Short Question (SQ1) (15%) Hal and Stu have started a small fund, investing S10 thousands of their own capital. Their quantitative strategy has identified 10 stocks to buy, and they plan to use their $10 thousands buy equal dollar amounts of each stock, that is, $1000 in each stock. They would like to short sell a hedging portfolio constructed with the S&P 500 portfolio and the risk-free asset to make their overall portfolio market-neutral. Assume there is no initial maintenance margin requirement or any kind of restrictions on short-selling. For each stock, the two partners have estimated the single market index model of the form, R = a1 + B R + Et where it is a stock's excess return in month t, and Ride is the excess return on the S&P 500 index in month t. Across the 10 stocks that Hal and Stu want to buy, the partners estimate that the average a equals 0.02, and the average Bi equals 0.75. Based on historical estimates, they are also assuming that: the standard deviation of it equals 0.10 for the 10 stocks that Hal and Stu plan to buy. The correlation between and jt equals o for every possible pair for stocks that Hal and Stu want to buy the expected excess monthly return on the S&P 500 equals 0.005 the standard deviation of the monthly market return is 0.06 * Terminology A hedging portfolio here describes a position to be shorted to make the overall portfolio market neutral Overall portfolio describes the overall position combining the buy position and the short-sell position Market-neutral in the market index model indicates having zero beta on the market index (a) What is the dollar amount of the hedging portfolio should they short sell? (5%) (b) What is the expected dollar profit on the overall position over the next month? (5%) (C) What is the variance of the return on the overall position over the next month? (5%) Short Question (SQ1) (15%) Hal and Stu have started a small fund, investing S10 thousands of their own capital. Their quantitative strategy has identified 10 stocks to buy, and they plan to use their $10 thousands buy equal dollar amounts of each stock, that is, $1000 in each stock. They would like to short sell a hedging portfolio constructed with the S&P 500 portfolio and the risk-free asset to make their overall portfolio market-neutral. Assume there is no initial maintenance margin requirement or any kind of restrictions on short-selling. For each stock, the two partners have estimated the single market index model of the form, R = a1 + B R + Et where it is a stock's excess return in month t, and Ride is the excess return on the S&P 500 index in month t. Across the 10 stocks that Hal and Stu want to buy, the partners estimate that the average a equals 0.02, and the average Bi equals 0.75. Based on historical estimates, they are also assuming that: the standard deviation of it equals 0.10 for the 10 stocks that Hal and Stu plan to buy. The correlation between and jt equals o for every possible pair for stocks that Hal and Stu want to buy the expected excess monthly return on the S&P 500 equals 0.005 the standard deviation of the monthly market return is 0.06 * Terminology A hedging portfolio here describes a position to be shorted to make the overall portfolio market neutral Overall portfolio describes the overall position combining the buy position and the short-sell position Market-neutral in the market index model indicates having zero beta on the market index (a) What is the dollar amount of the hedging portfolio should they short sell? (5%) (b) What is the expected dollar profit on the overall position over the next month? (5%) (C) What is the variance of the return on the overall position over the next month? (5%)
