data, as they cannot be directly observed. Fortunately (and as discussed in Chapter 16), volatility and correlation estimation do not suffer from the same issues as expected return estimation. Historical data can be used to provide quite robust estimates of future volatility and correlation. As seen in Table 9.1, while the historical volatility figures were different in each of the decades, they were not nearly as sensitive as the average return estimates. Of course, investors would also like to know portfolio return in addition to portfolio risk. Fortunately, an equilibrium approach helps investors in this dimension as well. Chapter 6 discussed the linkage between portfolio weights, risk characteristics, and expected returns. To pin down the third from the first two, investors must assess the overall level of risk aversion. In turn, there is a mapping from the level of risk aversion to the market equity risk premium. Thus, an assessment of the equity premium (discussed in Chapter 5) gives investors a view on the level of risk aversion, which in turn drives expected returns on all other asset classes. The true benefit of an equilibrium approach is that it gives an internally consistent platform for portfolio analysis. On an ex post basis, an equilibrium approach helps us understand differences in investor behavior. On an ex ante basis, strategic asset allocations can be formed as deviations from the equilibrium portfolio. Investors will naturally deviate from the equilibrium portfolio if they believe that they can be adequately compensated for doing so. How would an investor analyze a deviation from equilibrium? One way is to follow the approach outlined in Chapter 7-that is, to specify a set of views and to apply the Black-Litterman model. If specific views are not well defined, then an alternative approach is to recognize that there is a mapping between views and optimal portfolios and to start with the latter; that is, propose a portfolio that represents a deviation from equilibrium. Using the same risk characteristics and equity risk premium, work backward to find the expected asset returns associated with the proposed portfolio. Next, calculate the difference between the new expected returns and the equilibrium returns. Finally, assess (on the basis of data analysis and financial economic theory) whether the differences seem reasonable. If so, then the proposed portfolio should be implemented. If not, then a new portfolio should be proposed. In the next several chapters, we show how an equilibrium approach can be applied to each of the key decisions in strategic asset allocation. The level of the bond/equity split, and its relation to liabilities, is discussed in Chapter 10. The impact of international diversification and currency hedging are discussed in Chapter 11. The application of an equilibrium approach to uncorrelated asset classes is addressed in Chapter 12.