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Currently the expected return on the market portfolio is 13%. The stock of XYZ Corp. has a beta of 1.2. Th expected return of the stock, based on the CAPM is 15%. What is the risk free rate?

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Question

Currently the expected return on the market portfolio is 13%. The stock of XYZ Corp. has a beta of 1.2. Th expected return of the stock, based on the CAPM is 15%. What is the risk free rate?

Solution

The formula, under CAPM =

Expected Retrun = Risk free rate + Beta ( Marktet Retrun - Risk free rate )

Expected Retrun = 15%

Beta = 1,2

Return on Market portfolio = 13%

Expected Retrun = Risk free rate + Beta ( Marktet Retrun - Risk free rate )

15% = Risk free rate + 1.2 ( 13% - Risk free rate )

0.15 = Risk free rate + 1.2 ( 0.13 - Risk free rate )

0.15 = Risk free rate + 0.156 - 1.2 * Risk free rate

Risk free rate - 1.2 * Risk free rate = 0.15 - 0.156 = - 0.006

Risk free Rate ( 1 - 1.2 ) = - 0.006

- 0.2 * Risk free Rate = - 0.006

Risk free rate = - 0.006 / - 0.2 = 0.03 = 3%

Risk Free rate = 3%

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