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Abstract:
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, 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.

Technical analysis, trading rules, asset allocation, predictability, learning

Abstract:
In this paper, we conduct a comprehensive study of tests for mean-variance spanning. Under the popular regression framework of Huberman and Kandel (1987), we provide geometric interpretations of three asymptotic tests (likelihood ratio, Wald, and Lagrange multiplier) of mean-variance spanning. Under normality assumption, we present their exact distributions and analyze their power comprehensively. Under general distributional assumptions, we review spanning tests based on the generalized method of moments (GMM), provide new GMM spanning test, and evaluate their performance. In addition, we compare the performance of various spanning tests in the regression framework with those cast in the stochastic discount factor framework. Our results suggest that the two set-ups have similar properties when returns are normally distributed, but the regression framework performs better when returns follow a multivariate Student-t distribution.

Abstract:
The modern portfolio theory pioneered by Markowitz (1952) is widely used in practice and taught in MBA texts. DeMiguel, Garlappi and Uppal (2007), however, show that, due to estimation errors, existing theory-based portfolio strategies are not as good as we once thought, and the estimation window needed for them to beat the naive $1/N$ strategy (that invests equally across N risky assets) is 'around 3000 months for a portfolio with 25 assets and about 6000 months for a portfolio with 50 assets.' In this paper, we modify the modern portfolio theory to account for estimation errors, so that the theory becomes more relevant in practice to yield positive gains over the naive 1/N strategy under realistic estimation windows. In particular, we provide new portfolio strategies that not only perform as well as the 1/N strategy in an exact one-factor model that favors the 1/N, but also outperform it substantially in a one-factor model with mispricing, in multi-factor models with and without mispricing, and in models calibrated from real data without any factor structures. We also find that the usual maximum likelihood (ML) estimator of the true portfolio rule can have Sharpe ratios higher than the 1/N in many cases, and hence, if one is concerned only about Sharpe ratios, the ML estimator is not as bad as one might have once believed.

Portfolio choice, parameter uncertainty, shrinkage, admissibility

Abstract:
In this paper, we conduct a simulation analysis of the Fama and MacBeth (1973) two-pass procedure, as well as maximum likelihood (ML) and generalized method of moments estimators of cross-sectional expected return models. We also provide some new analytical results on computational issues, the relations between estimators, and asymptotic distributions under model misspecification. The GLS estimator is often much more precise than the usual OLS estimator, but it displays more bias as well. A truncated form of ML performs quite well overall in terms of bias and precision, but produces less reliable inferences than the OLS estimator.

Fama and MacBeth, two-pass procedure, GLS, GMM

Abstract:
We analyze return predictability for components of the aggregate market, including portfolios sorted on industry, size, and book-to-market. Considering a variety of economic variables and lagged industry returns as predictors, both in-sample and out-of-sample tests highlight substantial differences in return predictability across components. Among industry portfolios, construction, textiles, apparel, furniture, printing, automobiles, and manufacturing exhibit the most predictability, while portfolios of small-cap and high book-to-market firms also display considerable predictability. Three key findings provide economic explanations for component predictability: (i) component predictability is markedly more evident during recessions, linking predictability to business-cycle fluctuations; (ii) based on a novel out-of-sample decomposition, time-varying macroeconomic risk premiums captured by the conditional CAPM and conditional Fama-French 3-factor model largely account for component predictability; (iii) industry concentration and market capitalization significantly explain differences in return predictability across industries, consistent with the information-flow frictions emphasized by Hong, Torous, and Valkanov (2007). We further show that predictability can be exploited to improve portfolio performance for component-rotation investment strategies.

Return predictability, Industries, Size, Book-to-market, Macroeconomic fundamentals and risk, Information-flow frictions

Abstract:
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, and also provide such tests for asymmetric betas and covariances. When stocks are sorted by size, book-to-market, and momentum, we find strong evidence of asymmetries for both size and momentum portfolios, but no evidence for book-to-market portfolios. Moreover, we evaluate the economic significance of incorporating asymmetries into investment decisions, and find that they can be of substantial economic importance for an investor with a disappointment aversion (DA) preference as described by Ang, Bekaert, and Liu (2005).

Abstract:
In this paper, we provide a model-free test for asymmetric correlations which suggest stocks tend to have greater correlations 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 asymmetric correlations by answering the question that what is the utility gain for an investor who switches from a belief of symmetric stock returns into a belief of asymmetric returns. Applying our methodology to three portfolios grouped by size, Fama and French's size and book-to-market, and industry, we find that asymmetries show up in sample estimates for all the portfolios, but they are statistically ignificant primarily for small size portfolios. Nevertheless, asymmetries are of substantial economic importance for an investor who switches her symmetry belief into an asymmetric one, irrespective of the portfolios.

Abstract:
While a host of economic variables have been identified in the literature with the apparent in-sample ability to predict the equity premium, Goyal and Welch (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.

portfolio performance between advised and self-directed investors

Abstract:
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.

limited participation, saving, consumption, insurance

Abstract:
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.

