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Walter Jasper currently manages a $500,000 portfolio
Walter Jasper currently manages a $500,000 portfolio. He is expecting to receive an additional $250,000 from a new client. The existing portfolio has a required return of 10.75 percent. The risk-free rate is 4 percent and the return on the market is 9 percent. If Walter wants the required return on the new portfolio to be 11.5 percent, what should be the average beta for the new stocks added to the portfolio?
Expert Solution
CAPM formula: Expected return = Risk-free rate + Beta * (Expected market return - Risk-free rate)
The existing portfolio is $500,000 with a required return of 10.75% or an annual return of $500,000 * 10.75% = $53,750.
The new portfolio will be $750,000 with a required return of 11.50% or an annual return of $750,000 * 11.50% = $86,250.
This means that the additional investment of $250,000 will have to generate an annual return of $86,250 - $53,750 = $32,500 or a return of $32,500/$250,000 = 13%.
Another approach is that $500,000 * 10.75% + $250,000 * x = $750,000 * 11.50%
Solving for this we also get that x = 13%
Using the CAPM formula:
13% = 4% + Beta * (9% - 4%)
Beta = 1.8
The new investment needs to be invested in stocks with an average beta of 1.8
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