Guofu   Zhou



  • Options & Futures, Derivatives (BSBA, MBA and PMBA); Real Option Valuation (MBA and PMBA); Advanced Topics in Finance (EMBA); Corporate Finance (BSBA); Financial Economics I & II (PhD discrete-time theory & empirical tests, and continuous-time theory); Data Analysis for Investments (MBA and MSF, implementing, via Matlab or Python or R, advanced portfolio strategies including factor models, big data forecasting and Black-Litterman model) and Mathematical Finance (MS in Finance, pricing derivatives under diffusion and jump processes).

Research Interests:

  • Investment strategies, big data, machine learning, forecasting, technical analysis, asset allocation, anomalies, asymmetric information, asset pricing tests and econometric methods.

Professional Service:

  • Associated Editor: Journal of Financial and Quantitative Analysis, 2000-present; Journal of Financial Markets; Journal of Empirical Finance, 2016-present; Editorial Board: Journal of Portfolio Management, 2008-present, Journal of Systematic Investing, 2020–present, and International Journal of Portfolio Analysis & Management, 2011–present; Director: Asian Finance Association, 2008--2010; Program Co-Chair: 2007 and 2008 China International Conference in Finance; Program Associate Chair: 2008 Meetings of the Financial Intermediation Research Society, 2002 Western Finance Association; Program Committee: Western Finance Association Annual Meetings, 1999--2015; China International Conference in Finance, 2002--2015. Referee for more than 60 journals.

Major Academic Contributions:

(a summary of the published and forthcoming papers)
    • Machine Learning/Big Data/Bitcoin/Textual Analysis :
      • Rapach, Strauss and Zhou (2013) is perhaps the first major academic study (published in a top finance journal) that applies LASSO in finance. They use it to select predictors from a large set ("big-data") of candidates for forecasting stock markets globally.
      • Rapach, Strauss Tu, and Zhou (2019), superseding an early 2014 version, apply Lasso to forecast industry returns with their lagged values, and find information diffusion may be responsible for the significant predictability.
      • Jiang, Lee, Martin and Zhou (2019) apply textual analysis to construct a manager sentiment index from firm tone of conference calls and financial statements ("big-data"). They find that manager sentiment drives both firm aggregate investments and market returns.
      • Rapach and Zhou (2019) apply the new cross sectional ML methods of Han, He, Rapach and Zhou (2019) to time series forecasting, and find they deliver the best empirical results compared with the currently most effective ones.
      • Detzel, Liu, Strauss, Zhou and Zhu (2020) propose perhaps the first equilibrium model that shows how technical analysis can arise endogenously via rational learning, providing a theoretical foundation of using technical analysis in practice. They document that ratios of prices to their moving averages forecast daily Bitcoin returns in- and out-of sample, and similar results hold for small-cap, young-firm, and low-analyst-coverage stocks as well as NASDAQ stocks during the dotcom era.
    • CAPM and APT :
      • Harvey and Zhou (1990) provide Bayesian multivariate tests of the CAPM (The Capital Asset Pricing Model) and find the probability that the market is mean-variance efficient is quite small for a range of plausible priors.
      • Zhou (1991) provides the first exact test of the zero-beta CAPM which allows for borrowing rates be higher than the lending rates (more complex than the usual CAPM, but more realistic) and finds even this extension will not explain the market inefficiency.
      • Zhou (1993) provides a finite sample test of the CAPM, with the exact P-value computed via simulations without unknown parameters for elliptical data, including in particular normal and t-distributions.
      • Harvey and Zhou (1993) provide GMM tests of the CAPM, which is robust to general distributions.
      • Geweke and Zhou (1994) provide an exact Bayesian framework for analyzing the arbitrage pricing theory (APT) and find the pricing errors are little changed with including more factors beyond the first one (the pricing errors there may be better weighted by using the asset inverse covariance matrix so that they will be invariant to portfolio repackaging).
      • Chou and Zhou (2006) provide bootstrap tests of the CAPM, which is robust to iid distributions and more accurate than usual asymptotic tests.
      • Kan and Zhou (2017) provide asymptotic tests the CAPM under t-distributions, in which the parameter estimates are efficiently obtained by using the EM-algorithm rather than the standard inefficient OLS estimator.
    • GMM :
      • Zhou (1994) provides the first GMM tests for patterned weighting matrices that allow analytically solutions in many finance applications (cited by Matyas (1999) in his GMM book; Cochrane (2001) presents a similar GMM test in his asset pricing book).
    • SDF :
      • Kan and Zhou (1999) show that the usual SDF (stochastic discount factor) approach provides unreliable risk premium estimate, later studies resolve this problem by adding factor moment conditions for which no more analytical solutions available.
      • Kan and Zhou (2006) provide the tightest lower bound on the SDF to date, showing that well known asset models do not have enough volatility in the SDF to pass this bound.
    • Two-pass Regressions :
      • Shanken and Zhou (2007) provide formal model misppecification tests in addition to a comprehensive theoretical and small sample study of the widely used Fama and MacBeth (1973) two-pass procedure that is fundamental in understanding to what extent cross-sectional expected returns/values are explained by certain factor attributes.
      • Jagannathan, Schaumburg and Zhou (2010) provide a survey of the literature on the two-pass procedure.
      • Bai and Zhou (2015) provide both the asymptotic theory for Fama and MacBeth (1973) two-pass regressions and new biased-adjusted OLS and GLS estimators in the common N>T case.
    • Predictability :
      • Lamoureux and Zhou (1996) show that a permanent and temporary decomposition of returns renders difficulty in predictions.
      • Rapach and Strauss and Zhou (2010) provide the first empirical evidence that: the US market risk premium is consistently predictable out-of-sample; they show it with macroeconomic variables via a combination forecast approach.
      • Neely, Rapach, Tu and Zhou (2014) show further that the predictive power of technical indicators matches or exceeds that of macroeconomic variables (note that technical indicators, such as moving averages of prices, can capture fundamental information too, such as world political stability, that are reflected in prices and not yet reflected in common macro variables).
      • Kong, Rapach, Strauss and Zhou (2011) analyze the predictability of market components.
      • Rapach and Strauss and Zhou (2013) find that the US stock market leads the world markets even at the monthly frequency.
      • Rapach and Zhou (2013) provide a survey of the literature on stock return predictability.
      • Huang, Jiang, Tu and Zhou (2015) find investor sentiment is a powerful predictor of the stock market.
      • Rapach, Ringgenberg and Zhou (2016) show that the aggregated short interest is another powerful predictor.
      • Lin, Wu and Zhou (2017) provide a new iterated combination forecast method (of which the PLS is a special case), and, with this new method, they find the predictability of corporate bonds is both economically and statistically significant.
      • Zhou (1999) improves Ross upper bound on predictability implied by asset pricing theory.
      • Huang and Zhou (2017) provide substantially tighter bounds and find major asset pricing models fail to explain the empirical predictability in the data due to inadequate state variables.
      • Jiang, Lee, Martin and Zhou (2019) find that a new manager sentiment index predicts strongly aggregate investments and market returns.
      • Gao, Han, Li and Zhou (2018) discover an intraday predictive pattern: the first half-hour return on the market predicts the last half-hour return.
      • Huang, Li, Wang and Zhou (2019) show that time-series momentum (TSM), the predictability of the past 12-month return on the next one-month return, is quite weak for the large cross section of assets, altering conclusion of the literature.
      • Chen, Tang, Yao and Zhou (2020) propose an investor attention index and find its predictive power on the stock market due to likely the reversal of temporary price pressure.
    • Momentum/Technical Analysis :
      • Zhu and Zhou (2010) provide perhaps the first theoretical study to show that technical analysis, specifically the widely used moving averages, can add value to asset allocation under uncertainty about predictability or uncertainty about the true model governing the stock price.
      • Han and Yang and Zhou (2013) find that technical analysis, applied to portfolios sorted by volatility or other info proxies, can outperform the buy-and-hold strategy substantially, and yield abnormal returns over 20% annually, which cannot be explained by market timing ability, investor sentiment, default and liquidity risks.
      • Olszweski and Zhou (2014) show that combining both technicals and macro/fundamentals offers a significant improvement in risk-adjusted returns.
      • Han, Zhou and Zhu (2016) provide perhaps the first general equilibrium model on moving averages to justify their predictability, and to understand the role of technical traders; they also propose a trend factor to capture simultaneously all three stock price trends (the short-, intermediate- and long-term), which outperforms substantially existing factors, such as the momentum, by more than doubling their Sharpe ratios.
      • Gao, Han, Li and Zhou (2018) discover perhaps the first intraday momentum pattern: the first half-hour return on the market predicts the last half-hour return.
    • Anomalies :
      • Chou, Li and Zhou (2006) study how anomalies help an investor to beat the market.
      • The trend factor of Han, Zhou and Zhu (2016), based on technical analysis measures of trends across time horizons, is one of the greatest anomalies ever in terms of return and Sharpe ratio.
      • Han, Huang and Zhou (2020) provide a simple dynamic monthly trading strategy to improve substantially existing anomalies that are formed on an annual basis.
    • Asymmetry :
      • Hong, Tu and Zhou (2007) provide the first model-free test for asymmetric correlations (and betas) to see if stocks move more often with the market when the market goes down than when it goes up.
      • Jiang, Wu and Zhou (2018) provide a general asymmetry test based on entropy, and find significant asymmetry risk premium.
    • Portfolio Choice :
      • Kan and Zhou (2007) derive, for the first time, an explicit expression for the expected utility loss under parameter estimation risk for normally-distributed returns.
      • Fabozzi, Huang and Zhou (2010) provide provide a survey of the literature on robust portfolios.
      • Tu and Zhou (2011) propose portfolio strategies that beat the 1/N rule in almost all scenarios except cases when the true weights are happen to be close to 1/N.
    • Bayesian Portfolio Choice :
      • Zhou (2009) provides an extension of the popular Black-Litterman model.
      • Tu and Zhou (2004) show how to select an optimal mean-variance portfolios under a realistic t-distribution and under asset pricing model priors, and they find that, tough the utility level does not change much vs normality assumption, but portfolio weights are drastically different to achieve that.
      • Tu and Zhou (2010) show how economic objectives can serve as useful priors that yield superior portfolios, which, in particular, perform generally better than the well known 1/N rule.
      • Avramov and Zhou (2010) provide a survey of the literature on Bayesian portfolio analysis.
    • Volatility :
      • Zhou and Zhu (2010) show how to select portfolios under short- and long-term volatility risks and find huge impacts vs the commonly used one volatility factor model.
      • Zhou and Zhu (2015) extend the long-run risks model of Bansal and Yaron (2004) by allowing both a long- and a short-run volatility components in the evolution of economic fundamentals. With the extension, the new model not only is consistent with the volatility literature that the stock market is driven by two, rather than one, volatility factors, but also provides significant improvements in explaining various puzzles of equity and options data.
      • Liu, Tang and Zhou (2019) show that, contrary to some previous studies, volatility-timing strategies do not work when applied to the aggregate stock market, once correcting a look-ahead bias.
    • Active Portfolio Management :
      • Zhou (2008a, b) extends the fundamental law of active portfolio management pioneered by Grinold (1989) to the case of estimation errors and the case of conditional performance.
      • Zhou (2009) provides an extension of the popular Black-Litterman model by incorporating information from the data (such as the dynamics of how the market moves) beyond combining views with equilibrium.
    • Behavior Finance :
      • Huang, Jiang, Tu and Zhou (2015) provide a new investor sentiment index that is aligned with the purpose of predicting the aggregate stock market. By eliminating a common noise component in sentiment proxies, the new index has much greater predictive power than existing sentiment indices both in- and out-of-sample, outperforms well recognized macroeconomic variables and can also predict cross-sectional stock returns sorted by industry, size, value, and momentum.
      • Jiang, Lee, Martin and Zhou (2019) provide a manager sentiment index based on the aggregated textual tone of conference calls and financial statements. They find that manager sentiment differs from investor sentiment in driving firm aggregate investments and market returns.
      • Zhou (2018) provides a review on various measures of investor sentiment based on market, survey, and media data, respectively, and discusses various potential extensions and a number of issues for future research.
      • Chen, Tang, Yao and Zhou (2020) propose an investor attention index and find its predictive power on the stock market due to likely the reversal of temporary price pressure.
    • Household Finance :
      • Gormley, Liu and Zhou (2010) show both theoretically and empirically that insurance (of large wealth shocks) plays an important role in household investment and savings decisions.
    • Chinese Markets and Monetary Policy :
      • Jiang, Rapach, Strauss, Tu and Zhou (2011) find that the Chinese stock market is twice as predictable as the US.
      • Han, Wang, Zhou and Zou (2014) show momentum exists in China, but on a short-term basis only.
      • Fan, Li and Zhou (2013) analyze its supply factor in the Chinese bond market.
      • Fan, Jiang and Zhou (2014) provide an overview of the Chinese bond market.
      • Liu, Tu, Zou and Zhou (2018) examine impacts of China's unique monetary policies in the perspective of the DSGE Model and Taylor rule.

