# Assignment 8 Explanation

Topics: Rate of return, Capital asset pricing model, Risk-free interest rate Pages: 1 (256 words) Published: May 1, 2013
Assignment 8 Question #8 (10 points) Suppose CAPM works, and you know that the expected returns on Walmart and Amazon are estimated to be 12% and 10%, respectively. You have just calculated extremely reliable estimates of the betas of Walmart and Amazon to be 1.30 and 0.90, respectively. Given this data, what is a reasonable estimate of the risk-free rate (the return on a long-term government bond)? (No more than two decimals in the percentage return, but do not enter the % sign.) First start by writing out the CAPM formula: Stock return=Risk free rate (RFR) + Stock’s beta * Market Risk Premium (MRP) In this question, we are given the stock return and the stock beta, and we are asked to solve for the risk free rate. However, we also don’t know what the market risk premium is. But we can set up two separate equations and rearrange them to represent the MRP in terms of the RFR. The Walmart stock return can be written as: 0.12=RFR + 1.3*MRP And Amazon: 0.10= RFR + 0.9*MRP Rearranging the Amazon equation, we can isolate the MRP as a function of the RFR: (0.10-RFR)/0.9=MRP. Now we can plug this into the Walmart equation and solve for the RFR. So we re-write the Walmart equation using the above formula in place of MRP, as follows: 0.12=RFR+1.3*[(0.10-RFR)/0.9]. Then you should be able to solve for the RFR!

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