Suppose you have a risk-aversion coefficient of 3.0, and utility function of, U = E[r] A02, that uses your estimate of annual arithmetic returns (APR) and variance. Which index would you invest in? 2 5.) Assume that only a single risky asset exists (the Global index), and a single risk-free rate (the 1- month US risk-free rate) at which investors can borrow and lend. Assume the risk-free rate is equal to its time-series average and has zero variance. Also assume the utility function provided in the previous problem, with a risk-aversion coefficient of 3.0. For all parts use your estimate of annualized arithmetic average returns (APR) and annualized variance. a. Plot the capital allocation line (CAL) in the expected return-standard deviation plane. What does moving up and down the CAL represent about the allocation between the two assets? What is the intercept of the line? What is its slope? What is the economic significance of the intercept and slope? b. Plot the investor's utility of the complete portfolio as a function of the allocation to the risky asset. What does the curve suggest about the investor's approximate optimal allocation to the risky asset? c. On the same plot as the CAL in (a), plot the indifference curve in the expected return- standard deviation plane corresponding to a utility level of 0.03 for an investor with a risk aversion coefficient of 3. Plot a second indifference curve corresponding to the utility level suggested by (b). How does the second indifference curve differ from the first? What is the relation of the second indifference curve with respect to the CAL? d. What is the exact allocation to the risky asset in the complete portfolio that maximizes the utility of the investor? Global Date 199007 199008 199009 199010 199011 199012 199101 199102 199103 199104 199105 199106 199107 199108 199109 199110 199111 199112 199201 199202 199203 199204 199205 199206 199207 199208 199209 199210 199211 199212 199301 199302 199303 199304 199305 199306 199307 199308 199309 199310 199311 199312 199401 199402 199403 199404 199405 North_America -0.82% -8.93% -5.41% -1.33% 6.43% 3.11% 4.73% 7.70% 2.80% 0.34% 4.16% -4.27% 4.42% 2.62% -1.29% 1.84% -3.76% 10.30% -0.34% 1.28% -2.30% 1.53% 0.65% -1.81% 3.99% -2.04% 0.97% 1.10% 3.70% 1.80% 0.99% 0.70% 2.58% -2.28% 3.02% 0.44% -0.12% 3.78% -0.18% 1.96% -1.52% 1.95% 3.15% -2.36% -4.41% 0.93% 1.03% Japan 0.78% -11.25% -17.43% 25.59% -13.52% 2.34% 1.67% 12.81% -3.76% 2.68% -1.59% -6.61% 1.85% -6.79% 9.10% 4.47% -8.14% 2.85% -5.33% -6.95% -11.13% -7.39% 9.02% -8.73% -3.00% 16.61% -2.59% -5.17% 2.07% -0.73% -0.63% 4.55% 16.04% 16.93% 5.21% -3.96% 6.94% 2.41% -4.96% -2.34% -15.98% 2.22% 17.06% 4.08% -1.97% 3.57% 1.54% Asia_exJapan 4.85% -7.82% -8.25% -1.58% -2.29% -0.61% 6.03% 9.26% 2.13% 3.24% -0.40% -0.50% 6.04% -1.48% 1.16% 4.33% -0.26% 1.58% 1.36% 1.85% 0.22% 5.67% 7.73% -1.05% -3.64% -6.22% -2.56% 2.41% -1.32% 1.31% 0.94% 8.22% 2.84% 5.70% 5.04% -2.58% 2.69% 6.82% 0.18% 15.95% -2.18% 20.28% 1.32% -6.21% -9.72% 2.48% 4.48% Europe 5.05% -10.20% -11.74% 7.27% 0.17% -0.95% 2.12% 7.78% -6.34% -0.21% 1.13% -7.02% 5.94% 1.86% 3.42% -2.33% -1.89% 6.61% -0.03% 0.15% -3.27% 5.45% 5.43% -0.90% -3.81% -0.35% -2.67% -7.39% -0.24% 1.41% 1.13% 1.48% 5.83% 2.17% 1.10% -2.90% 1.27% 8.89% -0.43% 2.66% -2.01% 7.20% 6.28% -3.23% -2.28% 4.02% -3.70% 1.47% -10.10% -11.64% 10.26% -3.30% 1.63% 2.99% 9.57% -1.93% 1.13% 1.22% -5.65% 3.93% -0.94% 3.34% 1.78% -4.75% 6.56% -1.86% -1.61% -5.14% 0.16% 4.41% -3.44% -0.36% 2.85% -1.14% -2.86% 2.07% 1.00% 0.59% 2.17% 7.02% 4.70% 3.35% -1.91% 2.55% 4.62% -1.78% 1.33% -6.06% 4.23% 7.61% -0.90% -3.37% 2.62% 0.11% Rf 0.68% 0.66% 0.60% 0.68% 