    Go To: (click on any of the items below or scroll down)

    Working papers


    Anomalies and the Expected Market Return

    with Xi Dong, Yan Liu and David Rapach (current Version: March, 2020).

    (On-line Appendix)

    We provide the first systematic evidence on the link between long-short anomaly portfolio returns—a cornerstone of the cross-sectional literature—and the time-series predictability of the aggregate market excess return. Using 100 representative anomalies from the literature, we employ a variety of shrinkage techniques (including machine learning, forecast combination, and dimension reduction) to efficiently extract predictive signals in a high-dimensional setting. We find that long-short anomaly portfolio returns evince statistically and economically significant out-of-sample predictive ability for the market excess return. Economically, the predictive ability of anomaly portfolio returns appears to stem from asymmetric limits of arbitrage and overpricing dominance.



    An Economic Specification Test of Asset Pricing Models with A Large Number of Assets

    with Ai He and Dashan Huang (current Version: June, 2020).

    (On-line Appendix)

    We find a pricing error profitability pattern for well-known asset pricing models: the CAPM, Fama-French, Hou-Xue-Zhang, Stambaugh-Yuan, and Daniel-Hirshleifer-Sun. A trading strategy that buys low pricing error stocks and sells high pricing error ones earns significant average and risk-adjusted returns, and it performs similarly across all the models. This fact applies to a large set of models with factors extracted from 105 anomalies. The profitability is unexplained by investor sentiment, limits-to-arbitrage, prospect theory, and expectation extrapolation, suggesting that new factors are needed to better understand the cross section of stock returns.

    Presented at 2020 AFA in San Diego; Winner of 2019 Chicago Quantitative Alliance Conference: 3rd Prize.



    Firm Characteristics and Expected Stock Returns

    with Yufeng Han, Ai He and David Rapach (current Version: July, 2020).

    We analyze the joint out-of-sample predictive ability of a comprehensive set of 299 firm characteristics for cross-sectional stock returns. We develop a cross-sectional out-of-sample R2 statistic that provides an informative measure of the accuracy of cross-sectional return forecasts in terms of mean squared forecast error. To improve cross-sectional return forecasts based on a large number of firm characteristics, we propose an E-LASSO approach that implements shrinkage in a flexible manner. Our new approach produces significant cross-sectional out-of-sample R2 gains on a consistent basis over time and provides the most accurate out-of-sample estimates of cross-sectional expected returns to date. The E-LASSO approach also generates substantial economic value in the context of long-short portfolios. Finally, we present evidence that more characteristics work better than fewer with respect to forecasting cross-sectional stock returns.

    Presented at 2019 AFA in Atlanta



    Fundamental Extrapolation and Stock Returns

    with Dashan Huang, Huacheng Zhang and Yingzi Zhu (current version: August, 2020).

    We explore the effects of fundamental extrapolation on stock returns. Empirically, we propose a novel approach to extrapolate firms' fundamental information and find that a strategy based on fundamental extrapolation earns an average return of 0.80% per month. Theoretically, we show that fundamental extrapolation has dual effects on stock price: a cash flow effect and a discount rate effect. The former pushes stock price up relative to its fundamental value, whereas the latter increases the representative investor's expected volatility and depresses today's stock price. Our empirical results suggest that the discount rate effect dominates the cash flow effect overall.



    Firm Fundamentals and the Cross Section of Implied Volatility Shapes

    with Ding Chen and Biao Guo (current Version: June, 2020).

    We investigate whether firm fundamentals can explain the shape of option implied volatility (IV) curve. Extending Geske's (1997) compound option model, we link firm fundamentals to the prices of equity and equity options, and show how the shape of IV curve can vary across firms with leverage, dividend policy and cost of capital. Using options of S&P 500 constituent companies, we show further empirically that firm fundamentals are important determinants of the IV curve even after controlling for historical volatility, risk-neutral skewness, kurtosis and systematic risk ratio. Fundamentals not only provide statistically and economically explanatory power on the IV curve, but also help reconcile with some stylized facts and puzzles.



    Trend Factor in China: The Role of Large Individual Trading

    with Yang Liu and Yingzi Zhu (current Version: May, 2020).


    We propose a 4-factor model for the Chinese stock market by adding a trend factor to Liu, Stambaugh, and Yuan's (2019) 3-factor model, which consists of the market, size, and value. Accounting for the fact that individual investors contribute about 80% of the total trading volume, the trend factor captures salient relevant price and volume trends, and earns a monthly Sharpe ratio of 0.48 --much greater than that of the market (0.11), size (0.20), and value (0.28). Our 4-factor model explains all reported Chinese anomalies --including turnover and reversal-- that are difficult to explain by existing models. Our model also outperforms strongly the replication of Fama and French's (2015) 5-factor model and Hou, Xue, and Zhang's (2015) 4-factor model in terms of both the Sharpe ratio and explanatory power. Moreover, our model can also explain mutual fund returns, working as an analogue of Carhart's (1997) 4-factor model in China.



    Volume and Return: The Role of Mispricing

    with Yufeng Han, Dashan Huang and Dayong Huang (current Version: May, 2018).

    Trading volume is positively related to future returns among underpriced stocks and negatively related to future returns among overpriced stocks. Consequently, the degree of mispricing among high volume stocks is three times as high as that among low volume stocks. This heterogenous volume-return relation is consistent with the theory of Atmaz and Basak (2018) if trading volume measures investor disagreement, whose effect on a stock's price depends on investors' average expectation bias. When the average bias is negative, the stock is undervalued and higher volume indicates more underpricing. In contrast, when the average bias is positive, the stock is overpriced and higher volume indicates more overpricing. Overall, our finding suggests that any equilibrium model on trading volume should consider its heterogeneous relation with stock returns.

    Presented at the 2018 SFS Finance Cavalcade Asia-Pacific.



    Lottery Preference and Anomalies

    with Lei Jiang, Quan Wen, and Yifeng Zhu (current version: May 2020).

    We construct a lottery factor that aggregates the information of 16 commonly used lottery features. The lottery factor significantly improves the explanatory power of the four-factor q model in Hou, Xue, and Zhang (2015) and explains all but a few major anomaly returns. In assessing the implication of lottery preference on profitability of anomaly-based trading strategies, we find that anomaly returns are significantly stronger among stocks with strong lottery preference. Moreover, the anomaly spread portfolios are mainly driven by the short leg among stocks with stronger lottery preference. The effect of lottery feature on anomalies is not driven by financial distress and is related to investors being reluctant to short sell stocks with high lottery features due to the high upside risk.



    Shrinking Factor Dimension: A Reduced-Rank Approach

    with Dashan Huang and Jiaen Li (current Version: January, 2019).

    (Matlab Program)

    (Python Program)

    (On-line Appendix)

    We propose a reduced-rank approach (RRA) to reduce a large number of factors to a few parsimonious ones. In contrast to principal component analysis and partial least squares, the RRA factors are designed to explain the cross section of stock returns, not to maximize factor variations or factor covariances with returns. Out of 70 factor proxies, we find that the number of RRA factors, which are the best linear combinations of the 70, improves little in model performance beyond a number of 5. The five RRA factors outperform the Fama-French (2015) five factors for pricing industry portfolios, and also do better than the Hou, Xue and Zhang (2015) four factors. But the RAA factor models do not gain much for pricing individual stocks. Our results suggest that new factors are wanted to reduce pricing errors at the firm level.

    Presented at Booth-EDHEC-RFS conference "New Methods for the Cross Section" in Chicago in September, 2018.


    Investor Sentiment and the Cross-Section of Corporate Bond Returns

    with Xu Guo, Hai Lin and Chunchi Wu (current version: September, 2019).

    This paper constructs an investor sentiment measure at both individual bond and aggregate levels, uncovering the first evidence that investor sentiment has strong cross- sectional predictive power for corporate bond returns. High bond investor sentiment leads to low future returns. A portfolio that longs low sentiment bonds and shorts high sentiment ones generates an average monthly return of 0.87% for top-quality bonds and 1.48% for speculative-grade bonds. The results are robust to controlling for risk factors and bond characteristics. The cross-sectional predictability of bond returns is countercyclical, and the predictability appears to stem from its predictive power on macroeconomic conditions.



    Exchange Rate Prediction with Machine Learning and a Smart Carry Trade Portfolio

    with Ilias Filippou, David Rapach and Mark Taylor (current version: August, 2020)


    We establish the predictability of monthly exchange rates via machine learning techniques, made possible with 70 predictors capturing country characteristics, global economic variables, and their interactions. To guard against overfitting, we use the elastic net to estimate panel predictive regressions and find that the resulting forecast consistently outperforms the naive no-change benchmark, which has proven difficult to beat in the literature. The forecast also markedly improves the performance of a carry trade portfolio, especially during and after the global financial crisis. When we allow for more complex deep learning models, nonlinearities do not appear substantial in the data.



    An Information Factor: Can Informed Traders Make Abnormal Profits?

    with Matthew Ma, Xiumin Martin and Matthew Ringgenberg (current Version: September, 2019).

    We construct an information factor (INFO) using the informed stock buying of corporate insiders and the informed selling of short sellers and option traders. INFO strongly predicts future stock returns -- a long-short portfolio formed on INFO earns monthly alphas of 1.24%, substantially outperforming existing strategies including momentum. INFO explains hedge fund returns in the time-series and cross-section. Higher values of INFO are associated with increases in aggregate hedge fund value. Moreover, funds with higher covariation between their returns and INFO outperform by 0.28% per month. The results show information processing skill is an important source of return variation.



    Twin Momentum: Fundamental Trends Matter

    with Dashan Huang, Huacheng Zhang and Yingzi Zhu (current version: January, 2019).

    (On-line Appendix)

    Using time-series trends of a set of firms’ major fundamentals, we find that there is a fundamental momentum in the stock market. Buying stocks in the top quintile of fundamental trends and selling stocks in the bottom quintile earns a monthly average return of 0.88%, whose magnitude is comparable to price momentum. Combining price momentum and fundamental momentum produces a twin momentum, earning an average return that exceeds the sum of the two momentum returns. Our results show that firm fundamental trends play an economically much more important role than previously thought. Theoretically, we show that investors can learn from fundamental trends about future stock returns in an equilibrium model, providing an economic rationale for fundamental momentum.



    Extracting Information from Corporate Yield Curve: A Machine Learning Approach

    (with Xu Guo, Hai Lin and Chunchi Wu current version: January, 2019).

    (Data and SAS Program)

    (Internet Appendix)

    We document strong evidence on the cross-sectional predictability of corporate bond returns based on 48 yield predictors that capture the information in the yield curve one to 48 months ahead. In addition to standard regression forecasts, we generate forecasts based on machine learning, which improves the forecast performance especially for junk bonds, and find that short- and long-term predictors are most informative. Return predictability is economically and statistically significant, and is robust to various controls. The pronounced bond anomaly uncovered in this paper joins a host of equity anomalies that challenge rational pricing models.

