Chapter 8 portfolio beta problems

Chapter 8 portfolio beta problems - If she goes ahead with...

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Chapter 8 Portfolio Beta Problem 1. You hold a diversified portfolio consisting of $7,500 in 20 different stocks. The portfolio beta is 1.12. You want to sell one stock with a beta of 1 for $7,500 and purchase another stock with a beta of 1.75. What is your portfolio’s new beta? Size of portfolio = 20 x 7500 = $150,000 old portfolio rest of portfolio 7500 142500 1 150000 150000 x β = + β 1/20 of 150,000 = 7,500 19/20 of 150,000 = 142,500 1.12 = .05 x 1 + .95 x β rest 1.07 = .95β Β = 1.1263 New portfolio beta: β = .05 x 1.75 + 0.95 x 1.1263 = 1.16 2. Assume that the risk-free rate is 5.5% and the market risk premium is 6%. A money manager has $10 million invested in a portfolio that has a required return of 12%. The manager plans to sell $3 million of stock with a beta of 1.6 that is part of the portfolio. She plans to reinvest this $3 million into another stock that has a beta of 0.7.
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Unformatted text preview: If she goes ahead with this planned transaction, what will be the required return of her new portfolio? Calculate the portfolios current beta: R = r rf + (r m r rf ) 12 = 5.5 + 6 1.0833 = The portfolio beta is the weighted average of the betas of the individual stocks in the portfolio. If you sell $3 million of a stock that has a beta of 1.6, what will be the beta of the remaining stocks? Calculate the beta of the remaining stocks in the portfolio: 1.0833 = (3/10)(1.6) + (7/10)X 0.6033 = 0.7X 0.8619 = X 0.8619 is the beta of the $7 million of stocks that remain. Now what happens to the portfolio beta when the new stock is added? Calculate the new portfolios beta = (7/10)(0.8619) + (3/10)(0.7) = 0.6033 + 0.21 = 0.8133 Calculate the new portfolios required return: R = r rf + (r m r rf ) = 5.5 + ^ x 0.8133 = 10.38%...
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