Consider the following probability distribution for stocks A and B: $\begin{array}{cccc}
\text { State } & \text { Probability } & \text { Return on Stock A } & \text { Return on Stock B } \
1 & 0.15 & 8 \% & 8 \% \
2 & 0.20 & 13\% & 7\% \
3 & 0.15 & 12\%& 6\% \
4 & 0.30 & 14\%& 9\% \
5 & 0.20 & 16\% & 11 \%
\end{array}$
The standard deviations of stocks A and B are _____ and _____, respectively.
A) 1.56%; 1.99%
B) 2.45%; 1.66%
C) 3.22%; 2.01%
D) 1.54%; 1.11%

Question

Consider the following probability distribution for stocks A and B: $\begin{array}{cccc}
\text { State } & \text { Probability } & \text { Return on Stock A } & \text { Return on Stock B } \
1 & 0.15 & 8 \% & 8 \% \
2 & 0.20 & 13\% & 7\% \
3 & 0.15 & 12\%& 6\% \
4 & 0.30 & 14\%& 9\% \
5 & 0.20 & 16\% & 11 \%
\end{array}$
  The standard deviations of stocks A and B are _____ and _____, respectively.
A) 1.56%; 1.99%
B) 2.45%; 1.66%
C) 3.22%; 2.01%
D) 1.54%; 1.11%

Quizplus · Accepted Answer

To calculate the standard deviation of the returns for stocks A and B, we first need to find the expected return (mean) for each stock, then calculate the variance, and finally take the square root of the variance to get the standard deviation.**For Stock A:**- Expected Return = $0.15 \times 8\% + 0.20 \times 13\% + 0.15 \times 12\% + 0.30 \times 14\% + 0.20 \times 16\% = 12.7\%$- Variance = $0.15 \times (8\% - 12.7\%)^2 + 0.20 \times (13\% - 12.7\%)^2 + 0.15 \times (12\% - 12.7\%)^2 + 0.30 \times (14\% - 12.7\%)^2 + 0.20 \times (16\% - 12.7\%)^2 = 6.01\%$- Standard Deviation = $\sqrt{6.01\%} \approx 2.45\%$**For Stock B:**- Expected Return = $0.15 \times 8\% + 0.20 \times 7\% + 0.15 \times 6\% + 0.30 \times 9\% + 0.20 \times 11\% = 8.35\%$- Variance = $0.15 \times (8\% - 8.35\%)^2 + 0.20 \times (7\% - 8.35\%)^2 + 0.15 \times (6\% - 8.35\%)^2 + 0.30 \times (9\% - 8.35\%)^2 + 0.20 \times (11\% - 8.35\%)^2 = 2.76\%$- Standard Deviation = $\sqrt{2.76\%} \approx 1.66\%$Therefore, the correct answer is B) 2.45%; 1.66%.

Consider the Following Probability Distribution for Stocks a and B