Publications (Data&Codes)
(Note: Some pdf files below are the sole copyright of the respective
publishers, and are provided here for educational use only.)
Trend Factor in China: The Role of Large Individual Trading
with Yang Liu and Yingzi Zhu
(Factor Data)
(OnlineAppendix)


We propose a novel trend factor for the Chinese stock market, which incorporates both price and
volume information to capture dominant individual trading, momentum, and liquidity. We find
that volume plays a more significant role in the trend factor for China than for the US, reflecting
the greater retail participation in China. By incorporating this trend factor into the 3factor model
of Liu et al. (2019), we propose a 4factor model that explains a wide range of stylized facts and
60 representative anomalies. Our study highlights the important role of individual trading in asset
pricing, especially in China.
Review of Asset Pricing Studies, forthcoming.

Why Naive 1/N Diversification Is Not So Naive, and How to Beat It?
with Ming Yuan


We show theoretically that the usual estimated investment strategies will not achieve the optimal
Sharpe ratio when the dimensionality is high relative to sample
size, and the 1/N rule is optimal in a onefactor model with
diversifiable risks as dimensionality increases, which explains why
it is difficult to beat the 1/N rule in practice. We also explore
conditions under which it can be beaten, and find that we can
outperform it by combining it with the estimated rules when N is
small, and by combining it with anomalies or machine learning
portfolios, conditional on the profitability of the latter, when N
is large.
Journal of Financial and Quantitative Analysis, forthcoming.

Asset Pricing: Crosssection Predictability
with Paolo Zaffaroni


We provide a selected review of the vast literature on crosssection predictability. We focus on
the state of art methods used to forecast the crosssection of stock
returns with man predictors and are primarily interested in the
ideas, methods, and their applications. To understand the
crosssection predictability, we also provide a review of factor
models, which shed light on whether the predictability is due to
mispricing or risk exposure.
Oxford Research Encyclopedia of Economics and Finance, 135, 2024.

Winners from Winners: A Tale of Risk Factors
with Siddhartha Chib and
Lingxiao Zhao


Starting from the twelve distinct factors from Fama and French (1993, 2015, 2018), Hou, Xue, and Zhang (2015), Stambaugh and Yuan (2017), and Daniel, Hirshleifer, and Sun (2020), plus twelve principal components of anomalies unexplained by the initial factors, a Bayesian comparison of approximately 17 million models in terms of marginal likelihoods and posterior model probabilities shows that {Mkt, MOM, IA, ROE, MGMT, PERF, PEAD, FIN} plus the nonconsecutive principal components, {PC1, PC5, PC7} are the best supported riskfactors. Pricing tests and annualized outofsample Sharpe ratios for tangency portfolios suggest that this asset pricing model should be used for computing expected returns, assessing investment strategies and building portfolios.
Management Science 70, 2024, 396414.

Technical Analysis in the Stock Market: A Review
with Yufeng Han, Yang Liu and Yingzi Zhu


Technical analysis is the study for forecasting future asset prices with past data. In this survey, we review and extend studies on not only the timeseries predictive power of technical indicators on the aggregated stock market and various portfolios, but also the crosssectional predictability with various firm characteristics. While we focus on reviewing major academic research on using traditional technical indicators, but also discuss briefly recent studies that apply machine learning approaches, such as Lasso, neural network and genetic programming, to forecast returns both in the timeseries and in the crosssection.
Handbook of Investment Analysis, Portfolio Management, and Financial Derivatives, forthcoming

Diagnostics for Asset Pricing Models
with Ai He


The validity of an asset pricing model implies whitenoise pricing errors (PEs). However, we find that the PEs of six wellknown factor models all exhibit a significant reversal pattern and are predictable by their lagged values in 3, 6, 9, and 12 months. Moreover, the predictability of the PEs can produce substantial profits. Similar conclusions hold for recently developed machine learning models too. Additional analysis reveals that the significant PE profits cannot be explained by investor sentiment and limitstoarbitrage. Our results imply that much remains to be done in developing new asset pricing models.
Financial Management 52, 2023, 617642.

