Facts About Factors via SSRN

Paula Cocoma

State Street Corporation

Megan Czasonis

State Street Corporation

Mark Kritzman

Massachusetts Institute of Technology (MIT) – Sloan School of Management

David Turkington

State Street Associates

April 6, 2015

MIT Sloan Research Paper No. 5128-15

Abstract:

It has become fashionable to allocate portfolios to factors rather than to assets. The often stated motivation for this approach is that factors are less correlated with each other than assets; therefore, factors afford greater opportunity for diversification. This argument is specious, of course, because ultimately the portfolio must be invested in assets. It is, therefore, impossible to produce a better in-sample portfolio by describing the portfolio as a set of factors than assets. There are several potentially legitimate arguments, though, for favoring factor stratification over asset stratification. It could be that factors are easier to forecast than assets, because investors are better able to relate current information to future factor behavior than to future asset behavior. Unfortunately, we have no way of testing this conjecture generically. But there are several testable conjectures. Perhaps risk estimated from high-frequency returns predicts risk over longer horizons more reliably for factors than for assets. Or the statistical properties of large samples may predict the statistical properties of small samples more reliably for factors than for assets. Or, for the same sample size, the statistical properties of factors may be more stationary from one sample to the next than they are for assets. Finally, it may be that reducing the dimensionality of a large set of assets to a smaller set of factors reduces noise more effectively than reducing dimensionality to a smaller set of assets. We offer empirical evidence of the validity, or lack thereof, of these testable conjectures.

Facts About Factors

It has recently become fashionable to allocate portfolios across factors instead of assets, but the motivation for doing so is often misguided. For example, some claim that factors are less correlated with each other than assets; hence, they enable investors to achieve greater diversification. What is often overlooked, however, is that the asset combinations used to mimic factors include both long and short positions. It is the inclusion of short positions that give factors the appearance of lower correlations. The reality is that it is impossible to produce more efficient portfolios, in sample, by expressing exposures as factors instead of assets, as long as the investable units are the same in both cases.

Is there any advantage to factor allocation? Yes, potentially. Investors may be able to predict factor behavior more dependably than asset behavior for several reasons. Perhaps some investors are better able to relate current information to future factor performance than they are to asset performance. Unfortunately, we are unable to test this conjecture generically, as this skill varies from investor to investor. Or it may be that risk estimated from highfrequency returns gives more reliable estimates of risk over longer horizons for factors than for assets.2 Or perhaps the statistical properties of large samples may better predict the statistical properties of small samples more dependably for factors than for assets. Or, for the same sample size, the statistical properties of factors may be more stationary from one sample to the next than they are for assets. Finally, it may be that reducing the dimensionality of a large set of assets to a small set of factors reduces noise more effectively than reducing dimensionality to a small set of assets. If these conjectures are true, factor stratification will dominate asset stratification, because factors will produce more reliable results across return intervals or from large samples to small samples or across independent samples. Otherwise, factor allocation may be yet another fad in a long history of investment fads.

We begin by repudiating the notion that factors offer superior diversification benefits. We then introduce our metrics for evaluating stationarity. Next we define the assets and factors used in our analysis, and we describe the data. We then present our results, which quantify four types of estimation error: interval error, small?sample error, independent?sample error, and noise arising from redundant dimensionality. We conclude with a summary of the relative merits of asset and factor allocation.

The Diversification Benefits of Factors – or Not

Some investors believe that factors offer superior diversification benefits relative to assets because factors are less correlated with each other. This argument is specious if the factors represent regroupings of the assets, even if these regroupings are less correlated with each other than the component assets. The factors would be less correlated only because they would include some short exposures to the assets. Exhibit 1 reveals that assets deliver the same degree of efficiency as factors.

Factors

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