1) A mutual fund manager has a $20 million portfolio with a beta of 0.95. The risk-free rate is 3.75%, and the market risk premium is 5.6%. The manager expects to receive an additional $5 million, which she plans to invest in a number of stocks. After investing the additional funds, she wants the fund’s required return to be 9.75%. What should be the average beta of the new stocks added to the portfolio? Hint: calculate the beta of the portfolio AFTER the additional investment, then use that to calculate the average beta of the additional investment. You must show your work to receive full credit.
2) Stock A has an expected return of 7%, a standard deviation of expected returns of 35%, a correlation coefficient with the market of -0.3, and a beta coefficient of -0.5. Stock B has an expected return of 12%, a standard deviation of returns of 10%, a 0.7 correlation with the market, and a beta coefficient of 1.0. Which security is riskier? Why?
3) A stock has a required return of 11.2%, the risk-free rate is 4.2%, and the market risk premium is 4.2%. What is the stock’s beta? You must show your work to receive full credit.
4) Calculate the required rate of return for Aggies Enterprises assuming that investors expect a 4.6% rate of inflation in the future. The real risk-free rate is 3.3%, and the market risk premium is 7.1%. Aggie has a beta of 0.77, and its realized rate of return has averaged 13.2% over the past 5 years. You must show your work to receive full credit.