0.57% 0.60% 0.52% 0.48% 0.44% 0.53% 0.47% 0.42% 0.49% 0.46% 0.46% 0.42% 0.39% 0.38% 0.34% 0.28% 0.34% 0.32% 0.28% 0.32% 0.31% 0.26% 0.26% 0.23% 0.23% 0.28% 0.23% 0.22% 0.25% 0.24% 0.22% 0.25% 0.24% 0.25% 0.26% 0.22% 0.25% 0.23% 0.25% 0.21% 0.27% 0.27% 0.32% 0.32% 0.31% 0.28% 0.37% 0.37% 0.38% 0.37% 0.44% 0.42% 0.40% 0.46% 0.44% 0.54% 199405 199406 199407 199408 199409 199410 199411 199412 199501 199502 199503 199504 199505 199506 199507 199508 199509 199510 199511 199512 199601 199602 199603 199604 199605 199606 199607 199608 199609 199610 199611 199612 199701 199702 199703 199704 199705 199706 199707 199708 199709 199710 199711 199712 199801 199802 199803 199804 1.03% -2.81% 3.04% 4.38% -1.69% 1.52% -3.67% 1.33% 1.80% 4.07% 2.72% 2.63% 3.49% 2.98% 4.08% 0.89% 3.66% -1.05% 4.27% 1.54% 2.78% 1.69% 1.22% 2.42% 2.57% -0.59% -5.25% 3.27% 5.32% 1.81% 6.75% -1.19% 5.50% 0.02% 4.48% 4.43% 7.08% 4.27% 7.73% -3.71% 5.86% -3.33% 2.96% 1.84% 0.47% 7.41% 5.19% 1.27% 1.54% 6.33% -3.80% 0.09% -2.85% 2.59% -6.16% 2.05% -6.44% -5.25% 9.08% 4.10% -6.23% -4.16% 6.31% -2.67% -1.16% -3.92% 4.52% 4.90% -1.26% -1.47% 3.01% 6.84% 4.48% 0.35% -4.70% 4.30% 2.85% -6.88% 0.64% -7.06% -10.75% 1.84% -3.68% 1.88% 13.56% 5.83% -3.98% -9.38% -2.55% -7.67% -8.04% -7.59% 10.98% 1.23% -6.54% -1.89% 4.48% -6.07% 5.02% 3.99% -2.16% 1.42% -7.85% -0.86% -7.17% 6.19% 0.92% 1.56% 4.58% -1.84% 5.24% -1.08% 2.13% -0.31% 1.22% 3.26% 8.54% 0.76% -0.54% 2.04% 1.09% -1.72% -4.96% 4.24% 2.72% 2.64% 6.83% -0.12% -1.64% 1.18% -4.22% 0.27% 7.34% 2.69% 2.18% -8.00% 4.41% -21.72% -0.87% -1.04% -7.33% 11.76% -1.45% -5.07% -3.70% -0.84% 4.93% 2.33% -3.23% 4.02% -4.14% 0.52% -1.07% 2.38% 3.90% 3.00% 2.28% 1.51% 4.48% -3.57% 2.79% -0.23% 0.19% 2.37% 0.98% 2.30% 1.36% 1.11% 1.96% 0.68% -1.38% 2.65% 1.55% 1.94% 4.47% 2.49% 0.06% 0.99% 2.48% -0.43% 4.48% 4.10% 3.37% -4.80% 9.16% -4.14% 1.09% 2.73% 3.73% 7.72% 7.32% 2.72% 0.11% 0.47% 1.35% 2.47% -2.48% 2.49% 4.77% 1.23% -1.92% 0.97% 4.72% 3.11% 0.38% 0.40% 4.82% -1.36% 2.10% -1.52% 3.07% 2.68% 1.52% 1.01% 1.62% 3.16% 0.51% -0.08% 4.07% 1.33% 3.59% -0.07% 4.83% -1.31% 0.47% 0.66% -2.35% 2.34% 7.45% 4.43% 4.11% -5.16% 5.40% -5.03% 0.68% 0.77% 2.48% 6.83% 4.16% 1.18% 0.47% 0.45% 0.47% 0.43% 0.47% 0.42% 0.49% 0.43% 0.39% 0.39% 0.46% 0.42% 0.40% 0.45% 0.41% 0.44% 0.42% 0.41% 0.46% 0.45% 0.39% 0.43% 0.43% 0.49% 0.37% 0.43% 0.41% 0.44% 0.42% 0.39% 0.48% 0.43% 0.39% 0.39% 0.43% 199804 199805 199806 199807 199808 199809 199810 199811 199812 199901 199902 199903 199904 199905 199906 199907 199908 199909 199910 199911 199912 200001 200002 200003 200004 200005 200006 200007 200008 200009 200010 200011 200012 200101 200102 200103 200104 200105 200106 200107 200108 200109 200110 200111 200112 200201 200202 200203 1.27% -2.41% 3.30% -2.30% -15.79% 6.48% 7.39% 6.08% 6.30% 3.63% -3.77% 3.85% 4.63% -1.81% 5.08% -2.98% -0.92% -2.31% 6.04% 3.21% 7.29% -3.94% 1.96% 7.51% 4.31% -2.97% 4.08% -1.65% 7.52% -4.85% -2.28% -9.71% 2.05% 3.72% -9.44% -6.85% 8.07% 1.17% -1.67% -1.73% -5.90% -8.96% 2.43% 8.11% 1.78% -1.70% -2.01% 4.49% -1.89% -4.50% 0.69% -1.24% -8.82% -3.44% 16.49% 3.91% 3.14% 1.14% -2.26% 14.01% 5.04% 4.96% 10.80% 10.30% 3.26% 7.21% 6.66% 7.55% 4.06% -4.99% -1.33% 6.63% -8.61% -7.06% 6.29% -11.68% 6.95% -4.32% -6.95% -2.50% -9.35% -0.30% -5.16% -3.87% 9.08% 0.17% -5.02% -8.63% -2.39% -7.39% 0.99% -1.63% -8.09% -7.71% 5.26% 5.73% -5.07% -10.47% -5.33% -3.10% -12.90% 10.89% 18.07% 5.09% -2.17% 0.23% -0.98% 8.39% 16.91% -5.13% 9.29% -1.79% -2.01% -1.87% 1.55% 7.40% 9.12% -6.76% -0.58% 0.87% -5.77% -8.00% 11.23% -0.17% 2.56% -6.97% -5.44% -0.53% 4.44% 3.32% -3.37% -12.87% 6.89% 0.12% 1.67% -3.57% -0.81% -14.26% 6.25% 2.72% 2.72% -0.11% 