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

Rate of Return Probability Return Expected Return Boom Normal Bust Boom Normal Bust Boom Normal Bust X           0.20           0.15                -   25% 60% 15%           0.05           0.09                -             0.14 Y           0.35           0.10         -0.30 25% 60% 15%           0.09           0.06         -0.05           0.10 Z           0.60           0.05         -0.40 25% 60% 15%           0.15           0.03         -0.06           0.12 Security Weight Expected Return ER* Weight X 30% 0.14 4.20% Y 30% 0.1025 3.08% Z 40% 0.12 4.80% Portfolio Return 12.08%

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