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We survey recent methodological contributions in asset pricing using factor models and machine learning. We organize these results based on their primary objectives: estimating expected returns, factors, risk exposures, risk premia, and the stochastic discount factor, as well as model comparison and alpha testing. We also discuss a variety of asymptotic schemes for inference. Our survey is a guide for financial economists interested in harnessing modern tools with rigor, robustness, and power to make new asset pricing discoveries, and it highlights directions for future research and methodological advances.

Machine learning for asset management faces a unique set of challenges that differ markedly from other domains where machine learning has excelled. Understanding these differences is critical for developing impactful approaches and realistic expectations for machine learning in asset management. We discuss a variety of beneficial use cases and potential pitfalls, and emphasize the importance of economic theory and human expertise for achieving success through financial machine learning.

We use a large cross-section of equity returns to estimate a rich affine model of equity prices, dividends, returns and their dynamics. Using the model, we price dividend strips of the aggregate market index, as well as any other well-diversified equity portfolio. We do not use any dividend strips data in the estimation of the model; however, model-implied equity yields generated by the model match closely the equity yields from the traded dividend forwards reported in the literature. Our model can therefore be used to extend the data on the term structure of discount rates in three dimensions: (i) over time, back to the 1970s; (ii) across maturities, since we are not limited by the maturities of actually traded dividend claims; and most importantly, (iii) across portfolios, since we generate a term structure for any portfolio of stocks (e.g., small or value stocks). The new term structure data generated by our model (e.g., separate term structures for value, growth, investment and other portfolios, observed over a span of 45 years that covers several recessions) represent new empirical moments that can be used to guide and evaluate asset pricing models.

In this article, we review the literature studying interactions between climate change and financial markets. We first discuss various approaches to incorporating climate risk in macrofinance models. We then review the empirical literature that explores the pricing of climate risks across a large number of asset classes, including real estate, equities, and fixed income securities. In this context, we also discuss how investors can use these assets to construct portfolios that hedge against climate risk. We conclude by proposing several promising directions for future research in climate finance.

We reconsider the idea of trend-based predictability using methods that flexibly learn price patterns that are most predictive of future returns, rather than testing hypothesized or pre-specified patterns (e.g., momentum and reversal). Our raw predictor data are images—stock-level price charts—from which we elicit the price patterns that best predict returns using machine learning image analysis methods. The predictive patterns we identify are largely distinct from trend signals commonly analyzed in the literature, give more accurate return predictions, translate into more profitable investment strategies, and are robust to a battery of specification variations. They also appear context-independent: Predictive patterns estimated at short time scales (e.g., daily data) give similarly strong predictions when applied at longer time scales (e.g., monthly), and patterns learned from US stocks predict equally well in international markets.

Stock momentum, long-term reversal, and other past return characteristics that predict future returns also predict future realized betas, suggesting these characteristics capture time-varying risk compensation. We formalize this argument with a conditional factor pricing model. Using instrumented principal components analysis, we estimate latent factors with time-varying factor loadings that depend on observable firm characteristics. We show that factor loadings vary significantly over time, even at short horizons over which the momentum phenomenon operates (one year), and this variation captures reliable conditional risk premia missed by other factor models commonly used in the literature. Our estimates of conditional risk exposure can explain a sizable fraction of momentum and long-term reversal returns and can be used to generate even stronger return predictions.

We propose a new latent factor conditional asset pricing model. Like Kelly, Pruitt, and Su (KPS, 2019), our model allows for latent factors and factor exposures that depend on covariates such as asset characteristics. But, unlike the linearity assumption of KPS, we model factor exposures as a flexible nonlinear function of covariates. Our model retrofits the workhorse unsupervised dimension reduction device from the machine learning literature—autoencoder neural networks—to incorporate information from covariates along with returns themselves. This delivers estimates of nonlinear conditional exposures and the associated latent factors. Furthermore, our machine learning framework imposes the economic restriction of no-arbitrage. Our autoencoder asset pricing model delivers out-of-sample pricing errors that are far smaller (and generally insignificant) compared to other leading factor models.