1.95% -11.64% 4.34% 6.78% 4.50% 3.25% 0.29% -1.94% 0.27% 3.20% -3.38% 2.03% 1.52% 1.75% 0.08% 2.10% 3.07% 9.66% -6.78% 6.30% 1.15% -5.16% 0.45% 1.11% -1.15% -1.07% -4.44% -2.16% -3.99% 6.28% 0.76% -8.19% -8.85% 7.67% -4.67% -3.26% -0.39% -1.77% -11.24% 3.45% 4.29% 1.91% -4.57% 0.52% 5.22% 1.18% -1.20% 1.64% -0.78% -13.58% 1.71% 8.40% 5.29% 4.71% 2.20% -2.96% 3.96% 4.60% -2.77% 5.00% 0.05% 0.43% -0.21% 4.79% 3.97% 7.52% -5.05% 2.64% 5.24% -5.27% -2.73% 3.69% -2.84% 4.64% -4.72% -2.93% -6.88% 1.92% 2.30% -8.37% -7.32% 8.03% -0.78% -2.45% -2.22% -4.11% -9.65% 2.68% 5.83% 0.78% -3.06% -0.55% 4.84% 0.43% 0.40% 0.41% 0.40% 0.43% 0.46% 0.32% 0.31% 0.38% 0.35% 0.35% 0.43% 0.37% 0.34% 0.40% 0.38% 0.39% 0.39% 0.39% 0.36% 0.44% 0.41% 0.43% 0.47% 0.46% 0.50% 0.40% 0.48% 0.50% 0.51% 0.56% 0.51% 0.50% 0.54% 0.38% 0.44% 0.39% 0.32% 0.28% 0.30% 0.31% 0.28% 0.22% 0.17% 0.15% 0.14% 0.13% 0.13% 8.63% 2.62% 1.68% -1.45% 4.55% 0.91% 2.24% -5.44% -6.13% 0.14% -7.38% 4.83% 2.79% -3.01% 1.62% -1.13% -0.48% 4.65% 200204 200205 200206 200207 200208 200209 200210 200211 200212 200301 200302 200303 200304 200305 200306 200307 200308 200309 200310 200311 200312 200401 200402 200403 200404 200405 200406 200407 200408 200409 200410 200411 200412 200501 200502 200503 200504 200505 200506 200507 200508 200509 200510 200511 200512 200601 200602 200603 -5.21% -0.96% -7.10% -8.04% 0.24% -9.99% 7.66% 5.97% -5.33% -2.33% -1.59% 0.91% 8.21% 6.37% 1.55% 2.17% 2.53% -0.99% 6.08% 1.52% 4.61% 2.11% 1.54% -1.06% -1.91% 1.20% 2.18% -3.67% 0.19% 2.17% 1.79% 4.76% 3.41% -2.45% 2.36% -1.47% -2.65% 3.61% 1.18% 4.27% -0.44% 1.19% -2.23% 4.16% 0.47% 3.85% -0.18% 1.78% 5.37% 7.26% -4.67% -5.92% -1.26% -4.74% -6.60% 3.18% -2.29% -3.38% 1.55% -2.84% 1.08% 4.63% 7.22% 3.49% 9.83% 7.46% 4.01% -3.68% 6.57% 2.03% 0.00% 14.94% -4.54% -3.16% 5.33% -6.49% 1.12% -2.96% 2.52% 3.92% 5.09% -1.07% 1.95% -1.27% -1.96% -2.30% 0.92% 0.83% 7.09% 8.33% -0.08% 3.25% 9.52% 3.99% -2.12% 3.00% 7.06% 3.96% 3.34% 6.31% 5.24% 6.06% 0.08% 5.29% 4.55% 3.70% -1.34% -5.29% 0.06% 0.59% 1.06% 2.76% 5.48% 3.39% 8.09% 3.01% 0.19% 4.14% -3.02% -0.24% -0.16% 4.48% 3.64% 0.40% 4.18% -5.86% 3.32% 2.14% 6.50% 0.06% 2.31% -0.13% 0.54% -2.37% -10.37% 0.34% -13.01% 8.75% 4.97% -2.67% -3.28% -3.30% -1.32% 13.27% 7.68% 1.19% 1.83% 0.16% 2.94% 6.29% 4.57% 7.34% 2.55% 3.13% -3.22% -1.13% 1.44% 2.06% -3.08% 0.44% 4.13% 4.13% 6.99% 4.46% -1.09% 4.70% -2.31% -2.36% 0.23% 1.74% 4.04% 2.35% 1.74% -3.09% 1.65% 4.12% 6.72% 0.89% 4.38% -2.41% 0.50% -5.30% -8.47% 0.09% -10.20% 6.09% 5.24% 4.11% -2.60% -1.75% -0.24% 8.80% 6.62% 2.10% 2.25% 2.73% 1.39% 5.89% 1.76% 5.71% 2.33% 1.95% 0.05% -2.15% 0.67% 2.47% -3.67% 0.48% 2.27% 2.68% 5.51% 3.93% -1.73% 3.16% -1.80% -2.37% 1.61% 1.47% 3.77% 1.35% 2.36% -2.39% 3.21% 2.86% 4.89% -0.10% 2.81% 0.15% 0.14% 0.13% 0.15% 0.14% 0.14% 0.14% 0.12% 0.11% 0.10% 0.09% 0.10% 0.10% 0.09% 0.10% 0.07% 0.07% 0.08% 0.07% 0.07% 0.08% 0.07% 0.06% 0.09% 0.08% 0.06% 0.08% 0.10% 0.11% 0.11% 0.11% 0.15% 0.16% 0.16% 0.16% 0.21% 0.21% 0.24% 0.23% 0.24% 0.30% 0.29% 0.27% 0.31% 0.32% 0.35% 0.34% 0.37% 200603 200604 200605 200606 200607 200608 200609 200610 200611 200612 200701 200702 200703 200704 200705 200706 200707 200708 200709 200710 200711 200712 200801 200802 200803 200804 200805 200806 200807 200808 200809 200810 200811 200812 200901 200902 200903 200904 200905 200906 200907 200908 200909 200910 200911 200912 201001 201002 1.78% 1.52% -2.95% -0.13% -0.33% 2.55% 1.73% 3.71% 2.16% 1.06% 1.70% -1.46% 1.35% 4.30% 4.07% -1.32% -3.02% 1.05% 4.09% 2.69% -5.08% -0.30% -6.16% -2.14% -1.11% 4.90% 2.57% -7.73% -1.44% 1.13% -9.84% -18.15% -7.72% 1.40% -7.37% -9.84% 8.75% 10.47% 6.63% -0.20% 8.11% 