12

Asset Classes Versus Risk Factors and Something About Dr. Strange

While volatilities are easy to visualize, covariances are more difficult. Academics have standardized the measure into the concept of beta, which is easier to interpret.

—JPP

BACK IN 2010, A FEW WEEKS AFTER I JOINED PIMCO, MARK Taborsky—who was a multi-asset portfolio manager at the time—suggested that we compare the diversification properties of risk factors with traditional asset classes. We eventually published an editorial in 2011 in the Journal of Portfolio Management on the topic. To my surprise, our two-pager received a lot of attention (unlike most of my publications) and was the most downloaded article in the Journal of Portfolio Management for over a year. It has been cited by 16 subsequent articles . . . although not all of them are complimentary.

When they think of risk factors, most people think of equity-based, Fama-French factors such as market beta, size, value, momentum, and quality. Some comprehensive models also include sector and country factors.

But fixed income portfolio managers have long decomposed portfolios into risk factors as well, probably even before equity investors did so. Almost all fixed income risk models are factor-based. Duration is a risk factor (or to be more precise, the interest rate is the risk factor, and duration is the exposure to it, or beta). Over time, many fixed income investors have expanded their factor-based approach to multi-asset portfolio management. To do so, they have connected two separate sets of factors (equity and fixed income), typically housed in two separate systems.

This process is not as complicated as it seems. We just need to measure the correlations between fixed income and equity factors. It can be made very complicated if we try to remeasure exposures across asset classes. For example, we can try to assign interest rate duration to stocks, equity beta to credit bonds, etc. In my experience, it’s better to keep it simple. It’s OK to allow for correlated factors. The correlation matrix will add up the risks in a consistent manner.

It’s in that multi-asset context that Mark Taborsky and I wanted to help institutional investors with their asset allocation decisions. If asset classes are combinations of risk factors, why not diversify the portfolio directly across these factors? And if we diversify across factors, are the portfolios more resilient to market turbulence than are those allocated across asset classes?

To investigate, first I compiled returns for various factors. I used equity factors such as market beta, size, value, and momentum. For fixed income, I used interest rate duration, two slope factors, and a few flavors of credit spreads. I also added real estate and commodity as alternative factors. There is no industry consensus on how to map asset classes to risk factors. In a monograph I mentioned earlier, “Factor Investing and Asset Allocation: A Business Cycle Perspective” (2016), my coauthors and I provide an overview of methodologies to define factors, which include statistical methods (principal components analysis, regression analysis, etc.), fixed income mathematics, and long-short equity portfolio construction. (Earlier in this book, we also discussed macro factors. While they drive asset returns, these factors are not directly investable. You can’t invest in GDP growth.)

For asset classes, I used the traditional building blocks: large and small cap US stocks, international stocks, core bonds, etc. We found that the average correlation across risk factors was much lower than the average correlation across asset classes. Also, during periods of market stress, the average correlation across risk factors did not jump by nearly as much as the correlation across classes.

This result was to be expected, because several of the factors were represented by long-short portfolios, while asset classes were all long-only benchmarks. If we allow for short positions, we can drastically lower correlations and make the portfolio’s volatility more stable. When we discussed extreme correlations in Chapter 9, I mentioned that there’s nothing magical about risk factors. If we constrain risk factors to be linear combinations of asset classes and allow for short positions in both asset classes and risk factors, we arrive at the same portfolio optimization result. No efficiency gains.

The problem is that we didn’t explain this nuance in the editorial. I worry that we contributed to the hype around risk premiums as asset classes, which was not our goal. However, the fact remains that risk factors are often less constrained than asset classes. They are typically defined as long-short portfolios. And they sometimes cover a broader investment universe than asset classes, which also leads to efficiency gains.

Importantly, as we discussed in the context of scenario analysis, asset classes’ exposures to risk factors change over time. Examples of such changes abound. For instance, the interest rate duration of the Barclays U.S. Aggregate has increased by more than 40% since the 2008 crisis (from 4.5 to 6 years). Before the global financial crisis, the financials and energy sectors represented 31% of the S&P 500 index. They now represent only 19% of the index. Six years ago, energy and materials represented about 25% of the emerging markets equity index, while technology represented less than 15%. These percentages have now flipped.

