with No Asset Class Portfolio Shorting Constraint Japanese government bonds -202.7% 0.0% European government bonds -321.1 0.0 U.S. government bonds ^84.4 0.0 U.S. equities -11.3 0.0 Global fixed income 1493.2 0.0 European equities -258.0 0.0 U.S. high-grade corporate bonds -385.8 0.0 EAFE 314.3 0.0 Hedge fund portfolio 58.1 55.3 U.S. high yield -9.9 36.3 Private equity 0.5 0.0 Emerging debt -28.8 0.0 REITs 4.3 7.7 Japanese equities -71.7 0.7 Emerging market equities 3.1 0.0 Portfolio volatility 4.9% 5.1% Portfolio expected return 18.2 8.4 from a mathematical point of view they each optimize the problem that was posed. Given the input forecasts, a large number of relatively tight minimum and maximum holdings would have to be specified (indeed, this is the usual approach) in order to get reasonable-looking answers out of the optimizer. In this situation the optimizer is obviously not adding a lot of value. In the Black-Litterman approach we don't start with a set of expected returns for all asset classes. Instead, we start with equilibrium expected returns, which lead to the optimal portfolio having market capitalization weights. Though perhaps reasonable looking, this market capitalization portfolio doesn't change very much over time, and the obvious question is how to use an optimizer to tilt away from this portfolio in order to take advantage of perceived opportunities. We create a simple equity-only example in order to illustrate how sensitive the optimized portfolio is to small changes in expected returns. Equity markets are not as highly correlated as fixed income markets and currencies; if we were to use a more complete set of assets it would only compound the problem. The equity-only equilibrium expected excess returns, shown in Table 7.3 along with market capitalization, differ slightly from those shown for the more complete global market portfolio in Table 6.5. However, since equities dominate the risk of the market portfolio the differences are not that great. Consider a hypothetical situation in which an investor believes that over the next three months the German economic growth will be slightly weaker than expected and German equity will underperform relative to equilibrium expectations. We suppose that the investor quantifies this view as a 20 basis point lower than equilibrium expected return on the German equity market over the next three