Alternative Investments - Black Keith H.

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off from an operating company, while in other cases, it might be funded with what is known as legacy wealth, which refers to a second or third generation of family members that have inherited their wealth from a prior source of capital generation. The financial resources of a family office can be used for a variety of purposes, from maintaining the family's current standard of living to providing benefits for many future generations to distributing all or a portion of it through philanthropic activities in the current generation. Family offices tend to have relatively long time horizons and are typically large enough to invest in a full menu of assets, including alternative asset classes.

      1.4 Objectives and Constraints

      As already discussed, different asset owners have their own particular objectives in managing their assets and face various constraints, which could be internal or external. An objective is a preference that distinguishes an optimal solution from a suboptimal solution. A constraint is a condition that any solution must meet. Internal constraints are imposed by the asset owner and may be a function of the owner's time horizon, liquidity needs, and desire to avoid certain sectors. External constraints result from market conditions and regulations. For instance, an asset owner may be prohibited from investing in certain asset classes, or fees and due diligence costs may prevent the owner from considering all available asset classes. The next sections describe the issues that must be considered while attempting to develop a systematic understanding of asset owners' objectives and constraints.

      1.5 Investment Policy Objectives

      Asset owners' objectives must be expressed in terms of consistent risk-adjusted performance values. In other words, it is safe to assume that asset owners would prefer to earn a high rate of return on their assets. However, higher rates of return are associated with higher levels of risk. Therefore, asset owners should present their objectives in terms of combinations of risks and returns that are consistent with market conditions and their level of risk tolerance. For instance, the objective of earning 30 % per year on a portfolio that has 8 % annual volatility is not consistent with market conditions. Such a high return would require a much higher level of volatility. Also, if the asset owner states that her objective is to earn 25 % per year with no reference to the level of risk that she is willing to assume, then it could lead the portfolio manager to create a risky portfolio that is entirely inconsistent with her risk tolerance. Therefore, asset owners and portfolio managers need to communicate in a clear language regarding return objectives and risk levels that are acceptable to the asset owner and are consistent with current market conditions.

      1.5.1 Evaluating Objectives with Expected Return and Standard Deviations

      Consider the following two investment choices available to an asset owner:

      

investment A will increase by 10 % or decrease by 8 % over the next year, with equal probabilities.

      

Investment B will increase by 12 % or decrease by 10 % over the next year, with equal probabilities.

      

The expected return on both investments is 1 % (found as the probability weighted average of their potential returns); however, their volatilities will be different (see Equation 4.9 of CAIA Level I).

      

Investment A: Standard deviation =

      

Investment B: Standard deviation =

      If an asset owner expresses a preference for investment A over investment B, then we can claim that the asset owner is risk averse. Although it is rather obvious to see why a risk-averse asset owner would prefer A to B, it will not be easy to determine whether a risk-averse investor would prefer C to D from the following example:

      

Investment C will increase by 10 % or decrease by 8 % over the next year, with equal probabilities.

      

Investment D will increase by 12 % or decrease by 9 % over the next year, with equal probabilities.

      In this case, compared to investment C, investment D has a higher expected return (1.5 % to 1 %) and a higher standard deviation (10.5 % to 9 %). Depending on their aversion to risk, some asset owners may prefer C to D, and others, D to C.

      1.5.2 Evaluating Risk and Return with Utility

      Different asset owners will have their own preferences regarding the trade-off between risk and return. Economists have developed a number of tools for expressing such preferences. Expected utility is the most common approach to specifying the preferences of an asset owner for risk and return. While a utility function is typically used to express preferences of individuals, there is nothing in the theory or application that would prevent us from applying this to institutional investors as well. Therefore, in the context of investments, we define utility as a measurement of the satisfaction that an individual receives from investment wealth or return. Expected utility is the probability weighted average value of utility over all possible outcomes. Finally, in the context of investments, a utility function is the relationship that converts an investment's financial outcome into the investor's level of utility.

      Suppose the initial capital available for an investment is W and that the utility derived from W is U(W). Thus, the expected utilities associated with investments A and B can be expressed as follows:

      (1.1)

      (1.2)

      The function U(•) is the utility function. The asset owner would prefer investment A to investment B if E[U(WA)] > E[U(WB)].

      Suppose the utility function can be represented by the log function, and assume that the initial investment is $100. Then:

      (1.3)

      (1.4)

      In this case the asset owner would prefer investment A to investment B because it has higher expected utility. Applying the same function to investments C and D, it can be seen that E[U(WC)] = 4.611 and E[U(WD)] = 4.615. In this case, the asset owner would prefer investment D to investment C.

      APPLICATION 1.5.2

      Suppose that an investor's utility is the following function of wealth (W):

      Find the current and expected utility of the investor if the investor currently has $100 and is considering whether to speculate all the money in an investment with a 60 % chance of earning 21 % and a 40 % chance of losing 19 %. Should the investor take the speculation rather than hold the cash?

      The current utility of holding the cash is 10, which can be found as

. The expected utility of taking the speculation is found as:

      Because the investor's expected utility of holding the cash is only 10, the investor would prefer to take the speculation, which has an expected utility of 10.2.

EXHIBIT 1.1 Logarithmic Utility Function

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