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, implementing advanced asset allocation strategies) and Mathematical Finance (MS in Finance, pricing derivatives under diffusion and jump processes).

Research Interests:

  • Portfolio choice, asset allocation, technical analysis, bubbles and crashes, anomalies, asymmetric information, asset pricing tests, Bayesian learning, model selection, econometric methods in finance, and real option.

Professional Service:

  • Associated Editor: Journal of Financial and Quantitative Analysis, 2000-present; Journal of Empirical Finance, 2016-present; Editorial Board: Journal of Portfolio Management, 2008-present, and International Journal of Portfolio Analysis & Management; 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 50 journals.

Major Academic Contributions:

(a summary of the published and forthcoming papers)
  • CAPM and APT : Harvey and Zhou (1990) provide the first 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. 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).
  • 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) provides 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) survey the literature. 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 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 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) survey the literature. Huang, Jiang, Tu and Zhou (2015) find investor sentiment is a powerful predictor of the stock market, and Rapach, Ringgenberg and Zhou (2015) show that the aggregated short interest is another powerful predictor. Lin, Wu and Zhou (2016) 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 that is implied by asset pricing theory, Huang and Zhou (2015) provide substantially tighter bounds and find major asset pricing models fail to explain the empirical predictability in the data due to inadequate state variables.
  • Momentum/Technical Analysis : Zhu and Zhou (2010) provide 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. Han, Zhou and Zhu (2016) provide perhaps the first general equilibrium model on the price moving averages to understand the roles of technical traders and to justify their predictability of, and propose a trend factor, which captures simultaneously all three stock price trends (the short-, intermediate- and long-term) and outperforms substantially existing factors, such as the momentum, by more than doubling their Sharpe ratios.
  • Asymmetry Tests : 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.
  • Portfolio Choice : Tu and Zhou (2009) show how to select an optimal mean-variance portfolio under the realistic t-distribution with asset pricing model priors and finds big differences in weights vs the normal case. Kan and Zhou (2007) solve analytically, for the first time, the expected utility/return loss under parameter estimation risk. Fabozzi, Huang and Zhou (2010) provide a survey. 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, and Tu and Zhou (2010) show how economic objectives can serve as useful priors that yield superior portfolios. Avramov and Zhou (2010) survey the literature.
  • Volatility Risks : 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 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 explaining various puzzles of equity and options data.
  • 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.
  • 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 Stock and Bond Markets : 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. For the Chinese bond market, Fan, Li and Zhou (2013) analyze its supply factor, and Fan, Jiang and Zhou (2014) provide an overall introduction.

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

Working papers


Optimal Portfolio Selection with and Without Risk-Free Asset

with Raymond Kan and Xiaolu Wang (current version: August, 2016).

In this paper, we consider optimal portfolio problems with and without risk-free asset, taking into account estimation risk. For the case with a risk-free asset, we derive the exact distribution of out-of-sample returns of various optimal portfolio rules, including the two-fund and three-fund rules suggested by Kan and Zhou (2007), and compare their out-of-sample performance with the equally weighted portfolio (i.e., 1/N rule). We find that the dominance of the 1/N rule over various optimal portfolio rules as documented by DeMiguel, Garlappi, and Uppal (2009) was due in part to the exclusion of risk-free asset in their construction of optimal portfolios, even though those optimal portfolio rules were designed to include the risk-free asset. In order to have a direct comparison with the 1/N rule of risky assets only, we also consider an optimal portfolio problem without risk-free asset and develop a new portfolio rule that is designed to mitigate estimation risk in this case. We show that our new portfolio rule performs well relative to the 1/N rule in both calibrations and real data sets.



Intraday Momentum: The First Half-Hour Return Predicts the Last Half-Hour Return

with Lei Gao, Yufeng Han and Sophia Zhengzi Li (current version: December, 2015).

In this paper, using intraday data from January 4, 1999 to December 31, 2012, we document an intraday momentum pattern that the first half-hour return on the market predicts the last half-hour return on the market. The predictability is both statistically and economically significant, and is stronger on more volatile days, recession days and some macroeconomic news release days. We interpret the trading behavior of daytraders and informed traders as the economic driving forces behind the intraday momentum.





Does Momentum Exist in Bonds of Different Ratings?

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

This paper investigates whether momentum exists in the corporate bond market. Instead of relying on the price information from just a single time horizon, we incorporate all trend signals in the short, intermediate and long terms simultaneously. Using this informationally ef?cient strategy, we uncover strong and signi?cant momentum for all bonds across ratings. Interestingly, bond momentum earns roughly the same amount of return as stock momentum, but has little correlation with the latter. The effect of bond momentum is robust to various controls of risk factors, bond characteristics, and transaction costs, and is stronger after the establishment of TRACE and during periods with low sentiment or low growth. Overall, mo mentum appears to be the most pronounced cross-sectional anomaly emerged from the bond market that challenges the existing rational pricing theory of corporate bonds.



Bond Return Predictability and Macroeconomy: The International Link

with Xiaoneng Zhu (current version: August, 2016).

This paper provides real-time out-of-sample evidence on the international link of macroeconomic risks for government bonds. Motivated by a simple production-based model, we construct a global macroeconomic factor (GMF) from a panel of international real-time macroeconomic variables that are not subject to future revisions or release delay. We find that the GMF, as an aggregate measure of world macro risks, predicts strongly bond risk premia across countries, with out-of-sample R2 up to $23%. In contrast, a local macroeconomic factor (LMF) extracted from local macroeconomic variables generate mixed results. The predictive power of the GMF is robust after controlling the Cochrane-Piazzesi factor and the global forward-rate factor. Overall, its predictability is not only significant statistically, but also important economically. Moreover, the GMF also contains information for predicting international stock returns and carry trade profitability.



