FBE441_Spring08_FinalExam_MW0204_SOLUTIONS

# FBE441_Spring08_FinalExam_MW0204_SOLUTIONS - FBE441:...

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FBE 441 Final Exam: Spring 2008 [SOLUTIONS] Page 2 1. (5 points) A stock has a perfect positive correlation of +1 with the market. Does this imply that the stock has a beta of 1? i) No, not always ii) Yes, always (no explanations necessary) SOLUTION: i).No, not always. Actually, only in very rare circumstances would beta be 1. In general, when constructing the Beta of a portfolio p versus the market Beta(p) = cov(p,M) / sigma(M) and this can be written as Beta(p) = corr(p.M) * [sigma(p) / sigma(M]), thus, unless the volatility of the market index [sigma(M)] and the portfolio [sigma(p)] are equal, the Beta is not 1. 2. You manage an equity fund with an expected risk premium of 10% and an expected standard deviation of 14%. The rate on T-bills is 6%. Your client chooses to invest \$600,00 of her portfolio in your equity fund and \$40,000 in a T-Bill money market fund. 2.a. (5 points) What is the expected return and standard deviation of return on your client’s portfolio? Expected Return of Overall Portfolio ________________ Standard Deviation of Overall Portfolio ________________ SOLUTION: Expected return for equity fund = T-bill rate + risk premium = 6% + 10% = 16% Expected return of client’s overall portfolio = (0.6 × 16%) + (0.4 × 6%) = 12% Standard deviation of client’s overall portfolio = 0.6 × 14% = 8.4% 2.b. (5 points) What is the reward-to-variability ratio for the equity fund? Sharpe Ratio ________________ SOLUTION : The Reward to variability ratio (Sharpe Ratio) = 10% / 14% = 0.71 3. (5 points) Stocks offer an expected rate of return of 18%, with a standard deviation of 22%. Gold offers an expected return of 10% with a standard deviation of 30%. When would you invest in Gold? i) Always ii) If the correlation between Gold and Stock equals 1. iii) If the correlation between Gold and Stock is low enough. iv) Never, Gold is inferior asset both in terms of means and volatility.
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## This note was uploaded on 04/26/2011 for the course FBE 441 taught by Professor Callahan during the Spring '07 term at USC.

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FBE441_Spring08_FinalExam_MW0204_SOLUTIONS - FBE441:...

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