Due to their short lifespans and migrating moneyness, options are notoriously difficult to study with the factor models commonly used to analyze the risk-return trade-off in other asset classes. Instrumented principal components analysis solves this problem by tracking contracts in terms of their pricing-relevant characteristics via time-varying latent factor loadings. We find that a model with three latent factors prices the cross-section of option returns and explains more than 85% of the variation in a panel of monthly S&P 500 option returns from 1996 to 2017. In particular, we show that the IPCA factors can be rationalized via an economically plausible three-factor model consisting of a level, slope and skew factor. Finally, out-of-sample trading strategies based on insights from the IPCA model have significant alpha over previously studied option strategies. Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

We study the pricing of shocks to uncertainty and volatility using a wide-ranging set of options contracts covering a variety of different markets. If uncertainty shocks are viewed as bad by investors, they should carry negative risk premia. Empirically, however, uncertainty risk premia are positive in most markets. Instead, it is the realization of large shocks to fundamentals that has historically carried a negative premium. In other words, we find that the return premium for gamma is negative while that for vega is positive. These results imply that it is jumps, for which exposure is measured by gamma, not forward-looking uncertainty shocks, measured by vega, that drive investors' marginal utility. In further support of the jump interpretation, the return patterns are more extreme for deeper out of the money options.

We propose and implement a procedure to dynamically hedge climate change risk. We extract innovations from climate news series that we construct through textual analysis of newspapers. We then use a mimicking portfolio approach to build climate change hedge portfolios. We discipline the exercise by using third-party ESG scores of firms to model their climate risk exposures. We show that this approach yields parsimonious and industry-balanced portfolios that perform well in hedging innovations in climate news both in sample and out of sample. We discuss multiple directions for future research on financial approaches to managing climate risk.

We perform a comparative analysis of machine learning methods for the canonical problem of empirical asset pricing: measuring asset risk premia. We demonstrate large economic gains to investors using machine learning forecasts, in some cases doubling the performance of leading regression-based strategies from the literature. We identify the best performing methods (trees and neural networks) and trace their predictive gains to allowance of nonlinear predictor interactions that are missed by other methods. All methods agree on the same set of dominant predictive signals which includes variations on momentum, liquidity, and volatility. Improved risk premium measurement through machine learning simplifies the investigation into economic mechanisms of asset pricing and highlights the value of machine learning in financial innovation.

Stock momentum, long-term reversal, and other past return characteristics that predict future returns also predict future realized betas, suggesting these characteristics capture time-varying risk compensation. We formalize this argument with a conditional factor pricing model. Using instrumented principal components analysis, we estimate latent factors with time-varying factor loadings that depend on observable firm characteristics. We show that factor loadings vary significantly over time, even at short horizons over which the momentum phenomenon operates (one year), and this variation captures reliable conditional risk premia missed by other factor models commonly used in the literature. Our estimates of conditional risk exposure can explain a sizable fraction of momentum and long-term reversal returns and can be used to generate even stronger return predictions.

We study how sophisticated investors, when faced with changes in information environment, adjust their information acquisition and trading behavior, and how these changes in turn affect market efficiency. We find that, after exogenous reductions of analyst coverage due to closures of brokerage firms, hedge funds scale up information acquisition. They trade more aggressively and earn higher abnormal returns on the affected stocks. Moreover, the participation of hedge fund significantly mitigates the impairment of market efficiency caused by coverage reductions. Our results show a substitution effect between sophisticated investors and public information providers in facilitating market efficiency in a causal framework.

In this article, the authors document robust momentum behavior in a large collection of 65 widely studied characteristic-based equity factors around the globe. They show that, in general, individual factors can be reliably timed based on their own recent performance. A time series “factor momentum” portfolio that combines timing strategies of all factors earns an annual Sharpe ratio of 0.84. Factor momentum adds significant incremental performance to investment strategies that employ traditional momentum, industry momentum, value, and other commonly studied factors. Their results demonstrate that the momentum phenomenon is driven in large part by persistence in common return factors and not solely by persistence in idiosyncratic stock performance.

We use textual analysis of high-dimensional data from patent documents to create new indicators of technological innovation. We identify important patents based on textual similarity of a given patent to previous and subsequent work: these patents are distinct from previous work but are related to subsequent innovations. Our importance indicators correlate with existing measures of patent quality but also provide complementary information. We identify breakthrough innovations as the most important patents—those in the right tail of our measure—and construct time-series indices of technological change at the aggregate and sectoral level. Our technology indices capture the evolution of technological waves over a long time span (1840 to the present) and cover innovation by private and public firms, as well as non-profit organizations and the US government. Advances in electricity and transportation drive the index in the 1880s; chemicals and electricity in the 1920s and 1930s; and computers and communication in the post-1980s.