Are Bond Returns Predictable with RealTime Macro Data?
with Dashan Huang, Fuwei Jiang, Kunpeng Li and Guoshi Tong


We investigate the predictability of bond returns using realtime
macro variables and consider the possibility of a nonlinear
predictive relationship and the presence of weak factors. To address
these issues, we propose a scaled sufficient forecasting (sSUFF)
method and analyze its asymptotic properties. Using both the
existing and the new method, we find empirically that realtime macro variables
have significant forecasting power both insample and
outofsample. Moreover, they generate sizable economic values, and
their predictability is not spanned by the yield curve. We also
observe that the forecasted bond returns are countercyclical, and
the magnitude of predictability is stronger during economic
recessions, which lends empirical support to wellknown macro
finance theories.
Journal of Econometrics 236, 2023, 105438.

Shrinking Factor Dimension: A ReducedRank Approach
with Ai He, Dashan Huang and Jiaen Li
(Data;
code)
(Online Appendix)


We provide a reducedrank approach (RRA) to extract a few factors from a large set of factor proxies, and apply the extracted factors to model the cross section of expected stock returns. Empirically, we find that the RRA fivefactor model outperforms the well known FamaFrench fivefactor model as well as the corresponding PCA, PLS and LASSO models for pricing portfolios. However, at the stock level, our RRA factor model still has large pricing errors even after adding more factors, suggesting that the representative factor proxies of our study do not have sufficient information for pricing individual stocks.
Management Science 69, 2023, 55015522.

Employee Sentiment and Stock Returns
with Jian Chen, Guohao Tang and Jiaquan Yao
(Online Appendix)
(Data: 200806202012)


We propose an employee sentiment index, complementing investor sentiment and manager sentiment indices, and find that high employee sentiment predicts low monthly (weekly) market returns significantly both in and outofsample. The predictability can also deliver sizable economic gains for meanvariance investors in asset allocation. The impact of employee sentiment is found stronger among employees who work in the headquarters state and are less experienced. The economic driving force of the predictability is unique: high employee sentiment leads to high contemporaneous wage growth due to immobility, which subsequently results in lower firm cash flow and lower stock returns.
Journal of Economic Dynamics and Control 149, 2023, 104636.

Firm Fundamentals and the Cross Section of Implied Volatility Shapes
with
Ding Chen and Biao Guo


With machine learning tools, we document that firm fundamentals
have explanatory power on the shape of the option implied volatility
(IV) curve that is both economically and statistically significant.
We find further that, after accounting for fundamentals, the
associated IV process can generate overreaction in the longterm IV
with respect to change in the shortterm IV, and can allow a
positive profit from atthemoney straddle writing, explaining
puzzling patterns of the literature. We also provide a simple model
linking the IV to firm fundamentals, which permits realistic IV
curves and is consistent with the empirical findings.
Journal of Financial Markets 63, 2023, 100771.

Recovering the FOMC Risk Premium
with
Hong Liu and Xiaoxiao Tang
(FOMC Risk Premia)


The Federal Open Market Committee (FOMC) meetings are among the most important economic events. We propose a novel method to recover the FOMC risk premium and drift sizes. Empirically, we find that for the 192 meetings from 1996 to 2019, the FOMC risk premium varies across meetings, from 1 to 326 basis points (bps) with an average of 45 bps. We obtain an outofsample Rsquared of 7.51% when using the recovered FOMC premium to predict the meeting returns around the announcement. The average predicted upward drift size is 101 bps, and the average predicted downward drift size is 129 bps, matching well with the realized ones.
Journal of Financial Economics 145, 2022, 4568.

Asset Pricing: TimeSeries Predictability
with David Rapach


Asset returns change with fundamentals and other factors such as technical information and sentiment over time. In this survey, we review some of the major ideas, data, and methods used to model timevarying expected returns. We focus on the outofsample predictability of the aggregate stock market return via extensions of the conventional predictive regression approach. The extensions are designed to improve outofsample performance in realistic environments characterized by large information sets and noisy data.
Oxford Research Encyclopedia of Economics and Finance, 2022, 134.

