The Three Types of Factors

Academic studies have identified a large number of factors that can be said to have predicted outsized returns over periods of time, depending on how you measure their effectiveness. Various firms have created indices based on a number of these factors, ranging from low volatility to momentum. Beyond that, investors have been looking at factors like the price-to-earnings ratio and the price-to-book ratio for a hundred years or so.

But what most investors overlook is that factors don’t all work the same way.

I classify factors into roughly three categories: direct, distributive, and augmentative. Here’s what I mean.

A direct factor, when tested by deciles over time, produces a chart that looks like this:

This is the performance of unlevered free cash flow to enterprise value in the Russell 3000 with a monthly rebalance and no slippage since 1999.

A distributed factor produces a chart like this:

This is the performance of operating margin growth (the difference between the most recent TTM operating margin and the twelve months before that), again in the Russell 3000 with a monthly rebalance and no slippage since 1999. I call it a distributed factor because the deciles fall into a normal distribution, more or less.

Now if you go long the top quintile of each factor and short the bottom quintile, which is the conventional way to measure the effectiveness of a factor, the first factor, using the Russell 3000 and rebalancing quarterly, will give you a result that looks like this:

And the second will give you a result that looks like this:

Now for most people who look at factors, this second factor clearly doesn’t work. But what if you go long the middle quintile and short the top and bottom deciles? Then you get a chart that looks like this:

That’s the kind of thing you have to do with a distributed factor.

Now let’s look at an augmentative factor: fully diluted market cap, with lower values ranking higher. (Most size factors are augmentative, but many quality factors are too, e.g. accrual ratios.)

Clearly, this is not going to produce good results if we take the top quintile long and the bottom quintile short. And even as a distributed factor, it’s pretty weak, since the middle deciles aren’t much higher than the top and bottom ones.

Now here’s a direct factor, operating income growth (the growth of the most recent quarter’s operating income compared with the same quarter last year):

I’m going to combine this direct factor with the augmentative factor, and weight them 60% operating income growth, 40% fully diluted market cap. Here’s what we get:

An augmentative factor increases the effectiveness of a direct factor.

Two things should be quite clear from this categorization of factors. First, a distributed factor can be converted into a direct factor by privileging middling results rather than high or low results. I do this for a lot of “growth” factors when I evaluate stocks. Second, an augmentative factor can be converted into a direct factor by combining it with another factor. So, for example, I can combine fully diluted market cap with operating income growth by using the former as a denominator and the latter as a numerator, ending up with a modified inverse PEG ratio. This solution, of course, only works if the denominator is always positive, but there are other ways to combine factors mathematically.

The problem with most factor studies is that they look at all possible factors as if they’re direct, and their tests are always along the lines of “go long the top quintile and short the bottom,” or “chart the excess returns of the top quintile over a benchmark.” Recognizing that factors can work in very different ways will increase the number of factors you can use—and your opportunities to use them.

CAGR since 1/1/16: 48%.

My top ten holdings right now: RCKY, IRMD, AUDC, INTT, ZYXI, WSTL, TRIB, XOXO, TZOO, RICK.

Comments

[Victor]

Hi Yuval. Interesting classification of factors. In your eyes, is there an objective way to determine whether a factor is augmentative, distributed or simply 'not significantly useful'? I can imagine that a first look at the marketcap factor would make one think it is a distrubuted factor, the same goes for some of the accruel factors.

A practical way I can think of myself is to first construct a ranking system (with one or more nodes) of 'direct' (linear) factors and subsequently add 'other factors' of which it is unclear whether they are distributed or augmentative. If using an 'other factor' in a way that punishes the top and bottom buckets results in better results for the ranking system than simply adding the plain 'other factor', this is a sign it is a distributed factor. And the oppositive way around. This test, plus some 'common sense' thinking (subjective test), where there is some intuition behind the top and bottom buckets underperforming (e.g. very large increases in margins being as bad as large very decreases because of instability of the businessmodel), should give a reasonable indication what type of factor you are dealing with.

Do you have an other (formal) process of determining the type of factor?

Best,

Victor

[Yuval Taylor]

No, I don't think there's an objective way to classify these factors. I think your conclusions in the second paragraph of your comment are absolutely sound.