Equilibrium Country Capitalization Expected Return Excess Return United States 53.98% 8.50% 4.00% United Kingdom 10.60 7.47 2.97 Japan 9.85 7.07 2.57 France 4.44 8.39 3.89 Switzerland 3.49 7.32 2.82 Germany 3.27 9.11 4.61 Netherlands 2.58 8.19 3.69 Canada 2.28 7.71 3.21 Italy 1.78 8.01 3.51 Australia 1.73 5.99 1.49 Spain 1.37 8.26 3.76 Sweden 0.87 9.59 5.09 Hong Kong 0.83 7.29 2.79 Finland 0.67 11.48 6.98 Belgium 0.48 6.71 2.21 Singapore 0.40 7.05 2.55 Denmark 0.36 6.69 2.19 Ireland 0.30 7.02 2.52 Norway 0.24 6.82 2.32 Portugal 0.19 6.40 1.90 Greece 0.14 6.82 2.32 Austria 0.07 5.20 0.70 New Zealand 0.06 5.35 0.85 months. The investor holds all other expected returns unchanged at their equilibrium values. Given this slight alteration in expected returns, in Table 7.4 we show two new optimal portfolios together with the deviations of these two portfolios from the market capitalization weights. The first portfolio is optimized with no constraints except that weights sum to 100 percent; the second portfolio includes constraints against shorting. When the portfolio is optimized without constraints the optimizer quickly recognizes a slight inconsistency between the expected return for Germany and the other equity markets and treats this inconsistency as an opportunity. It suggests a 54 percent short position in Germany offset by overweight positions in most of the other equity markets. Notice also, though, the odd short positions in Japan, Finland, Australia, Norway, and New Zealand. When no shorting constraints are imposed the opportunity is significantly reduced. The German equity position is zero and other deviations from market capitalization weights are reduced proportionately. This unconstrained optimal portfolio has an expected return of 8.1 percent and an annualized volatility of 15.2 percent. These compare to the equilibrium portfolio values of 8.1 percent and 16.2 percent, respectively. The view of a slightly lower expected return on German stocks has provided an opportunity to reduce risk,