    Presented at 2018 EFA in Warsaw



    Are Bond Returns Predictable with Real-Time Macro Data?

    with Dashan Huang, Fuwei Jiang, and Guoshi Tong (current version: March, 2019).

    We reaffirm the stylized fact that bond risk premia are time-varying with macroeconomic condition, even with real-time macro data instead of commonly used final revised data. While real-time data are noisier and render standard forecasts insignificant, we find that, with four efficient target-driven methods, they still contain enough information to predict bond returns significantly both in- and out-of-sample. The predictability can also yield substantial economic value to a mean-variance investor. Moreover, the factors extracted from real-time data predict future macroeconomic condition. Consistent with asset pricing theory, the predicted bond returns are countercyclical.



    Scaled PCA: A New Approach to Dimension Reduction

    with Dashan Huang, Fuwei Jiang, Kunpeng Li, and Guoshi Tong (current version: March, 2020).

    We propose a novel modification to the popular principal component analysis (PCA) by scaling each predictor with its predictive slope on the target to be forecasted. Unlike the PCA that maximizes the common variation of predictors, our scaled PCA, sPCA, puts more weights on those predictors that have stronger forecasting power. Asymptotically, we provide a set of sufficient conditions under which the sPCA forecast outperforms the PCA and partial least squares (PLS) forecasts. Simulated and real data show that the sPCA forecast outperforms the PCA forecast in general, and performs similarly as, and in some cases better than, the PLS forecast.



    Recovering the FOMC Risk Premium

    with Hong Liu and Xiaoxiao Tang (current version: April 2020).

    The Federal Open Market Committee (FOMC) meetings have significant impact on market returns. We propose a methodology to recover the risk premium associated with FOMC meetings from option prices. We also estimate the sizes of upward/downward market price jumps after an imminent FOMC meeting. In our empirical analysis, with observed price data for 67 meetings and with data backed out via machine learning for the remaining 109 meetings from 1996 to 2017, we find that the risk premium varies from 15 to 88 basis points (bps), with an average of 38 bps which is consistent with the average realized returns documented in the literature. The average upward jump size is 103 bps, and the average downward jump size is 87 bps.



    Momentum, Reversal, and the Firm Fundamental Cycle

    with Yufeng Han Zhaodan Huang, Weidong Tian (current version: Nov 2018).

    We link momentum and long-run return reversal to the cyclic behavior of firm fundamentals, which are represented by a fundamental index that summarizes succinctly and efficiently a broad range of business activities at firm level. In responding to repeated unanticipated positive (negative) shocks in fundamentals, investors continue to raise (lower) prices for winner (loser) firms, yielding momentum. However, due to the cyclicality of firm fundamentals, the unanticipated positive (negative) shocks decrease in magnitude overtime and eventually reverse, generating the reversal pattern. In addition, we find that firm fundamentals can explain stronger momentum in microcap stocks, and a long/short decile portfolio based on the firm fundament index outperforms the popular momentum portfolio substantially by doubling the Sharpe ratio and does not suffer crashes.

    Best Paper Award, The World Finance Conference, 2019



    Sparse Macro Factors

    with David Rapach (current version: January, 2019).

    We use machine learning to estimate sparse principal components (PCs) for 120 monthly macro variables spanning 1960:02 to 2018:06 from the FRED-MD database. For comparison, we also extract the first ten conventional PCs from the macro variables. Each of the conventional PCs is a linear combination of all the underlying macro variables, making them difficult to interpret. In contrast, each of the sparse PCs is a sparse linear combination, whose active weights allow for intuitive economic interpretations of the sparse PCs. The first ten sparse PCs can be interpreted as yields, inflation, production, housing, employment, yield spreads, wages, optimism, money, and credit. Innovations to the conventional (sparse) PCs constitute a set of conventional (sparse) macro factors. Robust tests indicate that only one of the conventional macro factors earns a significant risk premium. In contrast, three of sparse macro factors—corresponding to yields, housing, and optimism—earn significant risk premia. Compared to leading risk factors from the literature, mimicking portfolios for the yields, housing, and optimism factors deliver sizable Sharpe ratios. A four-factor model comprised of the market factor and mimicking portfolio returns for the yields, housing, and optimism factors performs on par with or better than leading multifactor models from the literature in accounting for numerous anomalies in cross-sectional stock returns.

    Best paper award, Inquire UK and Inquire Europe, 2019



    Employee Sentiment and Stock Returns

    with Jian Chen, Guohao Tang and Jiaquan Yao (current version: May, 2020).

    We propose an employee sentiment index, which complements investor sentiment and manager sentiment indices, and find that high employee sentiment predicts a subsequent low market return, significant both in- and out-of-sample. The predictability of the employee sentiment index can also deliver sizable economic gains for mean-variance investors in asset allocation. The employee sentiment’s impact is stronger among employees who work in the headquarters state and among less experienced employees. The economic driving force of the predictability is distinct from those of investor sentiment and manager sentiment: high employee sentiment leads to high contemporaneous wage growth due to immobility, which in turn results in subsequently lower firm cash flow and lower stock return.



    Optimal Portfolio Choice with Estimation Risk: No Risk-free Asset Case

    with Raymond Kan and Xiaolu Wang (current version: March, 2020).

    (Internet Appendix)

    For the popular mean-variance portfolio choice problem in the case without a risk-free asset, we develop a new optimal portfolio rule that is designed to mitigate estimation risk. We compare its out-of-sample performance, both theoretically and empirically, with that of other portfolio rules. In both calibrations and real datasets, we show that our new rule performs well relative to others. In addition, we derive the exact distribution of the out-of-sample returns and obtain explicit expressions for the out-of-sample expected utilities of various optimal portfolio rules, which offer analytical insights into portfolio construction and performance evaluation.



    Corporate Activities and the Market Risk Premium

    with Erik Lie, Bo Meng and Yiming Qian (current version: October, 2017).

    While existing asset pricing studies focus on macroeconomic variables to predict stock market risk premium, we find that an aggregate index of corporate activities has substantially greater predictive power both in- and out-of sample, and yields much greater economic gain for a mean-variance investor. The predictive ability of the corporate index stems from its information content about future cash flows. Cross-sectionally, the corporate index performs particularly well for stocks with great information asymmetry.



    Sentiment Across Asset Markets

    with Dashan Huang, Heikki Lehkonen and Kuntara Pukthuanthong (current version: June, 2018)

    In this paper, we study investor sentiment in five major asset markets: stocks, bonds, commodities, currencies, and housing. Based on Thomson Reuter's sentiment measures extracted from 235 news and social media sources, we find that each market is predicted by its own sentiment. Cross-markets, kitchen sink regressions reveal that the stock market is influenced only by bond sentiment, while bond market is affected just by currency market, which is largely unexplained by others; the commodities are related to currencies and housing, and housing can be predicted by stock and bond sentiment. In an efficient information aggregation by the partial least square (PLS), the predictability of each market increases substantially by using information of all markets vs using only its own sentiment.



    Cost Behavior and Stock Returns

    with Dashan Huang, Fuwei Jiang and Jun Tu (current version: April, 2017).

    This paper shows that investors do not fully incorporate cost behavior information into valuation. Firms with higher growth in operating costs generate substantially lower future stock returns. A long-short spread portfolio earns an average return of about 12% per year after controlling for extant risk factors and firm characteristics. Mean-variance spanning tests show that an investor can benefit from investing in this spread portfolio in addition to well-known factors. Firms with high cost growth also suffer from deteriorations in future operating performance. The negative cost growth-return relation is much stronger around earnings announcement days, among firms with lower investor attention, higher idiosyncratic volatility, and higher transaction costs, suggesting that investor underreaction and limits to arbitrage mainly drive the effect.



    Taming Momentum Crashes: A Simple Stop-loss Strategy

    with Yufeng Han and Yingzi Zhu (current version: August, 2015).

    In this paper, we propose a stop-loss strategy to limit the downside risk of the well-known momentum strategy. At a stop-level of 10%, we find, with data from January 1926 to December 2013, that the maximum monthly losses of the equal- and value-weighted momentum strategies go down from -49.79% to -11.36% and from -64.97% to -23.28%, while the Sharpe ratios are more than doubled at the same time. We also provide a general equilibrium model of stop-loss traders and non-stop traders and show that the market price differs from the price in the case of no stop-loss traders by a barrier option.



    Which Hedge Fund Styles Hedge Against Bad Times?

    with Charles Cao and David Rapach (current Version: February, 2015).

    We examine hedge fund style performance in bad versus good times defined as (1) up and down equity market regimes derived from the 200-day moving average of the S&P 500 price index or (2) nonstressed and stressed financial market regimes determined endogenously using the Federal Reserve Bank of Kansas City Financial Stress Index and threshold estimation. We show that hedge fund styles often exhibit significant changes in risk factor exposures across good and bad times. For certain hedge fund styles, changes in factor exposures represent valuable hedges against bad times; in contrast, other hedge fund styles become more exposed to risk factors during bad times in a manner that magnifies downside risk exposure. In the context of “balanced” 40-30-30 portfolios that allocate across U.S. stocks, bonds, and individual hedge fund styles, we find that the Global Macro, Managed Futures, and Multi-Strategy styles provide investors with especially valuable hedges against bad times.



    Forecasting Bond Risk Premia Using Technical Indicators

    with Jeremy Goh, Fuwei Jiang, and Jun Tu (current Version: July, 2013).

    While economic variables have been used extensively to forecast the U.S. bond risk premia, little attention has been paid to the use of technical indicators which are widely employed by practitioners. In this paper, we fill this gap by studying the predictive ability of using a variety of technical indicators vis-a-vis the economic variables. We find that the technical indicators have statistically and economically significant in- and out-of-sample forecasting power. Moreover, we find that utilizing information from both technical indicators and economic variables substantially increases the forecasting performances relative to using just economic variables.



    Forecasting Stock Returns During Good and Bad Times

    with Dashan Huang, Fuwei Jiang and Jun Tu (current version: May, 2015).

    We show that stock returns can be significantly predicted by past realized returns in both good and bad times, in and out of sample. We extend the model in Fama and French (1988) to show that stock returns display mean reversion and momentum over time, which is dependent on the market state. Specifically, past stock returns predict future returns negatively in good times and positively in bad times, which is consistent consistent with the change and level effects in P´astor and Stambaugh (2009).



    Hansen-Jagannathan Distance: Geometry and Exact Distribution

    with Raymond Kan; November, 2002.

    This paper provides an in-depth analysis of the Hansen-Jagannathan (HJ) distance, which is a measure that is widely used for diagnosis of asset pricing models, and also as a tool for model selection. In the mean and standard deviation space of portfolio returns, we provide a geometric interpretation of the HJ-distance. In relation to the traditional regression approach of testing asset pricing models, we show that the HJ-distance is a scaled version of the aggregate pricing errors, and it is closely related to Shanken's (1985) cross-sectional regression test (CSRT) statistic, with the only major difference in how the zero-beta rate is estimated. For the statistical properties, we provide the exact distribution of the sample HJ-distance and also a simple numerical procedure for computing its distribution function. In addition, we propose a new test of equality of HJ-distance for two nested models. Simulation evidence shows that the asymptotic distribution for sample HJ-distance is grossly inappropriate for typical number of test assets and time series observations, making the small sample analysis empirically relevant.


    Toward a Better Understanding of the Beta Method and the Stochastic Discount Factor Method

    with Raymond Kan; May, 2002.

