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

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    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?

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    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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