Question

There are two stocks in the market, Stock A and Stock B . The price of Stock A today is $85. The price of Stock A next year will be $74 if the economy is in a recession, $97 if the economy is normal, and $107 if the economy is expanding. The probabilities of recession, normal times, and expansion are .30, .50, and .20, respectively. Stock A pays no dividends and has a correlation of .80 with the market portfolio. Stock B has an expected return of 15.0 percent, a standard deviation of 35.0 percent, a correlation with the market portfolio of .34, and a correlation with Stock A of .46. The market portfolio has a standard deviation of 19.0 percent. Assume the CAPM holds.

b-1. What is the expected return of a portfolio consisting of 75 percent of Stock A and 25 percent of Stock B? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return % b-2. What is standard deviation of a portfolio consisting of 75 percent of Stock A and 25 percent of Stock B? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation % c. What is the beta of the portfolio in part (b)? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.) Beta of the portfolio

Answer 1

First let us find the expected return and standard deviation of stock A

The return for different situation for stock A is

Recession=(74-85)/85=-12.94%

normal=(97-85)/85=14.12%

Expanding=(107-85)/85=25.88%

Expected return of A=8.35%

std of A=14.63%

b2)beta of portfolio=correlation (portfolio,market)*(std of portfolio/std of market)