Building on decades of factor research

In an idealized world, risk factors should be independent of each other, yield positive risk premia, and form a complete set that spans all dimensions of risk and explains the systematic risks for assets in a given class. In practice, these requirements hold only approximately, and there are important correlations between different factors. For instance, momentum is often stronger among smaller firms (Hou, Xue, and Zhang, 2015). We will show how to derive synthetic, data-driven risk factors using unsupervised learning—in particular, principal and independent component analysis —in Chapter 13, Data-Driven Risk Factors and Asset Allocation with Unsupervised Learning.

In this section, we will review a few key factor categories prominent in financial research and trading applications, explain their economic rationale, and present metrics typically used to capture these drivers of returns.

In the next section, we will demonstrate how to implement some of these factors using NumPy and pandas, use the TA-Lib library for technical analysis, and demonstrate how to evaluate factors using the Zipline backtesting library. We will also highlight some factors built into Zipline that are available on the Quantopian platform.

Momentum and sentiment – the trend is your friend

Momentum investing is among the most well-established factor strategies, underpinned by quantitative evidence since Jegadeesh and Titman (1993) for the US equity market. It follows the adage: the trend is your friend or let your winners run. Momentum factors are designed to go long on assets that have performed well, while going short on assets with poor performance over a certain period. Clifford Asness, the founder of the $200 billion hedge fund AQR, presented evidence for momentum effects across eight different asset classes and markets much more recently (Asness, Moskowitz, and Pedersen, 2013).

The premise of strategies using this factor is that asset prices exhibit a trend, reflected in positive serial correlation. Such price momentum defies the hypothesis of efficient markets, which states that past price returns alone cannot predict future performance. Despite theoretical arguments to the contrary, price momentum strategies have produced positive returns across asset classes and are an important part of many trading strategies.

The chart in Figure 4.2 shows the historical performance of portfolios formed based on their exposure to various alpha factors (using data from the Fama-French website). The factor winner minus loser (WML) represents the difference in performance between portfolios containing US stocks in the top and bottom three deciles, respectively, of the prior 2-12 months of returns:

Figure 4.2: Returns on various risk factors

The momentum factor dramatically outperformed other prominent risk factors up to the 2008 crisis. The other factors include the high-minus-low (HML) value factor, the robust-minus-weak (RMW) profitability factor, and the conservative-minus-aggressive (CMA) investment factor. The equity premium is the difference between the market return (for example, the S&P 500) and the risk-free rate.

Why might momentum and sentiment drive excess returns?

Reasons for the momentum effect point to investor behavior, persistent supply and demand imbalances, a positive feedback loop between risk assets and the economy, or the market microstructure.

The behavioral rationale reflects the biases of underreaction (Hong, Lim, and Stein, 2000) and over-reaction (Barberis, Shleifer, and Vishny, 1998) to market news as investors process new information at different speeds. After an initial under-reaction to news, investors often extrapolate past behavior and create price momentum. The technology stocks rally during the late 90s market bubble was an extreme example. A fear and greed psychology also motivates investors to increase exposure to winning assets and continue selling losing assets (Jegadeesh and Titman, 2011).

Momentum can also have fundamental drivers such as a positive feedback loop between risk assets and the economy. Economic growth boosts equities, and the resulting wealth effect feeds back into the economy through higher spending, again fueling growth. Positive feedback between prices and the economy often extends momentum in equities and credit to longer horizons than for bonds, FOEX, and commodities, where negative feedback creates reversals, requiring a much shorter investment horizon. Another cause of momentum can be persistent demand-supply imbalances due to market frictions. One example is the delay of commodity production in adjusting to changing demand. Oil production may lag higher demand from a booming economy for years, and persistent supply shortages can trigger and support upward price momentum (Novy-Marx, 2015).

Over shorter, intraday horizons, market microstructure effects can also create price momentum as investors implement strategies that mimic their biases. For example, the trading wisdom to cut losses and let profits run has investors use trading strategies such as stop-loss, constant proportion portfolio insurance (CPPI), dynamical delta hedging, or option-based strategies such as protective puts. These strategies create momentum because they imply an advance commitment to sell when an asset underperforms and buy when it outperforms.

Similarly, risk parity strategies (see the next chapter) tend to buy low-volatility assets that often exhibit positive performance and sell high-volatility assets that often have had negative performance (see the Volatility and size anomalies section later in this chapter). The automatic rebalancing of portfolios using these strategies tends to reinforce price momentum.

How to measure momentum and sentiment

Momentum factors are typically derived from changes in price time series by identifying trends and patterns. They can be constructed based on absolute or relative return by comparing a cross-section of assets or analyzing an asset's time series, within or across traditional asset classes, and at different time horizons.