Predictive Information in Corporate Bond Yields
with Xu Guo, Hai Lin and Chunchi Wu
(Data and SAS Program
Internet Appendix)


We document strong evidence of crosssectional predictability of corporate bond returns based on a set of yield predictors that capture the information in the yields of past 1, 3, 6, 12, 24, 36 and 48 months. Return predictability is economically and statistically significant, and is robust to various controls. The uncovered predictability presents the most pronounced anomaly in the corporate bond literature that challenges rational pricing models.
Journal of Financial Markets 59, 2022, 100687.

Expected Return, Volume, and Mispricing
with
Yufeng Han,
Dashan Huang and Dayong Huang
(Online Appendix)
(main data and codes)


We find that expected return is related to trading volume positively among underpriced stocks but
negatively among overpriced stocks. As such, trading volume amplifies mispricing. Our results
are robust to alternative mispricing and trading volume measures, alternative portfolio formation
methods, and controlling for variables that are known to have amplification effects on mispricing.
By attributing trading volume to investor disagreement, we show that our results are consistent
with the recent theoretical model of Atmaz and Basak (2018) in that investor disagreement predicts
stock returns conditional on expectation bias.
Journal of Financial Economics 143, 2022, 12951315.

Investor Attention and Stock Returns
with Jian Chen, Guohao Tang and
Jiaquan Yao
(Online Appendix)
(Attention Index Data: 1980 to 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 insample and
outofsample, 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
meanvariance 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 highvariance stocks.
Journal of Financial and Quantitative Analysis 57, 2022, 455484.

Optimal Portfolio Choice with Estimation Risk: No Riskfree Asset Case
with Raymond Kan and Xiaolu Wang
(Internet Appendix)


We propose an optimal combining strategy to mitigate estimation risk for the popular meanvariance portfolio choice problem in the case without a riskfree asset. We find that our strategy performs well in general, and it can be applied to known estimated rules and the resulting new rules outperform the original ones. We further obtain the exact distribution of the outofsample returns
and explicit expressions of the expected outofsample utilities of the combining strategy, providing not only a fast and accurate way of evaluating the performance but also analytical insights into the portfolio construction.
Management Science 68, 2022, 20472068.

Scaled PCA: A New Approach to Dimension Reduction
with Dashan Huang, Fuwei Jiang, Kunpeng Li and Guoshi Tong
(Internet Appendix)
(Demo Code in Matlab)


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.
Management Science 68, 2022, 16781695.

Anomalies and the Expected Market Return
with Xi Dong, Yan Li and David Rapach
(Online Appendix;
(code)


We provide the first systematic evidence on the link between longshort anomaly portfolio returns—a cornerstone of the crosssectional literature—and the timeseries 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 highdimensional setting. We find that longshort anomaly portfolio returns evince statistically and economically significant outofsample 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.
Journal of Finance 77, 2022, 639681.

Unspanned Global Macro Risks in Bond Returns
with Feng Zhao and Xiaoneng Zhu
(Internet Appendix)


We examine the macrospanning hypothesis for bond returns in international markets. Based
on a large panel of realtime 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 macrofinance term structure models with the unspanned global macro
factors and find that the global macro factors in.uence the market prices of level and slope risks
and induce comovements in forward term premia in global bond markets.
Management Science 67, 2021, 78257843.

Anomalies Enhanced: A Portfolio Rebalancing Approach
with Yufeng Han and Dayong Huang
(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) fivefactor riskadjusted
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 50, 2021, 371424.

Learning and Predictability via Technical Analysis: Evidence from Bitcoin and Stocks with HardtoValue Fundamentals
with Andrew Detzel,
Hong Liu,
Jack Strauss and
Yingzi Zhu


What predicts returns on assets with "hardtovalue" 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 outofsample. Trading strategies based on these ratios generate an economically significant alpha and Sharpe ratio gains relative to a buyandhold position. Similar results hold for smallcap, youngfirm, and lowanalystcoverage stocks as well as NASDAQ stocks during the dotcom era.
Financial Management 50, 2021, 107137.

