7.15 Calculating the variance and standard deviation: Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be –25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.4, 0.5, and 0.1, respectively, then what are the expected return and the standard deviation for Kate’s investment?
7.20 Portfolios with more than one asset: Given the returns and probabilities for the three possible states listed here, calculate the covariance between the returns of Stock A and Stock B. For convenience, assume that the expected returns of Stock A and Stock B are 11.75 percent and 18 percent, respectively.
7.22 You are comparing stock A to stock B. Given the following information, which one of these two stocks should you prefer and why? Calculate expected return and standard deviation for each stock, and base your choice on return/risk characteristics.
7.24 Hatter Enterprise paid a dividend last year of $3.25, which is expected to grow at a constant rate of 7%. Hatter has a beta of 1.5 and their stock is currently selling for $62. If the market risk premium is 6% and the risk-free rate is 3%, should you purchase Hatter’s stock? Why or Why not? Show by comparing the current selling price to an “equilibrium” price (based on CAPM) of Hatter.