3.16% 4.50% -2.75% 5.76% 3.03% -3.58% 3.68% 3.00% 2.74% -6.97% -1.38% -1.64% 1.71% -1.60% 1.69% 0.22% 1.90% 0.84% 3.95% -1.16% -2.20% 0.84% -0.05% -0.04% -3.34% 1.78% 0.19% -1.92% -3.67% -4.70% 1.10% -3.58% 6.41% 2.24% -6.43% -2.96% -3.85% -10.73% -13.46% 0.03% 8.53% -6.50% -11.95% 1.46% 7.98% 11.05% 2.71% 4.05% 3.43% -0.89% -2.32% -2.07% 0.26% 2.81% 0.39% 2.31% 6.84% -5.56% 0.20% 1.40% 2.73% 0.03% 6.49% 5.00% 4.19% 2.36% 1.54% 5.10% 5.17% 3.58% 2.87% 1.52% -3.77% 13.33% 8.49% -6.07% -1.17% -10.16% 2.92% -5.16% 7.23% 3.39% -7.94% -5.16% -6.43% -17.35% -25.98% -6.62% 7.67% -7.64% -4.90% 11.04% 13.78% 18.58% 1.58% 12.74% 1.88% 8.80% 0.95% 2.68% 2.43% -6.50% 2.91% 4.38% 5.59% -3.19% 0.11% 1.40% 3.14% 1.10% 4.19% 4.19% 3.77% 1.09% -0.17% 4.12% 6.03% 1.96% 0.16% -1.82% -1.69% 5.11% 4.67% -3.73% -1.89% -9.72% 2.11% 0.43% 4.59% 1.05% -8.47% -3.58% -4.27% -14.97% -22.06% -7.02% 6.61% -10.97% -10.01% 7.05% 13.79% 12.86% -1.84% 10.26% 5.67% 5.37% -1.90% 3.00% 1.06% -5.36% -2.18% 2.81% 3.25% -3.69% -0.20% 0.17% 2.65% 1.00% 3.74% 2.75% 2.26% 1.40% -0.21% 2.19% 4.18% 2.89% -0.41% -1.99% -0.74% 4.70% 3.49% -4.31% -1.32% -7.56% 0.06% -1.06% 5.09% 2.02% -7.87% -2.62% -1.84% -12.19% -19.38% -6.51% 4.34% -8.48% -9.93% 7.32% 0.37% 0.36% 0.43% 0.40% 0.40% 0.42% 0.41% 0.41% 0.42% 0.40% 0.44% 0.38% 0.43% 0.44% 0.41% 0.40% 0.40% 0.42% 0.32% 0.32% 0.34% 0.27% 0.21% 0.13% 0.17% 0.18% 0.18% 0.17% 0.15% 0.13% 0.15% 0.08% 0.03% 0.09% 0.00% 0.01% 0.02% 0.01% 0.00% 0.01% 0.01% 0.01% 0.01% 0.00% 0.00% 0.01% 0.00% 0.00% 11.43% 9.93% -0.29% 8.61% 3.97% 4.41% -2.15% 3.66% 1.99% -3.70% 1.24% 201002 201003 201004 201005 201006 201007 201008 201009 201010 201011 201012 201101 201102 201103 201104 201105 201106 201107 201108 201109 201110 201111 201112 201201 201202 201203 201204 201205 201206 201207 201208 201209 201210 201211 201212 201301 201302 201303 201304 201305 201306 201307 201308 201309 201310 201311 201312 3.68% 6.33% 1.99% -7.83% -5.41% 6.94% -4.45% 9.44% 3.91% 0.84% 6.80% 1.99% 4.04% 0.41% 2.78% -1.50% -1.82% -2.25% -5.86% -8.48% 11.49% -0.51% 0.42% 5.19% 4.31% 2.33% -0.60% -6.69% 3.73% 1.05% 2.70% 2.82% -1.60% 0.66% 1.28% 5.31% 0.97% 3.70% 1.29% 2.49% -1.54% 5.68% -2.56% 3.78% 4.15% 2.78% 2.63% 0.39% 4.75% 0.52% -7.89% -0.64% 2.99% -2.56% 4.73% 1.42% 1.87% 7.57% 0.34% 4.78% -8.65% 0.74% -1.64% 2.49% 3.38% -7.05% -0.42% -1.19% -3.80% 1.16% 4.36% 3.61% 1.26% -1.94% -8.42% 4.74% -1.83% -0.63% 2.14% -1.86% 1.74% 3.90% 3.64% 2.85% 5.39% 8.53% -5.64% 1.03% 1.33% -2.39% 8.54% -0.14% 0.95% 0.76% 2.91% 7.65% 0.84% -12.31% -0.25% 9.58% -0.92% 12.73% 3.74% -1.37% 6.96% -0.91% 0.12% 2.32% 4.68% -2.54% -2.33% 1.28% -6.85% -15.47% 13.74% -6.52% -1.18% 9.82% 5.13% -2.27% 0.95% -11.22% 4.74% 5.03% 1.02% 4.24% 1.89% 1.52% 2.86% 5.36% 1.31% -0.46% 2.43% -6.28% -6.18% 3.74% -0.25% 6.72% 3.48% -2.34% -0.53% -2.18% 6.55% -1.92% -12.04% -0.93% 11.86% -4.24% 11.55% 5.11% -8.09% 8.98% 3.72% 3.06% -0.18% 8.09% -3.04% -2.02% -3.45% -10.12% -11.63% 11.05% -4.72% -2.15% 5.67% 1.24% 6.31% 0.45% -9.51% -3.11% 8.21% -3.92% 9.82% 4.02% -2.22% 7.58% 2.15% 3.53% -0.67% 4.43% -2.11% -1.49% -1.80% -7.46% -9.12% 10.01% -2.60% -0.39% 5.56% 4.92% 1.20% -1.13% -8.83% 4.86% 0.91% 2.78% 3.04% -0.39% 1.32% 2.34% 5.43% 0.11% 2.24% 3.01% 0.55% -2.50% 5.60% -1.84% 5.48% 3.75% 1.82% 2.16% 0.00% 0.01% 0.00% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.00% 0.00% 0.00% 0.00% 0.01% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 0.00% 0.00% 0.01% 0.01% 0.01% 0.01% 0.01% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 6.41% 0.06% -2.25% -12.30% 7.10% 0.63% 4.60% 3.48% 1.70% 2.25% 3.48% 6.25% -2.40% -0.49% 4.16% 1.13% -4.55% 7.42% -0.75% 7.09% 4.48% 1.40% 