*This post is available as a PDF download here.*

# Summary

- The Fama French three-factor model provides a powerful tool for assessing exposures to equity risk premia in investment strategies.
- In this note, we explore alternative specifications of the value (HML) and size (SMB) factors using price-to-earnings, price-to-cash flow, and dividend yield.
- Running factor regressions using these alternate specifications on a suite of value ETFs and Newfound’s Systematic Value strategy, lead to a wide array of results, both numerically and directionally.
- While many investors consider the uncertainty of the parameter estimates from the regression using the three-factor model, most do not consider the uncertainty that comes from the assumption of how you construct the equity factors in the first place.
- Understanding the additional uncertainty is crucial for manager and investors who must consider what risks they are trying to measure and control by using tools like factor regression and make sure their assumptions align with their goals.

In their 1992 paper, *The Cross-Section of Expected Stock Returns*, Eugene Fama and Kenneth French outlined their three-factor model to explain stock returns.

While the Capital Asset Pricing Model (CAPM) only describes asset returns in relation to their exposure to the market’s excess return through the stock’s beta and identifies any return beyond that as alpha, Fama and French’s three-factor model reattributed some of that supposed alpha to exposures to a value factor (High-minus-low or HML) based on returns stratified by price-to-book ratios and a size factor (small-minus-big or SMB) based on returns stratified by market capitalization.

This gave investors a tool to judge investment strategies based on the loadings to these risk factors. A manager with a seemingly high alpha may have simply been investing in value and small-cap stocks historically.

The notion of compensated risk premia has also opened the floodgate of many additional factors from other researchers (such as momentum, quality, low beta, etc.) and even two more factors from Fama and French (investment and profitability).

A richer factor universe opens up a wide realm of possibilities for analysis and attribution. However, setting further developments aside and going back to the original three-factor model, we would be remiss if we didn’t dive a bit further into its specification.

At the highest level, we agree with treating “value” and “size” as risk factors, but there is more than one way to skin a factor.

What is “value”?

Fama and French define it using the price-to-book ratio of a stock. This seems legitimate for a broad swath of stocks, especially those that are very capital intensive – such as energy, manufacturing, and financial firms – but what about industries that have structurally lower book values and may have other potential price drivers? For example, a technology company might have significant intangible intellectual property and some utility companies might employ leverage, which decreases their book value substantially.

To determine value in these sectors, we might utilize ratios that account for sales, dividends, or earnings. But then if we analyzed these strategies using the Fama French three-factor model as it is specified, we might misjudge the loading on the value factor.

“Size” seems more straightforward. Companies with low market capitalizations are small. However, when we consider how the size factor is defined based on the value factor, there might even be some differences in SMB using different value metrics.

In this commentary, we will explore what happens when we alter the definition of value for the value factor (and hence the size factor) and see how this affects factor regressions of a sample of value ETFs along with our Systematic Value strategy.

**HML Factor Definitions**

In the standard version of the Fama French 3-factor model, HML is constructed as a self-financing long/short portfolio using a 2×3 sort on size and value. The investment universe is split in half based on market capitalization and in three parts (30%/40%/30%) based on valuation, in this base case, price-to-book ratio.

Using additional data from the Kenneth French Data Library and the same methodology, we will construct HML factors using sorts based on size and:

- Price-to-earnings ratios
- Price-to-cash flow ratios
- Dividend yields

The common inception date for all the factors is June 1951.

The chart below shows the growth of each of the four value factor portfolios.

*Source: Kenneth French Data Library. Calculations by Newfound Research. **Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions. *

Over the entire time period – and for many shorter time horizons – the standard HML factor using price-to-book does not even have the most attractive returns. Price-to-earnings and price-to-cash flow often beat it out.

On the other hand, the HML factor formed using dividend yields doesn’t look so hot.

One of the reasons behind this is that the small, low dividend yield companies performed much better than the small companies that were ranked poorly by the other value factors. We can see this effect borne out in the SMB chart for each factor, as the SMB factor for dividend yield performed the best.

