What Is a Factor? The Impact of the Long-Only Constraint
Note: this blog post and paper were written in collaboration with Axioma colleagues Esther Mezey, PhD, Ipek Onat, MS and Dieter Vandenbussche, PhD.
Our recent paper “What, Exactly, Is a Factor?” examined various ways of constructing a portfolio used to calculate factor returns. We demonstrated that the absence or presence of a number of common constraints—such as a universe limitation—could have a large impact on a portfolio’s exposures and returns. We also showed how some methodologies, such as using just the top and bottom quintiles based on the chosen factor, can have a particularly distorting effect, since returns are no longer driven by the factor alone, but also by other exposures.
In a recent follow-up to the original paper—“What Is a Factor Part 2”—we drilled down into the impact of a long-only constraint. Many managers cannot short in their portfolios, yet their returns are measured against a “factor” that can. As in our earlier paper, we find that difference can have a substantial impact.
A factor-mimicking portfolio (FMP) is a long-short portfolio with unit exposure to the factor and no exposure to any other source of risk. It is rebalanced daily and encompasses a very broad investment universe. In the current study we created (using Axioma’s optimizer) what we call long-only FMPs: they have all the characteristics of the traditional FMP, except that a broad index—in this case using Axioma’s Global Developed Market portfolio—is used as a benchmark, and the portfolio can only be short up to the benchmark weight. In other words, the portfolio will look more like that of a typical long-only quantitatively driven portfolio or smart beta ETF. The analysis of these portfolios is based on the active return of our long-only FMP, and is thus directly comparable to the traditional long-short version.
In the paper we cover three major topics: 1) the impact the long-only constraint has on the whole portfolio, in that the inability to short also impacts the long positions, creating a more concentrated portfolio with more stock-specific risk; 2) how the level of tracking error impacts the portfolio’s concentration, its correlation with the traditional FMP and its performance; and 3) how this analysis can be used to determine whether the factor “works better” on the long side or the short side. We also compare another common technique of building a long-only portfolio, i.e., buying the capitalization-weighted average of the top 20% of stocks, to the optimized approach.
Our major findings were as follows.
- The active holdings of the long-only FMP are, indeed, more concentrated than the long-short FMP, and the portfolio does have more stock-specific risk.
- As we increase the tracking error of our long-only FMP, we find that holdings are less and less correlated with the long-short portfolio that might be viewed as the “ideal” expression of the factor. The portfolio comprising the top quintile of stocks has quite a low holdings correlation with the long-short FMP, and the returns are completely uncorrelated.
- The long-only constraint had a big impact, but results differed by factor.
- The long-only FMP, with its exposure to the underlying factor scaled to match the traditional FMP, had significantly worse performance than the traditional FMP for a few factors, suggesting much of the factor return came from the short side. The higher level of specific risk in these portfolios also contributed to the shortfall.
- The top quintile portfolio may have had the highest return, but it had the return with substantially more volatility.
- Not all factors exhibited the strength on the short side, however, and even those that did over the long term saw substantial differences from year to year.
The figures below show the returns for long-only FMPs run at different levels of tracking error using four factors from Axioma’s WW4 model and Axioma’s Global Developed Markets portfolio. Clearly, the inability to short detracts substantially from the Profitability and Momentum factors over time, and the impact gets larger as target tracking error rises. For Value, shorting also helps but the impact between tracking error levels is smaller. And for Earnings Yield, there is not much impact, but a lot more volatility for higher-tracking-error long-only FMPs.
Cumulative Active Return by Level of Target Tracking Error, Long-Only FMPs
Note: Benchmark and Investment Universe used was Axioma’s Global Developed Market portfolio.