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Financial Services questions: Relative Valuation, Analyzing a Portfolio, CAPM and more...

Can you please assist me with these questions -

1. Stock Betas - A stock has an expected return of 12.5%, the risk-free rate is 5%, and the market risk premium is 6%. What must the beta of this stock be?

8. Expected Returns - A stock has a beta of .7, the expected return on the market is 15%, and the risk-free rate is 6.5%. What must the expected return on this stock be?

10. Portfolio Weights A stock has a beta of .9 and expected return of 12%. A risk-free asset currently earns 6%.
a. What is the expected return on a portfolio that is equally invested in the two assets?
b. If a portfolio of the two assets has a beat of .5, what are the portfolio weights?
c. If a portfolio of the two assets has an expected return of 11%, what is its beta?
d. If a portfolio of the two assets has a beta of 1.80, what are the portfolio weights? How do you interpret the weights for the two assets in this case?

12. Relative Valuation - Stock Y has a beta of 1.45 and an expected return of 17%. Stock Z has a beta of .85 and an expected return of 12%. If the risk-free rate is 6% and the market risk premium is 7.5%, are these stocks correctly priced?

18. Analyzing a Portfolio - You have $100,000 to invest in a portfolio containing Stock X, Stock Y, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 16.5% and that has only 70% of the risk of the overall market. If X has an expected return of 28% and a beta of 1.7, Y has an expected return of 14% and a beta of 1.1, and the risk free rate is 7%, how much money will you invest in Stock Y? How do you interpret your answer?

21. CAPM - John Wilson, a portfolio manager, is evaluating the expected performance of two common stocks, Furhman Labs, Inc., and Garten Testing, Inc. The risk-free rate is 5%, the expected return on the market is 11.5%, and the betas of the two stocks are 1.5 and .8, respectively. Wilson's own forecasts of the returns on the two stocks are 13.25% for Furhman Labs and 11.25% for Garten. Calculate the required return for each stock. Is each stock undervalued, fairly valued, or overvalued?

Solution Preview

1. Stock Betas - A stock has an expected return of 12.5%, the risk-free rate is 5%, and the market risk premium is 6%. What

must the beta of this stock be?

From CAPM model, Re = Rf + Beta * risk premium
i.e., 12.5% = 5% + 6%*Beta
7.5% = 6%*Beta
Beta = 7.5% / 6% = 1.25

8. Expected Returns - A stock has a beta of .7, the expected return on the market is 15%, and the risk-free rate is 6.5%.

What must the expected return on this stock be?

CAPM model:
Re = Rf + Beta*(Rm - Rf)
= 6.5% + 0.7 * (15% - 6.5%)
= 0.1245 = 12.5%

10. Portfolio Weights A stock has a beta of .9 and expected return of 12%. A risk-free asset currently earns 6%.
a. What is the expected return on a portfolio that is equally invested in the two assets?
Weight of stock is Ws = 0.5
weight of Risk free asset is Wf = 0.5
Then Re = Ws * Rs + Wf * Rf
= 0.5*12% + 0.5*6%
= 9%

b. If a portfolio of the two assets has a beta of .5, what are the portfolio weights?
portfolio Beta = Ws * Beta
i.e. 0.5 = Ws * 0.9
Ws = 0.56
Thus, the weight of stock is 0.56, and weight of Risk free asset is Wf = 0.44

c. If a ...

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