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 Money Market 1007,8 Year Stocks 792,1 973,9 Bonds 1995 3287,3 1996 3291,6 1055,3 1997 1346,5 1670,1 2011,3 1837,4 3687,3 4220,2 3903,3 4575,3 1119,5 1165,2 1998 1999 1246,5 1313,1 2000 (a) Calculate the geometric means of rates of return for stocks, bonds, and money market. (b) Calculate the covariance matrix of rates of return. Table 2. Covariances between rates of return of securities |Covariance Stocks Bonds Money Market Stocks Bonds Money Market ? ? ? ? ? ? ? ? ? (c) Set the quadratic program to minimize the portfolio risk. It is assumed that shortsales are allowed.

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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
Bonds
3287,3
Money Market
1007,8
Year
Stocks
1995
792,1
1996
973,9
3291,6
1055,3
1997
1346,5
1670,1
2011,3
1837,4
3687,3
4220,2
3903,3
4575,3
1119,5
1165,2
1998
1999
1246,5
2000
1313,1
(a) Calculate the geometric means of rates of return for stocks, bonds, and money market.
(b) Calculate the covariance matrix of rates of return.
Table 2. Covariances between rates of return of securities
Covariance
Stocks
Stocks Bonds
Money Market
?
?
Bonds
?
?
?
Money Market
?
?
?
(c) Set the quadratic program to minimize the portfolio risk. It is assumed that shortsales are
allowed.
Transcribed Image Text: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 Bonds 3287,3 Money Market 1007,8 Year Stocks 1995 792,1 1996 973,9 3291,6 1055,3 1997 1346,5 1670,1 2011,3 1837,4 3687,3 4220,2 3903,3 4575,3 1119,5 1165,2 1998 1999 1246,5 2000 1313,1 (a) Calculate the geometric means of rates of return for stocks, bonds, and money market. (b) Calculate the covariance matrix of rates of return. Table 2. Covariances between rates of return of securities Covariance Stocks Stocks Bonds Money Market ? ? Bonds ? ? ? Money Market ? ? ? (c) Set the quadratic program to minimize the portfolio risk. It is assumed that shortsales are allowed.
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