Problem 11-27 Analyzing a Portfolio [LO 2] You want to create a portfolio equall
ID: 2724221 • Letter: P
Question
Problem 11-27 Analyzing a Portfolio [LO 2]
You want to create a portfolio equally as risky as the market, and you have $500,000 to invest. Information about the possible investments is given below:
How much will you invest in Stock C? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)
How much will you invest in the risk-free asset? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)
You want to create a portfolio equally as risky as the market, and you have $500,000 to invest. Information about the possible investments is given below:
Explanation / Answer
We know the total portfolio value and the investment of two stocks in the portfolio, so we can find the weight of these two stocks. The weights of Stock A and Stock B are:
w A = $135,000 / $500,000 = .27
Wb = 145000/500000 = .29
Since the portfolio is as risky as the market, the of the portfolio must be equal to one. We also know the of the risk-free asset is zero. We can use the equation for the of a portfolio to find the weight of the third stock. Doing so, we find: P = 1.0 = w A (0.80) + w B (1.25) + w C (1.40) + w Rf (0) 1.0 = 0.270(0.80) + 0.290(1.25) + w C (1.40)
w C = 0.301071
Invest in Stock C = 0.301071($500,000) Invest in Stock C = $150,535.71
We also know the total portfolio weight must be one, so the weight of the risk-free asset must be one minus the asset weight we know, or: 1 = w A + w B + w C + w Rf = 1 – 0.270 – 0.290 – 0.301071 – w Rf w Rf = 0.138929
Invest in risk-free asset = 0.138929($500,000) Invest in risk-free asset = $69,464.29