(Recall that we mentioned previously how the Fama French way of defining the size factor is dependent on which value metric we use.)

*Source: Kenneth French Data Library. Calculations by Newfound Research. **Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions.*

Looking at the statistical significance of each factor through its t-statistic, we can see that Price-to-Earnings and Price-to-Cash Flow yielded higher significance for the HML factor than Price-to-Book. And those two along with Dividend Yield all eclipsed the Price-to-Book construction of the SMB factor.

*T-Statistics for HML and SMB Using Various Value Metrics*

| Price-to-Book | Dividend Yield | Price-to-Earnings | Price-to-Cash Flow |

HML | 2.9 | 0.0 | 3.7 | 3.4 |

SMB | 1.0 | 2.4 | 1.6 | 1.9 |

Assuming that we do consider all metrics to be appropriate ways to assess the value of companies, even if possibly under different circumstances, how do different variants of the Fama French three-factor model change for each scenario with regression analysis?

**The Impact on Factor Regressions**

Using a sample of U.S. value ETFs and our Systematic Value strategy, we plot the loadings for the different versions of HML. The regressions are carried out using the trailing three years of monthly data ending on October 2019.

*Source: Tiingo, Kenneth French Data Library. Calculations by Newfound Research. **Past performance is not an indicator of future results. Returns represent live strategy results. Returns for the Newfound Systematic Value strategy are gross of all management fees and taxes, but net of execution fees. Returns for ETFs included in study are gross of any management fees, but net of underlying ETF expense ratios. Returns assume the reinvestment of all distributions.*

For each different specification of HML, the differences in the loading between investments is generally directionally consistent. For instance, DVP has higher loadings than FTA for all forms of HML.

However, sometimes this is not the case.

VLUE looks more attractive than VTV based on price-to-cash flow but not dividend yield. FTA is roughly equivalent to QVAL in terms of loading when price-to-book is used for HML, but it varies wildly when other metrics are used.

The tightest range for the four models for any of the investments is 0.09 (PWV) and the widest is 0.52 (QVAL). When we factor in that these estimates each have their own uncertainty, distinguishing which investment has the better value characteristic is tough. Decisions are commonly made on much smaller differences.

We see similar dispersion in the SMB loadings for the various constructions.

*Source: Tiingo, Kenneth French Data Library. Calculations by Newfound Research. **Past performance is not an indicator of future results. Returns represent live strategy results. Returns for the Newfound Systematic Value strategy are gross of all management fees and taxes, but net of execution fees. Returns for ETFs included in study are gross of any management fees, but net of underlying ETF expense ratios. Returns assume the reinvestment of all distributions.*

Many of these values are not statistically significant from zero, so someone who has a thorough understanding of uncertainty in regression would likely not draw a strict comparison between most of these investments.

However, one implication of this is that if a metric is chosen that does ascribe significant size exposure to one of these investments, an investor may make a decision based on not wanting to bear that risk in what they desire to be a large-cap investment.

**Can We Blend Our Way Out?**

One way we often mitigate model specification risk is by blending a number of models together into one.

By averaging all of our HML and SMB factors, respectively, we arrive at blended factors for the three-factor model.

*Source: Tiingo, Kenneth French Data Library. Calculations by Newfound Research. **Past performance is not an indicator of future results. Returns represent live strategy results. Returns for the Newfound Systematic Value strategy are gross of all management fees and taxes, but net of execution fees. Returns for ETFs included in study are gross of any management fees, but net of underlying ETF expense ratios. Returns assume the reinvestment of all distributions.*

All of the investments now have HML loadings in the top of their range of the individual model loadings, and many (FTA, PWV, RPV, SPVU, VTV, and the Systematic Value strategy) have loadings to the blended HML factor that exceed the loadings for all of the individual models.

The opposite is the case for the blended SMB factor: the loadings are in the low-end of the range of the individual model loadings.

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

So which is the correct method?

That’s a good question.