We propose a new modeling approach for the cross section of returns. Our method, Instrumented Principal Components Analysis (IPCA), allows for latent factors and time-varying loadings by introducing observable characteristics that instrument for the unobservable dynamic loadings. If the characteristics/expected return relationship is driven by compensation for exposure to latent risk factors, IPCA will identify the corresponding latent factors. If no such factors exist, IPCA infers that the characteristic effect is compensation without risk and allocates it to an "anomaly" intercept. Studying returns and characteristics at the stock-level, we find that four IPCA factors explain the cross section of average returns significantly more accurately than existing factor models and produce characteristic-associated anomaly intercepts that are small and statistically insignificant. Furthermore, among a large collection of characteristics explored in the literature, only eight are statistically significant in the IPCA specification and are responsible for nearly 100% of the model's accuracy. Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

An ever increasing share of human interaction, communication, and culture is recorded as digital text. We provide an introduction to the use of text as an input to economic research. We discuss the features that make text different from other forms of data, offer a practical overview of relevant statistical methods, and survey a variety of applications.

We propose a method for constructing conditional option return distributions. In our model, uncertainty about the future option return has two sources: Changes in the position and shape of the implied volatility surface that shift option values (holding moneyness and maturity fixed), and changes in the underlying price which alter an option's location on the surface and thus its value (holding the surface fixed). We estimate a joint time series model of the spot price and volatility surface and use this to construct an ex ante characterization of the option return distribution via bootstrap. Our "ORB" (option return bootstrap) model accurately forecasts means, variances, and extreme quantiles of S&P 500 index conditional option return distributions across a wide range of strikes and maturities. We illustrate the value of our approach for practical economic problems such as risk management and portfolio choice. We also use the model to illustrate the risk and return tradeoff throughout the options surface conditional on being in a high or low risk state of the world. Comparing against our less structured but more accurate model predictions helps identify misspecification of risks and risk pricing in traditional no-arbitrage option models with stochastic volatility and jumps.

The pricing of corporate credit can be succinctly understood via the credit-implied volatility (CIV) surface. We invert it each month from the firm-by-maturity panel of CDS spreads via the Merton model, transforming CDS spreads into units of asset volatility. The CIV surface facilitates direct comparison of credit spreads at different "moneyness" (firm leverage) and time to maturity. We use this framework to organize the behavior of corporate credit markets into three stylized facts. First, CIV exhibits a steep moneyness smirk: Low leverage (out-of-the money) CDS trade at a large implied volatility premium relative to highly levered (at-the-money) CDS, holding all other firm characteristics fixed. Second, the dynamics of credit spreads can be described with three clearly interpretable factors driving the entire CIV surface. Third, the cross section of CDS risk premia is fully explained by exposures to CIV surface shocks. Using a structural model for joint asset behavior of all firms, we show that the shape of the CIV surface implies that aggregate asset growth is subject to stochastic volatility and severe, time-varying downside tail risk. Lastly, we explore CIV of other credit instruments including corporate bonds and sovereign CDS.

We document a form of excess volatility that is irreconcilable with standard models of prices, even after accounting for variation in discount rates. We compare prices of claims on the same cash flow stream but with different maturities. Standard models impose precise internal consistency conditions on the joint behavior of long and short maturity claims and these are strongly rejected in the data. In particular, long maturity prices are significantly more variable than justified by the behavior at short maturities. Our findings are pervasive. We reject internal consistency conditions in all term structures that we study, including equity options, currency options, credit default swaps, commodity futures, variance swaps, and inflation swaps.

