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Chapter 20 of the CAIA Level I book discussed the Fundamental Law of Active Management (FLOAM). This model expresses the risk-adjusted value added by an active portfolio manager as a function of the manager's skill to forecast asset returns and the number of markets to which the manager's skill can be applied (breadth). In particular, we saw that

(2.1)

where IR is the information ratio and is equal to the ratio of the manager's alpha (i.e., expected outperformance) divided by the volatility of the alpha. IC is the information coefficient of the manager, which is a measure of the manager's skill, and represents the correlation between the manager's forecast of asset returns and the actual returns to those assets. BR is the strategy's breadth, which is defined as the number of independent forecasts that the manager can skillfully make during a given period of time (e.g., one year). Not surprisingly, the value added by active management increases with the ability of the manager to forecast returns and the number of independent markets to which the forecasting skill can be applied.

The FLOAM can be applied to security selection as well as asset class allocation. Clearly, when FLOAM is applied to the process of selecting securities from a universe of 5,000 or more, there should be greater potential for adding value, as the breadth could be large. This insight has been used as an argument against TAA. In other words, to add value through active asset allocation, a portfolio manager will need a much higher level of skill if that skill is to be applied to only a handful of independent asset classes.

APPLICATION 2.1.1

Suppose active manager A has the skill to select stocks from a universe of 2,000 securities and generate an information ratio (IR) of 1.2. This means that the expected alpha of this manager's portfolio is 20 % higher than the volatility of the alpha. Active manager B can generate the same information ratio (1.2) using 15 asset classes. What are the managers' information coefficients?

Using Equation 2.1:

Active manager A has an information coefficient of 0.027:

Active manager B has an information coefficient of 0.310:

In this example, active manager B has to be about 11.5 times more skillful using active management among asset classes than active manager A, who is using security selection to achieve the same IR. In Equation 2.1, any of the variables can be solved given the value of the other two.

An extension of FLOAM provides additional insights into the potential value-added properties of TAA. FLOAM assumes that the manager is unconstrained in the sense that she can apply her skills to all available securities. In reality, portfolio managers face a number of constraints, both internal and external. For instance, the manager is constrained by the limits imposed by SAA. In addition, there could be regulatory constraints on allocations to certain asset classes. Finally, there are implementation costs associated with active management. This is particularly important when considering alternative investments. The costs associated with changing allocations to private equity or some real assets could be prohibitive. Even altering allocations to more liquid segments of alternative investments, such as commodity trading advisers (CTAs) and some hedge fund strategies, could be costly. The next section models potential costs.