In the CAPM equilibrium, assets whose returns are not correlated with the market portfolio have zero expected excess return. This result, which was shown in Chapter 4, should give pause to those, such as ourselves, who hope to use uncorrected assets to add value to portfolios. The CAPM theory implies that in equilibrium uncorrelated assets have no particular value in portfolio construction. Uncorrelated assets can diversify portfolios, but if one reduces risk by switching from assets that have positive expected return into assets that do not, then the diversification has not improved the characteristics of the portfolio. Risk reduction is not an end in itself. Investors can most easily lower or raise portfolio risk by choosing to hold more or less cash. The value of uncorrelated assets is not their ability to reduce risk, but rather their potential to increase expected returns while at the same time reducing, or at least not increasing, risk. Uncorrelated assets that do provide a positive expected return can play, depending on the size of the expected return, a very valuable role in portfolios, but this capability depends crucially on the existence of some deviation from equilibrium. Active risk, the risk created by active management relative to a benchmark, suffers from a similar conundrum. Active risk almost always has zero expected correlation to the market, has no expected excess return in equilibrium, and thus does not contribute value to a portfolio. Any role for active risk in portfolio construction must reflect a deviation from equilibrium. In this chapter we will attempt to highlight two results: first, how important and valuable active risk and other sources of uncorrelated returns are in portfolio construction, and second, how the equilibrium approach guides and informs the search for positive returns associated with uncorrelated risks, returns that the theory itself suggests should not exist. The fact that an equilibrium approach does not provide a role for uncorrelated assets in a portfolio does not mean that an equilibrium approach is wrong or uninteresting. What the equilibrium does provide is a framework in which to identify opportunities. In other words, an equilibrium framework allows us to identify when it is the case that assets with various characteristics, such as being uncorre-