We find that shocks to the equity capital ratio of financial intermediaries—Primary Dealer counterparties of the New York Federal Reserve—possess significant explanatory power for crosssectional variation in expected returns. This is true not only for commonly studied equity and government bond market portfolios, but also for other more sophisticated asset classes such as corporate and sovereign bonds, derivatives, commodities, and currencies. Our intermediary capital risk factor is strongly pro-cyclical, implying counter-cyclical intermediary leverage. The price of risk for intermediary capital shocks is consistently positive and of similar magnitude when estimated separately for individual asset classes, suggesting that financial intermediaries are marginal investors in many markets and hence key to understanding asset prices.Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

I propose a new measure of common, time-varying tail risk for large cross sections of stock returns. Stock return tails are described by a power law in which the power law exponent is allowed to transition smoothly through time as a function of recent data. It is motivated by asset pricing theory and is estimable via quasi-maximum likelihood. Estimates indicate substantial time variation in stock return tails, and that the risk of extreme returns rises in weak economic conditions.

We empirically analyze the pricing of political uncertainty, guided by a theoretical model of government policy choice. To isolate political uncertainty, we exploit its variation around national elections and global summits. We find that political uncertainty is priced in the equity option market as predicted by theory. Options whose lives span political events tend to be more expensive. Such options provide valuable protection against the price, variance, and tail risks associated with political events. This protection is more valuable in a weaker economy and amid higher political uncertainty. The effects of political uncertainty spill over across countries.

We show that firms' idiosyncratic volatility obeys a strong factor structure and that shocks to the common factor in idiosyncratic volatility (CIV) are priced. Stocks in the lowest CIV-beta quintile earn average returns 5.4% per year higher than those in the highest quintile. The CIV factor helps to explain a number of asset pricing anomalies. We provide new evidence linking the CIV factor to income risk faced by households. These three facts are consistent with an incomplete markets heterogeneous-agent model. In the model, CIV is a priced state variable because an increase in idiosyncratic firm volatility raises the average household's marginal utility. The calibrated model matches the high degree of comovement in idiosyncratic volatilities, the CIV-beta return spread, and several other asset price moments.

This article evaluates a large collection of systemic risk measures based on their ability to predict macroeconomic downturns. We evaluate 19 measures of systemic risk in the US and Europe spanning several decades. We propose dimension reduction estimators for constructing systemic risk indexes from the cross section of measures and prove their consistency in a factor model setting. Empirically, systemic risk indexes provide significant predictive information out-of-sample for the lower tail of future macroeconomic shocks.

We forecast a single time series using many predictor variables with a new estimator called the three-pass regression filter (3PRF). It is calculated in closed form and conveniently represented as a set of ordinary least squares regressions. 3PRF forecasts converge to the infeasible best forecast when both the time dimension and cross section dimension become large. This requires only specifying the number of relevant factors driving the forecast target, regardless of the total number of common (and potentially irrelevant) factors driving the cross section of predictors. We derive inferential theory in the form of limiting distributions for estimated relevant factors, predictive coefficients and forecasts, and provide consistent standard error estimators. We explore two empirical applications that exemplify the many predictor problem: Forecasting macroeconomic aggregates with a large panel of economic indices, and forecasting stock market aggregates with many individual assets' price-dividend ratios. These, combined with a range of Monte Carlo experiments, demonstrate the 3PRF's forecasting power.

Returns and cash flow growth for the aggregate U.S. stock market are highly and robustly predictable. Using a single factor extracted from the cross section of book- to-market ratios, we find an out-of-sample return forecasting R-squared as high as 13% at the annual frequency (0.9% monthly). We document similar out-of-sample predictability for returns on value, size, momentum and industry-sorted portfolios. We present a model linking aggregate market expectations to disaggregated valuation ratios in a dynamic latent factor system. We find that spreads in growth and value portfolios’ exposures to economic shocks are key to identifying predictability and are consistent with duration-based theories of the value premium. Our findings suggest that discount rates are far less persistent, and their shocks far more volatile, than implied by leading asset pricing models.

We examine the pricing of financial crash insurance during the 2007-2009 financial crisis in U.S. option markets, and we show that a large amount of aggregate tail risk is missing from the cost of financial sector crash insurance during the crisis. The difference in costs between out-of-the-money put options for individual banks and puts on the financial sector index increases fourfold from its pre-crisis 2003-2007 level. We provide evidence that a collective government guarantee for the financial sector lowers index put prices far more than those of individual banks and explains the increase in the basket-index put spread.