    In a standardized factor model, Kan and Zhou (1999) show the stochastic discount factor (SDF) method yields less efficient estimates than the beta method when both are based on the generalized method of moments (GMM). By modifying the common use of the SDF [via adding more moment conditions to the practice before the publication of Kan and Zhou (1999)], Jagannathan and Wang (2001) and Cochrane (2000a,b) find that the two methods have the same asymptotic variance for the new GMM estimator (which no longer admits analytical solution). Moreover, their analysis relies on a joint normality assumption of both the asset returns and factors. In this paper, we show that: 1) once the normality assumption is relaxed, the modified SDF method is highly sensitive to factor skewness and kurtosis whereas the beta method is not, implying that the SDF estimates can be less reliable in realistic situations where the factors are leptokurtic; 2) in conditional asset pricing models, the modified SDF is in general still strictly dominated by the beta method in terms of estimation accuracy; 3) while it is not well understood and almost never used in the SDF formulation of an asset pricing model, the maximum likelihood method is well defined and has both strictly more efficient estimates and more powerful tests than the SDF method; 4) the SDF tests can have much less power than the beta method in conditional asset pricing models. In short, while the SDF set-up is an elegant theoretical formation, empirical estimation and tests should pay as much attention to the beta method as to the SDF if not more (one more reason is that, as shown by Jagannathan and Wang (2001), estimated model pricing errors have smaller variance by using the beta method than the SDF one).


    A Book


    Financial Economics

    with Frank Fabozzi and Ted Neave.

    A book of intermediate level, for advanced undergrads, MBAs, practitioners, and non-finance PhDs who want to learn more the economic theory and intuition without too much technical proofs or too many abstract concepts.

    Wiley, November, 2011.

    (Solution Manual and Support)



    Publications     (Note: All the pdf files of the articles below are the sole copyright of the respective publishers, and are provided here for educational use and information only.)



    Unspanned Global Macro Risks in Bond Returns

    with Feng Zhao and Xiaoneng Zhu (current version: August, 2020)


    We examine the macro-spanning hypothesis for bond returns in international markets. Based on a large panel of real-time macro economic variables that are not subject to revisions, we find that global macro factors have predictive power for bond returns unspanned by yield factors. Furthermore, we estimate macro finance term structure models with the unspanned global macro factors and find that the global macro factors influence the market prices of level and slope risks and induce co-movements in forward term premia in global bond markets.

    Management Science, forthcoming.



    Investor Attention and Stock Returns

    with Jian Chen, Guohao Tang and Jiaquan Yao (current version: August, 2020)


    (Attention Index data from Jan., 1980 to Dec., 2017)

    We propose an investor attention index based on proxies in the literature, and find that it predicts the stock market risk premium significantly, both in-sample and out-of-sample, while every proxy individually has little predictive power. The index is extracted by using the partial least squares, but the results are similar by using the scaled principal component analysis. Moreover, the index can deliver sizable economic gains for mean-variance investors in asset allocation. The predictive power of the investor attention index stems primarily from the reversal of temporary price pressure and from the stronger forecasting ability for high-variance stocks.

    Journal of Financial and Quantitative Analysis, forthcoming.



    Anomalies Enhanced: A Portfolio Re-balancing Approach

    with Yufeng Han and Dayong Huang (current version: March, 2019).

    (Internet Appendix)

    Many anomalies are based on firm characteristics and are rebalanced yearly, ignoring any information during the year. In this paper, we provide dynamic trading strategies to rebalance the anomaly portfolios monthly. For eight major anomalies, we find that these dynamic trading strategies substantially enhance their economic importance, with improvements in the Fama and French (2015) five-factor risk-adjusted abnormal return ranging from 0.40% to 0.75% per month. The results are robust to a number of controls. Our findings indicate that many well known anomalies are more profitable than previously thought, yielding new challenges for their theoretical explanations.

    Financial Management, forthcoming.



    Learning and Predictability via Technical Analysis: Evidence from Bitcoin and Stocks with Hard-to-Value Fundamentals

    with Andrew Detzel, Hong Liu, Jack Strauss and Yingzi Zhu (current version: January, 2020).

    What predicts returns on assets with "hard-to-value" fundamentals, such as Bitcoin and stocks in new industries? We propose perhaps the first equilibrium model that justifies the use of technical analysis endogenously via rational learning. We document that ratios of prices to their moving averages forecast daily Bitcoin returns in- and out-of-sample. Trading strategies based on these ratios generate an economically significant alpha and Sharpe ratio gains relative to a buy-and-hold position. Similar results hold for small-cap, young-firm, and low-analyst-coverage stocks as well as NASDAQ stocks during the dotcom era.

    Financial Management, forthcoming.



    Time-Series and Cross-Sectional Stock Return Forecasting: New Machine Learning Methods

    with David Rapach (current Version: August, 2019).

    This paper extends the machine learning methods developed in Han, He, Rapach and Zhou (2019) for forecasting cross-sectional stock returns to a time-series context. The methods use the elastic net to refine the simple combination return forecast from Rapach et al. (2010). In a time-series application focused on forecasting the US market excess return using a large number of potential predictors, we find that the elastic net refinement substantively improves the simple combination forecast, thereby providing one of the best market excess return forecasts to date. We also discuss the cross-sectional return forecasts developed in Han et al. (2019), highlighting how machine learning methods can be used to improve combination forecasts in both the time-series and cross-sectional dimensions. Overall, because many important questions in finance are related to time-series or cross-sectional return forecasts, the machine learning methods discussed in this paper should provide valuable tools to researchers and practitioners alike.

    "Machine Learning in Asset Management" (edited by Emmanuel Jurczenko, Wiley, 2020), 1--33.



    Time-Series Momentum: Is It There?

    with Dashan Huang. Jiangyuan Li, and Liyao Wang (current Version: April, 2019).

    (Data and Matlab Program)

    (Python Program)

    (Internet Appendix)

    Discussions at Alpha Architect)

    Time-series momentum (TSM), which refers to the predictability of the past 12-month return on the next one-month return, is the focus of quite a few recent influential studies. This paper shows, however, that asset by asset time-series regressions reveal little TSM both in- and out-of-sample. In a pooled regression, the usually used t-statistic can over-reject the no predictability hypothesis, and three versions of bootstrap corrected t-statistics show that there is no TSM. From an investment perspective, although the TSM strategy is known to be profitable, it performs the same as a similar strategy based on historical mean that does not require predictability. Overall, the evidence on TSM is quite weak, especially for the large cross section of assets.

    Journal of Financial Economics 135, 2020, 774--794.



    Stock Return Asymmetry: Beyond Skewness

    with Lei Jiang, Ke Wu, and Yifeng Zhu (current version: October, 2018).

    In this paper, we propose two asymmetry measures for stock returns. Unlike the popular skewness measure, our measures are based on the distribution function of the data rather than just the third central moment. We present empirical evidence that greater upside asymmetries calculated using our new measures imply lower average returns in the cross-section of stocks. In contrast, when using the skewness measure, the relationship between asymmetry and returns is inconclusive.

    Journal of Financial and Quantitative Analysis 55, 2020, 357--386



    Volatility-Managed Portfolio: Does It Really Work?

    with Fang Liu and Xiaoxiao Tang (current Version: December, 2018).

    (Data and Program)

    (On-line Appendix)

    In this article, the authors find that a typical application of volatility-timing strategies to the stock market suffers from a look-ahead bias, despite existing evidence on successes of the strategies at the stock level. After correcting the bias, the strategy becomes very difficult to implement in practice as its maximum drawdown is 68.93% in almost all cases. Moreover, the strategy outperforms the market only during the financial crisis period. The authors also consider three alternative volatility-timing strategies and find that they do not outperform the market either. Their results show that one cannot easily beat the market via timing the market alone.

    Journal of Portfolio Management 46 (1), 2019, 38--51



    Industry Return Predictability: A Machine Learning Approach

    with David Rapach, Jack Strauss and Jun Tu (current Version: 2019).

    (Internet Appendix)

    We use machine learning tools to analyze industry return predictability based on the information in lagged industry returns. Controlling for post-selection inference and multiple testing, we find significant in-sample evidence of industry return predictability. Lagged returns for the financial sector and commodity- and material-producing industries exhibit widespread predictive ability, consistent with the gradual diffusion of information across economically linked industries. Out-of-sample industry return forecasts that incorporate the information in lagged industry returns are economically valuable: controlling for systematic risk using leading multifactor models from the literature, an industry-rotation portfolio that goes long (short) industries with the highest (lowest) forecasted returns delivers an annualized alpha of over 8%. The industry-rotation portfolio also generates substantial gains during economic downturns, including the Great Recession.

    Journal of Financial Data Science 1 (3), 2019, 9--28.



    Manager Sentiment and Stock Returns

    with Fuwei Jiang, Joshua Lee and Xiumin Martin (current version: August, 2017).

    Updated paper (November 15, 2019)

    MS Index Data (updated to December, 2017)

    MS Index Data (updated to December, 2017)

    This paper constructs a manager sentiment index based on the aggregated textual tone of corporate financial disclosures. We find that manager sentiment is a strong negative predictor of future aggregate stock market returns, with monthly in-sample and out-of-sample R-squared of 9.75% and 8.38%, respectively, which is far greater than the predictive power of other previously-studied macroeconomic variables. Its predictive power is economically comparable and is informationally complementary to existing measures of investor sentiment. Higher manager sentiment precedes lower aggregate earnings surprises and greater aggregate investment growth. Moreover, manager sentiment negatively predicts cross-sectional stock returns, particularly for firms that are difficult to value and costly to arbitrage.

    Journal of Financial Economics 132, 2019, 126--149.



    Measuring Investor Sentiment

    (current version: October, 2017).

    Investor sentiment indicates how far an asset value deviates from its economic fundamentals. In this paper, we review various measures of investor sentiment based on market, survey, and media data, respectively. While much progress has been made that contributes to our understanding of the pricing of difficult to-value assets, anomalies, and predictability, much remains to done. We discuss various potential extensions and a number of issues for future research.

    Annual Review of Financial Economics 10, 2018, 239--259.



    Forecasting Corporate Bond Returns: An Iterated Combination Approach

    (with Hai Lin and Chunchi Wu current version: June, 2016).

    (On-line Appendix)

    Using a comprehensive data set and an array of 27 macroeconomic, stock and bond predictors, we find that corporate bond returns are highly predictable based on an iterated combination model. The large set of predictors outperforms traditional predictors substantially, and predictability generated by the model is both statistically and economically significant. Stock market and macroeconomic variables play an important role in forming expected bond returns. Return forecasts are closely linked to the evolution of real economy. Corporate bond premia have strong predictive power for business cycle and the primary source of this predictive power is from the low-grade bond premium.

    Management Science 64, 2018, 4218--4238.



    Asymmetry in Stock Comovements: An Entropy Approach

    with Lei Jiang and Ke Wu (current version: June, 2017).

    (On-line Appendix)

    We provide an entropy approach for measuring asymmetric comovement between the return on a single asset and the market return. This approach yields a model-free test for stock return asymmetry, generalizing the correlation-based test proposed by Hong, Tu, and Zhou (2007). Based on this test, we find that asymmetry is much more pervasive than previously thought. Moreover, our approach also provides an entropy-based measure of downside asymmetric comovement. In the cross-section of stock returns, we find an asymmetry premium: high downside asymmetric comovement with the market indicates higher expected returns.

    Journal of Financial and Quantitative Analysis 53, 2018, 1479--1507.



    Market Intraday Momentum

    with Lei Gao, Yufeng Han and Sophia Zhengzi Li (current version: June, 2017).

    (On-line Appendix)

    Based on high frequency data of the S&P 500ETF from 1993--2013, we document an intraday momentum pattern: the first half-hour return on the market predicts the last half-hour return. The predictability, both statistically and economically significant, is stronger on more volatile days, on higher volume days, on recession days, on major macroeconomic news release days, and with more institutional trading activities. This intraday momentum is also present for ten other most actively traded domestic and international ETFs in the US, and for two major international equity index futures during their own first and last half-hours of trading. Theoretically, the intraday momentum is consistent with not only Bogousslavsky's (2016) model of portfolio infrequent rebalancing, but also a model in which some investors are late-informed and trade near the market close.

    Journal of Financial Economics 129, 2018, 394--414.



