style="font-size:15px;"> APPLICATION 1.5.8
Suppose that an investor's optimal portfolio has an expected return of 10 %, which is 8 % higher than the riskless rate. If the variance of the portfolio is 0.04, what is the investor's degree of risk aversion, λ?
Using Equation 1.9, λ can be expressed as:
1.5.9 Managing Assets with Risk Aversion and Growing Liabilities
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.
1.6 Investment Policy Constraints
The previous section introduced the expected utility approach as a simple and yet flexible approach to modeling risk-return objectives of asset owners. This section discusses the typical set of constraints that must be taken into account when trying to select the investment strategy that maximizes the expected utility of the asset owner.
1.6.1 Investment Policy Internal Constraints
Internal constraints refer to those constraints that are imposed by the asset owner as a result of its specific needs and circumstances. Some of these internal constraints can be incorporated into the objective function previously discussed. For example, we noted how the constraint that allocations with positive skewness are preferred could be incorporated into the model. However, there are other types of constraints that may be expressed separately. Some examples of these internal constraints are:
LIQUIDITY. The asset owner may have certain liquidity needs that must be explicitly recognized. For example, a foundation may be anticipating a large outlay in the next few months and therefore would want to have enough liquid assets to cover those outflows. This will require the portfolio manager to impose a minimum investment requirement for cash and other liquid assets. Even if there are no anticipated liquidity events where cash outlays will be needed, the asset owner may require maintaining a certain level of liquidity by imposing minimum investment requirements for cash and cash-equivalent investments, and maximum investment levels for such illiquid assets as private equity and infrastructure.
TIME HORIZON. The asset owner's investment horizon can affect liquidity needs. In addition, it is often argued that investors with a short time horizon should take less risk in their asset allocation decisions, as there is not enough time to recover from a large drawdown. This impact of time horizon can be taken care of by changing the degree of risk aversion or by imposing a maximum limit on allocations to risky assets. Time horizon may impact asset allocation in other ways as well. For instance, certain asset classes are known to display mean reversion in the long run (e.g., commodities). As a result, an investor with a short time horizon may impose a maximum limit on the allocation to commodities, as there will not be enough time to enjoy the benefits of potential mean reversion.
SECTOR AND COUNTRY LIMITS. For a variety of reasons, an asset owner may wish to impose constraints on allocations to certain countries or sectors of the global economy. For instance, national pension plans may be prohibited from investing in certain countries, or a university endowment may have been instructed by its trustees to avoid investments in certain industries.
Asset owners may have unique needs and constraints that have to be accommodated by the portfolio manager. However, it is instructive to present asset owners with alternative allocations in which those constraints are relaxed. This will help asset owners understand the potential costs associated with those constraints.
1.6.2 Investment Policy and the Two Major Types of External Constraints
External constraints refer to constraints that are driven by factors that are not directly under the control of the investor. These constraints are mostly driven by regulations and the tax status of the asset owner.
1.7 Preparing an Investment Policy Statement
The next step in the process is to develop the overall framework of the asset allocation by preparing an investment policy statement (IPS)3.
1.7.1 Seven Common Components of an Investment Policy Statement
The policy may include a recommended strategic allocation as well. The following is an outline of a typical IPS based on seven common components.
1. BACKGROUND. A typical IPS begins with the background of the asset owner and its mission. It reminds all parties who the beneficiaries of the assets are.
2. OBJECTIVE. The overall goals of the asset owner are described. For instance, the IPS of a foundation may state that the broad objectives are to (1) maintain the purchasing power of the current assets and all future contributions, (2) achieve returns within reasonable and prudent levels of risk, and (3) maintain an appropriate asset allocation based on a total return policy that is compatible with a flexible spending policy while still having the potential to produce positive real returns. The IPS may also provide additional details about the level of risk tolerance, the investment