No Need to Build a New Optimizer—We Can Use Risk Factors Behind the Scenes

This instability in factor exposures has consequences for portfolio construction. It motivates the use of risk factor models (rather than asset class–based models) in portfolio optimization even if we continue to invest across asset classes. A typical multi-asset portfolio optimization process solves for the asset class weights that maximize the portfolio’s expected return for a given risk level. But if we can measure each asset class’s risk factor exposures, as well as the non-factor-based (“idiosyncratic”) risk, there is a simple mathematical transformation that allows us to estimate asset class volatilities, correlations, and tail risks from their current factor exposures. The intuition is that we can multiply current factor exposures with historical factor returns to rebuild an asset class return series. (We can simulate the non-factor-based volatility to scale up the risk accordingly.) Then we can use our traditional asset class–based portfolio optimization tools on asset class risk estimates that have been derived from risk factors. It all adds up beautifully. There’s no need to build a new optimizer.

The downside of this hybrid factor-based/asset class–based approach is that sometimes risk factor exposures can change rapidly. In these cases, point-in-time estimates may be misleading. Suppose you allocate to hedge funds. Hedge fund managers may shift their equity market beta up and down tactically as part of their mandate. If the manager has de-risked the portfolio and gone to cash, and you estimate volatility and correlations based on current factor exposures, you will underestimate exposure to loss. The solution is to measure how exposures change over time. If they change rapidly, it may be preferable to use average exposures over a longer period and assign the rest of the volatility to the non-factor-based bucket, which in this case represents market timing skill.

Remember that the goal, as always, is to forecast risk based on what we know about the asset class or strategy. What’s the most relevant risk estimate for the future? The answer may differ based on the length of our investment horizon. In the case of dynamic strategies like hedge funds, average exposures are more relevant for relatively long horizons. For an estimate of risk one day, one week, or one month ahead, current exposures often work best.

Smart Betas, Alt Betas, Style Premiums, Risk Premiums, and All the Hype

Beyond the commendable use of risk factor models to forecast risk, our industry has recently embraced direct investment in risk factors (or smart betas, alternative betas, style premiums, etc.). We discussed the theoretical foundations for this trend in Chapter 1. Factors should deliver a positive return if they represent compensation for undiversifiable risk (risk premiums) or a persistent anomaly caused by investor behavior. In that context, not all factors qualify as risk premiums. Most risk factor models include country, currency, yield curve slope, and sector factors. These types of factors help measure risk, but they’re not expected to deliver a risk premium.¹

Over time, equity markets deliver a risk premium (over bonds or cash), as modeled in the capital asset pricing model. Relative to bond investors, stock investors get compensated for their investment in the riskiest part of companies’ capital structure. Hence, equity market beta is the most basic risk premium.

Similar risk premium arguments have been made for value (long high book-to-market, short low book-to-market stocks), size (long small capitalization, short large capitalization stocks), momentum (long stocks with high recent returns, short stocks with low recent returns), and a variety of other factors. These factors, in theory, deliver returns that compensate for higher risk.²

But for factors such as momentum, we don’t know whether excess returns represent compensation for risk or a behavioral anomaly. Some authors have argued that momentum is caused by investors who extrapolate recent performance. These investors like to buy stocks that have gone up in price and sell stocks that have gone down in price.³ It’s easy to see how such behavior can create bubbles. Prices may increase for fundamental reasons, but then continue to increase due to momentum investors, which leads to further price appreciation, which leads to more demand by momentum investors, and so on. A vicious circle, of sorts. The same effect can occur on the downside, when a price decline precipitates sell orders, which leads to further price declines, which leads to . . . You catch my drift.

However, value-oriented investors often take the other side of the trade. They seek to buy low and sell high. They sell inflated assets that have levitated away from fundamentals and buy deflated assets at bargain prices. Momentum investors often buy high and want to sell higher. This push and pull between momentum and value investors should lead to some equilibrium. Only if momentum investors are more numerous or aggressive will the momentum risk premium persist. It will likely persist at a relatively short time horizon—typically one month, as I showed in Chapter 5 in the context of return forecasting. At longer horizons, prices tend to revert to fundamentals. This mean reversion rewards value investors. I suspect this difference in time horizon between momentum and value investors also explains why the value and momentum factors are uncorrelated month to month.