2.41% Suppose you have a risk-aversion coefficient of 3.0, and utility function of, U = E[r] A02, that uses your estimate of annual arithmetic returns (APR) and variance. Which index would you invest in? 2 5.) Assume that only a single risky asset exists (the Global index), and a single risk-free rate (the 1- month US risk-free rate) at which investors can borrow and lend. Assume the risk-free rate is equal to its time-series average and has zero variance. Also assume the utility function provided in the previous problem, with a risk-aversion coefficient of 3.0. For all parts use your estimate of annualized arithmetic average returns (APR) and annualized variance. a. Plot the capital allocation line (CAL) in the expected return-standard deviation plane. What does moving up and down the CAL represent about the allocation between the two assets? What is the intercept of the line? What is its slope? What is the economic significance of the intercept and slope? b. Plot the investor's utility of the complete portfolio as a function of the allocation to the risky asset. What does the curve suggest about the investor's approximate optimal allocation to the risky asset? c. On the same plot as the CAL in (a), plot the indifference curve in the expected return- standard deviation plane corresponding to a utility level of 0.03 for an investor with a risk aversion coefficient of 3. Plot a second indifference curve corresponding to the utility level suggested by (b). How does the second indifference curve differ from the first? What is the relation of the second indifference curve with respect to the CAL? d. What is the exact allocation to the risky asset in the complete portfolio that maximizes the utility of the investor? Global Date 199007 199008 199009 199010 199011 199012 199101 199102 199103 199104 199105 199106 199107 199108 199109 199110 199111 199112 199201 199202 199203 199204 199205 199206 199207 199208 199209 199210 199211 199212 199301 199302 199303 199304 199305 199306 199307 199308 199309 199310 199311 199312 199401 199402 199403 199404 199405 North_America -0.82% -8.93% -5.41% -1.33% 6.43% 3.11% 4.73% 7.70% 2.80% 0.34% 4.16% -4.27% 4.42% 2.62% -1.29% 1.84% -3.76% 10.30% -0.34% 1.28% -2.30% 1.53% 0.65% -1.81% 3.99% -2.04% 0.97% 1.10% 3.70% 1.80% 0.99% 0.70% 2.58% -2.28% 3.02% 0.44% -0.12% 3.78% -0.18% 1.96% -1.52% 1.95% 3.15% -2.36% -4.41% 0.93% 1.03% Japan 0.78% -11.25% -17.43% 25.59% -13.52% 2.34% 1.67% 12.81% -3.76% 2.68% -1.59% -6.61% 1.85% -6.79% 9.10% 4.47% -8.14% 2.85% -5.33% -6.95% -11.13% -7.39% 9.02% -8.73% -3.00% 16.61% -2.59% -5.17% 2.07% -0.73% -0.63% 4.55% 16.04% 16.93% 5.21% -3.96% 6.94% 2.41% -4.96% -2.34% -15.98% 2.22% 17.06% 4.08% -1.97% 3.57% 1.54% Asia_exJapan 4.85% -7.82% -8.25% -1.58% -2.29% -0.61% 6.03% 9.26% 2.13% 3.24% -0.40% -0.50% 6.04% -1.48% 1.16% 4.33% -0.26% 1.58% 1.36% 1.85% 0.22% 5.67% 7.73% -1.05% -3.64% -6.22% -2.56% 2.41% -1.32% 1.31% 0.94% 8.22% 2.84% 5.70% 5.04% -2.58% 2.69% 6.82% 0.18% 15.95% -2.18% 20.28% 1.32% -6.21% -9.72% 2.48% 4.48% Europe 5.05% -10.20% -11.74% 7.27% 0.17% -0.95% 2.12% 7.78% -6.34% -0.21% 1.13% -7.02% 5.94% 1.86% 3.42% -2.33% -1.89% 6.61% -0.03% 0.15% -3.27% 5.45% 5.43% -0.90% -3.81% -0.35% -2.67% -7.39% -0.24% 1.41% 1.13% 1.48% 5.83% 2.17% 1.10% -2.90% 1.27% 8.89% -0.43% 2.66% -2.01% 7.20% 6.28% -3.23% -2.28% 4.02% -3.70% 1.47% -10.10% -11.64% 10.26% -3.30% 1.63% 2.99% 9.57% -1.93% 1.13% 1.22% -5.65% 3.93% -0.94% 3.34% 1.78% -4.75% 6.56% -1.86% -1.61% -5.14% 0.16% 4.41% -3.44% -0.36% 2.85% -1.14% -2.86% 2.07% 1.00% 0.59% 2.17% 7.02% 4.70% 3.35% -1.91% 2.55% 4.62% -1.78% 1.33% -6.06% 4.23% 7.61% -0.90% -3.37% 2.62% 0.11% Rf 0.68% 0.66% 0.60% 0.68% 