Covariance complexity and rates of return on assets

This paper considers the estimation of the expected rate of return on a set of risky assets. The approach to estimation focuses on the covariance matrix for the returns. The structure in the covariance matrix determines shared information which is useful in estimating the mean return for each asset. An empirical Bayes estimator is developed using the covariance structure of the returns distribution. The estimator is an improvement on the maximum likelihood and Bayes–Stein estimators in terms of mean squared error. The effect of reduced estimation error on accumulated wealth is analyzed for the portfolio choice model with constant relative risk aversion utility.     

Predicting stock returns: A risk measurement perspective

This paper proposes a new and efficient model selection strategy to obtain significant stock returns predictability from a risk measurement perspective. The risk interval is defined as the distance between the current actual return and the returns' historical average. The model selection strategy involves switching stock return forecasting models according to different risk intervals from the mean reversion and extreme value theory. This new strategy generates encouraging results in the empirical analysis. A mean-variance investor can realize sizeable economic gains by allocating assets through this new approach relative to competing forecasting models. Furthermore, the strategy performs robustly under alternative settings from both statistical and economic perspectives.     

Out-of-Sample Predictability in International Equity Markets: A Model Selection Approach

For 13 major international stock markets, there is much evidence of out-of-sample predictability for growth stocks especially when evaluated with economic criteria, and to a noticeably lesser extent for general stock markets and value stocks. Our results shed light on the recent debate about stock return predictability, using different assets (growth-style indexes), forecasting variables (past returns), forecasting models (nonlinear models), and alternative forecasting evaluation criteria (economic criteria). Our analysis suggests that (growth) stock returns might be predictable.     

International capital asset pricing: Evidence from options

We study the risk dynamics and pricing in international economies through a joint analysis of the time-series returns and option prices on three equity indexes underlying three economies: the S&P 500 Index of the United States, the FTSE 100 Index of the United Kingdom, and the Nikkei-225 Stock Average of Japan. We develop an international capital asset pricing model, under which the return on each equity index is decomposed into two orthogonal jump-diffusion components: a global component and a country-specific component. We apply separate stochastic time changes to the two components so that stochastic volatility can come from both global and country-specific risks. For each economy, we assign separate market prices for the two return risk components and the two volatility risk components. Under this specification, we obtain tractable option pricing solutions. Model estimation reveals several interesting insights. First, global and country-specific return and volatility risks show different dynamics. Global return movements contain a larger discontinuous component, and global return volatility is more persistent than the country-specific counterparts. Second, investors charge positive prices for global return risk and negative prices for volatility risk, suggesting that investors are willing to pay positive premiums to hedge against downside global return movements and upside volatility movements. Third, the three economies contain different risk profiles and also price risks differently. Japan contains the largest idiosyncratic risk component and smallest global risk component. Investors in the Japanese market also price more heavily against future volatility increases than against future market downfalls.     

International stock return predictability: Evidence from new statistical tests

We investigate whether stock returns of international markets are predictable from a range of fundamentals including key financial ratios (dividend-price ratio, dividend-yield, earnings-price ratio, dividend-payout ratio), technical indicators (price pressure, change in volume), and short-term interest rates. We adopt two new alternative testing and estimation methods: the improved augmented regression method and wild bootstrapping of predictive model based on a restricted VAR form. Both methods take explicit account of endogeneity of predictors, providing bias-reduced estimation and improved statistical inference in small samples. From monthly data of 16 Asia-Pacific (including U.S.) and 21 European stock markets from 2000 to 2014, we find that the financial ratios show weak predictive ability with small effect sizes and poor out-of-sample forecasting performances. In contrast, the price pressure and interest rate are found to be strong predictors for stock return with large effect sizes and satisfactory out-of-sample forecasting performance.     