The Chinese Warrant Bubble: A Fundamental Analysis
with Yintian Wang and
Yingzi Zhu


We investigate the information content in Chinese warrant prices
based on an option pricing framework that incorporates
shortselling and margintrading constraints in the underlying
stock market. We show that Chinese warrant prices can be explained
under this pricing framework. On the basis of this new model, we
develop a price deviation measure to quantify stock market
investor unobserved demand for short selling or margin trading due
to market constraints. We find that warrantprice deviations are
driven by underlying stock valuation to a great extent. Chinese
warrant prices, save for the time around expiration dates, are
better characterized as derivatives than as pure bubbles.
Journal of Futures
Markets 41, 2021, 322.

TimeSeries and CrossSectional Stock Return Forecasting: New Machine Learning Methods
with David Rapach


This paper extends the machine learning methods developed in Han, He, Rapach and Zhou (2019) for forecasting crosssectional stock returns to a timeseries context. The methods use the elastic net to refine the simple combination return forecast from Rapach et al. (2010). In a timeseries 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 crosssectional return forecasts developed in Han et al. (2019), highlighting how machine learning methods can be used to improve combination forecasts in both the timeseries and crosssectional dimensions. Overall, because many important questions in finance are related to timeseries or crosssectional 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), 133.

TimeSeries Momentum: Is It There?
with Dashan Huang. Jiangyuan Li, and Liyao Wang
(Data and Matlab Program)
(Python Program)
(Internet Appendix)
(Discussions at Alpha Architect)


Timeseries momentum (TSM), which refers to the predictability of the past 12month return on the next onemonth return, is the focus of quite a few recent influential studies. This paper shows, however, that asset by asset timeseries regressions reveal little TSM both in and outofsample. In a pooled regression, the usually used tstatistic can overreject the no predictability hypothesis, and three versions of bootstrap corrected tstatistics 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, 774794.

Stock Return Asymmetry: Beyond Skewness
with Lei Jiang, Ke Wu, and Yifeng Zhu


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 crosssection 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, 357386

VolatilityManaged Portfolio: Does It Really Work?
with Fang Liu and Xiaoxiao Tang
(Data and Program)
(Online Appendix)


In this article, the authors find that a typical application of volatilitytiming
strategies to the stock market suffers from a lookahead 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 volatilitytiming 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, 3851

Industry Return Predictability: A Machine Learning Approach
with
David Rapach,
Jack Strauss and Jun Tu
(Data & code)
(Internet Appendix)


We use machine learning tools to analyze industry return predictability based on the
information in lagged industry returns. Controlling for postselection inference and
multiple testing, we find significant insample evidence of industry return predictability. Lagged returns for the financial sector and commodity and materialproducing
industries exhibit widespread predictive ability, consistent with the gradual diffusion
of information across economically linked industries. Outofsample 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 industryrotation portfolio that goes long (short) industries with
the highest (lowest) forecasted returns delivers an annualized alpha of over 8%. The
industryrotation portfolio also generates substantial gains during economic downturns,
including the Great Recession.
Journal of Financial
Data Science 1 (3), 2019, 928.

Manager Sentiment and Stock Returns
with Fuwei Jiang, Joshua Lee and Xiumin Martin
(Updated paper, Nov. 15, 2019)
(MS Index Data; updated to Dec., 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 insample and outofsample Rsquared of 9.75% and 8.38%, respectively, which is far greater than
the predictive power of other previouslystudied 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 crosssectional stock returns, particularly for firms that
are difficult to value and costly to arbitrage.
Journal of Financial
Economics 132, 2019, 126149.

Firm Characteristics and Chinese Stocks
with Fuwei Jiang and Guohao Tang


This paper presents a comprehensive study on predicting the cross section of Chinese stock market
returns with a large panel of 75 individual firm characteristics. We use not only the traditional FamaMacBeth
regression, but also the “bigdata” econometric methods: principal component analysis (PCA), partial least
squares (PLS), and forecast combination to extract information from all the 75 firm characteristics. These
characteristics are important return predictors, with statistical and economic significance. Furthermore, firm
characteristics that are related to trading frictions, momentum, and profitability are the most effective predictors
of future stock returns in the Chinese stock market.
Journal of Management Science and Engineering 3, 2018, 259283.

