historical averages for two reasons. First, assuming you want to optimize returns, implied returns analysis indicates what the return of an asset or currency must be before you'd be willing to bear the additional risk of taking a position in it. As a result, implied returns on assets and currencies are computed directly from the marginal contribution to risk analysis. Second, historical averages are notoriously poor predictors of expected returns, in part because estimates vary widely depending on which historical period is used. For example, the expected return on the yen/dollar exchange rate differs markedly if you use 1980-1990, rather than 1990-2000, as the basis for the historical average. Implied returns analysis can assess the currency returns of different hedging levels. In other words, working backward from a set of portfolio weights and an assumption about the currency hedging level, we can find the corresponding implied currency return. Assume that all investors hold a global capitalization weighted portfolio. The asset "weight" applied to currency is the unhedged currency position. For example, a yen investor who holds 20 percent of his or her portfolio in U.S. equities and hedges 50 percent of currency exposure would have an open U.S. dollar position of 10 percent. Figure 11.7 plots the relationship between implied currency returns and the level of currency hedging, from euro, sterling, U.S. dollar, and yen perspectives. The graphs show that the greater the currency hedging, the lower the implied currency return. For example, when euro-based investors leave all currency positions completely open, the implied return (excess) on the U.S. dollar is 3.3 percent. When all positions are hedged at the 50 percent level, however, the implied U.S. dollar return is approximately 2.1 percent. The relationship between implied currency returns and the level of currency hedging is not really surprising. Remember, Figure 11.6's risk decomposition analysis suggests that higher levels of currency hedging mean lower levels of portfolio risk attributable to currency. Thus, in order for it to be optimal for investors to hedge at higher levels, they must also believe that currency will have lower expected excess returns. The graphs in Figure 11.7 also indicate that at higher currency hedging levels, the implied excess return of some currencies actually becomes negative. For example, U.S. dollar investors who hedge 100 percent of their open currency positions are implying that returns to the yen will be negative. Although counterintuitive, this result can be explained by a negative correlation between excess currency returns and excess asset returns. Given this surprising result, a more detailed analysis of the historical correlation between currency and asset returns is warranted. Furthermore, if we assume that excess currency returns and excess asset returns are uncorrected, how is implied currency return affected? Figure 11.8 looks at the long-term correlation between currency and asset returns. It plots a beta time series from a regression of a basket of G-7 currency returns on a portfolio of G-7 asset returns. (The G-7 countries include Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States.) The regression was estimated on 90-day rolling windows over a 20-year period. The graph reveals two interesting features about the time series: First, the beta coefficients are