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Occam’s Razor Meets Factor Analysis

The resulting parsimonious factor lens can help investors focus on the risks the really matter.

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Two Sigma Investments

Two Sigma Investments

What happens if investment decision makers apply the principle of Occam’s razor in their thought processes? Let’s take a quick look.

Refresher course! William of Ockham, a 14th century philosopher, didn’t conceive the principle under consideration here, but he popularized it by frequent use, during which he posited that in searching for explanations or solutions to problems “entities should not be multiplied unnecessarily.” In other words, if various models arrive at the same outcome, you should choose the one with the fewest assumptions.

So, let’s say investment decision makers want to apply Occam’s razor while determining asset allocations and evaluating managers. In both cases, institutional investors may find it useful to focus on select risk factors that appear to drive the majority of risk and return in their portfolios.

One way to do so is to decompose the returns and risk of an investment portfolio using statistical regression techniques. This can involve developing a risk factor model, which is a lens through which the portfolio is analyzed. Based on our research at Venn, we believe that such a lens should be “parsimonious,” generally meaning:

  • It is constructed with as few factors as possible, and
  • Used in combination with statistical methods that limit the results to the most relevant factors.

We believe that parsimony in factor lens construction can both simplify the investment process and enhance the accuracy of factor-based analysis.
Using a small number of the most relevant factors in a “less-is-more” approach can simplify the investment process by allowing investors to focus on their portfolios’ most significant risk drivers.

Our research suggests that only a handful of core factors drive most of the risk in institutional portfolios. We believe that constructing a valid risk lens with a manageable number of factors, in combination

with a factor selection methodology, can help investors better understand what these essential factors are, and how they interact.

Why does this matter? While many investors analyze the historical returns of their investments or portfolios, perhaps an even more important task is estimating how portfolios will perform in the future.

Simplify Investment Process

Imagine trying to forecast portfolio performance using an unparsimonious set (e.g., dozens or even hundreds) of factors across asset classes, geographies, industries, sectors, and/or styles. Investors might have a view on how a few key markets, like stocks, government bonds, and credit spreads will perform in the future. After all, many industry experts publish capital market assumptions for many of these broad asset classes and indicators. However, investors may not have an informed view on more specific geographical factors, such as how certain regions or countries will perform relative to one another within an asset class like equities. It would likely prove harder still to develop forward-looking expectations for various sectors within all those geographies, such as consumer discretionary, healthcare, technology, and utilities. And what about market-neutral “style” factors? Investors may have views on a small number of aggregate factors like equity value, momentum, or quality, but maybe not for single-metric factors, such as how a book-to-price factor will perform versus a sales-to-price factor.

In our view, the merits of Occam’s razor in forecasting portfolio performance are clear: using a factor lens intended to boil down elemental risks in most institutional portfolios to a smaller number of factors (say around 10-20) can make forecasting portfolio performance much more manageable.

The advantages of parsimony extend beyond manageability. We believe that using an excessive number of factors to explain the risk of a dependent return stream can result in overfitting. That is to say, a model may do a great job of explaining investment performance over a particular analysis period in the past, but may not be a good predictor of future performance.

Enhance Accuracy

To demonstrate why this can be the case, imagine a “portfolio” whose “returns” result from 10 die rolls. The returns of this portfolio would be random noise, and in retrospect should be unexplainable. Yet, you could try to model the 10 die-roll returns using a combination of ostensibly explanatory factors, such as the weight of the die, the size of the die, the age of the die roller – although these factors have nothing to do with the outcome of the rolls. The resulting model, however, would be fit to the noise of the past die rolls and wouldn’t have any predictive power in determining what the next die roll would be. The greater the number of explanatory factors used, the worse the problem becomes, since one can always find some combination of variables that happen to “explain” the noise of die rolls.

A small number of data points (in this example, only 10 die rolls) can also be problematic. We believe that adding more factors to an analysis can increase the risk of spurious results, especially with small sample sizes. Unfortunately, limited sample sizes are quite a common constraint in the institutional space, where many managers report returns infrequently (monthly, and even sometimes quarterly) and/or have a limited track record.

When conducting factor analysis, we believe that investors should consider the “degrees of freedom” as an important determinant of how much confidence to put in the output of the analysis. At Venn, we define the degrees of freedom to be approximately equal to the number of return data points in the analysis minus the number of explanatory factors. We believe that a greater number of degrees of freedom provides correspondingly greater confidence in the estimated factor relationships. In other words, have as many return observations as possible, while limiting the number of factors included to those that one thinks really matter. A general rule of thumb among statisticians is to have about 10 times the number of return observations as factors.

How can one determine the “factors that really matter”? Statistical methods, such as the Akaike information criterion, can be used for variable selection. [1]This particular method weighs the tradeoff between the quality and simplicity of various models – or essentially approximating Occam’s razor.

Learn more

We believe that a parsimonious risk lens can benefit investors by helping them focus on the risks that appear to really matter to their portfolio. And that parsimony in factor analysis can allow investors to simplify investment processes, especially those that require forward-looking assumptions, and can significantly aid the interpretation and accuracy of factor analysis.

Does parsimony come at the expense of comprehensiveness? In our view, not necessarily. With thoughtful construction and variable-selection techniques, we believe that a factor lens with relatively few, yet relevant, factors can still cover the majority of risk in institutional portfolios.

Check out this further exploration of how the Two Sigma Factor Lens attempts to provide a parsimonious and holistic view of portfolio risks.

1 Cavanaugh, J. E. (1997). “Unifying the derivations of the Akaike and corrected Akaike information criteria”, Statistics & Probability Letters, Vol. 33, No. 2, pages 201-208.

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