Problem 11-27 Analyzing a Portfolio [LO 2] You want to create a portfolio equall
ID: 2725043 • 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
a) Portfolio is equally risky as the market then of the portfolio must be equal to 1. of the risk-free asset is zero Asset Investment Weights Beta Stock A $145,000 29.00% 0.9 Stock B $135,000 27.00% 1.35 Stock C ? 1.5 Risk-free asset ? 0 Total $500,000 100.00% Use the equation for the of a portfolio to find the weight of the Stock C p = 1.0 = .29(0.90) + .27(1.35) + wC(1.50) + wRf(0) p = 1.0 = wA(0.90) + wB(1.35) + wC(1.50) + wRf(0) Solving for the weight of Stock C ( wC ) 24.97% Investment in Stock C = $500,000 x 24.97% $124,833.33 b) Asset Investment Weights Stock A $145,000 29.00% Stock B $135,000 27.00% Stock C $124,833.33 24.97% Risk-free asset $95,166.67 19.03% Total $500,000 100.00% The weight of the risk-free asset must be 100% minus weight of Stock A,B and C 1 = wA + wB + wC + wRf = 1 – 0.29 – 0.27 – 0.2497 = wRf wRF 19.03% Investment in Risk Free Asset = $500,000 x 19.03% $95,166.67