1 Consider the following informationState Probability A BBoom 06 20 -5Bust 04 -10 10a What are the expected return and standard deviation of stock A 5b What are the expected return and standard deviat

a. Expected return of stock A = 0.6(20%) + 0.4(-5%) = 11%.

To calculate the standard deviation of stock A, first we need to calculate the variance:

Variance of stock A = [0.6(20%-11%)^2 + 0.4(-5%-11%)^2] = 0.0945

Standard deviation of stock A = square root of variance = √0.0945 = 0.3076 (rounded to four decimal places)

b. Expected return of stock B = 0.6(-10%) + 0.4(10%) = 2%.

To calculate the standard deviation of stock B, first we need to calculate the variance:

Variance of stock B = [0.6(-10%-2%)^2 + 0.4(10%-2%)^2] = 0.0968

Standard deviation of stock B = square root of variance = √0.0968 = 0.3111 (rounded to four decimal places)

c. Expected return of portfolio = 0.5(11%) + 0.5(2%) = 6.5%.

To calculate the standard deviation of the portfolio, we need to use the formula:

Standard deviation of portfolio = [(0.5)^2(0.3076)^2 + (0.5)^2(0.3111)^2 + 2(0.5)(0.5)(0.3076)(0.3111)(-0.25)]^(1/2) = 0.2473 (rounded to four decimal places)

d. Diversification helps to reduce the overall risk of a portfolio by investing in multiple assets with different risk and return characteristics. In this case, investing in both stocks A and B reduces the overall standard deviation of the portfolio from 0.3076 (stock A) and 0.3111 (stock B) to 0.2473. This is because the returns of the two stocks are not perfectly correlated, meaning that when one stock performs poorly, the other may perform well, and vice versa. By diversifying, the investor can potentially achieve a higher return for a given level of risk