*This post can be downloaded as a PDF here.*

**Summary**

- Factors such as value, size, and momentum are generally constructed using dollar-neutral portfolios in academic literature.
- The market beta exposure in these portfolios is often significant and can vary substantially over time. Each factor has gone through periods where these features have been beneficial or detrimental to performance.
- Constructing beta neutral factor portfolios can remove the dependence on market beta within the factors.
- However, factor investing may be a prudent way to control market exposure. The beta timing may be a feature, not a bug.

A few months ago, in our presentation All About Factors & Smart Beta[1], we introduced the basics of factor investing. The core concept is that securities are ranked based upon a scoring system, and a *self-financing *portfolio is built by short-selling poorly ranking securities and using the proceeds to buy high ranking securities.

The self-financing nature of the portfolios – also called “dollar neutral” portfolios – makes factor performance easy to calculate. It does, however, introduce an interesting quirk: the portfolios are not *beta *neutral.

In other words, if we look at our long/short factor portfolio as two separate legs – a long leg and a short leg – the sensitivity each leg has to overall market moves can be very different. Furthermore, the sensitivity of each leg can evolve over time. This means that the overall factor portfolio can not only end up with sensitivity to market moves, but time-varying sensitivity.

Consider, for example, the value factor. Below we plot the beta of the long leg minus the beta of the short leg.

*Source: Kenneth French Data Library. Calculations by Newfound Research.*

Not only do we see that the magnitude of the beta difference can be quite large, we see that it can vary drastically over time. In addition to a broad swing from +1 to -0.7 from the 1930s to the 1980s, there are many dramatic short-term swings as well.

This raises two interesting questions:

- Are factor returns a byproduct of non-zero beta exposure?
- Do factors benefit from time-varying beta exposure – i.e. “market timing”?

**Data & Methodology**

Data in this commentary comes from the Kenneth French data library. For value and size factors, we utilize the “Hi 30” and “Lo 30” portfolios provided. For the momentum factor, we equally-weight the top and bottom three deciles to create synthetic “Hi 30” and “Lo 30” portfolios.

To estimate betas, we run rolling 25-week regressions of Hi and Lo portfolio excess returns against market excess returns. We then apply a 12-week exponentially weighted smoothing process to help eliminate noise.

First, an important tangent…

It is worth pointing out that this is the wrong way to do this*.* To actually estimate the beta of each leg, we should first find the beta of each underlying stock and then calculating the weighted average across all stocks in the portfolio. Without access to the underlying components, however, we are using past realized returns as a proxy estimate for present value. This is likely okay for low turnover factors like value and size, but may make the estimate for a higher turnover factor like momentum less accurate.

Furthermore, beta is merely a statistical tool we use to conveniently summarize a relationship; it is not an intrinsic property of a company. So we are estimating something that, in and of itself, is an estimate based on past behavior. Even if our estimate is completely certain, the model may be completely wrong. Hence, this entire analysis may just be a big case of garbage in, garbage out. You’ve been warned!

Okay, back to the regularly scheduled programming.

To test whether factors benefit from long-term beta exposure, we’ll create a portfolio whose monthly excess return is:

Where

is the long-term average of monthly differences in betas for the Hi and Lo legs. By using the long-term average difference, we can capture the long-term beta exposure without incorporating timing effects of changing relative beta levels.

To test whether factors benefit from beta timing, we will calculate a portfolio whose monthly excess return is:

This return represents the difference between each month’s actual beta spread versus the long-term average. Deviation from this average captures the “timing” component of changes in the beta spreads.

We will also calculate a portfolio that captures the residual effects: the difference between the traditional factor portfolio returns and the returns accounted for by the average beta exposure and timing exposure. The residual return is essentially the beta-neutral factor exposure.

**The Value Factor**

*Source: Kenneth French Data Library. Calculations by Newfound Research.*

- On average, the value factor has had a positive beta. This long market exposure added about 0.48% per year to performance. We can think of this as overlapping exposure with the equity risk premium, and not actually due to the value factor itself.
- Beta timing added 1.23% per year. We can see that it was largely additive in the first 30 years, and then was a drag over the next 60. In fact, based on this data we could argue that the returns in the first 30 years of the value factor are due almost entirely to beta timing.
- The residual, or beta neutral portion of the factor, accounted for about 1.79% per year.

**The Size Factor**

*Source: Kenneth French Data Library. Calculations by Newfound Research.*

- Long-term average beta exposure was a positive contribution of about 0.41% per year, in line with the idea that small-caps typically have higher beta than large-caps.
- Beta timing was a drag of -0.18% per year. Again, we can see that the results here were very regime dependent. From the 1950s through the late 1990s, beta timing was a significant drag on performance. On the other hand, it has been a tailwind over the last 17 years.
- The residual, or beta neutral portion of the factor, accounted for the lion’s share of the return, clocking in at 2.60% annualized.

**The Momentum Factor**

*Source: Kenneth French Data Library. Calculations by Newfound Research.*

- Long-term average beta exposure added 0.13% per year.
- Beta timing was a drag of -0.54% per year. Again, this result is highly regime driven; from 12/31/1992 to 12/31/2008, the beta timing component returned 3.82% per year.
- Residual account for the lion’s share of the return, clocking in at 4.50% annualized.

Worth noting is that if any of these results are gibberish, it’s likely to be momentum as momentum portfolios are the least stable and therefore it is likely that using our past realized beta estimate as a forecast for current beta has the highest degree of error.

**Beta-Neutral Portfolios**

One way of addressing the confounding impacts of time-varying beta exposure is by attempting to construct factor portfolios that are beta neutral instead of dollar neutral. To do this, we scale each leg such that its beta is equal to 1 (lending and borrowing at the risk-free rate as necessary).

*Source: Kenneth French Data Library. Calculations by Newfound Research.*

*Source: Kenneth French Data Library. Calculations by Newfound Research.*

*Source: Kenneth French Data Library. Calculations by Newfound Research.*

Ann. Return | Ann. Volatility | Ann. Sharpe(rf = 0) | Max Drawdown | |

Value | 3.55% | 13.68% | 0.26 | 48.59% |

Beta Neutral Value | 2.17% | 11.06% | 0.20 | 52.51% |

Size | 2.94% | 16.49% | 0.18 | 72.23% |

Beta Neutral Size | 2.85% | 17.17% | 0.17 | 74.66% |

Momentum | 4.00% | 21.81% | 0.18 | 90.02% |

Beta Neutral Momentum | 5.37% | 15.86% | 0.34 | 67.60% |

We can see that “neutralizing” beta had varying effects. Most prominently, however, it decreased returns for the value factor by 138bp per year. Equally as interesting is the improvement to both return and risk for the momentum factor (again, acknowledging that if any of these results are a case of “garbage in, garbage out,” this would be it.)** **

**Conclusion**

So what’s the take away? Is value an overstated factor, buoyed by early help from beta timing? Is momentum safer if we balance the beta risk?

If past factor returns *are *predictive of future returns (why else would we bother with them?), does that include the average beta and beta timing components?

One potential argument here is that even if factors are driven *entirely *by beta timing, they could simply be capturing dynamic sentiment changes in the market and intelligently betting on it. For example, while beta timing drove a substantial amount of the total return of the value factor from 1927 to 1957, the methodology of value investing may have been an intelligent way of harvesting changing investor views on risk during the period.

In other words, beta timing may very well be a feature, and not a bug, of factor investing.

[1] https://blog.thinknewfound.com/2017/03/factors-smart-beta/

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