A stock has a beta of .9 and an expected return of 9 percent. A risk-free asset

Question

A stock has a beta of .9 and an expected return of 9 percent. A risk-free asset currently earns 4 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 .5, what are the portfolio weights?
c. If a portfolio of the two assets has an expected return of 8 percent, 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? Explain.

Explanation / Answer

a) Risk Free Asset return 4% Other Asset return 9% Return on portfolio in case of equal investment 4%*.5+9%*.5 Return on portfolio in case of equal investment 6.50% b) Beta of risk free asset 0 Beta of other asset 0.9 Beta 0.5 Let weight of other asset be x, then risk free asset weight will be (1-x) .5= X*.9 +0*(1-x) .5 = .9X x=.5/.9 = .5555 Weight of other asset 0.5555 Weight of risk free asset 0.4445 c) Return = 8% Let weight of other asset be x, then risk free asset weight will be (1-x) 8% = 9%*x + 4%*(1-x) .08= .09X + .04 -.04x .04=.05X Weight of other asset 80% Weight of risk free asset 20% Beta = .8*.9+.2*0=.72 d) Beta of risk free asset 0 Beta of other asset 0.9 Beta 1.8 Let weight of other asset be x, then risk free asset weight will be (1-x) 1.8= X*.9 +0*(1-x) 1.8 = .9X x=1.8/.9 = 2 Weight of other asset 2 Weight of risk free asset -1 In this case company has to make negative investment in risk free asset i.e. sell risk free asset

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