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quiz_solve05 - 6 Given $1000 describe how to construct a...

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FNCE 3010 (Durham). Fall 2007. Quiz 5. Given a series of monthly returns for JKL, Inc. and the S&P 500, suppose that we estimate the CAPM relationship R A - R f = β ( R M - R f ) + ² and obtain β = 2 . 5, and the standard deviation of the residuals is 1.1. 1. Using a market risk premium of 8% and risk-free rate of 5%, what is JKL’s risk premium? What is JKL’s expected return? 2. If the market goes up by 1% next month, what is the expected change in JKL’s stock? 3. If JKL actually goes up by 2%, what is JKL’s idiosyncratic return for that period? 4. If the standard deviation of the monthly market return is 1.5%, what are JKL’s systematic risk, idiosyncratic risk, and total risk (expressed as monthly standard deviations)? 5. What range would I expect JKL’s monthly return to fall within 95% of the time?
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Unformatted text preview: 6. Given $1000, describe how to construct a portfolio with a beta of 2 comprised of JKL stock and the risk-free asset. What is the expected annual return for this portfolio? Solution: 1. Risk premium = 2.5 x 8 = 20%. Expected return = 5 + (2.5 x 8) = 25%. 2. 5/12 + 2.5 x (1 - 5/12)= 1.875% 3. JKL’s idiosyncratic return was 2 - 1.875 = .125%. 4. Systematic risk = 2.5 x 1.5 = 3.75. Idiosyncratic risk = 1.1. Total risk = sqrt(3 . 75 2 + 1 . 1 2 ) = 3.91%. 5. Between 25/12 - (2 x 3.91) = -5.74% and 17/12 + (2 x 2.42) = 9.90%. 6. 2 = w * 2 . 5 + (1-w ) * 0, solve for w. You should get w=.8. So, put $800 in JKL and 200 in the risk-free asset. The expected return for this portfolio should be 5+2*8 = 21%....
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