Dynamic principal component CAW models for high-dimensional realized covariance matrices

We propose a new dynamic principal component CAW model (DPC-CAW) for time-series of high-dimensional realized covariance matrices of asset returns (up to 100 assets). The model performs a spectral decomposition of the scale matrix of a central Wishart distribution and assumes independent dynamics for the principal components' variances and the eigenvector processes. A three-step estimation procedure makes the model applicable to high-dimensional covariance matrices. We analyze the finite sample properties of the estimation approach and provide an empirical application to realized covariance matrices for 100 assets. The DPC-CAW model has particularly good forecasting properties and outperforms its competitors for realized covariance matrices.     

An alternative measure of the “world market portfolio”: Determinants, efficiency, and information content

The world market portfolio plays an important role in international asset pricing, but is unobservable in practice. We first propose a framework for constructing a market proxy that corresponds to the “market portfolio” of financial theory. We then construct this proxy, analyze its determinants and test its efficiency and explanatory power over the period 1975-2007 with respect to the return generating processes of a broad asset universe. We show that its major determinants are traded assets and that it is not efficient. However, it is significant for explaining individual asset returns over an asset universe that includes stocks, bonds, money markets and commodities. The explanatory information is incremental to what is available in traded asset prices and the significance of this information is robust with respect to diversified portfolios generated by factor analysis and to characteristic-sorted portfolios as well as to various model specifications, including the single-index model, the Fama-French (1992) three factor model for stocks, and various specifications of multi-index models hedged and unhedged for foreign currency risk.     

The dual contributions of information instruments in return models: magnitude and direction predictability

By partitioning asset return prediction errors, we show explicitly the dual role of magnitude and sign prediction of return instruments. We demonstrate analytically that sign prediction directly affects heteroskedasticity in asset returns; increases in precision attenuate the heteroskedasticity. Our findings with monthly asset returns are consistent with earlier evidence and indicate that our proposed analytical model captures the sign predictive component of returns. Our results are supportive of a nonlinear return generating model that can be thought of as the product of a model, perhaps linear, for forecasting return signs and a model for forecasting return magnitudes.     

Tactical Industry Allocation and Model Uncertainty

We use Bayesian model averaging to analyze industry return predictability in the presence of model uncertainty. The posterior analysis shows the importance of inflation and earnings yield in predicting industry returns. The out‐of‐sample performance of the Bayesian approach is, in general, superior to that of other statistical model selection criteria. However, the out‐of‐sample forecasting power of a naive i.i.d. forecast is similar to the Bayesian forecast. A variance decomposition into model risk, estimation risk, and forecast error shows that model risk is less important than estimation risk.     

Economic Significance of Predictable Variations in Stock Index Returns

Knowledge of the one-month interest rate is useful in forecasting the sign as well as the variance of the excess return on stocks. The services of a portfolio manager who makes use of the forecasting model to shift funds between bills and stocks would be worth an annual management fee of 2% of the value of the assets managed. During 1954:4 to 1986:12, the variance of monthly returns on the managed portfolio was about 60% of the variance of the returns on the value weighted index, whereas the average return was two basis points higher.     

International portfolio diversification and multilateral effects of correlations

Not only are investors biased toward home assets, but when they do invest abroad, they appear to favor countries with returns more correlated with home assets. Often attributed to a preference for familiarity, this ‘correlation puzzle’ further reduces effective diversification. We use a multi-country general equilibrium model of portfolio choice to study how bilateral equity holdings are affected by return correlations among alternative destination and source countries. From the theoretical model, we develop an empirical approach to estimate a gravity equation for equity holdings that incorporates the overall covariance structure in a theoretically rigorous yet tractable manner. Estimation using this approach resolves the correlation puzzle, and finds that international investors do seek the diversification benefits of low cross-country correlations, as theory would predict.     