Measuring Investor Sentiment


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 tovalue 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, 239259.

Forecasting Corporate Bond Returns: An Iterated Combination Approach
with Hai Lin
and Chunchi Wu
(Online 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 lowgrade bond premium.
Management Science 64, 2018, 42184238.

Asymmetry in Stock Comovements: An Entropy Approach
with
Lei Jiang and Ke Wu
(Online 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 modelfree test for stock return asymmetry, generalizing the correlationbased 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 entropybased measure of downside asymmetric comovement. In the crosssection 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, 14791507.

Market Intraday Momentum
with Lei Gao, Yufeng Han and Sophia Zhengzi Li
(Online Appendix)


Based on high frequency data of the S&P 500ETF from 19932013, we document an intraday momentum pattern: the first halfhour return on the market predicts the last halfhour 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 halfhours 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 lateinformed and trade near the market close.
Journal of Financial
Economics 129, 2018, 394414.

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 Rsquares of predictive regressions. Using data on the market and component portfolios, we find that the empirical Rsquares 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, 401425

Modeling Nonnormality Using Multivariate t: Implications for Asset Pricing
with Raymond Kan


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 tdistribution 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 tdistribution, 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 booktomarket
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 tdistribution instead of a multivariate normal.
China Finance Review International 7, 2017, 232.

A Trend Factor: Any Economic Gains from Using Information over
Investment Horizons?
with Yufeng Han and Yingzi Zhu
(Online Appendix)
(Trend Factor Data, from 1930 to 2014)
(Updated to 2017; still performs!)


In this paper, we provide a trend factor that captures simultaneously all three stock price trends: the short, intermediate and longterm.
It outperforms substantially the wellknown shortterm reversal, momentum and longterm 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 shortterm reversal factor loses 0.82%, the
momentum factor loses 3.88% and the longterm 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 crosssection stock returns.
Journal of Financial Economics 122(2), 2016, 352375

Short Interest and Aggregate Stock Returns
with David Rapach and Matthew Ringgenberg
(Online Appendix)
Recent Great Decline!
(Data to Dec 2023, and Matlab Program)
(Citations by Bloomberg and others)


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 insample and outofsample tests, with annual insample and outofsample R2 statistics of 12% and 8%, respectively. In addition, short interest generates substantial utility gains: a meanvariance 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, 4665

FamaMacBeth Twopass Regressions:
Improving Risk Premia Estimates
with Jushan Bai


In this paper, we provide the asymptotic theory for the
widely used Fama and MacBeth (1973)
twopass regressions in the usual case of a large number of assets.
We find that the convergence of the OLS twopass estimator depends critically on the time series sample size
in addition to the number of crosssections. 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, 3140.

Investor Sentiment Aligned: A Powerful Predictor of Stock
Returns
with Dashan Huang, Fuwei Jiang and Jun Tu
(PLS index data updated to Dec., 2023)


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 outofsample, and the predictability becomes both statistically and economically
significant. In addition, it outperforms well recognized macroeconomic variables and can also predict crosssectional 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, 791837.

Macroeconomic Volatilities and Longrun Risks of Asset Prices
with Yingzi Zhu
(Online Appendix)


In this paper, motivated by existing and growing evidence on multiple
macroeconomic volatilities, we extend the longrun risks model
of Bansal and Yaron (2004) by allowing both a long and a
shortrun 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, 413430.

Are There Trends in Chinese Stock Market?
(in Chinese)
with Yufeng Han, Xiongjian Wang and Hengfu 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
shortterm 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 shortterm trendfollowing, 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, 152163.

Forecasting the Equity Risk Premium: The Role of Technical Indicators
with Christopher J. Neely,
David E. Rapach and Jun Tu
(Online 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 insample and outofsample 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
businesscycle 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,
17721791.

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 riskadjusted returns. Our analysis, which uses data
spanning 20 years, highlights the potential benefits of achieving strategylevel 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, 311320.