    Upper Bounds on Return Predictability

    (with Dashan Huang)

    Can the degree of predictability found in the data be explained by existing asset pricing models? We provide two theoretical upper bounds on the R-squares of predictive regressions. Using data on the market and component portfolios, we find that the empirical R-squares are significantly greater than the theoretical upper bounds. Our results suggest that the most promising direction for future research should aim to identify new state variables that are highly correlated with stock returns, instead of seeking more elaborate stochastic discount factors.

    Journal of Financial and Quantitative Analysis 52, 2017, 401--425



    Modeling Non-normality Using Multivariate t: Implications for Asset Pricing

    with Raymond Kan; October, 2016.

    Many important findings in empirical finance are based on the normality assumption, but this assumption is firmly rejected by the data due to fat tails of asset returns. In this paper, we propose the use of a multivariate t-distribution as a simple and powerful tool to examine the robustness of results that are based on the normality assumption. In particular, we find that, after replacing the normality assumption with a reasonable t-distribution, the most efficient estimator of the expected return of an asset is drastically different from the sample average return. For example, the annual difference in the estimated expected returns under normal and t is 2.964% for the Fama and French's (1993, 1996) smallest size and book-to-market portfolio. In addition, there are also substantial differences in estimating Jensen's alphas, choosing optimal portfolios, and testing asset pricing models when returns follow a multivariate t-distribution instead of a multivariate normal.

    China Finance Review International 7, 2017, 2--32.



    A Trend Factor: Any Economic Gains from Using Information over Investment Horizons?

    (with Yufeng Han and Yingzi Zhu).

    (On-line Appendix)

    Trend Factor Data of the paper, from June 1930 to Dec 2014

    Updated to Dec 2017; continues to perform well

    In this paper, we provide a trend factor that captures simultaneously all three stock price trends: the short-, intermediate- and long-term. It outperforms substantially the well-known short-term reversal, momentum and long-term reversal factors, which are based on the three price trends separately, by more than doubling their Sharpe ratios. During the recent financial crisis, the trend factor earns 0.75% per month, while the market loses -2.03% per month, the short-term reversal factor loses -0.82%, the momentum factor loses -3.88% and the long-term reversal factor barely gains 0.03%. The performance of the trend factor is robust to alternative formations and to a variety of control variables. The trends over horizons are captured by moving averages of prices whose predictive power is justified by a proposed general equilibrium model. From an asset pricing perspective, the trend factor performs well in explaining cross-section stock returns.

    Journal of Financial Economics 122, 2016, 352--375



    Short Interest and Aggregate Stock Returns

    (with David Rapach and Matthew Ringgenberg).

    (On-line Appendix)

    (Data and Matlab Program)

    (Citations by Bloomberg and other practitioner  platforms)

    We show that short interest is arguably the strongest known predictor of aggregate stock returns. Short interest outperforms a host of popular return predictors from the literature in both in-sample and out-of-sample tests, with annual in-sample and out-of-sample R2 statistics of 12% and 8%, respectively. In addition, short interest generates substantial utility gains: a mean-variance investor would be willing to pay over 300 basis points per annum to have access to the information in short interest. We employ a VAR decomposition to explore the economic source of short interest’s predictive power and find that it stems almost entirely from a cash flow channel. Overall, our evidence indicates that short sellers are informed traders who anticipate changes in future aggregate cash flows and associated changes in future market returns.

    Journal of Financial Economics 121, 2016, 46--65



    Fama-MacBeth Two-pass Regressions: Improving Risk Premia Estimates

    (with Jushan Bai)

    In this paper, we provide the asymptotic theory for the widely used Fama and MacBeth (1973) two-pass regressions in the usual case of a large number of assets. We find that the convergence of the OLS two-pass estimator depends critically on the time series sample size in addition to the number of cross-sections. To accommodate typical relatively small time series length, we propose new OLS and GLS estimators that improve the small sample performances significantly.

    Finance Research Letters 15, 2015, 31--40.



    Investor Sentiment Aligned: A Powerful Predictor of Stock Returns

    (with Dashan Huang, Fuwei Jiang and Jun Tu)

    The PLS index data updated to Dec., 2018 (done on November 18, 2019)

    The sentiment proxies updated to Dec., 2018

    We propose a new investor sentiment index that is aligned with the purpose of predicting the aggregate stock market. By eliminating a common noise component in sentiment proxies, the new index has much greater predictive power than existing sentiment indices both in- and out-of-sample, and the predictability becomes both statistically and economically significant. In addition, it outperforms well recognized macroeconomic variables and can also predict cross-sectional stock returns sorted by industry, size, value, and momentum. The driving force of the predictive power appears stemming from investors' biased belief about future cash flows.

    Review of Financial Studies, 28, 2015, 791--837.



    Macroeconomic Volatilities and Long-run Risks of Asset Prices

    (with Yingzi Zhu)

    (On-line Appendix)

    In this paper, motivated by existing and growing evidence on multiple macroeconomic volatilities, we extend the long-run risks model of Bansal and Yaron (2004) by allowing both a long- and a short-run volatility components in the evolution of economic fundamentals. With the extension, the new model is not only consistent with the volatility literature that the stock market is driven by two, rather than one, volatility factors, but also provides significant improvements in fitting various patterns of equity and options data.

    Management Science, 61, 2015, 413--430.



    Are There Trends in Chinese Stock Market? (in Chinese)

    (with Yufeng Han, Xiongjian Wang and Heng-fu Zou)

    Most stock markets world wide have the momentum effect that stock prices tend to move in the same direction half or a year ago, but not in China. This is puzzling since Chinese stock market is neither one of the most information transparent countries in the world, nor dominated by institutional investors. However, once we consider short-term trends captured by technical analysis, we do find that the Chinese stock is as trending as most other markets, say the US. The abnormal returns from short-term trend-following, the alphas, are both economically and statistically significant. Our results suggest that behavior finance and investment theory with information inefficiency are as relevant in China as they are elsewhere in the world.

    Journal of Financial Research 12, 2014, 152--163.



    Forecasting the Equity Risk Premium: The Role of Technical Indicators

    (with Christopher J. Neely, David E. Rapach and Jun Tu)

    (On-line Appendix)

    (The Data and Matlab Programs)

    Academic research has extensively used macroeconomic variables to forecast the U.S. equity risk premium, with little attention paid to the technical indicators widely employed by practitioners. Our paper fills this gap by comparing the forecasting ability of technical indicators with that of macroeconomic variables. Technical indicators display statistically and economically significant in-sample and out-of-sample forecasting power, matching or exceeding that of macroeconomic variables. Furthermore, technical indicators and macroeconomic variables provide complementary information over the business cycle: technical indicators better detect the typical decline in the equity risk premium near business-cycle peaks, while macroeconomic variables more readily pick up the typical rise in the equity risk premium near cyclical troughs. In line with this behavior, we show that combining information from both technical indicators and macroeconomic variables significantly improves equity risk premium forecasts versus using either type of information alone. Overall, the substantial countercyclical fluctuations in the equity risk premium appear well captured by the combined information in macroeconomic variables and technical indicators.

    Management Science, 60, 2014, 1772--1791.



    Strategy Diversification: Combining Momentum and Carry Strategies within a Foreign Exchange Portfolio

    (with Francis Olszweski)

    Hedge funds, such as managed futures, typically use two different types of trading strategies: technical and macro/fundamental. In this article, we evaluate the impact of combining the two strategies, and focus on, in particular, two common foreign exchange trading strategies: momentum and carry. We find evidence that combining the strategies offers a significant improvement in risk-adjusted returns. Our analysis, which uses data spanning 20 years, highlights the potential benefits of achieving strategy-level diversification. The point of the paper is to advocate the investment strategy of combining technicals with fundamentals

    Journal of Derivatives and Hedge Funds, 19, 2014, 311--320.



    Forecasting Stock Returns

    (with David Rapach)

    (Data and Matlab Programs)

    We survey the literature on stock return forecasting, highlighting the challenges faced by forecasters as well as strategies for improving return forecasts. We focus on U.S. equity premium forecastability and illustrate key issues via an empirical application based on updated data. Some studies argue that, despite extensive in-sample evidence of equity premium predictability, popular predictors from the literature fail to outperform the simple historical average benchmark forecast in out-of-sample tests. Recent studies, however, provide improved forecasting strategies that deliver statistically and economically significant out-of-sample gains relative to the historical average benchmark. These strategies—including economically motivated model restrictions, forecast combination, diffusion indices, and regime shifts—improve forecasting performance by addressing the substantial model uncertainty and parameter instability surrounding the data-generating process for stock returns. In addition to the U.S. equity premium, we succinctly survey out-of-sample evidence supporting U.S. cross-sectional and international stock return forecastability. The significant evidence of stock return forecastability worldwide has important implications for the development of both asset pricing models and investment management strategies.

    Handbook of Economic Forecasting, Volume 2A, Graham Elliott and Allan Timmermann (Eds.), Amsterdam: Elsevier (September 2013), pp. 328–383.



    A New Anomaly: The Cross-Sectional Profitability of Technical Analysis

    (with Yufeng Han and Ke Yang)

    (The early working paper version)

    In this paper, we document that an application of a moving average timing strategy of technical analysis to portfolios sorted by volatility generates investment timing portfolios that outperform the buy-and-hold strategy substantially. For high volatility portfolios, the abnormal returns, relative to the CAPM and the Fama-French three-factor models, are of great economic significance, and are greater than those from the well known momentum strategy. Moreover, they cannot be explained by market timing ability, investor sentiment, default and liquidity risks. Similar results also hold if the portfolios are sorted based on other proxies of information uncertainty.

    Journal of Financial and Quantitative Analysis, 48, 2013, 1433--1461.



    The Supply Factor in the Bond Market: Implications for Bond Risk and Return

    (with Longzhen Fan and Canlin Li)

    Recent empirical studies suggest that demand and supply factors have important effects on bond yields. Both market segmentation and preferred habitat hypothesis are used to explain these demand and supply effects. In this paper, we use an affine preferred-habitat term structure model and the unique Chinese bond market data to study these two hypotheses. Chinese bond market is unique because there exists an official term structure of lending rates, set exogenously by the government, on preferred habitat investors' alternative investments on loans. We show that demands of both the preferred-habitat investors and the arbitrageurs affect bond yields and returns. Moreover, we also find that the preferred-habitat investors' alternative investment opportunities have expected effect on bond yields and returns. We further show that the preferred-habitat and demand factors improve bond pricing and return predictability in a no-arbitrage term structure model. Variance decomposition analysis shows that the preferred-habitat factor explains an important part of bond yield variations.

    Journal of Fixed Income, 23, 2013, 62--81.



    International Stock Return Predictability: What is the Role of the United States?

    (with David E. Rapach and Jack K. Strauss)

    (On-line Appendix)

    (The Data and Matlab Programs)

    We present significant evidence of out-of-sample equity premium predictability for a host of industrialized countries over the postwar period. There are important differences, however, in the nature of equity premium predictability between the United States and other developed countries. Taken collectively, U.S. economic variables are significant out-of-sample predictors of the U.S. equity premium, while lagged international stock returns have no predictive power. In contrast, lagged international stock returns-- especially lagged U.S. returns--substantially outperform economic variables as out-of-sample equity premium predictors for non-U.S. countries, pointing to a leading role for the United States with respect to international return predictability. The leading role of the United States is consistent with information frictions in international equity markets. In addition, the predictability patterns are enhanced during economic downturns, linking return predictability to business-cycle fluctuations and the diffusion of news on macroeconomic fundamentals across countries. The leading role of the United States stands out during the recent global financial crisis: lagged U.S. stock returns deliver especially sizable gains for forecasting the monthly equity premium in other countries, evidenced by out-of-sample R2 statistics of 10% or greater, more than triple the postwar average.

    Journal of Finance, 68, 2013, 1633--1662.



    Volatility Trading: What is the Role of the Long-Run Volatility Component?

