4) Now we will focus on the two efficient frontiers: one of three assets in Exhibit 5 and one of five assets in Exhibit 8. We know (from our chapter 6), the optimal portfolios are the tangency portfolios given the risk-free asset is STP (return of 3.2%). For simplicity, let find the optimal portfolio of three assets as the portfolio that have the highest Sharpe ratio out of the 12 portfolios in Exhibit 5. Let call this optimal portfolio O_3-asset. Similarly, find the optimal portfolio of five assets, portfolio O_5-asset, based on Exhibit 8.

- Draw a graph with the two efficient frontiers and show the two optimal portfolios.

- Report (in an easy-to-compare format) the risks, returns, Sharpe ratios, and weight of each of five assets for portfolios O_3-asset and O_5-asset.

14.0% US Equity Foreign Equity 12.0% Baseline LTP Commodities 10.0% REITS 8.0% Expected Return 6.0% Bonds 4.0% 2.0% 0.0% 0.0% 20.0% 5.0% 15.0% 10.0% Stdev Portfolio 2 Bonds 0.772 0.701 0.632 3 4 5 Expected Ret. 7.00% 7.50% 8.00% 8.50% 9.00% 9.50% 10.00% 10.50% 11.00% 11.50% 12.00% 12.50% 6 Asset Allocation US Equity Foreign Equity 0.000 0.228 0.000 0.299 0.038 0.330 0.087 0.348 0.136 0.367 0.185 0.386 0.234 0.404 0.283 0.423 0.332 0.442 0.381 0.460 0.430 0.479 0.479 0.497 Stdev 9.38% 9.14% 9.06% 9.10% 9.27% 9.55% 9.94% 10.43% 11.00% 11.64% 12.33% 13.08% 7 8 0.565 0.497 0.429 0.362 0.294 0.227 0.159 0.092 0.024 9 10 11 12 Portfolio Expected Ret. 1 7.00% 2 7.50% 3 8.00% 4 8.50% 5 9.00% 6 9.50% 7 10.00% 8 10.50% 9 11.00% 10 11.50% 11 12.00% Stdev 8.29% 7.89% 7.67% 7.64% 7.80% 8.08% 8.49% 8.99% 9.58% 10.24% 10.98% Asset Allocation US Equity Foreign Equity Bonds REITs 0.000 0.020 0.643 0.180 0.000 0.082 0.567 0.182 0.000 0.144 0.491 0.183 0.000 0.207 0.415 0.185 0.036 0.239 0.348 0.174 0.089 0.257 0.285 0.156 0.143 0.275 0.222 0.138 0.197 0.292 0.159 0.119 0.250 0.310 0.097 0.101 0.304 0.328 0.034 0.083 0.387 0.354 0.000 0.010 Commodities 0.158 0.170 0.181 0.193 0.203 0.213 0.223 0.232 0.242 0.251 0.250