You have decided to invest 30 percent in X; 30 percent in Y; and 40 percent in Z

Question

You have decided to invest 30 percent in X; 30 percent in Y; and 40 percent in Z. The probability of the state of the economy is Boom 25%; Normal 60%; and, Bust 15%. The rate of return for stock X is Boom .20; Normal .15; and, Bust .00. The rate of return for stock Y is Boom .35; Normal .10; and, Bust -.30. The rate of return for stock Z is Boom .60; Normal .05; Bust -.40.
A] What is the portfolio expected return?

B] If the expected T-bill rate is 1.5 percent, what is the expected risk premium on the portfolio?

Explanation / Answer

Estimated rate of return for stock X is 0.25*0.20 + 0.60*0.15 + 0.15*0.00 = 0.14 = 14%

Estimated rate of return for stock Y is 0.25*0.35 + 0.60*0.10 + 0.15*(-0.30) = 0.1025 = 10.25%

Estimated rate of return for stock Z is 0.25*0.60 + 0.60*0.05 + 0.15*(-0.40) = 0.12 = 12%

Total estimated return on Portfolio = 0.30(14%)+0.30(10.25%)+0.4(12%)=12.075%

If the expected T-bill rate is 1.5 percent, expected risk premium on the portfolio = 12.075-1.5=10.575%

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