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## Calculation of Beta through CAPM Model.

Bonus question. Question Background. Define a linear regression model consisdent with CAPM in the following way:

Where ri = Ri - Rf is security i\'s excess return, rM= RM - Rf is market M\'s excess erturn. Under standard linear regression assumptions, that is, when εi are independent and their means are equal to zero, it is the case that bi = βi. The prediction of CAPM is that, in equilibrium, ai = 0.

Problem. The expected value and standard deviation of the market portfolio are 8% and 12%, respectively. The expected return of security A is 6%. The standard deviation of security B is 18%, and its specific risk is (10%)2. A portfolio that invests 1/3 of ots value in A and 2/3 in B has a beta of 1. What are the risk-free rate and the expected return of B according to CAPM?

Hint: using (3), consider the covariance of ri with rM and the variance of ri. decompose the latter one into systematic and firm-specific risk. Now you have all the information to solve the problem!

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