0.57% 0.60% 0.52% 0.48% 0.44% 0.53% 0.47% 0.42% 0.49% 0.46% 0.46% 0.42% 0.39% 0.38% 0.34% 0.28% 0.34% 0.32% 0.28% 0.32% 0.31% 0.26% 0.26% 0.23% 0.23% 0.28% 0.23% 0.22% 0.25% 0.24% 0.22% 0.25% 0.24% 0.25% 0.26% 0.22% 0.25% 0.23% 0.25% 0.21% 0.27% 0.27% 0.32% 0.32% 0.31% 0.28% 0.37% 0.37% 0.38% 0.37% 0.44% 0.42% 0.40% 0.46% 0.44% 0.54% 199405 199406 199407 199408 199409 199410 199411 199412 199501 199502 199503 199504 199505 199506 199507 199508 199509 199510 199511 199512 199601 199602 199603 199604 199605 199606 199607 199608 199609 199610 199611 199612 199701 199702 199703 199704 199705 199706 199707 199708 199709 199710 199711 199712 199801 199802 199803 199804 1.03% -2.81% 3.04% 4.38% -1.69% 1.52% -3.67% 1.33% 1.80% 4.07% 2.72% 2.63% 3.49% 2.98% 4.08% 0.89% 3.66% -1.05% 4.27% 1.54% 2.78% 1.69% 1.22% 2.42% 2.57% -0.59% -5.25% 3.27% 5.32% 1.81% 6.75% -1.19% 5.50% 0.02% 4.48% 4.43% 7.08% 4.27% 7.73% -3.71% 5.86% -3.33% 2.96% 1.84% 0.47% 7.41% 5.19% 1.27% 1.54% 6.33% -3.80% 0.09% -2.85% 2.59% -6.16% 2.05% -6.44% -5.25% 9.08% 4.10% -6.23% -4.16% 6.31% -2.67% -1.16% -3.92% 4.52% 4.90% -1.26% -1.47% 3.01% 6.84% 4.48% 0.35% -4.70% 4.30% 2.85% -6.88% 0.64% -7.06% -10.75% 1.84% -3.68% 1.88% 13.56% 5.83% -3.98% -9.38% -2.55% -7.67% -8.04% -7.59% 10.98% 1.23% -6.54% -1.89% 4.48% -6.07% 5.02% 3.99% -2.16% 1.42% -7.85% -0.86% -7.17% 6.19% 0.92% 1.56% 4.58% -1.84% 5.24% -1.08% 2.13% -0.31% 1.22% 3.26% 8.54% 0.76% -0.54% 2.04% 1.09% -1.72% -4.96% 4.24% 2.72% 2.64% 6.83% -0.12% -1.64% 1.18% -4.22% 0.27% 7.34% 2.69% 2.18% -8.00% 4.41% -21.72% -0.87% -1.04% -7.33% 11.76% -1.45% -5.07% -3.70% -0.84% 4.93% 2.33% -3.23% 4.02% -4.14% 0.52% -1.07% 2.38% 3.90% 3.00% 2.28% 1.51% 4.48% -3.57% 2.79% -0.23% 0.19% 2.37% 0.98% 2.30% 1.36% 1.11% 1.96% 0.68% -1.38% 2.65% 1.55% 1.94% 4.47% 2.49% 0.06% 0.99% 2.48% -0.43% 4.48% 4.10% 3.37% -4.80% 9.16% -4.14% 1.09% 2.73% 3.73% 7.72% 7.32% 2.72% 0.11% 0.47% 1.35% 2.47% -2.48% 2.49% 4.77% 1.23% -1.92% 0.97% 4.72% 3.11% 0.38% 0.40% 4.82% -1.36% 2.10% -1.52% 3.07% 2.68% 1.52% 1.01% 1.62% 3.16% 0.51% -0.08% 4.07% 1.33% 3.59% -0.07% 4.83% -1.31% 0.47% 0.66% -2.35% 2.34% 7.45% 4.43% 4.11% -5.16% 5.40% -5.03% 0.68% 0.77% 2.48% 6.83% 4.16% 1.18% 0.47% 0.45% 0.47% 0.43% 0.47% 0.42% 0.49% 0.43% 0.39% 0.39% 0.46% 0.42% 0.40% 0.45% 0.41% 0.44% 0.42% 0.41% 0.46% 0.45% 0.39% 0.43% 0.43% 0.49% 0.37% 0.43% 0.41% 0.44% 0.42% 0.39% 0.48% 0.43% 0.39% 0.39% 0.43% 199804 199805 199806 199807 199808 199809 199810 199811 199812 199901 199902 199903 199904 199905 199906 199907 199908 199909 199910 199911 199912 200001 200002 200003 200004 200005 200006 200007 200008 200009 200010 200011 200012 200101 200102 200103 200104 200105 200106 200107 200108 200109 200110 200111 200112 200201 200202 200203 1.27% -2.41% 3.30% -2.30% -15.79% 6.48% 7.39% 6.08% 6.30% 3.63% -3.77% 3.85% 4.63% -1.81% 5.08% -2.98% -0.92% -2.31% 6.04% 3.21% 7.29% -3.94% 1.96% 7.51% 4.31% -2.97% 4.08% -1.65% 7.52% -4.85% -2.28% -9.71% 2.05% 3.72% -9.44% -6.85% 8.07% 1.17% -1.67% -1.73% -5.90% -8.96% 2.43% 8.11% 1.78% -1.70% -2.01% 4.49% -1.89% -4.50% 0.69% -1.24% -8.82% -3.44% 16.49% 3.91% 3.14% 1.14% -2.26% 14.01% 5.04% 4.96% 10.80% 10.30% 3.26% 7.21% 6.66% 7.55% 4.06% -4.99% -1.33% 6.63% -8.61% -7.06% 6.29% -11.68% 6.95% -4.32% -6.95% -2.50% -9.35% -0.30% -5.16% -3.87% 9.08% 0.17% -5.02% -8.63% -2.39% -7.39% 0.99% -1.63% -8.09% -7.71% 5.26% 5.73% -5.07% -10.47% -5.33% -3.10% -12.90% 10.89% 18.07% 5.09% -2.17% 0.23% -0.98% 8.39% 16.91% -5.13% 9.29% -1.79% -2.01% -1.87% 1.55% 7.40% 9.12% -6.76% -0.58% 0.87% -5.77% -8.00% 11.23% -0.17% 2.56% -6.97% -5.44% -0.53% 4.44% 3.32% -3.37% -12.87% 6.89% 0.12% 1.67% -3.57% -0.81% -14.26% 6.25% 2.72% 2.72% -0.11% 