value is positive, though at this level the value in terms of incremental expected excess return to the portfolio per unit sold has dropped slightly, from .17 to .1667. Again we might consider what is the expected excess return on international equities for which the investor would be indifferent to an additional purchase. The point of indifference is the value, ef, such that: (1.212-^-.055)=0 (2.18) That is, e, = 4.5. The hurdle rate to justify continued purchase of international equities has increased from 3.8 to 4.5 because the marginal contribution of international equities to portfolio risk has increased relative to that of domestic equities. Suppose the investor decides to keep only 10 percent of the portfolio value in domestic equity. In order to keep risk constant, the investor must purchase 56 percent of international equity. Using the new values d = .10 and f = .56 in the earlier formulas we can confirm that the volatility of the portfolio remains 10 percent and that Ad = .110 and A^ = . 159. The impact on expected excess return of the portfolio per unit sold at this point is given by f \ A   (2.19) which simplifies as (.691 .05 - .055) = -.012 (2.20) Now the investor has sold too much domestic equity. The value in terms of incremental expected excess return to the portfolio per unit sold has dropped so far that it has become negative. The negative impact on the portfolio expected return signals that at the margin the investor has too much risk coming from international equity and the expected excess return does not justify it. The hurdle rate to justify continued purchase of international equities is the value, ef, such that: (.691*ef -.055) = 0 (2.21) That is, ^=8.0%. Clearly this hurdle rate has continued to increase as the marginal contribution of international equities to portfolio risk has continued to increase relative to that of domestic equities. Throughout this example, we have assumed that the investor has a set of expected excess returns for domestic and international equities. In practice, few investors have such we 11-formulated views on all asset classes. Notice, however, that given an expected excess return on any one asset class, in this case domestic equities, we can infer the hurdle rate, or point of indifference for purchases or sales of every other asset. We refer to these hurdle rates as the implied views of the portfolio. Rather than following the traditional portfolio optimization strategy, which requires