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Beyond Equilibrium, the Black-Litterman Approach_______________________________ 81^ TABLE 7.4 Optimal Portfolio Given Bearish


View on German Equity Change from No Change from Country Unconstrained Market Cap Shorting Market C United States 57.6% 3.6% 54.2% 0.2% United Kingdom 11.7 1.1 10.6 0.1 Japan 8.4 -1.4 9.8 -0.1 France 18.9 14.4 5.3 0.9 Switzerland 9.2 5.7 3.8 0.3 Germany -53.7 -57.0 0.0 -3.3 Netherlands 11.5 8.9 3.1 0.5 Canada 2.9 0.6 2.3 0.0 Italy 14.6 12.9 2.5 0.7 Australia -2.7 -4.4 1.5 -0.2 Spain 3.8 2.4 1.5 0.1 Sweden 8.1 7.3 1.3 0.4 Hong Kong 3.0 2.2 1.0 0.1 Finland 0.1 -0.6 0.6 0.0 Belgium 1.9 1.4 0.6 0.1 Singapore 1.0 0.6 0.4 0.0 Denmark 1.1 0.7 0.4 0.0 Ireland 2.2 1.9 0.4 0.1 Norway -3.7 -3.9 0.0 -0.2 Portugal 2.8 2.6 0.4 0.2 Greece 0.7 0.5 0.2 0.0 Austria 1.2 1.1 0.1 0.1 New Zealand -0.4 -0.4 0.0 0.0 Volatility 15.2   16.2   Expected return 8.1   8.1   while holding expected return essentially unchanged. In this sense the optimizer is working as it should. If we compare the portfolio weights in the new unconstrained optimal portfolio with those of the global market capitalization weighted portfolio, however, the changes in country weights are very large, and in some cases inexplicable. This type of behavior is typical of an unconstrained mean-variance optimization. For this reason portfolio optimizations are usually run with many tight constraints on asset weights. Black-Litterman addresses this excessive sensitivity of portfolio optimizations without adding constraints. The Black-Litterman approach assumes there are two distinct sources of information about future excess returns: investor views and market equilibrium. Both sources of information are assumed to be uncertain and are expressed in terms of probability distributions. The expected excess returns that are used to drive the portfolio optimization are estimates that combine both sources of information. In the Black-Litterman model a view is a statement about the expected return