5. (10 points) Dybvig Incorporation stock has a beta of 1.13 and an expected ret

Question

5. (10 points) Dybvig Incorporation stock has a beta of 1.13 and an expected return of 12.1 percent. A risk-free asset currently earns 5 percent. 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 beta of .50, what are the portfolio weights? c. If a portfolio of the two assets has an expected return of 10 percent, what is its beta? If a portfolio of the two assets has a beta of 2.26, what are the portfolio weights? d. e. How do you interpret the weights for the two assets in case (d)? Explain.

Explanation / Answer

Let weight of Dybvig Incorporation Stock be x

weight of risk free asset is 56%(Rounded off)

weight of risk free asset is -100%

e. Weights of 200% and -100% in d interpret that, to borrow a sum equal to original fund available having the same characteristics as of risk free asset and to invest such borrowed sum together with the original fund available to stocks of Dybvig Incorporation.

a. Calculation of expected return of portfolio The return of a portfolio is the weighted average return of the securities which constitute the porfolio. Security Weight Expected Return Weight*Expected Return Dybvig Incorporation Stock 0.5 12.1 6.05 Risk free asset 0.5 5 2.5

Portfolio Return 8.55 b. Calculation of weights The beta of a portfolio is the weighted average beta of the securities which constitute the porfolio

Let weight of Dybvig Incorporation Stock be x

Security Weight Beta Weight*Expected Return Dybvig Incorporation Stock x 1.13 1.13x Risk free asset 1-x 0 0 1.13x = .5 x = .44 weight of Dybvig Incorporation Stock is 44% (Rounded off)

weight of risk free asset is 56%(Rounded off)

note: beta of risk free asset is zero c. Calculation of portfolio beta a) Find weight under given portfolio return Let weight of Dybvig Incorporation Stock be x Security Weight Expected Return Weight*Expected Return Dybvig Incorporation Stock x 12.1 12.1x Risk free asset 1-x 5 5(1-x) Portfolio Return 10 12.1x + 5 - 5x = 10 7.1x = 5 x = 70% weight of Dybvig Incorporation Stock is 70% (Rounded off) weight of risk free asset is 30% (Rounded Off) b) Calculation of portfolio beta Security Weight Beta Weight*Expected Return Dybvig Incorporation Stock 0.7 1.13 0.791 Risk free asset 0.3 0 0 Portfolio Beta 0.791 d. Calculation of weights Let weight of Dybvig Incorporation Stock be x Security Weight Beta Weight*Expected Return Dybvig Incorporation Stock x 1.13 1.13x Risk free asset 1-x 0 0 1.13x = 2.26 x = 2 weight of Dybvig Incorporation Stock is 200%

weight of risk free asset is -100%

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