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Volatility Forecasting with Fundamental Risk via Machine Learning
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This study investigates whether the direction of U.S. implied volatility, VIX index, can be forecast. Multiple forecasts are generated based on standard econometric models, but, more importantly, on several machine learning techniques. Their statistical significance is assessed by a plethora of performance evaluation measures, while real-time investment strategies are devised to appraise the investment implications of the underlying modeling approaches. The main conclusion of the analysis is that the implementation of machine learning techniques in implied volatility forecasting can be more effective compared to mainstream econometric models and model selection techniques, as they are superior both in a statistical and an economic evaluation setting.
We perform a comparative analysis of machine learning methods for the canonical problem of empirical asset pricing: measuring asset risk premiums. 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 allowing nonlinear predictor interactions missed by other methods. All methods agree on the same set of dominant predictive signals, a set that includes variations on momentum, liquidity, and volatility.
Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.
We propose a model selection method to systematically evaluate the contribution to asset pricing of any new factor, above and beyond what a high‐dimensional set of existing factors explains. Our methodology accounts for model selection mistakes that produce a bias due to omitted variables, unlike standard approaches that assume perfect variable selection. We apply our procedure to a set of factors recently discovered in the literature. While most of these new factors are shown to be redundant relative to the existing factors, a few have statistically significant explanatory power beyond the hundreds of factors proposed in the past.
We construct size and value factors in China. The size factor excludes the smallest 30% of firms, which are companies valued significantly as potential shells in reverse mergers that circumvent tight IPO constraints. The value factor is based on the earnings-price ratio, which subsumes the book-to-market ratio in capturing all Chinese value effects. Our three-factor model strongly dominates a model formed by just replicating the Fama and French (1993) procedure in China. Unlike that model, which leaves a 17% annual alpha on the earnings-price factor, our model explains most reported Chinese anomalies, including profitability and volatility anomalies.
This paper presents a comprehensive study on predicting the cross section of Chinese stock market returns with a large panel of 75 individual firm characteristics. We use not only the traditional Fama-MacBeth regression, but also the “big-data” econometric methods: principal component analysis (PCA), partial least squares (PLS), and forecast combination to extract information from all the 75 firm characteristics. These characteristics are important return predictors, with statistical and economic significance. Furthermore, firm characteristics that are related to trading frictions, momentum, and profitability are the most effective predictors of future stock returns in the Chinese stock market. Keywords: Partial least squares, Machine learning, Firm characteristics, Chinese stock market, Return predictability
We examine whether fundamental measures of volatility are incremental to market-based measures of volatility in (i) predicting bankruptcies (out of sample), (ii) explaining cross-sectional variation in credit spreads, and (iii) explaining future credit excess returns. Our fundamental measures of volatility include (i) historical volatility in profitability, margins, turnover, operating income growth, and sales growth; (ii) dispersion in analyst forecasts of future earnings; and (iii) quantile regression forecasts of the interquartile range of the distribution of profitability. We find robust evidence that these fundamental measures of volatility improve out-of-sample forecasts of bankruptcy and help explain cross-sectional variation in credit spreads. This suggests that an analysis of credit risk can be enhanced with a detailed analysis of fundamental information. As a test case of the benefit of volatility forecasting, we document an improved ability to forecast future credit excess returns, particularly when using fundamental measures of volatility.
We propose and evaluate explicit tests of the null hypothesis of no difference in the accuracy of two competing forecasts. In contrast to previously developed tests, a wide variety of accuracy measures can be used (in particular, the loss function need not be quadratic and need not even be symmetric), and forecast errors can be non-Gaussian, nonzero mean, serially correlated, and contemporaneously correlated. Asymptotic and exact finite-sample tests are proposed, evaluated, and illustrated.
We add to the emerging literature on empirical asset pricing in the Chinese stock market by building and analyzing a comprehensive set of return prediction factors using various machine learning algorithms. Contrasting previous studies for the US market, liquidity emerges as the most important predictor, leading us to closely examine the impact of transaction costs. The retail investors’ dominating presence positively affects short-term predictability, particularly for small stocks. Another feature that distinguishes the Chinese market from the US market is the high predictability of large stocks and state-owned enterprises over longer horizons. The out-of-sample performance remains economically significant after transaction costs.
