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You are trying to assess the risk and return of your portfolio. You put a quarter...

You are trying to assess the risk and return of your portfolio. You put a quarter of your money in small stocks with a beta of 2.8 and an expected return of 18%. You put half your money in large stocks with a beta of 1.8 and an expected return of 12%. You invest one-eighth of your money in a well-diversified portfolio like the S&P 500 index with a beta of 1 and an expected return of 8%, and the rest of your money is invested in risk-free T-bills. The expected return on the T-bills is 4%.

What is the expected return and systematic risk (beta) on your portfolio respectively?

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Answer #1

Weight of Small Stocks = 0.250
Weight of Large Stocks = 0.500
Weight of Well-Diversified Portfolio = 0.125
Weight of Risk-free T-Bills = 0.125

Beta of Portfolio = Weight of Small Stocks * Beta of Small Stocks + Weight of Large Stocks * Beta of Large Stocks + Weight of Well-Diversified Portfolio * Beta of Well-Diversified Portfolio + Weight of T-Bills * Beta of T-Bills
Beta of Portfolio = 0.250 * 2.80 + 0.500 * 1.80 + 0.125 * 1.00 + 0.125 * 0.00
Beta of Portfolio = 1.725

Expected Return of Portfolio = Weight of Small Stocks * Expected Return of Small Stocks + Weight of Large Stocks * Expected Return of Large Stocks + Weight of Well-Diversified Portfolio * Expected Return of Well-Diversified Portfolio + Weight of T-Bills * Expected Return of T-Bills
Expected Return of Portfolio = 0.250 * 18.00% + 0.500 * 12.00% + 0.125 * 8.00% + 0.125 * 4.00%
Expected Return of Portfolio = 12.00%

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