Consider the following: What is the expected return on an equally weighted portf
ID: 2724545 • Letter: C
Question
Consider the following:
What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)
What is the variance of a portfolio invested 28 percent each in A and B and 44 percent in C? (Do not round intermediate calculations. Round your answer to 5 decimal places (e.g., 32.16161).)
Rate of Return if State Occurs State of Probability of State Economy of Economy Stock A Stock B Stock C Boom .73 .11 .05 .41 Bust .27 .30 .36 –.21 Required: (a)What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)
Expected return % (b)What is the variance of a portfolio invested 28 percent each in A and B and 44 percent in C? (Do not round intermediate calculations. Round your answer to 5 decimal places (e.g., 32.16161).)
Variance of a portfolioExplanation / Answer
Answer:(a) To find the expected return of the portfolio, we need to find the return of the portfolio in each state of the economy. This portfolio is a special case since all three assets have the same weight. To find the expected return in an equally weighted portfolio, we can sum the returns of each asset and divide by the number of assets, so the expected return of the portfolio in each state of the economy is:
Boom: E(R p ) = (.11 + .05 + .41)/3 = .19 or 19%
Bust: E(R p ) = (.30 + .36 .21)/3 = .15 or 15%
To find the expected return of the portfolio, we multiply the return in each state of the economy by the probability of that state occurring, and then sum. Doing this, we find:
E(R p ) = .73(.19) + .27(.15) = .1792 or 17.92%
Answer:(b) This portfolio does not have an equal weight in each asset. We still need to find the return of the portfolio in each state of the economy. To do this, we will multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get:
Boom: E(R p )=.28(.11) +.28(.05) + .44(.41) =.2252 or 22.52%
Bust: E(R p ) =.28(.30) +.28(.36) + .44(.21) =0.0924 or 9.24%
And the expected return of the portfolio is:
E(R p ) = .73(.2252) + .27(0.0924) = .189344 or 18.9344%
To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, than add all of these up. The result is the variance. So, the variance and standard deviation of the portfolio is:
p 2 = .73(.2252 – .189344) 2 + .27(0.0924 – .189344) 2 = .003476