Most anomalies fail to hold up to currently acceptable standards for empirical finance. With microcaps mitigated via NYSE breakpoints and value-weighted returns, 65% of the 452 anomalies in our extensive data library, including 96% of the trading frictions category, cannot clear the single test hurdle of the absolute t-value of 1.96. Imposing the higher multiple test hurdle of 2.78 at the 5% significance level raises the failure rate to 82%. Even for replicated anomalies, their economic magnitudes are much smaller than originally reported. In all, capital markets are more efficient than previously recognized.
Received June 12, 2017; editorial decision October 29, 2018 by Editor Stijn Van Nieuwerburgh. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.
What capital allocation role can China’s stock market play? Counter to perception, stock prices in China have become as informative about future profits as they are in the US. This rise in stock price informativeness has coincided with an increase in investment efficiency among privately owned firms, suggesting the market is aggregating information and providing useful signals to managers. However, price informativeness and investment efficiency for state-owned enterprises fell below that of privately owned firms after the postcrisis stimulus, perhaps reflecting unpredictable subsidies and state-directed investment policy. Finally, evidence from realized returns suggests Chinese firms face a higher cost of equity capital than US firms.
We construct a robust stochastic discount factor (SDF) summarizing the joint explanatory power of a large number of cross-sectional stock return predictors. Our method achieves robust out-of-sample performance in this high-dimensional setting by imposing an economically motivated prior on SDF coefficients that shrinks contributions of low-variance principal components of the candidate characteristics-based factors. We find that characteristics-sparse SDFs formed from a few such factors—e.g., the four- or five-factor models in the recent literature—cannot adequately summarize the cross-section of expected stock returns. However, an SDF formed from a small number of principal components performs well.
We take up Cochrane's (2011) challenge to identify the firm characteristics that provide independent information about average U.S. monthly stock returns by simultaneously including 94 characteristics in Fama-MacBeth regressions that avoid overweighting microcaps and adjust for data-snooping bias. We find that while 12 characteristics are reliably independent determinants in non-microcap stocks from 1980 to 2014 as a whole, return predictability sharply fell in 2003 such that just two characteristics have been independent determinants since then. Outside of microcaps, the hedge returns to exploiting characteristics-based predictability also have been insignificantly different from zero since 2003. (JEL G12, G14)
Managed portfolios that take less risk when volatility is high produce large alphas, increase Sharpe ratios, and produce large utility gains for mean-variance investors. We document this for the market, value, momentum, profitability, return on equity, investment, and betting-against-beta factors, as well as the currency carry trade. Volatility timing increases Sharpe ratios because changes in volatility are not offset by proportional changes in expected returns. Our strategy is contrary to conventional wisdom because it takes relatively less risk in recessions. This rules out typical risk-based explanations and is a challenge to structural models of time-varying expected returns.
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Aggregate stock return volatility is both persistent and countercyclical. This paper tests whether it is possible to improve volatility forecasts at monthly and quarterly horizons by conditioning on additional macroeconomic variables. I find that several variables related to macroeconomic uncertainty, time-varying expected stock returns, and credit conditions Granger cause volatility. It is more difficult to find evidence that forecasts exploiting macroeconomic variables outperform a univariate benchmark out-of-sample. The most successful approaches involve simple combinations of individual forecasts. Predictive power associated with macroeconomic variables appears to concentrate around the onset of recessions.
The determination of the level of corporate borrowing and the choice of debt maturity are the two most important concerns in the management of capital structure. In this study, we examine analytically and empirically the impact of debt maturity changes on the expected returns of common stocks. Using the US stock market data and financial statement data, we examine the cross-sectional relation between expected returns and financial leverage ratios. We find reliable evidence that common stock expected returns are positively related to the extent of short-term debt financing. The positive relation is significant even after we control for systematic risk, total debt ratio and firm size. The results suggest that an increase in short-term debt which displaces the same amount of long-term debt increases the expected returns of common stocks, possibly because the substitution transfers risk from long-term debtholders to shareholders.
