to achieve a U.S. equity risk premium of 4 percent, as discussed in Chapter 5. This requires a risk aversion parameter, X, of 3.22, implying a degree of currency hedging of 69.0 percent. The resulting currency exposures are shown in the table as well. The annualized volatility of the portfolio is 8.30 percent. The annualized equilibrium risk premium of the global portfolio is 2.22 percent. Thus, the expected Sharpe ratio of the global portfolio is .268. Risk premiums are clearly a function of correlations with the market portfolio as well as volatilities. The Japanese equity market, for example, has a significantly higher volatility than does the U.S. equity market, but has a significantly lower risk premium reflecting its lower correlation with the global market portfolio. The highest risk premium belongs to the emerging markets equity asset class, which has both a high volatility and a relatively high correlation with the market portfolio. Finally, we should reiterate the point made earlier that we do not treat the risk premiums as forecasts or expectations, but rather as reference points or hurdle rates. In other words, we find the equilibrium framework interesting even though we do not treat it as necessarily being an accurate reflection of the current expectations built into market prices. We expect to have expectations that are at odds with the equilibrium risk premiums, and we will treat those situations as opportunities. 12Except in the case of emerging markets and high-yield assets in which data begins later. See Chapter 16 for a description of how we treat missing data and why we put more weight on more recent observations. In this example the half-life of our data decay is 6.5 years. Also, we treat the emerging markets equity and debt as dollar denominated; that is, we do not hedge their currency exposures.