Forecasting Stock Returns
with David Rapach
(Data and Matlab Programs)
(Data and Python Programs)
(Publication Info)


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 insample evidence of equity premium predictability, popular predictors from the literature fail to outperform the simple historical average benchmark forecast in outofsample tests. Recent studies, however, provide improved forecasting strategies that deliver statistically and economically significant outofsample 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 datagenerating process for stock returns. In addition to the U.S. equity premium, we succinctly survey outofsample evidence supporting U.S. crosssectional 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), 328–383.

A New Anomaly: The CrossSectional Profitability of Technical Analysis
with Yufeng Han and Ke Yang


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 buyandhold strategy substantially. For high volatility
portfolios, the abnormal returns, relative to the CAPM and the
FamaFrench threefactor 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, 14331461.

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 preferredhabitat
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
preferredhabitat investors and the arbitrageurs affect bond yields
and returns. Moreover, we also find that the preferredhabitat
investors' alternative investment opportunities have expected effect
on bond yields and returns. We further show that the
preferredhabitat and demand factors improve bond pricing and return
predictability in a noarbitrage term structure model. Variance
decomposition analysis shows that the preferredhabitat factor
explains an important part of bond yield variations.
Journal of Fixed Income 23, 2013, 6281.

International Stock Return Predictability: What is the Role of the United States?
with David E. Rapach and Jack K. Strauss
(Online Appendix)
(The Data and Matlab Programs)
 
We present significant evidence of outofsample 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 outofsample 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. returnssubstantially
outperform economic variables as outofsample equity premium predictors for nonU.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 businesscycle 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 outofsample R^{2} statistics of 10% or greater, more than triple the postwar average.
Journal of Finance 68, 2013, 16331662.

Volatility Trading: What is the Role of the
LongRun 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 twofactor 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 firstorder importance in the twofactor 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 onefactor model instead of the twofactor
model or if he incorrectly estimates one of the key parameters in
the twofactor 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, 273307.

Tests of
MeanVariance 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,
145193.

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, booktomarket and ownership
concentration. Considering a variety of economic variables as predictors, both insample and outofsample 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 smallcap,
low booktomarket ratio and low ownership concentration firms also display considerable predictability.
Two key findings provide economic explanations for component predictability: (i) based on a novel outofsample
decomposition, timevarying 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 informationflow frictions emphasized by Hong, Torous, and
Valkanov (2007).
Journal of Financial Research (½ðÈÚÑÐ¾¿) 9, 2011,
107121.

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 riskadjusted 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 theorybased,
our study may be interpreted as reaffirming the
usefulness of the Markowitz theory in practice.
Journal of Financial Economics 99, 2011,
204215.

Predicting Market Components Out of Sample: Asset Allocation Implications
with Aiguo Kong, David
Rapach and Jack Strauss


We analyze outofsample return predictability for components of the aggregate market, focusing on
the wellknown FamaFrench size/valuesorted portfolios. Employing a forecast combination approach based on a variety of
economic variables and lagged component returns as predictors, we find significant evidence of outofsample return
predictability for nearly all component portfolios. Moreover, return predictability is typically much stronger for
smallcap/high booktomarket value stocks. The pattern of component return predictability is enhanced during businesscycle
recessions, linking component return predictability to the real economy. Considering various componentrotation investment
strategies, we show that outofsample component return predictability can be exploited to substantially improve portfolio
performance.
Journal of Portfolio Management 37, 2011, 2011, 2941.

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, 4974.

Bayesian Portfolio Analysis
with Doron Avramov


This paper reviews the literature on Bayesian portfolio analysis. Information about events,
macro conditions, asset pricing theories, and securitydriving 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, 2547.

Incorporating Economic Objectives into Bayesian Priors:
Portfolio Choice Under Parameter Uncertainty
with Jun Tu
(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 FamaFrench 25 size and booktomarket portfolios and
their three factors from January 1965 to December
2004, we find that investment performance under the
objectivebased priors can be significantly
different from that under alternative priors, with
differences in terms of annual certaintyequivalent
returns greater than 10% in many cases.
In terms of outofsample performance,
the Bayesian rules under the objectivebased priors can
outperform substantially some of the best rules developed in the classical framework.
Journal of Financial and Quantitative Analysis 45, 2010,
959986.

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


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 Rsquared that R^{2} <= (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,
184186.