For some investments, it is situation-specific. If a strategy only uses price-to-earnings as its value metric, then putting it up against a three-factor model using the P/E ratio to construct the factors is appropriate for judging the efficacy of harvesting that factor.

However, if we are concerned more generally about the abstract concept of “value”, then the blended model may be the best way to go.

**Conclusion**

In this study, we have explored the impact of model specification for the value and size factor in the Fama French three-factor model.

We empirically tested this impact by designing a variety of HML and SMB factors based on three additional value metrics (price-to-earnings, price-to-cash flow, and dividend yield). These factors were constructed using the same rules as for the standard method using price-to-book ratios.

Each factor, with the possible exceptions of the dividend yield-based HML, has performance that could make it a legitimate specification for the three-factor model over the time that common data is available.

Running factor regressions using these alternate specifications on a suite of value ETFs and Newfound’s Systematic Value strategy, led to a wide array of results, both numerically and directionally.

While many investors consider the uncertainty of the parameter estimates from the regression using the three-factor model, most do not consider the uncertainty that comes from the assumption of how you construct the equity factors in the first place.

Understanding the additional uncertainty is crucial for decision-making. Managers and investors alike must consider what risks they are trying to measure and control by using tools like factor regression and make sure their assumptions align with their goals.

“Value” is in the eye of the beholder, and blind applications of two different value factors may lead to seeing double conclusions.

## Can Managed Futures Offset Equity Losses?

By Corey Hoffstein

On February 3, 2020

In Risk & Style Premia, Risk Management, Trend, Weekly Commentary

This post is available as a PDF download here.## Summary

Shortly after the 2008 crisis, the appetite for risk management strategies exploded. At the forefront of this trend was managed futures, which had already proven itself in the dot-com fallout. With the Societe Generale Trend Index

^{1}returning 20.9% in 2008, the evidence for CTAs to provide “crisis alpha”^{2}seemed un-debatable. AUM in these strategies sky-rocketed, growing from $200 billion in 2007 to approximately $325 billion by 2012.Source: http://managedfuturesinvesting.comSubsequent performance has, unfortunately, been lack-luster. Since 12/31/2011, the SG Trend Index has returned just 14.2% compared to the S&P 500’s 200.8% total return. While this is an unfair, apples-to-oranges comparison, it does capture the dispersion the strategy has exhibited to the benchmark most investors measure performance against during a bull market.

Furthermore, the allocation to managed futures had to come from somewhere. If investors reduced exposure to equities to introduce managed futures, the spread in performance captures the opportunity cost of that decision. There is hope yet: if the S&P 500 fell 50% over the next year, managed futures would have to return just 32% for their full-period performance (2011-2020) to equalize.

Yet how certain are we that managed futures would necessarily generate a positive return in an S&P 500 left-tail environment? Hurst, Ooi, and Pedersen (2017)

^{3}find that managed futures have generated anything from flat to meaningfully positive results during the top 10 largest drawdowns of a 60/40 portfolio since the late 1800s. This evidence makes a strong empirical case, but we should acknowledge the N=10 nature of the data.Perhaps we can lean into the mechanically convex nature of trend following. Trend following is a close cousin to the trading strategy that delta-hedges a strangle, generating the pay-off profile of a straddle (long an at-the-money put and call). Even without an anomalous premium generated by autocorrelation in the underlying security, the trading strategy itself should – barring trading frictions – generate a convex payoff.

Yet while mechanical convexity may be true on a contract-by-contract basis, it is entirely possible that the convexity we want to see emerge is diluted by trades across other contracts. Consider the scenario where the S&P 500 enters a prolonged and significant drawdown and our managed futures strategy goes short S&P 500 futures contract. While this trade may generate the hedge we were looking for, it’s possible that it is diluted by trades on other contracts such as wheat, the Japanese Yen, or the German Bund.

When we consider that many investors have portfolios dominated by equity risk (recall that equities have historically contributed 90% of the realized volatility for a 60/40 portfolio), it is possible that too much breadth within a managed futures portfolio could actually prevent it from providing negative beta during left-tail equity events.

