Capitalization Weights (May 2002) Equal Weights       Risk Risk   Risk Risk     Model A Model B   Model A Model B   Weights Risk Risk Weights Risk Risk Australia 1.75% 0.28% 1.18% 5.56% 1.45% 3.68% Austria 0.07 0.01 0.05 5.56 1.65 4.76 Belgium 0.49 0.28 0.35 5.56 4.74 3.97 Canada 2.31 1.87 2.46 5.56 4.86 5.13 Denmark 0.36 0.16 0.32 5.56 4.23 5.15 France 4.51 4.35 5.09 5.56 8.01 6.23 Germany 3.31 3.94 3.95 5.56 8.90 6.57 Hong Kong 0.85 0.23 1.21 5.56 3.40 8.02 Italy 1.80 1.59 1.86 5.56 7.23 6.17 Japan 9.99 5.56 7.89 5.56 3.88 3.82 Netherlands 2.62 2.51 2.83 5.56 8.15 5.90 Norway 0.24 0.12 0.25 5.56 4.58 6.10 Singapore 0.41 0.17 0.50 5.56 4.23 6.75 Spain 1.39 1.40 1.68 5.56 8.35 6.84 Sweden 0.88 1.01 1.19 5.56 9.78 7.49 Switzerland 3.54 2.18 3.31 5.56 5.43 5.02 United Kingdom 10.74 7.55 8.46 5.56 5.60 4.07 United States 54.73 66.80 57.43 5.56 5.50 4.33 Sum/VaR 100.00% $9.06 million $8.44 million 100.00% $7.37 million $9.36 millk estimator A, but become two of the top four contributors when using estimator B. In this case, the estimated VaR declines by more than 21 percent when switching from estimator B to estimator A. Another typical problem that uses the covariance matrix as an input is the asset allocation problem. We focus on this example because it is often argued that the main driver behind the construction of an optimal portfolio is a good set of expected returns, and that the risk model plays only a secondary role. The evidence from our examples suggests that this is clearly a misconception. We consider two portfolio managers who rebalance their assets at the end of each quarter, and attempt to maximize their expected returns subject to a tracking error constraint of 1 percent per quarter, relative to the same cash benchmark. We follow both managers from the first quarter of 1982 to the first quarter of 2002, for a total of 81 quarters. As in the previous example, the managers can form their optimal portfolios from a menu of 18 developed equity markets. They share the same views on the market in terms of expected returns, but use different models to estimate the covariance matrix. To provide direct evidence on the claim that a good forecasting model is likely to overcome any weakness of the risk model, we assume that the expected returns for each quarter are equal to the realized returns for that quarter. This is a model with perfect foresight and, therefore, superior to any realistic forecasting model