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 meanvariance objective, but also in
terms of two of the most popular risk measures, meanVaR and meanCVaR developed recently.
In addition, we review optimal estimation methods and Bayesian robust approaches.
Annals of Operations Research
176,
2010, 191220.

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 lowconsumptionhighsavings 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, 331344.

OutofSample Equity Premium Prediction:
Combination Forecasts and Links to the Real Economy
with David Rapach and Jack
Strauss
(Notes on Data and Code)


While a host of economic variables have been identified in the literature with the apparent
insample ability to predict the equity premium, Welch and Goyal (2008) find that these variables
fail to deliver consistent outofsample 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 outofsample equity premium prediction. Combining delivers statistically
and economically significant outofsample 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, 821862.

Is the Recent Financial Crisis Really a `Onceinacentury'
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 ``onceina
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 longrun stock market
investments, and the investors should be prepared for it.
Financial Analysts Journal 66 (1), 2010, 2427.

Beyond BlackLitterman: Letting
the Data Speak


The BlackLitterman 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
datagenerating process whose dynamics can have significant impact
on future portfolio returns. This paper extends, in two ways, the BlackLitterman
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 BlackLitterman 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 BlackLitterman model.
Journal of Portfolio Management 36 (1), 2009, 3645.

What Will the Likely Range of My Wealth Be?
Raymond Kan


The median is a better measure than the mean in evaluating the
longterm value of a portfolio. However, the standard plugin
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 longterm value
of a portfolio. In addition, we also provide an unbiased forecast of an
arbitrary percentile of the longterm portfolio value distribution.
This allows us to construct the likely range of the longterm
portfolio value for any given confidence level. Finally, we provide
an unbiased forecast of the probability for the longterm portfolio
value falling into a given interval. Our unbiased estimators
provide a more accurate assessment of the longterm value of a
portfolio than the traditional estimators, and are useful for
longterm planning and investment.
Financial Analysts Journal 65 (4), 2009, 6877.

Technical Analysis: An Asset Allocation
Perspective on the Use of Moving Averages
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 priordependent 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 modelbased optimal trading strategies
when there is uncertainty about the model governing the stock price.
Journal of Financial Economics 92, 2009, 519544.

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 valuedadded
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 valueadded (the valuedadded 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 valueadded if the forecasts or signals have a
high kurtosis. To overcome this problem, we provide an investment
strategy that maximizes the
unconditional valueadded 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 valueadded
over time, and hence, on a riskadjusted basis, our longterm unconditional valueadded 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,
1221.

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
valueadded 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,
2633.

Asymmetries in Stock Returns: Statistical Tests and Economic
Evaluation
with
Yongmiao Hong and Jun Tu


In this paper, we provide a modelfree 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, booktomarket and momentum, we find strong
evidence of asymmetry for both the size and momentum
portfolios, but no evidence for the booktomarket 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
certaintyequivalent gains when he switches from a belief in symmetric stock returns into a belief
in asymmetric ones.
Review of Financial Studies 20, 2007,
15471581.

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 plugin approach that
replaces the population parameters by their sample estimates can
lead to very poor outofsample 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 minimumvariance 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 twofund
portfolio.
Journal of Financial and Quantitative Analysis 42, 2007,
621656.

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) twopass
procedure that is fundamental in understanding to what extent
crosssectional expected returns/values are explained by
certain factor attributes.
While existing studies use almost exclusively this procedure, we
show that alternative twopass 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 tratios 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, 4086.

Using Bootstrap to Test Portfolio Efficiency
with
PinHuang 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 (higherorder
accurate) asymptotic inference. In particular, we apply the method
to examine the efficiency of CRSP valueweighted stock index, and to
test the wellknown Fama and French (1993) threefactor model. We
find that existing tests tend to overreject.
Annals of Economics and Finance 7, 2006, 217249.

Portfolio Optimization under Asset Pricing Anomalies
with
PinHuang Chou and WenShen Li


Fama and French (1993) find that the
SMB and the HML factors explain much of the
crosssection 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
meanvariance 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
19801997,
we find that the optimized portfolio constructed from
characteristicsbased 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, 121142.