## Replicating Managed Futures

We begin our study by first replicating a generic trend-following CTA index. We adopt an ensemble approach, which is effectively equivalent to holding a basket of managers who each implement a trend-following strategy with a different model and parameterization.

Specifically, we assume each manager implements using the same 47 contracts that represent a diversified basket of equities, rates, commodities, and currencies.

^{4}We implement with three different models (total return, price-minus-moving-average, and dual-moving-average-cross) and five potential lookback specifications (21, 42, 84, 168, and 336 days) for a total of 15 different implementations.

Each implementation begins by calculating an equal-risk contribution (“risk parity”) portfolio. Weights for each contract are then multiplied by their trend signal (which is simply either +1 or -1).

The weights for all 15 implementations are then averaged together to generate our index weights. Notional exposure of the aggregate weights is then scaled to target a 10% annualized volatility level. We assume that the index is fully collateralized using the S&P U.S. Treasury Bill Index.

Below we plot our index versus the SG Trend Index. The correlation of monthly returns between these two indices is 75% suggesting that our simple implementation does a reasonable job approximating the broad trend-following style of CTAs. We can also see that it captures the salient features of the SG Trend Index, including strong performance from 2001-2003, Q4 2008 and Q1 2009, and the 2014-2015 period. We can also see it closely tracks the shape the SG Trend Index equity curve from 2015 onward in all its meandering glory.

Source: Stevens Analytics. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions. These results do not reflect the returns of any strategy managed by Newfound Research.## Convexity versus Diversification

To explore the impact of diversification in managed futures versus convexity exhibited against the S&P 500, we will create a number of managed futures strategies and vary the number of contracts included. As we are attempting to create a convex payoff against the S&P 500, the S&P 500 futures contract will always be selected.

For example, a 2-contract strategy will always include S&P 500 futures, but the second contract could be 10-year U.S. Treasuries, the Nikkei, the Australian Dollar, Oil, or any of the other 42 futures contracts. Once selected, however, that pair defines the strategy.

For 2-, 4-, 8-, 16-, and 32- contract systems, we generate the performance of 25 randomly selected strategies. We then generate scatter plots with non-overlapping 6-month returns for the S&P 500 on the x-axis and non-overlapping 6-month returns for the managed futures strategies on the y-axis.

^{5}We then fit a 2^{nd}-degree polynomial line to visualize the realized convexity.(Note that for the single contract case – i.e. just the S&P 500 futures contract – we plot overlapping 6-month returns.)

Source: Stevens Analytics and Sharadar. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions. These results do not reflect the returns of any strategy managed by Newfound Research.There are two particularly interesting artifacts to note.

First, as the number of contracts goes up, the best-fit model turns from a “smile” to a “smirk,” suggesting that diversification dilutes positive convexity relationships with the S&P 500. This outcome should have been expected, as we generally know how managed futures has done over the 20-year period we’re examining. Namely, managed futures did quite well offsetting losses in 2000-2003 and 2008-2009, but has failed to participate in the 2010s.

Perhaps more interestingly, however, is the increase in left-tail performance of managed futures, climbing from 20% when just trading the S&P 500 futures contract to 150% in the 32-contract case. The subtle reason here is diversification’s impact on total notional exposure.

Consider this trivial example: Asset A and Asset B have constant 10% volatility and are uncorrelated with one another. As they are uncorrelated, any combination of these assets will have a volatility that is less than 10%. Therefore, if we want to achieve 10%, we need to apply leverage. In fact, a 50-50 mix of these assets requires us to apply 1.41x leverage to achieve our volatility target, resulting in 70.7% exposure to each asset.

As a more concrete example, when trading just the S&P 500 futures contract, achieving 10% volatility position in 2008 requires diluting gross notional exposure to just 16%. For the full, 47-contract model, gross notional exposure during 2008 dipped to 90% at its lowest point.