1.95% -11.64% 4.34% 6.78% 4.50% 3.25% 0.29% -1.94% 0.27% 3.20% -3.38% 2.03% 1.52% 1.75% 0.08% 2.10% 3.07% 9.66% -6.78% 6.30% 1.15% -5.16% 0.45% 1.11% -1.15% -1.07% -4.44% -2.16% -3.99% 6.28% 0.76% -8.19% -8.85% 7.67% -4.67% -3.26% -0.39% -1.77% -11.24% 3.45% 4.29% 1.91% -4.57% 0.52% 5.22% 1.18% -1.20% 1.64% -0.78% -13.58% 1.71% 8.40% 5.29% 4.71% 2.20% -2.96% 3.96% 4.60% -2.77% 5.00% 0.05% 0.43% -0.21% 4.79% 3.97% 7.52% -5.05% 2.64% 5.24% -5.27% -2.73% 3.69% -2.84% 4.64% -4.72% -2.93% -6.88% 1.92% 2.30% -8.37% -7.32% 8.03% -0.78% -2.45% -2.22% -4.11% -9.65% 2.68% 5.83% 0.78% -3.06% -0.55% 4.84% 0.43% 0.40% 0.41% 0.40% 0.43% 0.46% 0.32% 0.31% 0.38% 0.35% 0.35% 0.43% 0.37% 0.34% 0.40% 0.38% 0.39% 0.39% 0.39% 0.36% 0.44% 0.41% 0.43% 0.47% 0.46% 0.50% 0.40% 0.48% 0.50% 0.51% 0.56% 0.51% 0.50% 0.54% 0.38% 0.44% 0.39% 0.32% 0.28% 0.30% 0.31% 0.28% 0.22% 0.17% 0.15% 0.14% 0.13% 0.13% 8.63% 2.62% 1.68% -1.45% 4.55% 0.91% 2.24% -5.44% -6.13% 0.14% -7.38% 4.83% 2.79% -3.01% 1.62% -1.13% -0.48% 4.65% 200204 200205 200206 200207 200208 200209 200210 200211 200212 200301 200302 200303 200304 200305 200306 200307 200308 200309 200310 200311 200312 200401 200402 200403 200404 200405 200406 200407 200408 200409 200410 200411 200412 200501 200502 200503 200504 200505 200506 200507 200508 200509 200510 200511 200512 200601 200602 200603 -5.21% -0.96% -7.10% -8.04% 0.24% -9.99% 7.66% 5.97% -5.33% -2.33% -1.59% 0.91% 8.21% 6.37% 1.55% 2.17% 2.53% -0.99% 6.08% 1.52% 4.61% 2.11% 1.54% -1.06% -1.91% 1.20% 2.18% -3.67% 0.19% 2.17% 1.79% 4.76% 3.41% -2.45% 2.36% -1.47% -2.65% 3.61% 1.18% 4.27% -0.44% 1.19% -2.23% 4.16% 0.47% 3.85% -0.18% 1.78% 5.37% 7.26% -4.67% -5.92% -1.26% -4.74% -6.60% 3.18% -2.29% -3.38% 1.55% -2.84% 1.08% 4.63% 7.22% 3.49% 9.83% 7.46% 4.01% -3.68% 6.57% 2.03% 0.00% 14.94% -4.54% -3.16% 5.33% -6.49% 1.12% -2.96% 2.52% 3.92% 5.09% -1.07% 1.95% -1.27% -1.96% -2.30% 0.92% 0.83% 7.09% 8.33% -0.08% 3.25% 9.52% 3.99% -2.12% 3.00% 7.06% 3.96% 3.34% 6.31% 5.24% 6.06% 0.08% 5.29% 4.55% 3.70% -1.34% -5.29% 0.06% 0.59% 1.06% 2.76% 5.48% 3.39% 8.09% 3.01% 0.19% 4.14% -3.02% -0.24% -0.16% 4.48% 3.64% 0.40% 4.18% -5.86% 3.32% 2.14% 6.50% 0.06% 2.31% -0.13% 0.54% -2.37% -10.37% 0.34% -13.01% 8.75% 4.97% -2.67% -3.28% -3.30% -1.32% 13.27% 7.68% 1.19% 1.83% 0.16% 2.94% 6.29% 4.57% 7.34% 2.55% 3.13% -3.22% -1.13% 1.44% 2.06% -3.08% 0.44% 4.13% 4.13% 6.99% 4.46% -1.09% 4.70% -2.31% -2.36% 0.23% 1.74% 4.04% 2.35% 1.74% -3.09% 1.65% 4.12% 6.72% 0.89% 4.38% -2.41% 0.50% -5.30% -8.47% 0.09% -10.20% 6.09% 5.24% 4.11% -2.60% -1.75% -0.24% 8.80% 6.62% 2.10% 2.25% 2.73% 1.39% 5.89% 1.76% 5.71% 2.33% 1.95% 0.05% -2.15% 0.67% 2.47% -3.67% 0.48% 2.27% 2.68% 5.51% 3.93% -1.73% 3.16% -1.80% -2.37% 1.61% 1.47% 3.77% 1.35% 2.36% -2.39% 3.21% 2.86% 4.89% -0.10% 2.81% 0.15% 0.14% 0.13% 0.15% 0.14% 0.14% 0.14% 0.12% 0.11% 0.10% 0.09% 0.10% 0.10% 0.09% 0.10% 0.07% 0.07% 0.08% 0.07% 0.07% 0.08% 0.07% 0.06% 0.09% 0.08% 0.06% 0.08% 0.10% 0.11% 0.11% 0.11% 0.15% 0.16% 0.16% 0.16% 0.21% 0.21% 0.24% 0.23% 0.24% 0.30% 0.29% 0.27% 0.31% 0.32% 0.35% 0.34% 0.37% 200603 200604 200605 200606 200607 200608 200609 200610 200611 200612 200701 200702 200703 200704 200705 200706 200707 200708 200709 200710 200711 200712 200801 200802 200803 200804 200805 200806 200807 200808 200809 200810 200811 200812 200901 200902 200903 200904 200905 200906 200907 200908 200909 200910 200911 200912 201001 201002 1.78% 1.52% -2.95% -0.13% -0.33% 2.55% 1.73% 3.71% 2.16% 1.06% 1.70% -1.46% 1.35% 4.30% 4.07% -1.32% -3.02% 1.05% 4.09% 2.69% -5.08% -0.30% -6.16% -2.14% -1.11% 4.90% 2.57% -7.73% -1.44% 1.13% -9.84% -18.15% -7.72% 1.40% -7.37% -9.84% 8.75% 10.47% 6.63% -0.20% 8.11% 