Suppose you have a portfolio consisting of three stocks. You invest a total of $

Question

Suppose you have a portfolio consisting of three stocks. You invest a total of $200,000 in the stocks. The investments and beta for the stocks are shown in the following table. Use the table to complete parts (a) through (c) below. Stock Investment Beta 1 $60,000 1.25 2 $40,000 (0.5) 3 $100,000 1.5 (a) Assume the risk-free rate is 5.5% and the expected return for the market is 10%. Estimate the appropriate required rate of return for each stock. (b) Compute the portfolio beta. (c) Find the portfolio

Explanation / Answer

We use the Capital Asset Pricing Model (CAPM) to solve this question: The expected rate of return on any asset is given by,

r = rf + (rM - rf)

where rf is the risk-free rate, and rM is the expected return on the market portfolio. Given data:

rf = 5.5% and rM = 10%

Part (a): The expected returns for the 3 stocks are:

Stock 1: r1 = 0.055 + 1.25 * (0.1-0.055) = 0.11125 = 11.125%

Stock 2: r2 = 0.055 + (-0.5) * (0.1 - 0.055) = 0.0325 = 3.25% (less than the risk-free rate, because the for this stock is negative).

Stock 3: r3 = 0.055 + 1.5 * (0.1-0.055) = 0.1225 = 12.25%

Part (b): The of the portfolio can be calculated as the weighted average of the 3 components in the portfolio. The weights of the 3 components are:

w1 = $60,000/($60,000+$40,000+$100,000) = 0.3

w2 = $40,000/($60,000+$40,000+$100,000) = 0.2

w3 = $100,000/($60,000+$40,000+$100,000) = 0.5

portfolio = 1w1 + 2w2 + 3w3 = 0.3*1.25 + 0.2*(-0.5) + 0.5*1.5 = 1.025

Part (c): The expected return on the portfolio, can be calculated using the weighted average of the expected returns of each of the individual components of the portfolio:

rportfolio = r1w1 + r2w2 + r3w3 = 0.11125*0.3 + 0.0325*0.2 + 0.1225*0.5 = 0.101125 = 10.1125%

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