a. If your coefficient of risk-aversion is A = 1, find the portfolio weights in Bonds, Large Stocks, Small Stocks, and the Risk-free asset which maximize your utility. Report the portfolio weight for bonds 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 Risk-free Portfolio Weights Mean Return Standard Deviation b. Is this investor borrowing or lending at the risk-free rate? i. Borrowing, since the weight on the risk-free asset is positive. ii. Borrowing, since the weight on the risk-free asset is negative. iii. Lending, since the weight on the risk-free asset is positive. iv. Lending, since the weight on the risk-free asset is negative. c. If your coefficient of risk-aversion is A = 25, find the portfolio weights in Bonds, Large Stocks, Small Stocks, and the Risk-free asset which maximize your utility. Report the portfolio weight for bonds 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 Risk-free Portfolio Weights Mean Return Standard Deviation d. Is this investor borrowing or lending at the risk-free rate? i. Borrowing, since the weight on the risk-free asset is positive. ii. Borrowing, since the weight on the risk-free asset is negative. iii. Lending, since the weight on the risk-free asset is positive. iv. Lending, since the weight on the risk-free asset is negative. e. In Assignment 6, we found optimal complete portfolios by changing weights in all 3 assets (1 risk free, 2 risky). If we were to restrict the risk free asset to be a 0 weight utilizing the same method of maximizing utility, would our weights correspond to the optimal risky portfolio? i. Yes, always ii. Yes, for A below a certain value iii. Yes, for A above a certain value iv. Yes, for one specific value of A V. No 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% Risk- free Rate 3.34% E() T-Bnds 8.95% 10.44% LS 12.34% 17.05% SS 17.90% 23.34% S Covariance Matrix LS SS Bonds LS SS Bonds 0.0109 0.0000 0.0000 0.0291 0.0000 0.0545 Bordered Matrix Total 1.00 Bonds LS SS 0.33 0.33 0.33 Bonds 0.33 0.00121 0.00000 0.00000 LS 0.33 0.00000 0.00323 0.00000 SS 0.33 0.00000 0.00000 0.00605 Portfolio Risk and Return E(r_p) Var sup SR Complete Portfolio Risk and Return Portfolio Weights Total Risky 1.00 Risk-Free 0.00 1.00 E(r_p) Var_p s_p A Utility 25 0.00000 Final Portfolio Weights Bonds 0.33 LS 0.33 SS 0.33 Risk-Free 0.00 Total 1.0 a. If your coefficient of risk-aversion is A = 1, find the portfolio weights in Bonds, Large Stocks, Small Stocks, and the Risk-free asset which maximize your utility. Report the portfolio weight for bonds 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 Risk-free Portfolio Weights Mean Return Standard Deviation b. Is this investor borrowing or lending at the risk-free rate? i. Borrowing, since the weight on the risk-free asset is positive. ii. Borrowing, since the weight on the risk-free asset is negative. iii. Lending, since the weight on the risk-free asset is positive. iv. Lending, since the weight on the risk-free asset is negative. c. If your coefficient of risk-aversion is A = 25, find the portfolio weights in Bonds, Large Stocks, Small Stocks, and the Risk-free asset which maximize your utility. Report the portfolio weight for bonds 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 Risk-free Portfolio Weights Mean Return Standard Deviation d. Is this investor borrowing or lending at the risk-free rate? i. Borrowing, since the weight on the risk-free asset is positive. ii. Borrowing, since the weight on the risk-free asset is negative. iii. Lending, since the weight on the risk-free asset is positive. iv. Lending, since the weight on the risk-free asset is negative. e. In Assignment 6, we found optimal complete portfolios by changing weights in all 3 assets (1 risk free, 2 risky). If we were to restrict the risk free asset to be a 0 weight utilizing the same method of maximizing utility, would our weights correspond to the optimal risky portfolio? i. Yes, always ii. Yes, for A below a certain value iii. Yes, for A above a certain value iv. Yes, for one specific value of A V. No 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% Risk- free Rate 3.34% E() T-Bnds 8.95% 10.44% LS 12.34% 17.05% SS 17.90% 23.34% S Covariance Matrix LS SS Bonds LS SS Bonds 0.0109 0.0000 0.0000 0.0291 0.0000 0.0545 Bordered Matrix Total 1.00 Bonds LS SS 0.33 0.33 0.33 Bonds 0.33 0.00121 0.00000 0.00000 LS 0.33 0.00000 0.00323 0.00000 SS 0.33 0.00000 0.00000 0.00605 Portfolio Risk and Return E(r_p) Var sup SR Complete Portfolio Risk and Return Portfolio Weights Total Risky 1.00 Risk-Free 0.00 1.00 E(r_p) Var_p s_p A Utility 25 0.00000 Final Portfolio Weights Bonds 0.33 LS 0.33 SS 0.33 Risk-Free 0.00 Total 1.0