We revisit the relation between stock market volatility and macroeconomic activity using a new class of component models that distinguish short run from secular movements. We study long historical data series of aggregate stock market volatility, starting in the 19th century, as in Schwert (1989). We formulate models with the long term component driven by inflation and industrial production growth that are at par in terms of pseudo out-of-sample prediction for horizons of one quarter and are at par or out-perform more traditional time series volatility models at longer horizons. Hence, imputing economic fundamentals into volatility models pays off in terms of long horizon forecasting. We also find that at a daily level, inflation and industrial production growth, account for between 10 % and 35 % of one-day ahead volatility prediction. Hence, macroeconomic fundamentals play a significant role even at short horizons. Unfortunately, all the models -purely time series ones as well as those driven by economic variables -feature structural breaks over the entire sample spanning roughly a century and a half of daily data. Consequently, our analysis also focuses on subsamples -pre-WWI, the Great Depression era, and post-WWII (also split to examine the so called Great Moderation). Our main findings remain valid across subsamples.
This study maintains that the value relevance of accounting information cannot be measured solely by reference to Ball-Brown (ERC) analysis. The contribution of accounting information to return volatility is equally crucial. Synthesizing and generalizing results from earlier studies, this paper rigorously develops Ball-Brown (1968) and volatility measures of the information content of earnings from underlying primitives using the accounting return decomposition model of Vuolteenaho (2002). The well-known Ball-Brown metric is obtained by assuming that (i) the time series of (log deflated) earnings is stationary AR(1), (ii) other information shocks are non-existent and (iii) expected future discount rates are inter-temporally constant. This measure is initially extended to include other information shocks and dynamic discount rates that are also stationary AR(1). Generalized Ball-Brown and variance measures of information content are further obtained where the time series of earnings, other information and expected future discount rates follow either stationary ARMA(p,q) processes or a log-linear stationary VAR process. Closed form solutions of information content are also obtained for earnings components (e.g., cash flows and accruals). Applications of the theory are offered that show how this framework improves on extant empirical methodologies and suggests further lines of research.
We investigate the joint hypothesis that (1) tax expense contains information about core profitability that is incremental to reported earnings and (2) that information is reflected in stock prices with a delay. We find that seasonally differenced quarterly tax expense, our proxy for tax expense surprise, is related positively to future returns. This anomaly is separate from previously documented pricing anomalies based on financial and tax variables. Additional investigation reveals that tax expense surprise is related positively to changes in future quarterly earnings and tax expense, and both those future changes are related positively to future returns. While the returns to investing in predictable future earnings changes has been documented before, these results suggest that predicting changes in future tax expense also generates incremental future returns.
A fundamental assumption in cost accounting is that the relation between costs and volume is symmetric for volume increases and decreases. In this study, we investigate whether costs are “sticky”—that is, whether costs increase more when activity rises than they decrease when activity falls by an equivalent amount. We find, for 7,629 firms over 20 years, that selling, general, and administrative (SG&A) costs increase on average 0.55% per 1% increase in sales but decrease only 0.35% per 1% decrease in sales. Our analysis compares the traditional model of cost behavior in which costs move proportionately with changes in activity with an alternative model in which sticky costs occur because managers deliberately adjust the resources committed to activities. We test hypotheses about the properties of sticky costs and how the degree of stickiness of SG&A costs varies with firm circumstances.
A volatility model must be able to forecast volatility; this is the central requirement in almost all financial applications. In this paper we outline some stylized facts about volatility that should be incorporated in a model: pronounced persistence and mean-reversion, asymmetry such that the sign of an innovation also affects volatility and the possibility of exogenous or pre-determined variables influencing volatility. We use data on the Dow Jones Industrial Index to illustrate these stylized facts, and the ability of GARCH-type models to capture these features. We conclude with some challenges for future research in this area.
Recent explanations of aggregate stock market fluctuations suggest that countercyclical stock market volatility is consistent with rational asset evaluations. In this paper, I develop a framework to study the causes of countercyclical stock market volatility. I find that countercyclical risk premia do not imply countercyclical return volatility. Instead, countercyclical stock volatility occurs if risk premia increase more in bad times than they decrease in good times, thereby inducing price–dividend ratios to fluctuate more in bad times than in good. The business cycle asymmetry in the investors’ attitude toward discounting future cash flows plays a novel and critical role in many rational explanations of asset price fluctuations.
