1. Based on historical data, you have estimated the following probability distributions for the returns on two individual securities (SMALL and BIG) and the value-weighted market portfolio:
a) Calculate the expected return and standard deviation of return for Small, Big and the market portfolio b) Calculate the covariance between Small and Big; between Small and the market, and between Big and the market. c) Calculate the expected return and standard deviation of return for a portfolio that consists of ½ Big and ½ Small. d) Calculate the expected return and standard deviation of return for a portfolio that consists of 3/4 Big and 1/4 Small. e) Compare the five investment opportunities: the two portfolios in c) and d), the individual securities Small and Big, and the market portfolio. Without performing any calculations, can you recommend buying (or not buying) any of these investments?
2. The investment opportunity set above has been enhanced by the inclusion of a risk-free investment that pays 1%. Does access to this asset change your answer to 1e) above? Feel free to use calculations.
3. What is the beta of Small in the problem above? What is the beta of Big? If the CAPM is true, is Small in equilibrium, is it undervalued or is it overvalued? What about Big? You may continue to assume that the risk-free rate is 1%.
4. Download the spreadsheet labeled “Homework 3 Problem 4 Spreadsheet” from the course website. There are three columns of data: a monthly date, a closing price for an individual stock, and the market close.
a) Calculate a monthly return series from the closing monthly prices of both the market and the individual security. b) Calculate the arithmetic mean return and the standard deviation of the monthly return for both series. c) Calculate the...
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