Focus on the two efficient frontiers: one of three assets in Exhibit 5 and one of five assets in Exhibit 8. We know the optimal portfolios are the tangency portfolios given the risk-free asset is STP (return of 3.2%). Find the optimal portfolio of three assets as the portfolio that has 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. (Karen)

- Calculate the Sharpe ratios of the 12 portfolios in Exhibit 5. Show what portfolio is optimal (i.e. O_3-asset).

- Calculate the Sharpe ratios of the 12 portfolios in Exhibit 8. Show what portfolio is optimal (i.e. O_5-asset).

Portfolio 1 2 3 4 5 6 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% 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% 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 Bonds 0.772 0.701 0.632 0.565 0.497 0.429 0.362 0.294 0.227 0.159 0.092 0.024 7 8 9 10 11 12 Source: Thomson Financial Datastream. Exhibit 5b Risk-Return Plot of Optimal Portfolios with only U.S., Foreign, and Bonds 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% 5.0% 15.0% 20.0% 10.0% Stdev Exhibit 8 Array of Optimal Portfolios with All Five Asset Classes: U.S., Foreign, Bonds, REITs, and Commodities 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 0.000 0.020 0.643 0.000 0.082 0.567 0.000 0.144 0.491 0.000 0.207 0.415 0.036 0.239 0.348 0.089 0.257 0.285 0.143 0.275 0.222 0.197 0.292 0.159 0.250 0.310 0.097 0.304 0.328 0.034 0.387 0.354 0.000 REITS 0.180 0.182 0.183 0.185 0.174 0.156 0.138 0.119 0.101 0.083 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