Assume the probability of a pessimistic, most likely and optimistic state of nature is .25, .45 and .30, and the returns associated with those states of nature are 10%, 12%, and 16% for asset X. Based on this information, the expected return and standard deviation of return are:
A) 12.0% and 4.0%
B) 12.7% and 2.3%
C) 12.7% and 4.0%
D) 12.0% and 2.3%

Question

Quizplus · Accepted Answer

The expected return (ER) is calculated as the sum of each state's return multiplied by its probability: ER = (0.25 * 10%) + (0.45 * 12%) + (0.30 * 16%) = 2.5% + 5.4% + 4.8% = 12.7%. The standard deviation (SD) requires calculating the variance first, which involves the squared differences between each state's return and the ER, each weighted by its probability, and then taking the square root of the variance. The calculation for variance (Var) is: Var = (0.25 * (10% - 12.7%)^2) + (0.45 * (12% - 12.7%)^2) + (0.30 * (16% - 12.7%)^2). This simplifies to Var = (0.25 * 7.29) + (0.45 * 0.49) + (0.30 * 10.89) = 1.8225 + 0.2205 + 3.267 = 5.31. The square root of 5.31 gives the standard deviation, which is approximately 2.3%. Therefore, the expected return is 12.7% and the standard deviation is approximately 2.3%.

Assume the Probability of a Pessimistic, Most Likely and Optimistic