Portfolio choice, Parameter uncertainty, Bayesian priors

Abstract:
In this paper, we extend the long-run risks model of Bansal and Yaron (BY, 2004) to allow both a long- and a short-run volatility component in consumption growth, long-run risks, and dividend growth. Our two volatility model better captures macroeconomic volatility than a single volatility model, and can reconcile simultaneously the large negative market variance risk premium, differing predictability in excess returns, consumption, dividends, and stock market volatility, all of which are difficult to explain previously by the BY model.

Long-run Risk, Equity Risk Premium, Predictability, Variance Risk Premium

Abstract:
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 crisis, Once-in-a-Century event, drawndown probability

Abstract:
We test the mean-variance efficiency of a given portfolio with a Bayesian framework. Our test is more direct than Shanken's (1987), 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 using three distributions. The probability that the given portfolio is mean-variance efficient is small for a range of plausible priors. This is the working paper version of our 1990 Journal of Financial Economics article.

Asset pricing, CAPM, Bayesian finance, CAPM tests, market efficiency

Abstract:
The median is often 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.

long-term investment, median, quantiles

Abstract:
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.d.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.

This is the final working paper version of our 1993 publication in the Journal of Empirical Finance.

International asset pricing, CAPM, mean-variance efficiency, alternative distributions, mixtures of normals

Abstract:
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 R^2 <= (1 R_f)^2 Var(m) for a given asset pricing model with kernel m, where R_f is the risk-free 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.

Predictability, predictive regression, R-squared, stochastic discount factor

Abstract:
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.

Abstract:
In this paper, we conduct a simulation analysis of the Fama and MacBeth (1973) two-pass procedure, as well as maximum likelihood (ML) and generalized method of moments estimators of cross-sectional expected return models. We also provide some new analytical results on computational issues, the relations between estimators, and asymptotic distributions under model misspecification. The GLS estimator is often much more precise than the usual OLS estimator, but it displays more bias as well. A "truncated" form of ML performs quite well overall in terms of bias and precision, but produces less reliable inferences than the OLS estimator.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
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 R^2 statistics of 10% or greater, more than triple the postwar average.

Equity premium, Predictive regression model, Combination forecast, Information diffusion, Granger causality, Business cycle, Global financial crisis

Abstract:
The modern portfolio theory pioneered by Markowitz (1952, JF) is widely used in practice and taught in MBA texts. However, many studies, in the past and recent, e.g., Duchin and Levy (2009, JPM), find that the theory can be unreliable at all due to estimation errors (estimation risk). Especially, in a major paper in one of the top finance journals, DeMiguel, Garlappi and Uppal (2009, RFS) show that existing theory-based portfolio strategies are not as good as we once thought, and the estimation window needed for them to outperform the naive $1/N$ rule (that invests equally across N risky assets) is 'around 3000 months for a portfolio with 25 assets and about 6000 months for a portfolio with 50 assets;' and there are still many 'miles to go' before the gains promised by optimal portfolio choice can actually be realized out of sample."

My proposed study addresses three questions: \ {\bf 1)} for asset allocation decisions with up to 50 assets, theory-based portfolio strategies can be re-designed to incorporate estimation risk, so that they perform well, and outperform the naive $1/N$ rule in both simulations and real data sets when with sample size of 120 month (this has been done already, but significant revision is needed to accommodate more practical situations); {\bf 2)} When the number of assets is large, say $N=500$, most existing theory-based portfolio strategies do not apply because of 120 months of data cannot yield invertible covariance matrix of asset returns. But for the rule that does work, the idea of the approach still works as expected as confirmed by simulations. Future analytical extension of the existing theory strategies will be studies (doable, though takes substantial time), and then \underline{investment theory is useful after all} when $N$ is large or small; {\bf 3)} Pair trading, statistical arbitrage and index tracking strategies can all be modified to accommodate estimation risk.

There are potential many applications of the methodology of the proposed study in various portfolio management areas, such as asset allocation and benchmarking. The study of estimation risk, parameter and model uncertainties, can also shed light on many other issues of finance, such as the trading illiquidity and investor overreaction in financial crises.

Abstract:
The median is often a better measure than the mean in evaluating a portfolio’s long-term value. The standard plug-in estimate of the median, however, is too optimistic. It has a substantial upward bias that can easily exceed a factor of 2. This article provides an unbiased forecast of the median of a portfolio’s long-term value. It also provides an unbiased forecast of an arbitrary percentile of a portfolio’s long-term value distribution, which enables the construction of the likely range of a portfolio’s long-term value for any given confidence level. The article offers an unbiased forecast of the probability of a portfolio’s long-term value falling within a given interval. The article’s unbiased estimators give a more accurate assessment of a portfolio’s long-term value than do traditional estimators and are useful for long-term planning and investment.

Investment Theory, Portfolio Theory, Quantitative Tools, Econometric and Statistical Methods, Portfolio Management, Portfolio Construction, Rebalancing, and Implementation, Private Wealth Management, Investment Policy Formulation

Abstract:
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 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. The 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.

Black-Litterman, Bayesian, Mean-variance, Portfolio Choice, Views

Abstract:
This paper 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.

Abstract:
We propose alternative 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 model.

Abstract:
Within the past few years, several papers have suggested that returns on large equity portfolios may contain a significant predictable component at horizons of 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 paper 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.