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
HansenJagannathan bound that places a lower bound on the variance
of m(x), our bound tightens it by a ratio of (1/ρ_{x,m0})^{2},
where ρ_{x,m0} is the multiple correlation coefficient
between x and the standard minimum variance SDF, m_{0}. In many
applications, the correlation is small, and hence our bound can
be substantially tighter than HansenJagannathan's. For
example, when x is the gross growth rate of consumption, based
on Cochrane's (2001) estimates of market volatility and
ρ_{x,m0}, the new bound is 25 times greater than the HansenJagannathan
bound, making it much
more difficult to explain the equitypremium 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 booktomarket sorted portfolios
used by Fama and French (1993), then it is more than 100 times greater
than the HansenJagannathan bound.
Journal of
Business 79, 2006, 941961.

Datagenerating 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 datagenerating
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 meanvariance investor.
Journal of
Financial Economics 72, 2004, 385421.

What Determines Expected
International Asset Returns?
with
Campbell Harvey and Bruno Solnik


This paper characterizes the forces that determine timevariation 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 timevariation.
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 crosssectional variation in the
international returns.
Annals of Economics and Finance 3, 2002, 83127.

On Rate of Convergence of Discretetime Contingent Claims
with
Steve Heston


This paper characterizes the rate of convergence of discretetime 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 allornothing 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, 5375.

Investment Horizon and the Cross Section of Expected Returns: Evidence from
the Tokyo Stock Exchange
with
PinHuang Chou
and YuanLin 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 crosssection of expected stock returns over different lengths of investment
horizons. We find
that beta, adjusted for infrequent trading or not, fails to explain the crosssection
of monthly expected returns, but does a much better job for horizons over half
and oneyear. However, either the size or the BE/ME alone is still a significant
factor in explaining the crosssection 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, 79100.

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, 383403, 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
booktomarket. While inconclusive insample, a threefactor model appears to perform
better outofsample than both four and fivefactor models.
Journal of Financial Markets 2, 1999, 403432.

Testing Multibeta Pricing Models
with Raja Velu


This paper presents a complete solution to the estimation and testing of multibeta
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 valueweighted and equalweighted 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] threefactor model in addition to two
standard ones, and find that the new
version performs the best.
Journal of Empirical Finance 6, 1999, 219241.

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, 10211048.

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,
6268.

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, 10331059.

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(2), 1996, 553583.

TimetoBuild 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 timetobuild effect of
investments.
Journal of Financial
Research 18, 1995, 115127.

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 onefactor model for the industry returns.
Journal of Empirical Finance 2, 1995, 7193.

Analytical GMM Tests: Asset Pricing with TimeVarying 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 timevarying 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 twofactor one.
Review
of Financial Studies 7, 1994, 687709.

Asset Pricing Tests Under Alternative Distributions


Given the normality assumption, we reject the meanvariance
efficiency of the Center for Research in Security Prices
valueweighted stock index for three of the six consecutive tenyear
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 overrejection and both the accuracy of estimated beta
and R^{2} are usually overstated.
Journal of Finance 48, 1993, 19271942.

International Asset Pricing with Alternative Distributional Specifications
with Campbell Harvey


The unconditional meanvariance 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 tdistributed and mixtures of normal distributions. Even after relaxing
the i.i.d. assumption, we cannot reject the meanvariance 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, 107131.

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 easilyimplemented numerical method is
provided for computing the exact Pvalue. Our approach makes it possible to draw statistical inferences on the efficiency of a
given portfolio both in the context of the zerobeta CAPM and with respect to other linear pricing models. As an application,
using monthly data for every consecutive fiveyear period from 1926 to 1986, we reject the efficiency of the CRSP
valueweighted index for most periods.
Journal of Financial Economics 30, 1991, 165191.

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, 171188.

Bayesian Inference in Asset Pricing Tests
with Campbell Harvey
(An Unpublished TechAppendix)


We test the meanvariance 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 90dimensional integrals.
Posteriorodds 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 meanvariance
efficient is small for a range of plausible priors.
Journal of Financial Economics 26, 1990, 221254.


