Chapter 11 problems and solutions

Chapter 11 problems and solutions - Math 3650 Spring 2016...

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Math 3650 Spring 2016 Practice/Review for Chapter 11 1 .Define the Beta of a security. Give the formula for Beta. 2. Define covariance and correlation. How do we use correlation to help us achieve diversification within a portfolio? 3. Define the efficient frontier of a portfolio. 4. Define the Sharpe ratio. Give the formula. What can be said about the Sharpe ratio of an efficient portfolio? 5. You are given the following information concerning portfolios of large cap stocks, small cap stocks, and bonds. You are also given the risk free rate equals 1% Exp. Return Volatility Covariance with: Large Cap Small Cap Bonds Large cap 11.0% 17.5% 3.06% 3.08% 0.315% Small Cap 12.0% 22.0% 3.08% 4.84% 0.264% Bonds 4.5% 6.0% 0.315% 0.264% 0.360% a. Calculate the Correlation of Small cap stocks to Large cap stocks. Calculate the Correlation of Small Cap stocks to Bonds. If you held a portfolio of only Small cap stocks and wanted to lower your volatility, which other portfolio is the better diversifier? b. Calculate the expected return of a portfolio equally weighted with large cap stocks, small cap stocks, and bonds. c. The volatility of a portfolio equally weighted with large cap stocks, small cap stocks, and bonds is 13.2%. Using the answer you calculated in question 5b, calculate the Sharpe Ratio of this portfolio.
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6. The risk free rate is 3%. The equity risk premium for the stock market portfolio is 5%, and the variance of the market portfolio is 17.5%. The covariance of the returns of a firms stock and the market portfolio is 26.25%. Calculate the expected return of an investment in the firms stock using the CAPM. 7. What is the Beta of a portfolio of stocks? (Give the formula) 8. In class we did this example: The risk-free rate is 5%. The equity risk premium is 6%. We own 3 stocks: 20% of our portfolio is in stock ABC with a Beta of 0.75; 50% of our portfolio is
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