    (with Yingzi Zhu)

    In this paper, we study an investor's asset allocation problem with a recursive utility and with tradable volatility that follows a two-factor stochastic volatility model. Consistent with Liu and Pan (2003) and Egloff, Leippold, and Wu's (2009) finding under the additive utility, we show that volatility trading generates substantial hedging demand, and so the investor can benefit substantially from volatility trading. However, unlike existing studies, we find that the impact of elasticity of intertemporal substitution on investment decisions is of first-order importance in the two-factor stochastic volatility model when the investor has access to the derivatives market to optimally hedge the persistent component of the volatility shocks. Moreover, we study the economic impact of model and parameter misspecifications and find that an investor can incur substantial economic losses if he uses an incorrect one-factor model instead of the two-factor model or if he incorrectly estimates one of the key parameters in the two-factor model. In addition, we find that the elasticity of intertemporal substitution is a more sensible description of an investor's attitude toward model and parameter misspecifications than the risk aversion parameter.

    Journal of Financial and Quantitative Analysis, 47, 2012, 273--307.



    Tests of Mean-Variance Spanning

    (with Raymond Kan)

    (Matlab Programs)

    The paper presents a thorough study on the spanning: points out years old errors in the literature and provides geometrical/economic interpretations, small sample distributions and power analysis for likelihood ratio, Wald, and Lagrange multiplier tests, and a comparison among them and between the stochastic discount factor approach, in addition to a new sequential test that weighs explicitly economic significance into the size of the test.

    Annals of Economics and Finance, 13, 2012, 145-193.



    How Predictable Is the Chinese Stock Market? (in Chinese)

    (with Jiang Fuwei, David Rapach, Jack Strauss and Jun Tu)

    We analyze return predictability for the Chinese stock market, including the aggregate market portfolio and the components of the aggregate market, such as portfolios sorted on industry, size, book-to-market and ownership concentration. Considering a variety of economic variables as predictors, both in-sample and out-of-sample tests highlight significant predictability in the aggregate market portfolio of the Chinese stock market and substantial differences in return predictability across components. Among industry portfolios, Finance and insurance, Real estate, and Service exhibit the most predictability, while portfolios of small-cap, low book-to-market ratio and low ownership concentration firms also display considerable predictability. Two key findings provide economic explanations for component predictability: (i) based on a novel out-of-sample decomposition, time-varying systematic risk premiums captured by the conditional CAPM model largely account for component predictability; (ii) industry concentration significantly explain differences in return predictability across industries, consistent with the information-flow frictions emphasized by Hong, Torous, and Valkanov (2007).

    Journal of Financial Research (½ðÈÚÑо¿), 9, 2011, 107-121.



    Markowitz Meets Talmud: A Combination of Sophisticated and Naive Diversification Strategies

    (with Jun Tu)

    (The Longer 2008 EFA version)

    The modern portfolio theory pioneered by Markowitz (1952) is widely used in practice and extensively taught to MBAs. However, the estimated Markowitz's portfolio rule and most of its extensions not only underperform the naive 1/N rule (that invests equally across N assets) in simulations, but also lose money on a risk-adjusted basis in many real data sets. In this paper, we propose an optimal combination of the naive 1/N rule with one of the four sophisticated strategies--- the Markowitz rule, the Jorion (1986) rule, the MacKinlay and Pastor (2000) rule, and the Kan and Zhou (2007) rule--- as a way to improve performance. We find that the combined rules not only have a significant impact in improving the sophisticated strategies, but also outperform the 1/N rule in most scenarios. Since the combinations are theory-based, our study may be interpreted as reaffirming the usefulness of the Markowitz theory in practice.

    Journal of Financial Economics, 99, 2011, 204--215.



    Predicting Market Components Out of Sample: Asset Allocation Implications

    (with Aiguo Kong, David Rapach and Jack Strauss)

    We analyze out-of-sample return predictability for components of the aggregate market, focusing on the well-known Fama-French size/value-sorted portfolios. Employing a forecast combination approach based on a variety of economic variables and lagged component returns as predictors, we find significant evidence of out-of-sample return predictability for nearly all component portfolios. Moreover, return predictability is typically much stronger for small-cap/high book-to-market value stocks. The pattern of component return predictability is enhanced during business-cycle recessions, linking component return predictability to the real economy. Considering various component-rotation investment strategies, we show that out-of-sample component return predictability can be exploited to substantially improve portfolio performance.

    Journal of Portfolio Management, 37, 2011, 2011, 29--41.



    Cross Sectional Asset Pricing Tests

    (with Ravi Jagannathan and Ernst Schaumburg)

    A major problem in finance is to understand why different financial assets earn vastly different returns on average. In this paper, we survey various econometric approaches that have been developed to empirically examine various asset pricing models used to explain the difference in cross section of security returns. The approaches range from regressions to the generalized method of moments, and the associated asset pricing models are both conditional and unconditional. In addition, we review some of the major empirical studies.

    Annual Review of Financial Economics, 2, 2010, 49--74.



    Bayesian Portfolio Analysis

    (with Doron Avramov)

    This paper reviews the literature on Bayesian portfolio analysis. Information about events, macro conditions, asset pricing theories, and security-driving forces can serve as useful priors in selecting optimal portfolios. Moreover, parameter uncertainty and model uncertainty are practical problems encountered by all investors. The Bayesian framework neatly accounts for these uncertainties, whereas standard statistical models often ignore them. We review Bayesian portfolio studies when asset returns are assumed both independently and identically distributed as well as predictable through time. We cover a range of applications, from investing in single assets and equity portfolios to mutual and hedge funds. We also outline existing challenges for future work.

    Annual Review of Financial Economics, 2, 2010, 25--47.



    Incorporating Economic Objectives into Bayesian Priors: Portfolio Choice Under Parameter Uncertainty

    (with Jun Tu; The First Version, April 2004)

    (The Published Version)

    Economic objectives are often ignored when estimating parameters, though the loss of doing so can be substantial. This paper proposes a way to allow Bayesian priors to reflect the objectives. Using monthly returns of the Fama-French 25 size and book-to-market portfolios and their three factors from January 1965 to December 2004, we find that investment performance under the objective-based priors can be significantly different from that under alternative priors, with differences in terms of annual certainty-equivalent returns greater than 10% in many cases. In terms of out-of-sample performance, the Bayesian rules under the objective-based priors can outperform substantially some of the best rules developed in the classical framework.

    Journal of Financial and Quantitative Analysis, 45, 2010, 959--986.


    How Much Stock Return Predictability Can We Expect From an Asset Pricing Model?

    First draft, September, 2008.

    (The Published Version)

    Stock market predictability is of considerable interest in both academic research and investment practice. Ross (2005) provides a simple and elegant upper bound on the predictive regression R-squared that R2 <= (1 + R_f)2 Var(m) for a given asset pricing model with kernel m, where R_f is the riskfree rate of return. In this paper, we tighten this bound by a squared factor of the correlation between the default pricing kernel and the state variables of the economy. Since the correlation can be substantially smaller than one, our bound can be much tighter than Ross's. An empirical application illustrates that while Ross's bound is not binding, our bound does.

    Economics Letters, 108, 2010, 184--186.



    Robust Portfolios: Contributions from Operations Research and Finance

    (with Frank J. Fabozzi and Dashan Huang)

    In this paper we provide a survey of recent contributions to robust portfolio strategies from operations research and finance to the theory of portfolio selection. Our survey covers results derived not only in terms of the standard mean-variance objective, but also in terms of two of the most popular risk measures, mean-VaR and mean-CVaR developed recently. In addition, we review optimal estimation methods and Bayesian robust approaches.

    Annals of Operations Research, 176, 2010, 191--220.



    Limited Participation, Consumption, and Saving Puzzles: A Simple Explanation and the Role of Insurance

    (with Todd Gormley and Hong Liu)

    In this paper, we use a simple model to illustrate that the existence of a large, negative wealth shock and insufficient insurance against such a shock can potentially explain both the limited stock market participation puzzle and the low-consumption-high-savings puzzle that are widely documented in the literature. We then conduct an extensive empirical analysis on the relation between household portfolio choices and access to private insurance and various types of government safety nets, including social security and unemployment insurance. The empirical results demonstrate that a lack of insurance against large, negative wealth shocks is strongly correlated with lower participation rates and higher saving rates. Overall, the evidence suggests an important role of insurance in household investment and savings decisions.

    Journal of Financial Economics, 96, 2010, 331--344.


    Out-of-Sample Equity Premium Prediction: Combination Forecasts and Links to the Real Economy

    (with David Rapach and Jack Strauss)

    While a host of economic variables have been identified in the literature with the apparent in-sample ability to predict the equity premium, Welch and Goyal (2008) find that these variables fail to deliver consistent out-of-sample forecasting gains relative to the historical average. Arguing that substantial model uncertainty and instability seriously impair the forecasting ability of individual predictive regression models, we recommend combining individual model forecasts to improve out-of-sample equity premium prediction. Combining delivers statistically and economically significant out-of-sample gains relative to the historical average on a consistent basis over time. We provide two empirical explanations for the benefits of the forecast combination approach: (i) combining forecasts incorporates information from numerous economic variables while substantially reducing forecast volatility; (ii) combination forecasts of the equity premium are linked to the real economy. Top on the Most Read List as of June 2017

    Review of Financial Studies, 23, 2010, 821--862.


    Is the Recent Financial Crisis Really a `Once-in-a-century' Event?

    (with Yingzi Zhu)

    (The Longer working paper version)

    In the recent financial crisis, the Dow Jones stock market index dropped about 54% from a high of 14164.53 on October 9, 2007 to a low of 6547.05 on March 9, 2009. Alan Greenspan calls this a ``once-in-a century" crisis. While we do not know how he drew his conclusion, we show that the probability of a stock market drop of 50% from its high within a century is about 90% based on the popular random walk model of the stock prices. With a broad market index of the S&P500 and a more sophisticated asset pricing model which captures more risks in the economy, the probability rises to above 99%. The message of this paper is that a market drop of 50% or more is very likely in long-run stock market investments, and the investors should be prepared for it.

    Financial Analysts Journal, 66 (1), 2010, 24--27.


    Beyond Black-Litterman: Letting the Data Speak

    The Black-Litterman model is a popular approach for asset allocation by blending an investor's proprietary views with the views of the market. However, their model ignores the data-generating process whose dynamics can have significant impact on future portfolio returns. This paper extends, in two ways, the Black-Litterman model to allow Bayesian learning to exploit all available information-- the market views, the investor's proprietary views as well as the data. Our framework allows practitioners to combine insights from the Black-Litterman model with the data to generate potentially more reliable trading strategies and more robust portfolios. Further, we show that many Bayesian learning tools can now be readily applied to practical portfolio selections in conjunction with the Black-Litterman model.

    Journal of Portfolio Management, 36 (1), 2009, 36--45.


    What Will the Likely Range of My Wealth Be?

    (with Raymond Kan)

    The median is a better measure than the mean in evaluating the long-term value of a portfolio. However, the standard plug-in estimate of the median is too optimistic. It has a substantial upward bias that can easily exceed a factor of two. In this paper, we provide an unbiased forecast of the median of the long-term value of a portfolio. In addition, we also provide an unbiased forecast of an arbitrary percentile of the long-term portfolio value distribution. This allows us to construct the likely range of the long-term portfolio value for any given confidence level. Finally, we provide an unbiased forecast of the probability for the long-term portfolio value falling into a given interval. Our unbiased estimators provide a more accurate assessment of the long-term value of a portfolio than the traditional estimators, and are useful for long-term planning and investment.

    Financial Analysts Journal, 65 (4), 2009, 68--77.


    Technical Analysis: An Asset Allocation Perspective on the Use of Moving Averages

    (with Yingzi Zhu)

    (The Longer 2007 EFA version)

    In this paper, we analyze the usefulness of technical analysis, specifically the widely used moving average trading rule from an asset allocation perspective. We show that when stock returns are predictable, technical analysis adds value to commonly used allocation rules that invest fixed proportions of wealth in stocks. When there is uncertainty about predictability which is likely in practice, the fixed allocation rules combined with technical analysis can outperform the prior-dependent optimal learning rule when the prior is not too informative. Moreover, the technical trading rules are robust to model specification, and they tend to substantially outperform the model-based optimal trading strategies when there is uncertainty about the model governing the stock price.