Another risk premium that comes with a plausible story is the low-risk anomaly. There are several versions of the strategy, and a variety of smart beta products provide exposure to it (minimum volatility, low beta, etc.). The main idea is that low-risk/low-beta stocks tend to outperform high-beta stocks due to investors’ leverage constraints. As Frazzini and Pedersen (2014) explain in “Betting Against Beta”:

Many investors—such as individuals, pension funds, and mutual funds—are constrained in the leverage that they can take, and they therefore overweight risky securities instead of using leverage. . . . This behavior of tilting toward high-beta assets suggests that risky high-beta assets require lower risk-adjusted returns than low-beta assets, which require leverage.

Makes sense. The authors show that a strategy that levers low-risk assets and shorts high-risk assets (“betting against beta”) delivers “significant positive risk-adjusted returns” across markets. Even lower-risk Treasury and corporate bonds seem to outperform their higher-beta counterparts. They make a credible case. They control for other factor exposures such as size, value, momentum, and liquidity, and they uncover similar risk premiums across a wide range of assets, including country bond indexes, commodities, and currencies.

Still, to rely on this strategy, we must reject the CAPM’s idea that risk is rewarded. In a recent paper with the amusing title “Betting Against Betting Against Beta,” Robert Novy-Marx and Mihail Velikov (2018) disagree with the interpretation that low-beta assets offer a free lunch. But first they acknowledge the success of the paper:

Frazzini and Pedersen’s “Betting Against Beta” (2014) is an unmitigated academic success. It is, at the time of this writing, the fourth most downloaded article from the Journal of Financial Economics over the last 90 days, and its field-weighted citation impact suggests it has been cited 26 times more often than the average paper published in similar journals. Its impact on practice has been even greater. It is one of the most influential articles on “defensive equity,” a class of strategies that has seen massive capital inflows and is now a major investment category for institutional investors.

Then comes the hammer. Novy-Marx and Velikov describe the concept as a “fairly simple idea” (which may sound like an insult in the academic world, but for experienced practitioners, simple is good), and add that the risk premium’s “astonishing performance cannot be achieved in practice.” The methodology, partly because of its weighting scheme as well as how it uses leverage, “achieves its large, highly significant alpha, by hugely overweighting micro- and nano-cap stocks. . . . These stocks have limited capacity and are expensive to trade.”

Nonetheless, since its discovery several decades ago, the low-risk anomaly has persisted over time.⁴ As with most risk premiums, investors just need to temper their expectations. Good results are achievable in practice, but for due diligence purposes, they should require live track records rather than backtests.

Covered call writing, which we discussed in Chapter 7,⁵ is a strategy that delivers another risk premium with sound theoretical foundations and persistence over time: the volatility risk premium. There are several options strategies to access this risk premium, and it works across asset classes. The big picture is that investors who sell insurance get compensated over time, in exchange for exposure to tail risk. They can (and should) also hedge directional market risk. With such a “delta hedging” program, they capture the difference between implied and realized volatility. This difference tends to be positive across markets and over time, but it is also sensitive to tail events.

The Diversification Argument, Once Again

Part of the appeal (and the hype) behind risk premiums as building blocks for portfolio construction is their low correlation with each other and with traditional asset classes. The main reason for this low correlation, of course, is that most risk premiums employ short positions. Yet many of them, as we discussed in Chapter 9 in the context of our research on when diversification fails, are “long carry,” “long credit,” or “short optionality,” which means they have implied equity beta, especially when markets sell off.

The study titled “Value and Momentum Everywhere” (2013) by Cliff Asness, Toby Moskowitz, and Lasse Heje Pedersen shows the power of diversification across risk premiums. When the authors combine value and momentum strategies across markets (individual US, UK, European, and Japanese stocks, equity country indexes, currencies, global government bonds, and commodity futures), they obtain a stratospheric, hardly-ever-seen-in-practice Sharpe (return-to-risk) ratio of 1.59.

Of note, value and momentum strategies that invest from the top down, across countries’ indexes, government bonds, and currencies, are essentially a form of systematic GTAA (global tactical asset allocation). These strategies are often referred to as “style premiums” because they differ from other risk premiums that are constructed as long-short portfolios of individual stocks. A carry factor—which is another way to measure value—can be added to style premium strategies to capitalize on the predictive power of yields that we discussed in Chapter 2.

