dollar S$/US$ currency forward 3.35 1.38 10.46 15.72 -15.15 11.44 -2.64 -0.09 3.96% 47.48%   100.00% 2.48%   0.02   0.18   Swedish krona Swedish krona/US$ currency forward Swiss franc Swiss franc/US $ currency forward British pound Pound/US$ currency forward Total Total active risk Equity beta extension Bond beta extension At the time of this portfolio snapshot, we held active positions in 35 different securities in the overlay portfolio with a predicted tracking error of 2.48 percent. We held large equity overweights in the United States, Hong Kong, and Japan partially offset by large underweights in Australia, the United Kingdom, and Singapore. In bonds, overweights in the United States and Canada were offset by underweights in Japan, Euroland, and the United Kingdom. Our major currency positions were long the Swedish krona and Norwegian krone, and short the Swiss franc and U.K. pound sterling, with a net underweight in the U.S. dollar overall. The position sizes were determined using the optimization problem described earlier, where returns are maximized subject to a total tracking error constraint as well as constraints on the tracking errors within each of the four GTAA strategies. Despite the very simple optimization problem, the portfolio's risk budget is fairly well balanced, as seen in the tracking error decomposition in the rightmost column. At the individual security level, there are 11 positions contributing more than 5 percent of risk in absolute terms. That this well-balanced portfolio can result from a simple optimization problem is a testament to the Black-Litterman asset allocation model, which was developed primarily to address the problem of unbalanced portfolio optimizations. Leverage Finally, note that in asset class timing, we held a beta extension of 0.02 in equities and 0.18 in bonds. By an equity beta extension of 0.02, we mean that the beta of our global equity portfolio with respect to the equity benchmark was 1.02. This implies that for every 10 percent increase in the MSCI World Index, our global equity portfolio should outperform by 0.20 percent. Beta extension better represents the market timing position in equities than the sum of weights because the weights themselves may indicate a misleading position. For example, a 2x overweight in a country with half the beta of second country where a lx underweight is held actually represents a beta-neutral position, and therefore would not be expected to outperform when the global equity market increases or decreases.