Question

Suppose Autodesk stock has a beta of 2.16​, whereas Costco stock has a beta of 0.69. If the​ risk-free interest rate is 4 % and the expected return of the market portfolio is 10.0 %​, what is the expected return of a portfolio that consists of 60 % Autodesk stock and 40 % Costco​ stock, according to the​ CAPM?

Answer 1

Answer:

The portfolio return is 13.432%

Explanation:

The required return using CAPM

First we will calculate the required rate of return for both the stocks using the CAPM equation.

Let rA be the required rate of return for Autodesk stock and rB be the required rate of return for Costco stock.

For Autodesk, rA = 0.04 + 2.16 * (0.10 - 0.04) = 0.1696 or 16.96%

For Costco, rB = 0.04 + 0.69 * (0.10 - 0.04) = 0.0814 or 8.14%

The portfolio return is the weighted average return of stocks in the portfolio.

rP or return of portfolio = 0.6 * 0.1696 + 0.4 * 0.0814 = 0.13432 or 13.432%

Answer 2

Based on the information given the expected return of a portfolio is 13.43%.

First step is to calculate the expected return using this formula

Expected return= risk-free rate +Beta×(market rate- risk-free rate )

Expected return of Autodesk=4+2.16×(10-4)

Expected return of Autodesk=16.96%

Expected return of Costco=4+0.69×(10-4)

Expected return of Costco=8.14%

Second step is to calculate the expected return of portfolio using this formula

Expected return of portfolio=Respective return× Respective investment weights

Expected return of portfolio=(16.96×0.6)+(8.14×0.4)

Expected return of portfolio=13.43%(Approximately)

Inconclusion  the expected return of a portfolio is 13.43%.

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