    Journal of Financial Economics, 92, 2009, 519--544.


    On the Fundamental Law of Active Portfolio Management: How to Make Conditional Investments Unconditionally Optimal?

    The fundamental law of active portfolio management tells an active manager how to transform his alpha forecasts into the valued-added of his active portfolio by using a linear strategy with active positions proportional to the forecasts. This linear strategy is conditionally optimal because it is optimal each period conditional on the forecasts at that time. However, the unconditional value-added (the valued-added over the long haul or over multiple periods) is what usually the manager strives earnestly for. Under this unconditional objective, the linear strategy can approach zero value-added if the forecasts or signals have a high kurtosis. To overcome this problem, we provide an investment strategy that maximizes the unconditional value-added with the optimal use of conditional information. Our strategy is nonlinear in the forecasts, but has a simple economic interpretation. When the alpha forecasts are high, we invest less aggressively than the linear strategy, and when the forecasts are low, we invest more aggressively. In this way, we tend to smooth our value-added over time, and hence, on a risk-adjusted basis, our long-term unconditional value-added will in most cases be substantially higher than that based on the linear strategy, particularly when the alpha forecasts experience high kurtosis.

    Journal of Portfolio Management, 35 (1), 2008, 12--21.


    On the Fundamental Law of Active Portfolio Management: What Happens if Our Estimates Are Wrong?

    The fundamental law of active portfolio management pioneered by Grinold (1989) provides profound insights on the value creation process of managed funds. However, a key weakness of the law and its various extensions is that they ignore the estimation risk associated with the parameter inputs of the law. We show that the estimation errors have a substantial impact on the value-added of an actively managed portfolio, and they can easily destroy all the value promised by the law if they are not dealt with carefully. For bettering the chance of active managers to beat benchmark indices, we propose two methods, scaling and diversification, that can be used effectively to minimize the impact of the estimation errors significantly.

    Journal of Portfolio Management, 34 (4), 2008, 26--33.


    Asymmetries in Stock Returns: Statistical Tests and Economic Evaluation

    (with Yongmiao Hong and Jun Tu)

    In this paper, we provide a model-free test for asymmetric correlations in which stocks move more often with the market when the market goes down than when it goes up. We also provide such tests for asymmetric betas and covariances. In addition, we evaluate the economic significance of incorporating asymmetries into investment decisions. When stocks are sorted by size, book-to-market and momentum, we find strong evidence of asymmetry for both the size and momentum portfolios, but no evidence for the book-to-market portfolios. Moreover, the asymmetries can be of substantial economic importance for an investor with a disappointment aversion preference of Ang, Bekaert and Liu (2005). If the investors's felicity function is of the power utility form and if his coefficient of disappointment aversion is between 0.55 and 0.25, he can achieve over 2% annual certainty-equivalent gains when he switches from a belief in symmetric stock returns into a belief in asymmetric ones.

    Review of Financial Studies, 20, 2007, 1547--1581.


    Optimal Portfolio Choice with Parameter Uncertainty

    (with Raymond Kan)

    In this paper, we analytically derive the expected loss function associated with using sample means and covariance matrix of returns to estimate the optimal portfolio. Our analytical results show that the standard plug-in approach that replaces the population parameters by their sample estimates can lead to very poor out-of-sample performance. We further show that with parameter uncertainty, holding the sample tangency portfolio and the riskless asset is never optimal. An investor can benefit by holding some other risky portfolios that help reduce the estimation risk. In particular, we show that a portfolio that optimally combines the riskless asset, the sample tangency portfolio, and the sample global minimum-variance portfolio dominates a portfolio with just the riskless asset and the sample tangency portfolio, suggesting that the presence of estimation risk completely alters the theoretical recommendation of a two-fund portfolio.

    Journal of Financial and Quantitative Analysis, 42, 2007, 621--656.


    Estimating and Testing Beta Pricing Models: Alternative Methods and Their Performance in Simulations

    (with Jay Shanken)

    (A typo correction on the LR Estimator)

    In this paper, we provide a comprehensive theoretical and small sample study of the Fama and MacBeth (1973) two-pass procedure that is fundamental in understanding to what extent cross-sectional expected returns/values are explained by certain factor attributes. While existing studies use almost exclusively this procedure, we show that alternative two-pass methods can have better small sample performance. In addition, we provide tractable GMM approaches that accommodate conditional heteroscedasticity of the data. Moreover, the risk premium estimates and t-ratios of the Fama and MacBeth procedure provide no information on whether the model is misspecified or not, and they can be misleadingly interpreted if the model is indeed misspecified. We not only provide formal model misppecification tests, but also how that various estimation methods are useful in detecting model misppecification.

    Journal of Financial Economics, 84, 2007, 40--86.


    Using Bootstrap to Test Portfolio Efficiency

    (with Pin-Huang Chou)

    To facilitate wide use of the bootstrap method in finance, this paper shows by intuitive arguments and by simulations how it can improve upon existing tests to allow less restrictive distributional assumptions on the data and to yield more reliable (higher-order accurate) asymptotic inference. In particular, we apply the method to examine the efficiency of CRSP value-weighted stock index, and to test the well-known Fama and French (1993) three-factor model. We find that existing tests tend to over-reject.

    Annals of Economics and Finance, 7, 2006, 217--249.


    Portfolio Optimization under Asset Pricing Anomalies

    (with Pin-Huang Chou and Wen-Shen Li)

    Fama and French (1993) find that the SMB and the HML factors explain much of the cross-section stock returns that are unexplained by the CAPM, whereas Daniel and Titman (1997) show that it is the characteristics of the stocks that are responsible rather than the factors. But both arguments are largely based only on expected return comparisons, and little is known about how important each of the two explanations matters to an investor's investment decisions in general and portfolio optimization in particular. In this paper, we show that a mean-variance maximizing investor who exploits the asset pricing anomaly of the CAPM can achieve substantial economic gains than simply holding the market index. Indeed, using Japanese data over the period 1980-1997, we find that the optimized portfolio constructed from characteristics-based model and based on the first 200 largest stocks is the best performing one and has monthly returns more than 0.81% (10.16% annualized) over the Nikkei 225 index with no greater risk.

    Japan & The World Economy, 18, 2006, 121--142.


    A New Variance Bound on the Stochastic Discount Factor

    (with Raymond Kan)

    In this paper, we construct a new variance bound on any stochastic discount factor (SDF) of the form m=m(x) where x is a vector of random state variables. In contrast to the well known Hansen-Jagannathan bound that places a lower bound on the variance of m(x), our bound tightens it by a ratio of (1/ρx,m0)2, where ρx,m0 is the multiple correlation coefficient between x and the standard minimum variance SDF, m0. In many applications, the correlation is small, and hence our bound can be substantially tighter than Hansen-Jagannathan's. For example, when x is the gross growth rate of consumption, based on Cochrane's (2001) estimates of market volatility and ρx,m0, the new bound is 25 times greater than the Hansen-Jagannathan bound, making it much more difficult to explain the equity-premium puzzle based on existing asset pricing models. Another example is applying the new bound, with the growth rate of consumption as a state variable, to the 25 size and book-to-market sorted portfolios used by Fama and French (1993), then it is more than 100 times greater than the Hansen-Jagannathan bound.

    Journal of Business, 79, 2006, 941--961.


    Data-generating Process Uncertainty: What Difference Does It Make in Portfolio Decisions?

    (with Jun Tu)

    As the usual normality assumption is firmly rejected by the data, investors encounter a data-generating process (DGP) uncertainty in making investment decisions. In this paper, we propose a novel way to incorporate uncertainty about the DGP into portfolio analysis. We find that accounting for fat tails leads to nontrivial changes in both parameter estimates and optimal portfolio weights, but the certainty–equivalent losses associated with ignoring fat tails are small. This suggests that the normality assumption works well in evaluating portfolio performance for a mean-variance investor.

    Journal of Financial Economics, 72, 2004, 385--421.


    What Determines Expected International Asset Returns?

    (with Campbell Harvey and Bruno Solnik)

    This paper characterizes the forces that determine time-variation in expected international asset returns. We offer a number of innovations. By using the latent factor technique, we do not have to prespecify the sources of risk. We solve for the latent premiums and characterize their time-variation. We find evidence that the first factor premium resembles the expected return on the world market portfolio. However, the inclusion of this premium alone is not sufficient to explain the conditional variation in the returns. We find evidence of a second factor premium which is related to foreign exchange risk. Our sample includes new data on both international industry portfolios and international fixed income portfolios. We find that the two latent factor model performs better in explaining the conditional variation in asset returns than a prespecified two factor model. Finally, we show that differences in the risk loadings are important in accounting for the cross-sectional variation in the international returns.

    Annals of Economics and Finance, 3, 2002, 83--127.


    On Rate of Convergence of Discrete-time Contingent Claims

    (with Steve Heston)

    This paper characterizes the rate of convergence of discrete-time multinomial option prices. We show that it depends on the smoothness of option payoff function, and is much lower than commonly believed because the payoff functions are often all-or-nothing type and not continuously differentiable. We propose two methods, one of which is to smooth the payoff function, that help to yield the same rate of convergence as smooth payoff functions.

    Mathematical Finance, 10, 2000, 53--75.


    Investment Horizon and the Cross Section of Expected Returns: Evidence from the Tokyo Stock Exchange

    (with Pin-Huang Chou and Yuan-Lin Hsu)

    Using data from the Tokyo Stock Exchange, we study how beta, size, and ratio of book to market equity (BE/ME) account for the cross-section of expected stock returns over different lengths of investment horizons. We find that beta, adjusted for infrequent trading or not, fails to explain the cross-section of monthly expected returns, but does a much better job for horizons over half- and one-year. However, either the size or the BE/ME alone is still a significant factor in explaining the cross-section expected returns, but the size significantly diminishes for longer horizons when beta is included as an additional independent variable.

    Annals of Economics and Finance, 1, 2000, 79--100.


    Security Factors as Linear Combinations of Economic Variables

    A new framework is proposed to find the best linear combinations of economic variables that optimally forecast security factors. In particular, we obtain such combinations from Chen et al. (Journal of Business 59, 383--403, 1986) five economic variables, and obtain a new GMM test for the APT which is more robust than existing tests. In addition, by using Fama and French's (1993) five factors, we test whether fewer factors are sufficient to explain the average returns on 25 stock portfolios formed on size and book-to-market. While inconclusive in-sample, a three-factor model appears to perform better out-of-sample than both four- and five-factor models.

    Journal of Financial Markets, 2, 1999, 403--432.


    Testing Multi-beta Pricing Models

    (with Raja Velu)

    This paper presents a complete solution to the estimation and testing of multi-beta models by providing a small sample likelihood ratio test when the usual normality assumption is imposed and an almost analytical GMM test when the normality assumption is relaxed. Using 10 size portfolios from January 1926 to December 1994, we reject the joint efficiency of the CRSP value-weighted and equal-weighted indices. We also apply the tests to analyze a new version of Fama and French [Fama, E.F., French, K.R. 1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33, 3–-56] three-factor model in addition to two standard ones, and find that the new version performs the best.

    Journal of Empirical Finance, 6, 1999, 219--241.


    A Critique of the Stochastic Discount Factor Methodology

    (with Raymond Kan)

    In this paper, we point out that the widely used stochastic discount factor (SDF) methodology ignores a fully specified model for asset returns. As a result, it suffers from two potential problems when asset returns follow a linear factor model. The first problem is that the risk premium estimate from the SDF methodology is unreliable. The second problem is that the specification test under the SDF methodology has very low power in detecting misspecified models. Traditional methodologies typically incorporate a fully specified model for asset returns, and they can perform substantially better than the SDF methodology.

    Journal of Finance, 54, 1999, 1021--1048.


