Consider the following probability distribution for stocks A and B: If you invest 35% of your money in A and 65% in B, what would be your portfolio's expected rate of return and standard deviation?

Question

Consider the following probability distribution for stocks A and B:  If you invest 35% of your money in A and 65% in B, what would be your portfolio's expected rate of return and standard deviation?

Quizplus · Accepted Answer

Firstly, to calculate the portfolio's expected rate of return, we need to take a weighted average of the expected returns of A and B:
Expected Return = (0.35 x 12%) + (0.65 x 8%) = 9.2%
To calculate the portfolio's standard deviation, we use the following formula:
Portfolio Standard Deviation = SQRT[(Weight of A)^2 x (Standard Deviation of A)^2 + (Weight of B)^2 x (Standard Deviation of B)^2 + 2 x (Weight of A) x (Weight of B) x (Covariance between A and B)]
Using the given data, the portfolio standard deviation is calculated as follows:
Portfolio Standard Deviation = SQRT[(0.35)^2 x (16%)^2 + (0.65)^2 x (1%)^2 + 2 x (0.35) x (0.65) x (-2%)] = 1.7%
Therefore, the portfolio's expected rate of return is 9.2% and its standard deviation is 1.7%. The closest option is C - 10%; 1.7%.

Consider the Following Probability Distribution for Stocks a and B