3.16% 4.50% -2.75% 5.76% 3.03% -3.58% 3.68% 3.00% 2.74% -6.97% -1.38% -1.64% 1.71% -1.60% 1.69% 0.22% 1.90% 0.84% 3.95% -1.16% -2.20% 0.84% -0.05% -0.04% -3.34% 1.78% 0.19% -1.92% -3.67% -4.70% 1.10% -3.58% 6.41% 2.24% -6.43% -2.96% -3.85% -10.73% -13.46% 0.03% 8.53% -6.50% -11.95% 1.46% 7.98% 11.05% 2.71% 4.05% 3.43% -0.89% -2.32% -2.07% 0.26% 2.81% 0.39% 2.31% 6.84% -5.56% 0.20% 1.40% 2.73% 0.03% 6.49% 5.00% 4.19% 2.36% 1.54% 5.10% 5.17% 3.58% 2.87% 1.52% -3.77% 13.33% 8.49% -6.07% -1.17% -10.16% 2.92% -5.16% 7.23% 3.39% -7.94% -5.16% -6.43% -17.35% -25.98% -6.62% 7.67% -7.64% -4.90% 11.04% 13.78% 18.58% 1.58% 12.74% 1.88% 8.80% 0.95% 2.68% 2.43% -6.50% 2.91% 4.38% 5.59% -3.19% 0.11% 1.40% 3.14% 1.10% 4.19% 4.19% 3.77% 1.09% -0.17% 4.12% 6.03% 1.96% 0.16% -1.82% -1.69% 5.11% 4.67% -3.73% -1.89% -9.72% 2.11% 0.43% 4.59% 1.05% -8.47% -3.58% -4.27% -14.97% -22.06% -7.02% 6.61% -10.97% -10.01% 7.05% 13.79% 12.86% -1.84% 10.26% 5.67% 5.37% -1.90% 3.00% 1.06% -5.36% -2.18% 2.81% 3.25% -3.69% -0.20% 0.17% 2.65% 1.00% 3.74% 2.75% 2.26% 1.40% -0.21% 2.19% 4.18% 2.89% -0.41% -1.99% -0.74% 4.70% 3.49% -4.31% -1.32% -7.56% 0.06% -1.06% 5.09% 2.02% -7.87% -2.62% -1.84% -12.19% -19.38% -6.51% 4.34% -8.48% -9.93% 7.32% 0.37% 0.36% 0.43% 0.40% 0.40% 0.42% 0.41% 0.41% 0.42% 0.40% 0.44% 0.38% 0.43% 0.44% 0.41% 0.40% 0.40% 0.42% 0.32% 0.32% 0.34% 0.27% 0.21% 0.13% 0.17% 0.18% 0.18% 0.17% 0.15% 0.13% 0.15% 0.08% 0.03% 0.09% 0.00% 0.01% 0.02% 0.01% 0.00% 0.01% 0.01% 0.01% 0.01% 0.00% 0.00% 0.01% 0.00% 0.00% 11.43% 9.93% -0.29% 8.61% 3.97% 4.41% -2.15% 3.66% 1.99% -3.70% 1.24% 201002 201003 201004 201005 201006 201007 201008 201009 201010 201011 201012 201101 201102 201103 201104 201105 201106 201107 201108 201109 201110 201111 201112 201201 201202 201203 201204 201205 201206 201207 201208 201209 201210 201211 201212 201301 201302 201303 201304 201305 201306 201307 201308 201309 201310 201311 201312 3.68% 6.33% 1.99% -7.83% -5.41% 6.94% -4.45% 9.44% 3.91% 0.84% 6.80% 1.99% 4.04% 0.41% 2.78% -1.50% -1.82% -2.25% -5.86% -8.48% 11.49% -0.51% 0.42% 5.19% 4.31% 2.33% -0.60% -6.69% 3.73% 1.05% 2.70% 2.82% -1.60% 0.66% 1.28% 5.31% 0.97% 3.70% 1.29% 2.49% -1.54% 5.68% -2.56% 3.78% 4.15% 2.78% 2.63% 0.39% 4.75% 0.52% -7.89% -0.64% 2.99% -2.56% 4.73% 1.42% 1.87% 7.57% 0.34% 4.78% -8.65% 0.74% -1.64% 2.49% 3.38% -7.05% -0.42% -1.19% -3.80% 1.16% 4.36% 3.61% 1.26% -1.94% -8.42% 4.74% -1.83% -0.63% 2.14% -1.86% 1.74% 3.90% 3.64% 2.85% 5.39% 8.53% -5.64% 1.03% 1.33% -2.39% 8.54% -0.14% 0.95% 0.76% 2.91% 7.65% 0.84% -12.31% -0.25% 9.58% -0.92% 12.73% 3.74% -1.37% 6.96% -0.91% 0.12% 2.32% 4.68% -2.54% -2.33% 1.28% -6.85% -15.47% 13.74% -6.52% -1.18% 9.82% 5.13% -2.27% 0.95% -11.22% 4.74% 5.03% 1.02% 4.24% 1.89% 1.52% 2.86% 5.36% 1.31% -0.46% 2.43% -6.28% -6.18% 3.74% -0.25% 6.72% 3.48% -2.34% -0.53% -2.18% 6.55% -1.92% -12.04% -0.93% 11.86% -4.24% 11.55% 5.11% -8.09% 8.98% 3.72% 3.06% -0.18% 8.09% -3.04% -2.02% -3.45% -10.12% -11.63% 11.05% -4.72% -2.15% 5.67% 1.24% 6.31% 0.45% -9.51% -3.11% 8.21% -3.92% 9.82% 4.02% -2.22% 7.58% 2.15% 3.53% -0.67% 4.43% -2.11% -1.49% -1.80% -7.46% -9.12% 10.01% -2.60% -0.39% 5.56% 4.92% 1.20% -1.13% -8.83% 4.86% 0.91% 2.78% 3.04% -0.39% 1.32% 2.34% 5.43% 0.11% 2.24% 3.01% 0.55% -2.50% 5.60% -1.84% 5.48% 3.75% 1.82% 2.16% 0.00% 0.01% 0.00% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.00% 0.00% 0.00% 0.00% 0.01% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 0.00% 0.00% 0.01% 0.01% 0.01% 0.01% 0.01% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 6.41% 0.06% -2.25% -12.30% 7.10% 0.63% 4.60% 3.48% 1.70% 2.25% 3.48% 6.25% -2.40% -0.49% 4.16% 1.13% -4.55% 7.42% -0.75% 7.09% 4.48% 1.40% 2.41%