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Assume both portfolios A and B are well diversified, that E ( r A ) = 14% and E ( r B ) = 14.8%. If the economy has only one factor, andβA= 1 whileβB = 1.1, what must be the risk-free rate?

Short Answer

Expert verified

The correct answer for risk free rate rf= 6%

Step by step solution

01

Given Information

E(rA) = 14%

E(rB) = F

βA = 1

βB = 1.1

02

Solution for ‘a’

To obtain the risk-free rate (rf ) and the factor return (F), lets substitute the portfolio returns and betas in the expected return-beta relationship

E(r) = rfi[E(rM) - rf ]

14% = rf +1 x[F - rf ]

F = 14%

Let’s substitute the value of F in the below given equation:

14.8 % = rfi[F - rf ]

14.8 % = rf +1.1[14% - rf ]

rf= 6%

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