Читать книгу Alternative Investments - Black Keith H. - Страница 21

As mentioned earlier in the chapter, most asset owners are concerned with funding future obligations using the income generated by the assets. In the previous example, the DB plan has liabilities that will need to be met using the fund's assets. Suppose the current value of these liabilities is L euros. Further, suppose the rate of growth in liabilities is given by G, which could be random. In this case, the objective function of Equation 1.8 can be restated as:

(1.10)

In this case, the DB plan wishes to maximize the expected rate of return on the fund's assets, subject to its aversion toward deviations between the return on the fund and the growth in the fund's liabilities. In other words, the risk of the portfolio is measured relative to the growth in liabilities. Later in this chapter, we will demonstrate how this problem can be solved.

One final comment about evaluating investment choices: Although the framework outlined here is a flexible and relatively sound way of modeling preferences for risk and return, the presentation considered only one-period investments and decisions. Economists have developed methods for extending the framework to more than one period, where the investor has to withdraw some income from the portfolio. These problems are extremely complex and beyond the scope of this book. However, in many cases, the solutions that are based on the single-period approach provide a reasonable approximation of the solutions obtained under approaches that are more complex.