Question 4) There are three type of investment in a portfolio: S&P 500 index, 10-year treasury bond index, cash invested in money market a 1-day federal fund rate. Table 1 represents S&P 500 index for return on stocks, 10-year treasury bond index for return on bonds and cash invested in money market a 1-day federal fund rate. Table 1. S&P 500 Index, Bond Index and Money Market Year Stocks Bonds Money Market 1995 792,1 3287,3 1007,8 1996 973,9 3291,6 1055,3 1997 3687,3 1998 1999 2011,3 2000 1837,4 45753 1346,5 1670,1 4220,2 3903,3 1119,5 1165,2 1246,5 1313,1 (a) Calculate the geometric means of rates of return for stocks, bonds, and money market. (6 p.) (b) Calculate the covariance matrix of rates of return. (12 p.) Table 2. Covariances between rates of return of securities Covariance Stocks Bonds Money Market Stocks Bonds ? Money Market ? ? ? 3 (c) Set the quadratic program to minimize the portfolio risk. It is assumed that shortsales are allowed. (12 p.) Question 4) There are three type of investment in a portfolio: S&P 500 index, 10-year treasury bond index, cash invested in money market a 1-day federal fund rate. Table 1 represents S&P 500 index for return on stocks, 10-year treasury bond index for return on bonds and cash invested in money market a 1-day federal fund rate. Table 1. S&P 500 Index, Bond Index and Money Market Year Stocks Bonds Money Market 1995 792,1 3287,3 1007,8 1996 973,9 3291,6 1055,3 1997 3687,3 1998 1999 2011,3 2000 1837,4 45753 1346,5 1670,1 4220,2 3903,3 1119,5 1165,2 1246,5 1313,1 (a) Calculate the geometric means of rates of return for stocks, bonds, and money market. (6 p.) (b) Calculate the covariance matrix of rates of return. (12 p.) Table 2. Covariances between rates of return of securities Covariance Stocks Bonds Money Market Stocks Bonds ? Money Market ? ? ? 3 (c) Set the quadratic program to minimize the portfolio risk. It is assumed that shortsales are allowed. (12 p.)