Forecast evaluation often compares a parsimonious null model to a larger model that nests the null model. Under the null that the parsimonious model generates the data, the larger model introduces noise into its forecasts by estimating parameters whose population values are zero. We observe that the mean squared prediction error (MSPE) from the parsimonious model is therefore expected to be smaller than that of the larger model. We describe how to adjust MSPEs to account for this noise. We propose applying standard methods [West, K.D., 1996. Asymptotic inference about predictive ability. Econometrica 64, 1067–1084] to test whether the adjusted mean squared error difference is zero. We refer to nonstandard limiting distributions derived in Clark and McCracken [2001. Tests of equal forecast accuracy and encompassing for nested models. Journal of Econometrics 105, 85–110; 2005a. Evaluating direct multistep forecasts. Econometric Reviews 24, 369–404] to argue that use of standard normal critical values will yield actual sizes close to, but a little less than, nominal size. Simulation evidence supports our recommended procedure.
We survey and interview more than 400 executives to determine the factors that drive reported earnings and disclosure decisions. We find that managers would rather take economic actions that could have negative long-term consequences than make within-GAAP accounting choices to manage earnings. A surprising 78% of our sample admits to sacrificing long-term value to smooth earnings. Managers also work to maintain predictability in earnings and financial disclosures. We also find that managers make voluntary disclosures to reduce information risk and boost stock price but at the same time, try to avoid setting disclosure precedents that will be difficult to maintain.
This paper performs a financial statement analysis that combines a large set of financial statement items into one summary measure which indicates the direction of one-year-ahead earnings changes. Positions are taken in stocks on the basis of this measure during the period 1973–1983, which involve canceling long and short positions with zero net investment. The two-year holding-period return to the long and short positions is in the order of 12.5%. After adjustment for ‘size effects’ the return is about 7.0%. These returns cannot be explained by nominated firm risk characteristics.
This article presents a dynamic, rational expectations equilibrium model of asset prices where the drift of fundamentals (dividends)
shifts between two unobservable states at random times. I show that in equilibrium, investors' willingness to hedge against
changes in their own “uncertainty” on the true state makes stock prices overreact to bad news in good times and underreact
to good news in bad times. I then show that this model is better able than conventional models with no regime shifts to explain
features of stock returns, including volatility clustering, “leverage effects,” excess volatility, and time-varying expected
returns.
We model consumption and dividend growth rates as containing (1) a small long-run predictable component, and (2) fluctuating economic uncertainty (consumption volatility). These dynamics, for which we provide empirical support, in conjunction with Epstein and Zin's (1989) preferences, can explain key asset markets phenomena. In our economy, financial markets dislike economic uncertainty and better long-run growth prospects raise equity prices. The model can justify the equity premium, the risk-free rate, and the volatility of the market return, risk-free rate, and the price-dividend ratio. As in the data, dividend yields predict returns and the volatility of returns is time-varying. Copyright 2004 by The American Finance Association.
Lawrence R. Klein pioneered the work on aggregation, in particular in production functions, in the 1940s. He paved the way for researchers to establish the conditions under which a series of micro production functions can be aggregated so as to yield an aggregate production function. This work is fundamental in order to establish the legitimacy of theoretical (neoclassical) growth models and empirical work in this area (e.g., growth accounting exercises, econometric estimation of aggregate production functions). This is because these models depend on the assumption that the technology of an economy can be represented by an aggregate production function, i.e., that the aggregate production function exists. However, without proper aggregation one cannot interpret the properties an aggregate production function. The aggregation literature showed that the conditions under which micro production functions can be aggregated so as to yield an aggregate production function are so stringent that it is difficult to believe that actual economies can satisfy them. These results question the legitimacy of growth models and their policy implications. Scientifi c work cannot proceed as if production functions existed. For this reason, the profession should pause before continuing to do theoretical and applied work with no sound foundations and dedicate some time to studying other approaches to estimating the impact of economic policies in order to understand what questions can legitimately be posed to the empirical aggregate data. Lawrence R. Klein fue uno de los pioneros del campo de la agregaci�n, en particular en el �rea de las funciones de producci�n, durante la d�cada de los 40. Sus contribuciones ayudaron a defi nir el problema de la agregaci�n para que investigadores posteriores establecieran formalmente las condiciones formales bajo las que funciones de producci�n microecon�micas con propiedades neocl�sicas pudieran ser agregadas con el fi n de generar una funci�n
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