Can managers influence the liquidity of their firms’ shares? We use plausibly exogenous variation in the supply of public information to show that firms actively shape their information environments by voluntarily disclosing more information than regulations mandate and that such efforts improve liquidity. Firms respond to an exogenous loss of public information by providing more timely and informative earnings guidance. Responses appear motivated by a desire to reduce information asymmetries between retail and institutional investors. Liquidity improves as a result and in turn increases firm value. This suggests that managers can causally influence their cost of capital via voluntary disclosure.

Investors in option markets price in a substantial collective government bailout guarantee in the financial sector, which puts a floor on the equity value of the financial sector as a whole, but not on the value of the individual firms. The guarantee makes put options on the financial sector index cheap relative to put options on its member banks. The basket-index put spread rises fourfold from 0.8 cents per dollar insured before the financial crisis to 3.8 cents during the crisis for deep out-of-the-money options. The spread peaks at 12.5 cents per dollar, or 70% of the value of the index put. The rise in the put spread cannot be attributed to an increase in idiosyncratic risk because the correlation of stock returns increased during the crisis. The government's collective guarantee partially absorbs financial sector-wide tail risk, which lowers index put prices but not individual put prices, and hence can explain the basket-index spread. A structural model with financial disasters quantitatively matches these facts and attributes as much as half of the value of the financial sector to the bailout guarantee during the crisis. The model solves the problem of how to measure systemic risk in a world where the government distorts market prices.

We provide evidence for the importance of information asymmetry in asset pricing by using three natural experiments. Consistent with rational expectations models with multiple assets and multiple signals, we find that prices and uninformed demand fall as asymmetry increases. These falls are larger when more investors are uninformed, turnover is larger and more variable, payoffs are more uncertain, and the lost signal is more precise. Prices fall partly because expected returns become more sensitive to liquidity risk. Our results confirm that information asymmetry is priced and imply that a primary channel that links asymmetry to prices is liquidity. (JEL G12, G14, G17, G24) Theoretical asset pricing models routinely assume that investors have heterogeneous information. The goal of this article is to establish the empirical relevance of this assumption for equilibrium asset prices and investor demands. To do so, we exploit a novel identification strategy that allows us to infer changes in the distribution of information among investors and hence to quantify the effect of information asymmetry on prices and demands. Our results suggest that information asymmetry has a substantial effect on prices and demands and affects assets through a liquidity channel. Asymmetric-information asset pricing models typically rely on a noisy rational expectations equilibrium (REE) in which prices, due to randomness in the risky asset’s supply, only partially reveal the better-informed investors’ information. Random supply might reflect the presence of “noise traders” whose demands are independent of information. Prominent examples of such models include Grossman and Stiglitz (1980), Hellwig (1980), Admati (1985), Wang (1993), and Easley and O’Hara (2004).

We present a volatility forecasting comparative study within the ARCH class of models. Our goal is to identify successful predictive models over multiple horizons and to investigate how predictive ability is influenced by choices for estimation window length, innovation distribution, and frequency of parameter re-estimation. Test assets include a range of domestic and international equity indices and exchange rates. We find that model rankings are insensitive to forecast horizon and suggestions for estimation best practices emerge. While our main sample spans 1990-2008, we take advantage of the near-record surge in volatility during the last half of 2008 to ask if forecasting models or best practices break down during periods of turmoil. Surprisingly, we find that volatility during the 2008 crisis was well approximated by predictions one-day ahead, and should have been within risk managers' 1% confidence intervals up to one month ahead.

We estimate the value added by sell-side equity research analysts and explore the links between analyst research, informational efficiency, and asset prices. We identify the value of research from exogenous changes in analyst coverage. On announcement that a stock has lost all coverage, share prices fall by around 110 basis points or $8.4 million on average. The share price reaction is attenuated the more analysts continue to cover the stock, suggesting that there are diminishing returns to coverage at the margin. The adverse effect of coverage terminations is proportional to the analyst's reputation and experience and to the size of the broker's retail sales force. Exogenous reductions in coverage are followed by: less efficient pricing and lower liquidity; greater earnings surprises and more volatile trading around subsequent earnings announcements; increases in required returns; and reduced return volatility. Simulations suggest investors can trade profitably on the volatility changes. Finally, retail investors sell and large institutional investors buy around coverage terminations, suggesting that different investor clienteles have different demands for analyst research.