Now consider that trend following tends to transform the underlying distributions of assets to generate positive skewness. Increasing leverage can help push those positive trades even further out in the tails.

But here’s the trade-off: the actual exposure to S&P 500 futures contracts, specifically, still remains much, much higher in the case where we’re trading it alone. In practice, the reason the diversified approach was able to generate increased returns during left-tail equity events – such as 2008 – is due to the fact correlations crashed to extremes (both positive and negative) between global equity indices, rates, commodities, and currencies. This allowed the total notional exposure of directionally similar trades (e.g. short equities, long bonds, and short commodities in 2008) to far exceed the total notional exposure achieved if we were just trading the S&P 500 futures contract alone.

Source: Stevens Analytics. Calculations by Newfound Research.Our confidence in achieving negative convexity versus equity left-tail events, therefore, is inherently tied to our belief that we will see simultaneously trends across a large number of assets during such environments.

Another interpretation of this data is that because negative trends in the S&P 500 have historically coincided with higher volatility, a strategy that seeks to trade just the S&P 500 futures with constant volatility will lose convexity in those tail events. An alternative choice is to vary the volatility of the system to target the volatility of the S&P 500, whose convexity profile we plot below.

Source: Stevens Analytics and Sharadar. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions. These results do not reflect the returns of any strategy managed by Newfound Research.This analysis highlights a variety of trade-offs to consider:

Perhaps, then, we should consider approaching the problem from another angle: given exposure to managed futures, what would be a better core portfolio to hold? Given that most managed futures portfolios start from a risk parity core, the simplest answer is likely risk parity.

As an example, we construct a 10% target volatility risk parity index using equity, rate, and commodity contracts. Below we plot the convexity profile of our managed futures strategy against this risk parity index and see the traditional “smile” emerge. We also plot the equity curves for the risk parity index, the managed futures index, and a 50/50 blend. Both the risk parity and managed futures indices have a realized volatility of level of 10.8%; the blended combination drops this volatility to just 7.6%, achieving a maximum drawdown of just -10.1%.

Source: Stevens Analytics and Sharadar. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions. These results do not reflect the returns of any strategy managed by Newfound Research.## Conclusion

Managed futures have historically generated significant gains during left-tail equity events. These returns, however, are by no means guaranteed. While trend following is a mechanically convex strategy, the diversified nature of most managed futures programs can potentially dilute equity-crisis-specific returns.

In this research note, we sought to explore this concept by generating a large number of managed futures strategies that varied in the number of contracts traded. We found that increasing the number of contracts had two primary effects: (1) it reduced realized convexity from a “smile” to a “smirk” (i.e. exhibited less up-side participation with equity markets); and (2) meaningfully increased returns during negative equity markets.

The latter is particularly curious but ultimately the byproduct of two facts. First, increasing diversification allows for increased notional exposure in the portfolio to achieve the same target volatility level. Second, during past crises we witnessed a large number of assets trending simultaneously. Therefore, while increasing the number of contracts reduced notional exposure to S&P 500 futures specifically, the total notional exposure to trades generating positive gains during past crisis events was materially higher.

While the first fact is evergreen, the second may not always be the case. Therefore, employing managed futures specifically as a strategy to provide offsetting returns during an equity market crisis requires the belief that a sufficient number of other exposures (i.e. equity indices, rates, commodities, and currencies) will be exhibiting meaningful trends at the same time.

Given its diversified nature, it should come as no surprise that managed futures appear to be a natural complement to a risk parity portfolio.

Investors acutely sensitive to significant equity losses – e.g. those in more traditional strategic allocation portfolios – might therefore consider strategies designed more specifically with such environments in mind. At Newfound, we believe that trend equity strategies are one such solution, as they overlay trend-following techniques directly on equity exposure, seeking to generate the convexity mechanically and not through correlated assets. When overlaid with U.S. Treasury futures – which have historically provided a “flight-to-safety” premium during equity crises – we believe it is a particularly strong solution.