Prospect theory–based portfolio optimization: an empirical study and analysis using intelligent algorithms

The behaviourally based portfolio selection problem with investor’s loss aversion and risk aversion biases in portfolio choice under uncertainty is studied. The main results of this work are: developed heuristic approaches for the prospect theory model proposed by Kahneman and Tversky in 1979 as well as an empirical comparative analysis of this model and the index tracking model. The crucial assumption is that behavioural features of the prospect theory model provide better downside protection than traditional approaches to the portfolio selection problem. In this research the large-scale computational results for the prospect theory model have been obtained for real financial market data with up to 225 assets. Previously, as far as we are aware, only small laboratory tests (2–3 artificial assets) have been presented in the literature. In order to investigate empirically the performance of the behaviourally based model, a differential evolution algorithm and a genetic algorithm which are capable of dealing with a large universe of assets have been developed. Specific breeding and mutation, as well as normalization, have been implemented in the algorithms. A tabulated comparative analysis of the algorithms’ parameter choice is presented. The prospect theory model with the reference point being the index is compared to the index tracking model. A cardinality constraint has been implemented to the basic index tracking and the prospect theory models. The portfolio diversification benefit has been found. The aggressive behaviour in terms of returns of the prospect theory model with the reference point being the index leads to better performance of this model in a bullish market. However, it performed worse in a bearish market than the index tracking model. A tabulated comparative analysis of the performance of the two studied models is provided in this paper for in-sample and out-of-sample tests. The performance of the studied models has been tested out-of-sample in different conditions using simulation of the distribution of a growing market and simulation of the t-distribution with fat tails which characterises the dynamics of a decreasing or crisis market.     

Bayesian realized-GARCH models for financial tail risk forecasting incorporating the two-sided Weibull distribution

The realized-GARCH framework is extended to incorporate the two-sided Weibull distribution, for the purpose of volatility and tail risk forecasting in a financial time series. Further, the realized range, as a competitor for realized variance or daily returns, is employed as the realized measure in the realized-GARCH framework. Sub-sampling and scaling methods are applied to both the realized range and realized variance, to help deal with inherent micro-structure noise and inefficiency. A Bayesian Markov Chain Monte Carlo (MCMC) method is adapted and employed for estimation and forecasting, while various MCMC efficiency and convergence measures are employed to assess the validity of the method. In addition, the properties of the MCMC estimator are assessed and compared with maximum likelihood, via a simulation study. Compared to a range of well-known parametric GARCH and realized-GARCH models, tail risk forecasting results across seven market indices, as well as two individual assets, clearly favour the proposed realized-GARCH model incorporating the two-sided Weibull distribution; especially those employing the sub-sampled realized variance and sub-sampled realized range.     

The empirical relationship between risk and return: evidence from the UK stock market

Previous studies reach no consensus on the relationship between risk and return using data from one market. We argue that the world market factor should not be ignored in assessing the risk-return relationship in a partially integrated market. Applying a bivariate generalized autoregressive conditional heteroscedasticity in mean (GARCH-M) model to the weekly stock index returns from the UK and the world market, we document a significant positive relationship between stock returns and the variance of returns in the UK stock market after controlling for the covariance of the UK and the world market return. In contrast, conventional univariate GARCH-M models typically fail to detect this relationship. Nonnested hypothesis tests supplemented with other commonly used model selection criteria unambiguously demonstrate that our bivariate GARCH-M model is more likely to be the true model for UK stock market returns than univariate GARCH-M models. Our results have implications for empirical assessments of the risk-return relationship, expected return estimation, and international diversification.     

Mean–variance and mean–semivariance portfolio selection: a multivariate nonparametric approach

While univariate nonparametric estimation methods have been developed for estimating returns in mean-downside risk portfolio optimization, the problem of handling possible cross-correlations in a vector of asset returns has not been addressed in portfolio selection. We present a novel multivariate nonparametric portfolio optimization procedure using kernel-based estimators of the conditional mean and the conditional median. The method accounts for the covariance structure information from the full set of returns. We also provide two computational algorithms to implement the estimators. Via the analysis of 24 French stock market returns, we evaluate the in-sample and out-of-sample performance of both portfolio selection algorithms against optimal portfolios selected by classical and univariate nonparametric methods for three highly different time periods and different levels of expected return. By allowing for cross-correlations among returns, our results suggest that the proposed multivariate nonparametric method is a useful extension of standard univariate nonparametric portfolio selection approaches.     

