Annual Return, 1991-2007 Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 Bonds 18.39% 7.79% 15.48% -7.18% 31.67% -0.81% 15.08% 13.52% -8.74% 20.27% 4.21% 16.79% 2.38% 7.71% 6.50% -1.21% 10.25% Large Stocks 30.66% 7.71% 9.87% 1.29% 37.71% 23.07% 33.17% 28.58% 21.04% -9.10% -11.89% -22.10% 28.69% 10.88% 4.91% 11.78% 3.53% Small Stocks 49.09% 21.11% 19.01% -5.59% 34.01% 16.54% 23.82% -7.36% 40.55% -6.20% 29.25% -11.77% 74.75% 14.36% 3.26% 17.69% -8.26% Mystery Fund 16.17% 13.71% 10.75% 10.55% 12.03% 12.07% 13.12% 12.53% 13.28% 10.67% 9.84% 8.43% 7.28% 6.45% 7.26% 9.39% 7.35% Bonds 8.95% 10.44% E() Risk- free Rate 3.34% LS 12.34% 17.05% SS 17.90% 23.34% Mystery 10.64% 2.73% 0 Covariance Matrix LS SS Mystery Bonds LS SS Mystery Bonds 0.0109 0.0000 0.0000 0.0000 0.0291 0.0000 0.0000 0.0545 0.0000 0.0007 Bordered Matrix Total 1.00 Bonds LS SS Mystery 0.25 0.25 0.25 0.25 Bonds 0.25 0.00068 0.00000 0.00000 0.00000 LS 0.25 0.00000 0.00182 0.00000 0.00000 SS 0.25 0.00000 0.00000 0.00340 0.00000 Mystery 0.25 0.00000 0.00000 0.00000 0.00005 Portfolio Risk and Return E(r_p) Var_p O_P SR Complete Portfolio Risk and Return Portfolio Weights Risky Total Risk-Free 0.00 1.00 1.00 E(r_p) Var_P O_P SR A Utility 25 0.00000 Final Portfolio Weights Bonds 0.25 LS 0.25 SS Mystery 0.25 0.25 Risk-Free Total 0.00 1.0 2. For Question 2, use the "Mystery 1991-2007" tab. a. If your coefficient of risk-aversion is A = 1, find the portfolio weights in Bonds, Large Stocks, Small Stocks, the Mystery fund, and the Risk-free asset which maximize your utility. Report the portfolio weight for Mystery Fund for this optimal complete portfolio, and report the mean return and standard deviation of returns on this portfolio. (report weights raw numbers rounded to the 2nd decimal place, e.g. X.XX, report mean and std as percent rounded to the nearest 1 decimal place, so if the answer is 0.0122, report 1.2.) Bonds Large Stocks Small Stocks Mystery Fund Risk-free Portfolio Weights Mean Return Standard Deviation b. Interpret the portfolio weight on the risk-free asset. i. Borrowing a lot, since the weight on the risk-free asset is highly positive. ii. Borrowing a lot, since the weight on the risk-free asset is highly negative. iii. Lending a lot, since the weight on the risk-free asset is highly positive. iv. Lending a lot, since the weight on the risk-free asset is highly negative. C. If your coefficient of risk-aversion is A = 25, find the portfolio weights in Bonds, Large Stocks, Small Stocks, the Mystery fund, and the Risk-free asset which maximize your utility. Report the portfolio weight for Mystery Fund for this optimal complete portfolio, and report the mean return and standard deviation of returns on this portfolio. (report weights raw numbers rounded to the 2nd decimal place, e.g. X.XX, report mean and std as percent rounded to the nearest 1 decimal place, so if the answer is 0.0122, report 1.2.) Mystery Bonds Large Stocks Small Stocks Risk-free Fund Portfolio Weights Mean Return Standard Deviation Annual Return, 1991-2007 Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 Bonds 18.39% 7.79% 15.48% -7.18% 31.67% -0.81% 15.08% 13.52% -8.74% 20.27% 4.21% 16.79% 2.38% 7.71% 6.50% -1.21% 10.25% Large Stocks 30.66% 7.71% 9.87% 1.29% 37.71% 23.07% 33.17% 28.58% 21.04% -9.10% -11.89% -22.10% 28.69% 10.88% 4.91% 11.78% 3.53% Small Stocks 49.09% 21.11% 19.01% -5.59% 34.01% 16.54% 23.82% -7.36% 40.55% -6.20% 29.25% -11.77% 74.75% 14.36% 3.26% 17.69% -8.26% Mystery Fund 16.17% 13.71% 10.75% 10.55% 12.03% 12.07% 13.12% 12.53% 13.28% 10.67% 9.84% 8.43% 7.28% 6.45% 7.26% 9.39% 7.35% Bonds 8.95% 10.44% E() Risk- free Rate 3.34% LS 12.34% 17.05% SS 17.90% 23.34% Mystery 10.64% 2.73% 0 Covariance Matrix LS SS Mystery Bonds LS SS Mystery Bonds 0.0109 0.0000 0.0000 0.0000 0.0291 0.0000 0.0000 0.0545 0.0000 0.0007 Bordered Matrix Total 1.00 Bonds LS SS Mystery 0.25 0.25 0.25 0.25 Bonds 0.25 0.00068 0.00000 0.00000 0.00000 LS 0.25 0.00000 0.00182 0.00000 0.00000 SS 0.25 0.00000 0.00000 0.00340 0.00000 Mystery 0.25 0.00000 0.00000 0.00000 0.00005 Portfolio Risk and Return E(r_p) Var_p O_P SR Complete Portfolio Risk and Return Portfolio Weights Risky Total Risk-Free 0.00 1.00 1.00 E(r_p) Var_P O_P SR A Utility 25 0.00000 Final Portfolio Weights Bonds 0.25 LS 0.25 SS Mystery 0.25 0.25 Risk-Free Total 0.00 1.0 2. For Question 2, use the "Mystery 1991-2007" tab. a. If your coefficient of risk-aversion is A = 1, find the portfolio weights in Bonds, Large Stocks, Small Stocks, the Mystery fund, and the Risk-free asset which maximize your utility. Report the portfolio weight for Mystery Fund for this optimal complete portfolio, and report the mean return and standard deviation of returns on this portfolio. (report weights raw numbers rounded to the 2nd decimal place, e.g. X.XX, report mean and std as percent rounded to the nearest 1 decimal place, so if the answer is 0.0122, report 1.2.) Bonds Large Stocks Small Stocks Mystery Fund Risk-free Portfolio Weights Mean Return Standard Deviation b. Interpret the portfolio weight on the risk-free asset. i. Borrowing a lot, since the weight on the risk-free asset is highly positive. ii. Borrowing a lot, since the weight on the risk-free asset is highly negative. iii. Lending a lot, since the weight on the risk-free asset is highly positive. iv. Lending a lot, since the weight on the risk-free asset is highly negative. C. If your coefficient of risk-aversion is A = 25, find the portfolio weights in Bonds, Large Stocks, Small Stocks, the Mystery fund, and the Risk-free asset which maximize your utility. Report the portfolio weight for Mystery Fund for this optimal complete portfolio, and report the mean return and standard deviation of returns on this portfolio. (report weights raw numbers rounded to the 2nd decimal place, e.g. X.XX, report mean and std as percent rounded to the nearest 1 decimal place, so if the answer is 0.0122, report 1.2.) Mystery Bonds Large Stocks Small Stocks Risk-free Fund Portfolio Weights Mean Return Standard Deviation