Portfolio Percent Deviation Country Returns Equilibrium Weights from Market United States 3.71% -0.29% 53.98% 0.00% United Kingdom 2.59 -0.38 3.96 -6.64 Japan 2.72 0.14 16.49 6.64 France 3.44 -0.46 4.44 0.00 Switzerland 2.48 -0.34 3.49 0.00 Germany 4.04 -0.57 -2.27 -5.54 Netherlands 3.25 -0.45 2.58 0.00 Canada 2.94 -0.26 2.28 0.00 Italy 3.09 -0.42 1.78 0.00 Australia 1.41 -0.09 1.73 0.00 Spain 3.33 -0.43 1.37 0.00 Sweden 4.56 -0.53 0.87 0.00 Hong Kong 2.58 -0.22 0.83 0.00 Finland 6.27 -0.71 0.67 0.00 Belgium 1.93 -0.28 0.48 0.00 Singapore 2.40 -0.15 0.40 0.00 Denmark 1.98 -0.22 0.36 0.00 Ireland 2.25 -0.26 0.30 0.00 Norway 2.08 -0.24 0.24 0.00 Portugal 1.70 -0.21 0.19 0.00 Greece 2.10 -0.23 0.14 0.00 Austria 0.60 -0.10 0.07 0.00 New Zealand 0.79 -0.06 0.06 0.00 model is the market equilibrium portfolio plus a weighted sum of the portfolios about which the investor has views. We will now investigate how changes in some of the Black-Litterman parameters affect the optimal portfolio tilts. In this simple unconstrained optimization environment,4 we can characterize the deviations of the optimal portfolios from the market capitalization portfolio by the weights, iv1 and w2> on the two view portfolios. For example, in Table 7.7, wx = 5.54 andw2 = 6.64. In Table 7.8 we show how these weights vary with changes in the expected excess returns of the view portfolios {q1 and q2), the degrees of confidence (l/co1 and l/co2), and the correlation between the views. Notice that a view portfolio is given zero weight not when it has zero expected return, but rather when it has a return equal to that implied by a combination of equilibrium and all other views. Thus, adding a view creates a positive tilt toward that view portfolio only when the view is more bullish than the expected return implied by the Black-Litterman model without this particular view. In an unconstrained optimization environment the Black-Litterman model is, in some respects, a complex tool for solving a relatively straightforward problem. 4See He and Litterman (1999).