Consider a stock that has a 40 percent chance of a return of 5 percent, and a 60 percent change of a return of 10 percent. The standard deviation of this probability distribution is closest to:
A) 0.6 percent.
B) 2.5 percent.
C) 3.6 percent.

Question

Quizplus · Accepted Answer

The expected return (E(R)) is calculated as: $E(R) = (0.4 \times 5\%) + (0.6 \times 10\%) = 2\% + 6\% = 8\%$.The variance ($\sigma^2$) is calculated as: $\sigma^2 = (0.4 \times (5\% - 8\%)^2) + (0.6 \times (10\% - 8\%)^2) = (0.4 \times (-3\%)^2) + (0.6 \times 2\%^2) = (0.4 \times 0.0009) + (0.6 \times 0.0004) = 0.00036 + 0.00024 = 0.0006$.The standard deviation ($\sigma$) is the square root of the variance: $\sigma = \sqrt{0.0006} \approx 0.0245$ or 2.45%, which rounds to approximately 2.5%, making the initial selection incorrect based on the calculation provided. The correct calculation leads to an answer not listed exactly as provided, indicating a need for clarification in the calculation or the options provided. However, based on the standard approach to calculating standard deviation in a probability distribution context, the process involves calculating the expected return, determining the variance by considering the squared differences from the expected return weighted by their probabilities, and then taking the square root of the variance to find the standard deviation.

Consider a Stock That Has a 40 Percent Chance of a Return