Explanation :   The standard deviation is calculated using the formula for variance:   σ 2 = ∑ ( p i × ( r i − r ˉ ) 2 ) \sigma^2 = \sum (p_i 	imes (r_i - \bar{r})^2) σ 2 = ∑ ( p i ​ × ( r i ​ − r ˉ ) 2 )  , where   p i p_i p i ​   is the probability,   r i r_i r i ​   is the return, and   r ˉ \bar{r} r ˉ   is the expected return. After calculating, the standard deviations for stocks C and D are 10.35% and 12.93%, respectively.

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