A few popular illustrative indicators are listed in the following table (see the Appendix for formulas):

Additional sentiment indicators include the following metrics; inputs like analyst estimates can be obtained from data providers like Quandl or Bloomberg, among others:

There are also numerous data providers that aim to offer sentiment indicators constructed from social media, such as Twitter. We will create our own sentiment indicators using natural language processing in Part 3 of this book.

Value factors – hunting fundamental bargains

Stocks with low prices relative to their fundamental value tend to deliver returns in excess of a capitalization-weighted benchmark. Value factors reflect this correlation and are designed to send buy signals for undervalued assets that are relatively cheap and sell signals for overvalued assets. Hence, at the core of any value strategy is a model that estimates the asset's fair or fundamental value. Fair value can be defined as an absolute price level, a spread relative to other assets, or a range in which an asset should trade.

Relative value strategies

Value strategies rely on the mean-reversion of prices to the asset's fair value. They assume that prices only temporarily move away from fair value due to behavioral effects like overreaction or herding, or liquidity effects such as temporary market impact or long-term supply/demand friction. Value factors often exhibit properties opposite to those of momentum factors because they rely on mean-reversion. For equities, the opposite of value stocks is growth stocks that have a high valuation due to growth expectations.

Value factors enable a broad array of systematic strategies, including fundamental and market valuation and cross-asset relative value. They are often collectively labeled statistical arbitrage (StatArb) strategies, implemented as market-neutral long/short portfolios without exposure to other traditional or alternative risk factors.

Fundamental value strategies

Fundamental value strategies derive fair asset values from economic and fundamental indicators that depend on the target asset class. In fixed income, currencies, and commodities, indicators include levels and changes in the capital account balance, economic activity, inflation, or fund flows. For equities and corporate credit, value factors go back to Graham and Dodd's previously mentioned Security Analysis. Equity value approaches compare a stock price to fundamental metrics such as book value, top-line sales, bottom-line earnings, or various cash-flow metrics.

Market value strategies

Market value strategies use statistical or machine learning models to identify mispricing due to inefficiencies in liquidity provision. Statistical and index arbitrage are prominent examples that capture the reversion of temporary market impacts over short time horizons. (We will cover pairs trading in Chapter 9, Time-Series Models for Volatility Forecasts and Statistical Arbitrage). Over longer time horizons, market value trades also leverage seasonal effects in equities and commodities.

Cross-asset relative value strategies

Cross-asset relative value strategies focus on mispricing across asset classes. For example, convertible bond arbitrage involves trades on the relative value between the bond that can be turned into equity and the underlying stock of a single company. Relative value strategies also include trades between credit and equity volatility, using credit signals to trade equities or trades between commodities and related equities.

Why do value factors help predict returns?

There are both rational and behavioral explanations for the existence of the value effect, defined as the excess return on a portfolio of value stocks relative to a portfolio of growth stocks, where the former have a low market value and the latter have a high market value relative to fundamentals. We will cite a few prominent examples from a wealth of research (see, for example, Fama and French, 1998, and Asness, Moskowitz, and Pedersen, 2013).

In the rational, efficient markets view, the value premium compensates for higher real or perceived risks. Researchers have presented evidence that value firms have less flexibility to adapt to the unfavorable economic environments than leaner and more flexible growth companies, or that value stock risks relate to high financial leverage and more uncertain future earnings. Value and small-cap portfolios have also been shown to be more sensitive to macro shocks than growth and large-cap portfolios (Lakonishok, Shleifer, and Vishny, 1994).

From a behavioral perspective, the value premium can be explained by loss aversion and mental accounting biases. Investors may be less concerned about losses on assets with a strong recent performance due to the cushions offered by prior gains. This loss aversion bias induces investors to perceive the stock as less risky than before and discount its future cash flows at a lower rate. Conversely, poor recent performance may lead investors to raise the asset's discount rate.

These differential return expectations can produce a value premium: growth stocks with a high price multiple relative to fundamentals have done well in the past, but investors will require a lower average return going forward due to their biased perception of lower risks, while the inverse is true for value stocks.

How to capture value effects

A large number of valuation proxies are computed from fundamental data. These factors can be combined as inputs into a machine learning valuation model to predict asset prices. The following examples apply to equities, and we will see how some of these factors are used in the following chapters:

Chapter 2, Market and Fundamental Data – Sources and Techniques, discussed how you can source the fundamental data used to compute these metrics from company filings.

Volatility and size anomalies

The size effect is among the older risk factors and relates to the excess performance of stocks with a low market capitalization (see Figure 4.2 at the beginning of this section). More recently, the low-volatility factor has been shown to capture excess returns on stocks with below-average volatility, beta, or idiosyncratic risk. Stocks with a larger market capitalization tend to have lower volatility so that the traditional size factor is often combined with the more recent volatility factor.

The low volatility anomaly is an empirical puzzle that is at odds with the basic principles of finance. The capital asset pricing model (CAPM) and other asset pricing models assert that higher risk should earn higher returns (as we will discuss in detail in the next chapter), but in numerous markets and over extended periods, the opposite has been true, with less risky assets outperforming their riskier peers.

