# LO 66.2: Evaluate the methods and motivation for refining alphas in the

LO 66.2: Evaluate the methods and motivation for refining alphas in the implementation process.
A portfolio can be optimized, based on the inputs, using mean-variance analysis. In most cases there are significant constraints imposed on the asset weights, either by client or manager requirements. A client (or regulations) may prohibit short sales. A manager may impose an upper limit on active risk or on maximum deviations from benchmark weights. As more constraints are introduced, simple mean-variance analysis, maximizing active return minus a penalty for active risk, can become quite complex.
An alternative approach is to adjust the managers estimated alphas (an input into a mean- variance optimization analysis) in ways that effectively impose the various constraints. Consider an account for which short selling is prohibited. Rather than performing an optimization that constrains asset weights to be non-negative, we can use the optimization
2018 Kaplan, Inc.
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Topic 66 Cross Reference to GARP Assigned Reading – Grinold and Kahn, Chapter 14
equations (in reverse) to solve for the set of alphas that would produce non-negative weights in an unconstrained mean-variance optimization. The optimal weights are moved toward benchmark weights. This method allows us to focus on the effects of a specific constraint on alphas, the key input for active portfolio construction.
Before we examine refining alphas to satisfy other constraints, such as a constraint on the beta of the active portfolio, we consider two techniques that are often employed after refining alphas for various client or manager imposed constraints: scaling and trimming.
An often used equation for alpha is:
alpha = (volatility) x (information coefficient) x (score)
Where volatility refers to residual risk, the information coefficient (IC) measures the linear relationship between the managers forecasted asset alphas and actual asset returns, and score is expected to be approximately normally distributed with a mean of 0 and a standard deviation of 1. Considering that volatility (residual risk) and information coefficient (IC) are relatively constant, we can see that the standard deviation (scale) of portfolio alphas is proportional to the standard deviation of the score variable. Alphas will have a mean of zero and a scale approximately equal to volatility x information coefficient when score follows a standard normal distribution. With an information coefficient of 0.10 and residual risk of 30%, the scale of the alphas will be 0.10 x 30% = 3%; the alphas will have a mean of zero and a standard deviation of 3%.
If we compare the scale (standard deviation) of the refined alphas from our earlier discussion of a prohibition on short sales to the scale of the original unconstrained alphas, we can calculate the decrease in the information coefficient that results from the decrease in the scale of the alphas due to the imposition of the constraint. If the adjusted alphas do not have the appropriate scale, they can be rescaled.
Another refinement to manager alphas is to reduce large positive or negative alpha values, a process called trimming. The threshold for large values might be three times the scale of the alphas. For large alpha values, the reasons supporting these values are re-examined. Any alphas found to be the result of questionable data are set to zero. Additionally, the remaining large alphas may be reduced to some maximum value, typically some multiple of the scale of the alphas.