A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability

We present a simulation-based method for solving discrete-timeportfolio choice problems involving non-standard preferences,a large number of assets with arbitrary return distribution,and, most importantly, a large number of state variables withpotentially path-dependent or non-stationary dynamics. The methodis flexible enough to accommodate intermediate consumption,portfolio constraints, parameter and model uncertainty, andlearning. We first establish the properties of the method forthe portfolio choice between a stock index and cash when thestock returns are either iid or predictable by the dividendyield. We then explore the problem of an investor who takesinto account the predictability of returns but is uncertainabout the parameters of the data generating process. The investorchooses the portfolio anticipating that future data realizationswill contain useful information to learn about the true parametervalues.     

INTERNATIONAL DIVERSIFICATION OF EQUITIES AND FIXED-INCOME SECURITIES

Portfolio selection models have been applied principally to common stocks traded in the United States and in foreign stock markets. This study examines the efficient set of portfolios selected from a choice set that includes returns derived from domestic and international corporate bond and government bond indices as well as domestic and international stock indices. To assess the benefits of international multi-asset diversification, the authors examine the following issues: (1) the extent to which international and domestic fixed-income securities are included in efficient portfolios; (2) the effect on efficient set composition of using the Sharpe portfolio selection model as compared to the Markowitz portfolio selection model; (3) the sensitivity of efficient set characteristics produced from a single-index based portfolio selection model to alternative world market indices; and (4) the correspondence between expected and realized portfolio risk and return for the different portfolio selection models.     

Common Volatility: An Empirical Investigation of Closed-End Country Funds

The study of international integration of equity markets has received a great deal of interest. This paper investigates whether returns of forty-one closed-end country funds share a common volatility process with three comparable return series: the underlying net asset value (NAV), U.S. stock market returns, and foreign stock market returns. Country funds are a natural setting to test for international market integration, as they are traded in the U.S. market, whereas their underlying assets are traded in foreign stock markets. Our results indicate that only a few emerging markets' country funds share common volatility processes with their comparable asset returns. This, in turn, suggests weak linkages through the second moment of related assets.     

Sampling interval and estimated betas: Implications for the presence of transitory components in stock prices

We provide a theoretical framework to explain the empirical finding that the estimated betas are sensitive to the sampling interval even when using continuously compounded returns. We suppose that stock prices have both permanent and transitory components. The discrete time representation of the beta depends on the sampling interval and two components labeled “permanent and transitory betas”. We show that if no transitory component is present in stock prices then no sampling interval effect occurs. However, the presence of a transitory component implies that the beta is an increasing (decreasing) function of the sampling interval for more (less) risky assets. In our framework, assets are labeled risky if their “permanent beta” is greater than their “transitory beta” and vice versa for less risky assets. Simulations show that our theoretical results provide good approximations for the estimated betas in small samples. We provide empirical evidence about the presence of negative serial correlation and mean reversion in the returns of the portfolios considered. We discuss why our model is better able to provide an explanation for this sampling interval effect than other models in the literature.     

Betting against beta

We present a model with leverage and margin constraints that vary across investors and time. We find evidence consistent with each of the model's five central predictions: (1) Because constrained investors bid up high-beta assets, high beta is associated with low alpha, as we find empirically for US equities, 20 international equity markets, Treasury bonds, corporate bonds, and futures. (2) A betting against beta (BAB) factor, which is long leveraged low-beta assets and short high-beta assets, produces significant positive risk-adjusted returns. (3) When funding constraints tighten, the return of the BAB factor is low. (4) Increased funding liquidity risk compresses betas toward one. (5) More constrained investors hold riskier assets.