Consider the following information on a portfolio of three stocks: If your portf

Question

Consider the following information on a portfolio of three stocks: If your portfolio is invested 44 percent each in A and B and 12 percent in C, what is the portfolio's expected return, the variance, and the standard deviation? (Do not round intermediate calculations. Round your variance answer to 5 decimal places (e.g., 32.16161) and input your other answers as a percentage rounded to 2 decimal places (e.g., 32.16).) If the expected T-bill rate is 4.2 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Explanation / Answer

a) We need to find the return on the portfolio in each state of economy. To do this, we will multyply the return of each asset by its portfolio wweight and then sum the products to get the portfolio return in each state of economy. Doing so we get

To calculate the standard deviation, we first need to calculate the variance. To find the variance we need to find the square deviations from the expected return. We then multiply each possible squared deviation by its probability and then sum. The result is variance. So ,Variiance and standard deviationof portfolio are:

Variance = (0.14*(0.268-.1286)2+(.51*(.2108-0.1286)2+(.35*(-0.047-.1286)2

= 0.0169343

Sd = Variance 0.5 = 0.130131961 or 13.013%

b) Expected Risk Premium = Expected return of a risky asset minus risk free asset

= 0.1286 -0.042

= 0.086578 or 8.66%

Boom E(Rp) = (0.44*0.11)+(0.44*0.36)+(0.12*0.51) = 0.268 or 26.8 % Normal E(Rp) = (0.44*0.19)+(0.44*0.21)+(0.12*0.29) = 0.2108 or 21.08 % Bust E(Rp) = (0.44*0.20)+(0.44*-0.20)+(0.12*-0.39) = -0.047 or -4.68 % And the Expected return of the portfolio is E(Rp) = (0.14*0.268)+(.51*.2108)+(.35*-0.047)= 0.1286 or 12.86 %

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