Final Answer:
a) The expected rate of return, r^y, for stock Y is 14%.
b) It is not possible that most investors will regard stock Y as being less risky than stock X.
Step-by-step explanation:
a) To calculate the expected rate of return, r^y, for stock Y, we multiply the probability of each return by the corresponding return and sum them up.
The calculations are as follows:
= (0.1 * -35%) + (0.2 * 0%) + (0.4 * 20%) + (0.2 * 25%) + (0.1 * 45%)
= -3.5% + 0% + 8% + 5% + 4.5%
= 14%
Therefore, the expected rate of return, r^y, for stock Y is 14%.
b) To calculate the standard deviation of expected returns, Qx, for stock X, we need to calculate the variance first.
The calculations are as follows:
= ((0.1 * (10% - 12%)^2) + (0.2 * (2% - 12%)^2) + (0.4 * (12% - 12%)^2) + (0.2 * (20% - 12%)^2) + (0.1 * (38% - 12%)^2))^0.5
= ((0.01 * (-2%)^2) + (0.04 * (-10%)^2) + (0.04 * (0%)^2) + (0.04 * (8%)^2) + (0.01 * (26%)^2))^0.5
= (0.0004 + 0.004 + 0 + 0.00256 + 0.00676)^0.5
= 0.01372^0.5
= 0.1171
Therefore, the standard deviation of expected returns, Qx, for stock X is 11.71%.
To calculate the coefficient of variation for stock Y, we divide the standard deviation of stock Y (Qy = 20.35%) by the expected rate of return for stock Y (r^y = 14%) and multiply by 100 to express it as a percentage.
Coefficient of variation (CV) = (Qy / r^y) * 100
CV = (20.35% / 14%) * 100
CV = 145.36
Based on the coefficient of variation, we can compare the riskiness of different stocks. If the coefficient of variation is higher, it indicates higher relative risk. In this case, stock Y has a coefficient of variation of 145.36, which is higher than the coefficient of variation for stock X. This suggests that stock Y is regarded as more risky compared to stock X.