    Going to Extremes: Correcting Simulation Bias in Exotic Option Valuation

    (with Phil Dybvig and David Beaglehole)

    Monte Carlo simulation is widely used in practice to value exotic options for which analytical formulas are not available. When valuing those options that depend on extreme values of the underlying asset, convergence of the standard simulation is slow as the time grid is refined, and even a daily simulation interval produces unacceptable errors. This article suggests approximating the extreme value on a subinterval by a random draw from the known theoretical distribution for an extreme of a Brownian bridge on the same interval. This approach provides reliable option values and retains the flexibility of simulations, in that it allows great freedom in choosing a price process for the underlying asset or a joint process for the asset price, its volatility, and other asset prices.

    Financial Analysts Journal, 53, 1997, 62--68.


    Temporary Components of Stock Returns: What Do the Data Tell Us?

    (with Chris Lamoureux)

    Within the past few years several articles have suggested that returns on large equity portfolios may contain a significant predictable component at horizons 3 to 6 years. Subsequently, the tests used in these analyses have been criticized (appropriately) for having widely misunderstood size and power, rendering the conclusions inappropriate. This criticism however has not focused on the data, it addressed the properties of the tests. In this article we adopt a subjectivist analysis - treating the data as fixed - to ascertain whether the data have anything to say about the permanent/temporary decomposition. The data speak clearly and they tell us that for all intents and purposes, stock prices follow a random walk.

    Review of Financial Studies, 9, 1996, 1033--1059.


    Measuring the Pricing Error of the Arbitrage Pricing Theory

    (with John Geweke)

    This article provides an exact Bayesian framework for analyzing the arbitrage pricing theory (APT). Based on the Gibbs sampler, we show how to obtain the exact posterior distributions for functions of interest in the factor model. In particular, we propose a measure of the APT pricing deviations and obtain its exact posterior distribution. Using monthly portfolio returns grouped by industry and market capitalization, we find that there is little improvement in reducing the pricing errors by including more factors beyond the first one.

    Review of Financial Studies, 9, 1996, 553--583.


    Time-to-Build Effects and the Term Structure

    (with Jack Strauss)

    This paper shows that real macroeconomic variables have power in predicting movements in the term structure of interest rates, complementing recent studies on the links of structure to expected stock returns. We find that up to 86 percent of the variation in the term premia are due to changes in the macroeconomy. The predictive power can be attributed to time-to-build effect of investments.

    Journal of Financial Research, 18, 1995, 115--127.


    Small Sample Rank Tests with Applications to Asset Pricing

    This paper proposes small sample tests for rank restrictions that arise in many asset pricing models, economic fields and others, complementing the usual asymptotic theory which can be unreliable. Using monthly portfolio returns grouped by industry and using two sets of instrumental variables, we cannot reject a one-factor model for the industry returns.

    Journal of Empirical Finance, 2, 1995, 71--93.


    Analytical GMM Tests: Asset Pricing with Time-Varying Risk Premiums

    We propose alternative generalized method of moments (GMM) tests that are analytically solvable in many econometric models, yielding in particular analytical GMM tests for asset pricing models with time-varying risk premiums. We also provide simulation evidence showing that the proposed tests have good finite sample properties and that their asymptotic distribution is reliable for the sample size commonly used. We apply our tests to study the number of latent factors in the predictable variations of the returns on portfolios grouped by industries. Using data from October 1941 to September 1986 and two sets of instrumental variables, we find that the tests reject a one factor model but not a two-factor one.

    Review of Financial Studies, 7, 1994, 687--709.


    Asset Pricing Tests Under Alternative Distributions

    Given the normality assumption, we reject the mean-variance efficiency of the Center for Research in Security Prices value-weighted stock index for three of the six consecutive ten-year subperiods from 1926 to 1986. However, the normality assumption is strongly rejected by the data. Under plausible alternative distributional assumptions of the elliptical class, the efficiency can no longer be rejected. When the normality assumption is violated but the ellipticity assumption is maintained, many tests tend to be biased toward over-rejection and both the accuracy of estimated beta and R2 are usually overstated.

    Journal of Finance, 48, 1993, 1927--1942.


    International Asset Pricing with Alternative Distributional Specifications

    (with Campbell Harvey)

    The unconditional mean-variance efficiency of the Morgan Stanley Capital International world equity index is investigated. Using data from 16 OECD countries and Hong Kong and maintaining the assumption of multivariate normality, we cannot reject the efficiency of the benchmark. However, residual diagnostics reveal significant departures from normality. We test the sensitivity of the results by specifying error structures that are t-distributed and mixtures of normal distributions. Even after relaxing the i.i.d. assumption, we cannot reject the mean-variance efficiency of the world portfolio. Our results suggest that differences in country risk exposure, measured against the MSCI world portfolio, will lead to differences in expected returns.

    Journal of Empirical Finance, 1, 1993, 107--131.


    Small Sample Tests of Portfolio Efficiency

    This paper presents an eigenvalue test of the efficiency of a portfolio when there is no riskless asset, complementing the test of Gibbons, Ross, and Shanken (1989). Besides optimal upper and lower bounds, an easily-implemented numerical method is provided for computing the exact P-value. Our approach makes it possible to draw statistical inferences on the efficiency of a given portfolio both in the context of the zero-beta CAPM and with respect to other linear pricing models. As an application, using monthly data for every consecutive five-year period from 1926 to 1986, we reject the efficiency of the CRSP value-weighted index for most periods.

    Journal of Financial Economics, 30, 1991, 165--191.


    Algorithms for the Estimation of Possibly Nonstationary Time Series

    This paper presents efficient algorithms for computing time series projections, the maximum likelihood function and its gradient in possibly nonstationary vector times series model (VARMA).

    Journal of Time Series Analysis, 13, 1991, 171--188.


    Bayesian Inference in Asset Pricing Tests

    (with Campbell Harvey)

    (An Unpublished TechAppendix)

    We test the mean-variance efficiency of a given portfolio using a Bayesian framework. Our test is more direct than Shanken's (1987b), because we impose a prior on all the parameters of the multivariate regression model. The approach is also easily adapted to other problems. We use Monte Carlo numerical integration to accurately evaluate 90-dimensional integrals. Posterior-odds ratios are calculated for 12 industry portfolios from 1926–1987. The sensitivity of the inferences to the prior is investigated by using three different distributions. The probability that the given portfolio is mean-variance efficient is small for a range of plausible priors.

    Journal of Financial Economics, 26, 1990, 221--254.


    Some Finance, Economics, and Statistics Journals


    American Economic Review up to a few years ago(JSTOR) Go its web for recent ones: AER
    Annals of Applied Probability up to a few years ago(JSTOR) Go its web for recent ones: AAP
    Annals of Probability up to a few years ago(JSTOR) Go its web for recent ones: AP
    Annals of Statistics up to a few years ago(JSTOR) Go its web for recent ones: AS
    Applied Statistics up to a few years ago(JSTOR) Go its web for recent ones: APS
    Biometrika up to a few years ago(JSTOR) since 1996
    Econometrica up to a few years ago(JSTOR) More Recent (ProQuest) Web
    Econometric Reviews since 1998
    Econometrics Journal since 1998
    Econometric Theory since 1997
    Economic Journal up to a few years ago(JSTOR)
    Economics Letters since 1995
    Finance and Stochastics All
    Financial Analysts Journal since 11/1987 Web
    Financial Management since 1989
    International Economic Review up to a few years ago(JSTOR) More Recent (ProQuest) Web
    Journal of Applied Corporate Finance Publisher
    Journal of Applied Econometrics since 1997
    Journal of Banking and Finance Publisher
    Journal of Business up to a few years ago(JSTOR) OlinDownload
    Journal of Business and Economic Statistics All since 1996, some 1995
    A HREF=""> Olin download
    Journal of Derivatives since 1997
    Journal of Econometrics since 1995
    Journal of Economic Dynamics and Control since 1995
    Journal of Economic Literature up to a few years ago(JSTOR)
    Journal of Economic Theory since 1993
    Journal of Economics and Business since 1999
    Journal of Empirical Finance since 1995
    Journal of Finance up to 3 years ago last few years forthcoming papers
    Journal of Financial Econometrics Web
    Journal of Financial Economics since 1995 forthcoming papers
    Journal of Financial Markets since 1999
    Journal of Financial and Quantitative Analysis up to 4 years ago since 1990 Web
    Journal of Financial Research Web
    Journal of Fixed Income up to a few years ago Publisher
    Journal of Forecasting since 1996
    Journal of Political Economy up to a few years ago(JSTOR) since 1987
    Journal of the American Statistical Association up to a few years ago(JSTOR) Web
    Journal of the Royal Statistical Society Series A (Statistics in Society) up to a few years ago(JSTOR) Web
    Journal of the Royal Statistical Society Series B (Statistical Methodology) up to a few years ago(JSTOR) Web
    Journal of Time Series Analysis Web
    Mathematical Finance since 1997
    NBER Working Papers All
    Quarterly Journal of Economics up to a few years ago(JSTOR) since 1987
    Review of Economic Studies up to a few years ago(JSTOR) since 1996
    Review of Economics and Statistics up to a few years ago(JSTOR) since 2000
    Review of Financial Economics since 1999
    Review of Financial Studies All

    Some Big Link Pages:

    Ohio State Finance Sites
    An Econometric Link
    Worldwide Directory of Finance Faculty

    Some useful links for Olin Students:

  • Vaultreports: interview questions/answers and job info
  • Wetfeet: more interview Q/A, company and job info
  • McKinsey's various business publications
  • Fed: info and policy news, etc
  • NY Fed: info and data on interest rates, etc
  • Chicago Fed: info and reports, etc
  • St. Louis Fed: info and reports, etc
  • Cleveland Fed: Useful info on Fed Funds Rate
  • Harvard cases
  • Cases from Ivey Publishing
  • Cases from ECCH
  • Paper Trading 1: InvestmentChallenge: real-time (one type of accounts is free and another costs about $20)
    Warning: An individual (v.s. institutions) has less research, info, time and capital, but higher transactions cost. May also be lack of discipline. The only advantages seem that the individual may come-in and -out of the market faster and be able to endure a greater calculated risk (assume he knows how to calculate the risk!). Nevertheless, empirical studies show that trading is hazardous to wealth: to beat the mkt, most individuals are beaten by the market! Try the paper trading first to see whether you are an exception before put down your hard-earned money!
  • Paper Trading 2: Stock-Trak: real-time stocks, futures & options trading
  • CNN Financial News
  • CNBC Financial News
  • Bloomberg Financial News
  • CBS.MarketWatch: mkt info
  • Yahoo! Finance: various mkt info and calendar for economic data release
  • CNN News
  • CNN Fin News
  • Zacks Investment Research
  • Quote, charts and data, etc
  • The Chicago Mercantile Exchange
  • The Chicago Board of Trade
  • The Chicago Board Options Exchange
  • The New York Stock Exchange
  • The Nasdaq-Amex Stock Market
  • The New York Mercantile Exchange
  • Iowa Electronic Futures Mkts (small political bets)
  • Links to all futures exchanges
  • US securities and exchange commission
  • Warren E. Buffett's company and his writings
  • Financial scandals
  • Applied Futures Trading: a free web magazine
  • LARGE-LARGE-LARGE info and links on finance
  • An Option Pricer: European and implied volatility
  • Option Pricer 2: many useful stuff
  • Option Pricer 3: standard and exotic options
  • Hugh's Mortgage and Financial Calculators
  • TradeStation Commissions seem the lowest; an on-line trading platform for speculating on futures, options and stocks. Unless you trade actively, a monthly fee of $99 may be charged for accessing all the real-time info.
    A Warning: (The #1 advice of Bernard Baruch, a legendary speculator) Don't speculate unless you do it full time.
  • Interactive Brokers A competitor with TradeStation, but the platform is not as good.
  • Scottrade A traditional broker with on-line capabilities; free real-time streaming quotes (no need to open brokerage accounts!)
  • Treasuries buy and cash them on line for your fixed-income allocations.
  • Faculty page
    John M. Olin School of Business| Washington University in St. Louis| Links page