Cost Behavior and Stock Returns

with Dashan Huang, Fuwei Jiang and Jun Tu (current version: October, 2016).

This paper shows that investors fail to fully incorporate cost behavior information into valuation. Firms with higher growth in operating costs generate substantially lower future stock returns and operating performance. A spread portfolio of long stocks with low cost growth and short stocks with high cost growth earns an average abnormal return of about 12% per year, which cannot been explained by extant factor models 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 deterioration in operating performance. The negative cost growth-return relation is stronger among firms with lower investor attention, higher valuation uncertainty, and higher transaction costs, and therefore, mispricing plays an important role.



Manager Sentiment and Stock Returns

with Fuwei Jiang, Joshua Lee and Xiumin Martin (current version: October, 2015).

In this paper, we construct a manager sentiment index based on the aggregated textual tone of conference calls and financial statements. 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-square 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 also stronger than and is complimentary to the popular investor sentiment indexes. Moreover, manager sentiment also negatively predicts future aggregate earnings and cross-sectional stock returns, particularly for those firms that are either hard to value or difficult to arbitrage.



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.



Stock Return Asymmetry: Beyond Skewness

with Lei Jiang, Ke Wu and Yifeng Zhu (current version: October, 2016).

In this paper, we propose two asymmetry measures of stock returns. In contrast to the popular skewness measure, our improved asymmetry measures are based on the distribution function of the data instead of just the third moment. Empirically, we find that, with our new measures, greater upside asymmetries imply lower average returns in the cross section of stocks, while it can be inconclusive with skewness. Our results are consistent with recent theoretical models that analyze asymmetries such as Han and Hirshleifer (2015) and Goulding (2016).



Anomalies Enhanced: The Value of Higher Frequency Information

with Yufeng Han and Dayong Huang (current version: August, 2015).

Many anomalies are based on low frequency attributes, such as annual characteristics, that ignore higher frequency information. In this paper, we provide a simple strategy to incorporate the higher frequency information. We find that there is significant economic value-added. For eight major anomalies, we find that the enhanced anomalies can double the average returns while having similar or lower risks. The results are robust to a number of controls.





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.



Does Monetary Policy Moderate or Exacerbate the Economic Fluctuations and Stock Market Volatility in China?

with Wei Tu, Hongkui Liu and Heng-fu Zou (current version: January, 2015).

Based on a SVAR model, which integrates monetary policy behavior with the banking system, demand for money aggregate, and the real economy, the paper reexamines the relationship between the credit cycle and the business cycle in China. Different from the existing research, we distinguish between the 'required reserve rate' and the 'open market operation', and identify the impacts of the two policy instruments simultaneously. The empirical results show that the PBC's responsibility for controlling inflation and stabilizing the aggregate demand is mainly represented by the adjustment of the required reserve rate, and the 'open market operation' accounts for the monetary authority's concern on the liquidity management of commercial banks. Furthermore, we find that monetary policy shock is not the main driving force for the business cycles in China, whereas a large fraction of the variation in monetary policy is attributable to the systematic reactions of policy authority to the state of the economy. We also find that the interdependence between China's monetary policy and stock market is fairly limited at present.



Asymmetry in Stock Comovements: An Entropy Measure

with Lei Jiang and Ke Wu (current version: March, 2015).

In this paper, we provide an entropy measure for asymmetric comovements between an asset return and the market return. This measure yields a model-free test for asymmetry in stock returns that has greater power than 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. In the cross-section of stock returns, we find a risk premium (discount) for stocks with high downside (upside) comovement with the market. Moreover, downside comovement premium is almost twice as large as downside beta premium. Our findings are consistent with theoretical implications of a representative agent model with disappointment aversion preferences.



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).



Industry Interdependencies and Cross-Industry Return Predictability

With David Rapach, Jack Strauss and Jun Tu (current Version: February, 2015).

We use the adaptive LASSO from the statistical learning literature to identify economically connected industries in a general framework that accommodates complex industry interdependencies. Our results show that lagged returns of interdependent industries are significant predictors of individual industry returns, consistent with gradual information diffusion across industries. Using network analysis, we find that industries with the most extensive predictive power are key central nodes in the production network of the U.S. economy. Further linking cross-return predictability to the real economy, lagged employment growth for the interdependent industries predicts individual industry employment growth. We also compute out-of-sample industry return forecasts based on the lagged returns of interdependent industries and show that cross-industry return predictability is economically valuable: an industry-rotation portfolio that goes long (short) industries with the highest (lowest) forecasted returns exhibits limited exposures to common equity risk factors, delivers a substantial alpha of over 11% per annum, and performs very well during business-cycle recessions, especially the recent Great Recession.



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 in parameter estimation. But 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, Nov., 2011 (the left link provides more details).



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.)


Forecasting Corporate Bond Returns: An iterated combination approach

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

(An 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 (forthcoming)



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 Internationa (forthcoming)



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 (forthcoming)



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

(with Yufeng Han and Yingzi Zhu).

(An On-line Appendix)

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 Market Returns

(with David Rapach and Matthew Ringgenberg).

(An On-line Appendix)

(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)

[BW Index and our PLS index, updated to Dec., 2014 (free download for academic research only; a link of more data and new proxies for commercial use will be posted shortly)]

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)

(An 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)

(An 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)

(An 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.

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