Backtest Buyer Beware

Risk premium strategies are too easy to build. It has been estimated that there are at least 300 published factors, with roughly 40 newly discovered factors announced each year.⁶ In the real world, it’s not that easy to beat markets on a risk-adjusted basis. In the paper “Will Your Factor Deliver?” (2016), Noah Beck, Jason Hsu, Vitali Kalesnik, and Helge Kostka explain the issue as follows:

Few serious investors are likely to believe that all the 300-odd factor strategies would actually deliver reliable premiums in the future. Aside from a few egregious cases of research “mistakes” in which a claimed factor premium could not be replicated by other researchers, there are many other reasons to question the validity of the various exotic new sources of excess returns, which some academics mock as a “zoo of factors.” Skeptics argue that many of the documented factor premiums are the fruit of massive, intentional data mining.

After they apply several robustness tests, which include a more realistic assessment of transaction costs, they find that size and quality, two of the most prominent risk premiums, show “weak robustness,” while momentum, illiquidity, and low beta are more robust. But they add that “liquidity- demanding factors, such as illiquidity and momentum, are associated with significantly higher trading costs than other factors. Investors may be better off accessing these factors through active management rather than indexation.”

Even well-intentioned researchers often fall into the trap of data mining/overfitting. And when they don’t, they most likely rely on prior studies that were data-mined.⁷ Out-of-sample backtests are never truly out-of-sample, because researchers can look at simulated results and tweak their models to improve performance. Even if model inputs rely only on data that would have been available at the time, researchers get several passes at history. Wouldn’t it be nice in the real world to be able to say: “Wait, I think I should have bought the top 5 and bottom 5 stocks instead of the top 10 and bottom 10, and I should have weighted them based on volatility rather than use equal weights. Let’s ask Doctor Strange⁸ to reverse time, so I can get another pass”? In such a world, we’d see as many realized Sharpe ratios of 1.5 as we see in paper backtests.

To be fair, it can be useful to look at backtest data to improve a model, if we have a good reason to believe the improvement is going to work in the future. Data mining is not a black-and-white issue. It’s tricky. It helps if we can add truly out-of-sample analysis, with untouched data from another time period or from another market.

But another issue with risk premiums is that they can get crowded. As investors pile on these strategies, performance deteriorates. In the paper “Does Academic Research Destroy Stock Return Predictability,” R. David McLean and Jeffrey Pontiff (2016) show that after publication, risk premium performance deteriorates by 58%. They attribute 26% of this deterioration to data mining and the remaining 32% to crowding, or “publication-informed trading.” They also raise two other red flags related to risk premium backtests: postpublication declines are greater for predictors with higher in-sample returns, and returns are higher for portfolios concentrated in stocks with high idiosyncratic risk and low liquidity.

Risk factors won’t replace asset classes for portfolio construction. Investors should use the factor approach in risk models and roll up factor-based risk forecasts to the asset class level. (They can continue to use asset class–based portfolio optimization tools.) They should consider small allocations to risk premiums if they believe they can identify a handful of robust strategies. These risk premiums provide access to long-short portfolios and dynamic, uncorrelated sources of returns. But if someone shows you a backtest, don’t buy all the hype. Ask for a live track record and the theoretical foundations behind the risk premiums, as well as an analysis of tail risks and tail correlations—and be mindful of crowding.

Notes

1.   For example, in “Factor Investing and Asset Allocation: A Business Cycle Perspective” (2016), we show that adding sector, regional, and currency effects improves the CAPM’s fit to month-to-month data.

2.   See, for example, Fama and French (1992 and 2012) and Asness, Moskowitz, and Pedersen (2013).

3.   For a recent review of the literature on momentum, see Dhankar and Maheshwari (2016).

4.   A quick overview of the massive literature on the subject is available at https://en.wikipedia.org/wiki/Low-volatility_anomaly.

5.   Page 102 provides references.

6.   See Beck et al. (2016) and Harvey, Liu, and Zhu (2016).

7.   See McQueen and Thorley (1999).

8.   My son Charlie is 11, and he’s a Marvel fan, so I’m “forced” to sit through comic book movies with him. At least, that’s my excuse.