Читать книгу Alternative Investments - Black Keith H. - Страница 35

The results from a mean-variance optimization can be extremely sensitive to the assumptions, as small changes in the mean return or covariance matrix (i.e., the set of all variances and covariances) can lead to enormously different prescribed portfolio weights. The high sensitivity of portfolio optimizers to the input data has led to approaches that attempt to harness the power of optimization to identify diversification potential without generating extreme portfolio weights. In addition, in most cases, portfolio managers want to adjust the historical estimates to reflect their views about the estimated parameters going forward. For instance, a portfolio manager may want to incorporate her view that the health care sector is likely to do better than indicated by its historical track record. Perhaps the most popular modification to account for views and obtain reasonable estimates of weights is described by Black and Litterman.

The first problem addressed by the Black-Litterman approach is the tendency of the user's estimates of mean and variance to generate extreme portfolio weights in a mean-variance optimizer. Note that if a security truly and clearly offered a large expected return, low risk, and high diversification potential, then demand for the security would drive its price upward and its expected return downward until the demand for the security equaled the quantity available. In competitive markets, securities prices tend toward offering a perceived combination of risk and return in line with other assets.

The key to understanding the Black-Litterman approach is to understand that if a security offers an equilibrium expected return, then the demand for the asset will equal the supply. Further, the optimal allocation of the asset into every well-diversified portfolio will be equal to the weight of the asset in the market portfolio (i.e., the market weight). Thus, an equilibrium expected return for a security is the expected return that causes the optimal weight of that security in investor portfolios to equal its market weight.

This observation means that if the portfolio manager has no views about the future performance of a particular asset class, then its market weight should be used. For instance, a market-cap-weighted portfolio of global equities would be optimal. However, since market cap weights are not well defined for some asset classes, the Black-Litterman approach will need to be adjusted for application to alternative assets.

The primary innovation of the Black-Litterman approach is that it allows the investor to blend asset-specific views of each asset's expected return with views that would be consistent with market weights in a market equilibrium model.

Whereas some asset allocators employ advanced techniques such as the Black-Litterman approach to reduce the sensitivity of the weights to the expected risks and returns, a much larger number of asset allocators choose to add additional constraints to the optimization model to circumvent the difficulties and sensitivities of mean-variance optimization. Common additional constraints include the following:

Limits on estimated correlation between the return on the optimal portfolio and the return on a predefined benchmark

Limits on divergences of portfolio weights from benchmark weights

Limits or ranges on the prescribed portfolio weights

The last constraint, limits on portfolio weights, is the most popular. These constraints can prescribe upper or lower weights, outside of which the asset allocator will not invest. The portfolio optimizer is forced to generate weights within those ranges. In practice, however, many investors use so many constraints that the constraints have more influence on the final asset allocation than does the mean-variance optimization process. While each of the added constraints may help the asset allocator avoid extreme weights, the approach may ultimately lead to having the constraints define the allocation rather than the goal of diversification.