M Homework 3 C ezto.mheducation.com/hm.tpx 31 1.00 points Problem 11-27 Analyzin
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M Homework 3 C ezto.mheducation.com/hm.tpx 31 1.00 points Problem 11-27 Analyzing a Portfolio ILO 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: Asset Investment Beta 136,000 Stock A 81 1.26 Stock B 144,000 Stock C 1.41 Risk-free asset Requirement 1: How much will you invest in Stock C? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Investment in Stock C Requirement 2: 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 Investment in risk-free asset References eBook & Resources Difficulty: Intermediate Worksheet Learning objective: 11-02 Explain the Problem 11-27 Analyzing a Portfolio [Lo 21 impact of diversification e G 4:52 PM 5/11/2016Explanation / 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 = $136,000 / $500,000 = .272
Wb = 144000/500000 = .288
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 (0.81) + w B (1.26) + w C (1.41) + w Rf (0) 1.0 = 0.272(0.81) + 0.288(1.26) + w C (1.41)
w C = 0.295
Invest in Stock C = 0.295($500,000) Invest in Stock C = $147801.4
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 – 0.295 – w Rf w Rf = 0.=.144
Invest in risk-free asset = 0.144($500,000) Invest in risk-free asset = 72198.58
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