noted in Chapter 2, all one needs to have in order to solve for this internal measure of value is the expected excess return for one asset class. One suggestion is to normalize on the expected excess return of the market portfolio. In any case, given one reference for an expected excess return, we can solve for the implied views-that is, the set of expected excess returns for every other asset class in the portfolio such that the existing portfolio is optimal relative to those expected excess returns. As mentioned in Chapter 2, the implied views provide a natural set of hurdle rates against which to gauge whether the positions in the portfolio are sized appropriately. As a first step in analyzing a portfolio, it makes sense to compare the implied views with the equilibrium expected excess returns. When implied views differ from equilibrium values, the implication is that the investor has identified an opportunity, a situation where an asset is expected to return more or less than the equilibrium risk premium consistent with its risk characteristics. The investor may want to compare the deviations of expected excess returns imbedded in the implied views against the equilibrium values as a way to identify any inconsistencies or opportunities embedded in the portfolio. Just as an asset that is uncorrelated with the market portfolio has an equilibrium risk premium of zero, an asset whose returns are uncorrelated with the returns of a particular portfolio has an implied view of zero expected excess return. In this situation the investor may often want to ask, does the size of this exposure really make sense? When an investor has a positive weight in an asset, it usually exists because the investor has a positive outlook for the returns of that asset. If, in this situation, the implied view is zero or negative, that usually is associated with a circumstance in which the investor would be better off increasing the size of the position to more accurately reflect a positive outlook. The second step in portfolio analysis is to understand the risk contributions of each asset to the overall portfolio and to know what is the risk-minimizing position for each asset. The risk contributions are useful in sizing positions appropriately given the investor's views. Most investors find it hard to give with any confidence an estimate of the expected excess return for an asset. They can with much more confidence suggest a percentage of the portfolio risk that they would feel comfortable with coming from that asset. One drawback of looking only at risk contributions, however, is that it's not always obvious how to change a position if one wants to increase or decrease its risk contribution. Understanding where the risk-minimizing position is located is important in this regard. The risk-minimizing position is the position in a particular asset for which the portfolio risk is minimized, holding all other positions unchanged. The risk-minimizing position is also the position for which the returns of an asset would be uncorrelated with those of the portfolio, and, as noted earlier, this position has an implied view of zero expected excess return. If the current position is greater than the risk-minimizing position, then the current position represents a positive expected excess return, and adding to the position increases risk and increases expected return. Similarly, if the current position is less than the risk-minimizing position, then the current position represents a negative expected excess return, and selling the position increases risk and increases expected return. There is no reason for the risk-minimizing position to be a zero weight. One can easily have a positive weight in an asset, or an overweight position relative to a