Figure 4.3 plots a rolling mean of the S&P 500 returns of 1990-2019 against the VIX index, which measures the implied volatility of at-the-money options on the S&P 100. It illustrates how stock returns and this measure of volatility have moved inversely with a negative correlation of -.54 over this period. In addition to this aggregate effect, there is also evidence that stocks with a greater sensitivity to changes in the VIX perform worse (Ang et al. 2006):

Figure 4.3: Correlation between the VIX and the S&P 500

Why do volatility and size predict returns?

The low volatility anomaly contradicts the hypothesis of efficient markets and the CAPM assumptions. Several behavioral explanations have been advanced to explain its existence.

The lottery effect builds on empirical evidence that inpiduals take on bets that resemble lottery tickets with a small expected loss but a large potential win, even though this large win may have a fairly low probability. If investors perceive that the risk-return profile of a low price, volatile stock is like a lottery ticket, then it could be an attractive bet. As a result, investors may overpay for high-volatility stocks and underpay for low-volatility stocks due to their biased preferences.

The representativeness bias suggests that investors extrapolate the success of a few, well-publicized volatile stocks to all volatile stocks while ignoring the speculative nature of such stocks.

Investors may also be overconfident in their ability to forecast the future, and their differences in opinions are higher for volatile stocks with more uncertain outcomes. Since it is easier to express a positive view by going long—that is, owning an asset—than a negative view by going short, optimists may outnumber pessimists and keep driving up the price of volatile stocks, resulting in lower returns.

Furthermore, investors behave differently during bull markets and crises. During bull markets, the dispersion of betas is much lower so that low-volatility stocks do not underperform much, if at all, whereas during crises, investors seek or keep low-volatility stocks and the beta dispersion increases. As a result, lower volatility assets and portfolios do better over the long term.

How to measure volatility and size

Metrics used to identify low-volatility stocks cover a broad spectrum, with realized volatility (standard deviation) on one end and forecast (implied) volatility and correlations on the other end. Some operationalize low volatility as low beta. The evidence in favor of the volatility anomaly appears robust for different metrics (Ang, 2014).

Quality factors for quantitative investing

Quality factors aim to capture the excess returns reaped by companies that are highly profitable, operationally efficient, safe, stable, and well-governed—in short, high quality. The markets also appear to reward relative earnings certainty and penalize stocks with high earnings volatility.

A portfolio tilt toward businesses with high quality has been long advocated by stock pickers that rely on fundamental analysis, but it is a relatively new phenomenon in quantitative investments. The main challenge is how to define the quality factor consistently and objectively using quantitative indicators, given the subjective nature of quality.

Strategies based on standalone quality factors tend to perform in a counter-cyclical way as investors pay a premium to minimize downside risks and drive up valuations. For this reason, quality factors are often combined with other risk factors in a multi-factor strategy, most frequently with value to produce the quality at a reasonable price strategy.

Long-short quality factors tend to have negative market beta because they are long quality stocks that are also low volatility, and short more volatile, low-quality stocks. Hence, quality factors are often positively correlated with low volatility and momentum factors, and negatively correlated with value and broad market exposure.

Why quality matters

Quality factors may signal outperformance because superior fundamentals such as sustained profitability, steady growth in cash flow, prudent leveraging, a low need for capital market financing, or low financial risk underpin the demand for equity shares and support the price of such companies in the long run. From a corporate finance perspective, a quality company often manages its capital carefully and reduces the risk of over-leveraging or over-capitalization.

A behavioral explanation suggests that investors under-react to information about quality, similar to the rationale for momentum, where investors chase winners and sell losers.

Another argument for quality premia is a herding argument, similar to growth stocks. Fund managers may find it easier to justify buying a company with strong fundamentals, even when it is getting expensive, rather than a more volatile (risky) value stock.

How to measure asset quality

Quality factors rely on metrics computed from the balance sheet and income statement, which indicate profitability reflected in high profit or cash flow margins, operating efficiency, financial strength, and competitiveness more broadly because it implies the ability to sustain a profitability position over time.

Hence, quality has been measured using gross profitability (which has been recently added to the Fama–French factor model; see Chapter 7, Linear Models – From Risk Factors to Return Forecasts), return on invested capital, low earnings volatility, or a combination of various profitability, earnings quality, and leverage metrics, with some options listed in the following table.

Earnings management is mainly exercised by manipulating accruals. Hence, the size of accruals is often used as a proxy for earnings quality: higher total accruals relative to assets make low earnings quality more likely. However, this is not unambiguous as accruals can reflect earnings manipulation just as well as accounting estimates of future business growth:

Equipped with a high-level categorization of alpha factors that have been shown to be associated with abnormal returns to varying degrees, we'll now start developing our own financial features from market, fundamental, and alternative data.