Using the 'bucketizer' feature in the Axioma Portfolio to better examine non-linearities in portfolio exposures, and to build optimal portfolios

Many clients have discovered and commented on the usefulness of the Axioma Portfolio 'bucketizer' feature.

The bucketizer is an easy way to examine potential non-linearities in portfolio exposures. The feature allows users to construct quantiles of any attribute in a workspace, using either vendor provided or proprietary data imported into the system. The separate buckets, be they quintiles or deciles or some other user defined segment, can then become dimensions for graphing or reporting these portfolio characteristics.

Let's look at an example. We begin by constructing return forecasts, or alphas, that are independent of other common characteristics. Our goal is to construct a long-short market-neutral portfolio that uses the information in our alphas, while staying hedged along other dimensions, such as industry and style factors.

Next we create deciles of the forecasted alpha, setting the details in the dialog box in Exhibit 1. We name the new Classification, specify 10 equal buckets, and keep the "weights" (which means, in this case, we keep the values of the original alphas associated with each stock).

Exhibit 1: New Classification dialog box

In a similar manner, we create deciles of Specific Risk, i.e., the risk idiosyncratic to each individual security, unrelated to common factors, according to the Axioma US Robust Risk Model.

We then create several candidate portfolios using Axioma Portfolio, neutralizing Common Factor risk, but not constraining Specific Risk. The resulting distribution of the long and short portfolio holdings across the Deciles of Alpha is shown in Exhibit 2. Note the surprising 'barbell' nature of the distribution. If we were less confident in our own alphas, we could establish new constraints to enforce a gentler monotonic weighting of the alpha deciles.

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Exhibit 2: Distribution across alpha deciles.

Next, let's evaluate the distribution of Specific Risk, as this was an uncontrolled item in the portfolio construction process. Consistent with our intuition and preference, the resulting portfolio had larger holdings, both long and short, in the higher decile Specific Risk buckets than in the lower Specific Risk deciles. The net of the long and short positions is shown in Exhibit 3.

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Exhibit 3: Distribution across specific-risk deciles

The buckets in the above examples utilized the functionality in Axioma Portfolio to divide the source attribute into equally weighted groupings. An additional feature of the bucketize function allows us to define our own custom buckets, defining the breakpoints in the buckets. For example, one could create market capitalization buckets to evaluate and determine the portfolio exposures, either net or relative to a benchmark, to ensure bets are consistent with our intuition. Exhibit 4 provides an example of this approach.

Exhibit 4: Capitalization buckets creating breakpoints for Micro Cap (under $500 MM), Small Cap ($500 MM to $2B), Mid Cap ($2B to $8B), and Large Cap (Over $8B).

While the ability to create and evaluate buckets based on custom definitions is powerful, Axioma Portfolio also provides the ability to translate these settings into the optimization problem. We can easily use custom groupings as the basis for constraints by setting up a Limit Holding Constraint, which ensures that the optimal portfolio is within an upper and lower bound according the user-defined categories. Exhibit 5 shows an example of setting a constraint, ensuring the portfolio remains neutral along each of the capitalization buckets that were created previously.

Exhibit 5: Constraints as defined by user defined buckets

Summary

The bucketize feature of Axioma Portfolio enables us to construct quantile groupings, which, in turn, allows us to view a portfolio's distribution, identify bets, and set constraints during optimization. Whether bucketizing Axioma-supplied attributes, proprietary, or third-party content, the resulting reports and graphs can highlight sometimes surprising non-linear aspects of a portfolio. By enabling these buckets during optimization, the manager can decide if such insights are consistent with the intentional strategy, or if rebalancing the portfolio should be considered to better reflect the strategy objectives.

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