Читать книгу Alternative Investments - Black Keith H. - Страница 47
Part 1
Asset Allocation and Institutional Investors
CHAPTER 2
Tactical Asset Allocation, Mean-Variance Extensions, Risk Budgeting, Risk Parity, and Factor Investing
2.2 Extensions to the Mean-Variance Approach
2.2.2 Adjustment of the Mean-Variance Approach for Factor Exposure
ОглавлениеIn the process of asset allocation, whether strategic or tactical, the investor may wish to limit the exposure of the portfolio to certain sources of risk (and potentially some returns) other than or in addition to the risk of the overall market. For example, the investor may wish to cap the exposure of the portfolio to changes in the price of oil. As long as an observable factor representing the source of risk exists, the constraints on factor exposures can be incorporated into the mean-variance approach with little difficulty.
The first step is to estimate the factor exposures of the assets that are being considered for inclusion in the portfolio. To do this, a linear regression of the following form is run:
(2.6)
Here, Rit is the rate of return on asset i; ai and bi are the intercept and the slope of the regression, respectively; Ft is the risk factor that is of interest; and ϵit is the residual. For example, Ft might be the percentage change in the price of oil. In this regression, bi measures the factor exposure of asset i. Since the factor exposure of the portfolio is a weighted average of the individual asset's exposures, the factor exposure of the portfolio can be expressed as . The following constraint can now be added to the mean-variance optimization of Equation 2.4:
(2.7)
In this case, the constraint is that the total factor exposure of a potential portfolio must be less than or equal to the target, , in order for the portfolio to be a feasible solution. The impact of imposing this constraint is to reduce allocations to those asset classes that have large exposures to the source of risk being considered. It is important to note that since short sales are not allowed, it may not be feasible to create a portfolio with the desired level of factor exposure. For example, suppose an investor decides to have a negative exposure of the portfolio to the equity risk of the overall equity market. It may not be possible to create a negative equity beta portfolio when short positions are not permitted.
