Question

Consider the following information: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock B Stock C Boom .20 .31 .41 .32 Good .50 .18 .12 .11 Poor .25 −.04 −.07 −.05 Bust .05 −.15 −.27 −.08 a.

Your portfolio is invested 28 percent each in A and C, and 44 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculaitons. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return

b-1 What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.) Variance=

b-2 What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation=

Answer 1

The expected return of the portfolio is 28.08%. The variance of the portfolio is 0.028731, and the standard deviation is 16.96%.

Step-by-step explanation:

To calculate the expected return of the portfolio, we need to multiply the rate of return for each stock by the weight of that stock in the portfolio, and then sum up the results. The expected return of the portfolio can be calculated as follows:

Expected Return = (Weight of Stock A * Rate of Return for Stock A) + (Weight of Stock B * Rate of Return for Stock B) + (Weight of Stock C * Rate of Return for Stock C)

Expected Return = (0.28 * 0.31) + (0.44 * 0.18) + (0.28 * 0.41)

Expected Return = 0.0868 + 0.0792 + 0.1148

Expected Return = 0.2808

Therefore, the expected return of the portfolio is 28.08%.

To calculate the variance of the portfolio, we need to calculate the weighted sum of the squared deviations from the expected return for each stock, and then multiply that by the weights of the stocks in the portfolio. The variance can be calculated as follows:

Variance = (Weight of Stock A * (Rate of Return for Stock A - Expected Return)^2) + (Weight of Stock B * (Rate of Return for Stock B - Expected Return)^2) + (Weight of Stock C * (Rate of Return for Stock C - Expected Return)^2)

Variance = (0.28 * (0.31 - 0.2808)^2) + (0.44 * (0.18 - 0.2808)^2) + (0.28 * (0.41 - 0.2808)^2)

Variance = 0.007784 + 0.011737 + 0.009210

Variance = 0.028731

Therefore, the variance of the portfolio is 0.028731.

To find the standard deviation of the portfolio, we take the square root of the variance. The standard deviation can be calculated as follows:

Standard Deviation = √Varianc

Standard Deviation = √0.028731

Standard Deviation = 0.1696

Therefore, the standard deviation of the portfolio is 16.96%.

Answer 2

The expected return of a portfolio is calculated using the weights of the stocks and their expected returns in different economic states. Variance and standard deviation measure the risk of the portfolio's returns deviating from the expected return. The steps include calculating the weighted expected returns and then the dispersion measures.

Step-by-step explanation:

The student is working on a problem involving portfolio analysis, specifically, calculating the expected return, variance, and standard deviation of a portfolio consisting of three stocks (A, B, and C). The expected return of the portfolio is calculated by multiplying the returns of each stock by the probability of each economic state occurring and by the portfolio weight, then summing these results. Variance and standard deviation offer measures of the portfolio's risk. They show how spread out the returns may be from the expected return; a higher value indicates more risk.

To calculate the expected return (E(R)): E(R) = (28% × E(Ra)) + (44% × E(Rb)) + (28% × E(Rc)), where E(Ra), E(Rb), and E(Rc) are the expected returns of stocks A, B, and C respectively.

To find the variance and standard deviation, we need to calculate the weighted sum of the squares of the deviations from the expected return for each possible state, and then take the square root of the variance for the standard deviation.