A Time-Series Model of Stock Returns with a Positive Short-Term Correlation and a Negative Long-Term Correlation

We study portfolio stock return behavior that exhibits both a positive autocorrelation over short horizons and a negative autocorrelation over long horizons. These autocorrelations are more significant in small size portfolios. Among various forms of temporary components in stock prices, an AR(2) component is the simplest model compatible with this pattern of returns, which yields an ARMA(2,2) model of stock returns. We show that the significance of this model is that it requires the presence of feedback trading, which is a form of irrational trades, and the market's slow adjustment to the market fundamentals, which is consistent with recent modelings of stock prices. We find that the variation of the temporary component becomes greater as the firm size gets smaller. This implies that the deviation from the market fundamentals is larger in small size portfolios than in large size portfolios.     

A transactions data analysis of nonsynchronous trading

Weekly returns of stock portfolios exhibit substantial autocorrelation.Analytical studies suggest that nonsynchronous trading is capableof explaining from 5% to 65% of the autocorrelation. The varyingimportance of nonsynchronous trading in these studies arisesprimarily from differing assumptions regarding nontrading periodsof stocks. We simulate the effects of nonsynchronous tradingby sampling stock returns from a return generating process usingtransactions data to obtain the precise time of each stock'slast trade. We find that simulated weekly portfolio returnsexhibit autocorrelations that are roughly 25% that of theirobserved (CRSP) weekly returns.     

The impact of portfolio diversification on mean reverting components of stock indices

Positive autocorrelations are introduced into stock index portfolios when they are formed from individual stock indices while negative autocorrelations are induced in returns by increasing the investment horizon. Using monthly data of six international stock indices, this paper examines the diversification effect with different investment horizons on autocorrelations of stock index portfolios. The results show that portfolio diversification does not alter the impact of the investment horizon on autocorrelations. Different investment horizons, however, have great impact on the diversification effect on autocorrelations. With short (long) horizons, the average autocorrelation coefficient increases (decreases) with an increase in the portfolio size, suggesting that mean-reverting component dominates the delayed adjustment effect in long horizons and vice versa in short horizons. Our results are robust across two 10-year sub-periods.The author would like to thank an anonymous referee of this Journal for the comments on an earlier version of this paper and the Research Committee of Hong Kong Baptist University for the financial support in this research.     

THE CROSS-AUTOCORRELATION OF SIZE-BASED PORTFOLIO RETURNS IS NOT AN ARTIFACT OF PORTFOLIO AUTOCORRELATION

Prior studies find evidence of asymmetric size-based portfolio return cross-autocorrelations where lagged large firm returns lead current small firm returns. However, some studies question whether this economic relation is independent of the effect of portfolio return autocorrelation. We formally test for this independence using size-based portfolios of New York Stock Exchange and American Stock Exchange securities and, separately, portfolios of Nasdaq securities. Results from causality regressions indicate that, across all markets, lagged large firm returns predict current small firm returns, even after controlling for autocorrelation in small firm returns. These cross-autocorrelation patterns are stronger for Nasdaq securities.     

Trading Volume: Implications of an Intertemporal Capital Asset Pricing Model

We derive an intertemporal asset pricing model and explore its implications for trading volume and asset returns. We show that investors trade in only two portfolios: the market portfolio, and a hedging portfolio that is used to hedge the risk of changing market conditions. We empirically identify the hedging portfolio using weekly volume and returns data for U.S. stocks, and then test two of its properties implied by the theory: Its return should be an additional risk factor in explaining the cross section of asset returns, and should also be the best predictor of future market returns.     

Portfolio Returns,Market Volatility,and Seasonality

This paper examines three important issues related to the relationship between stock returns and volatility. First, are Duffee's (1995) findings of the relationship between individual stock returns and volatility valid at the portfolio level? Second, is there a seasonality of the market return volatility? Lastly, do size portfolio returns react symmetrically to the market volatility during business cycles? We find that the market volatility exhibits strong autocorrelation and small size portfolio returns exhibit seasonality. However, this phenomenon is not present in large size portfolios. For the entire sample period of 1962–1995, the highest average monthly volatility occurred in October, followed by November, and then January. Examining the two sub-sample periods, we find that the average market volatility increases by 15.4% in the second sample period of 1980–1995 compared to the first sample period of 1962–1979. During the contraction period, the average market volatility is 60.9% higher than that during the expansion period. Using a binary regression model, we find that size portfolio returns react asymmetrically with the market volatility during business cycles. This paper documents a strongly negative contemporaneous relationship between the size portfolio returns and the market volatility that is consistent with the previous findings at the aggregate level, but is inconsistent with the findings at the individual firm level. In contrast with the previous findings, however, we find an ambiguous relationship between the percentage change in the market volatility and the contemporaneous stock portfolio returns. This ambiguity is attributed to strongly negative contemporaneous and one-month ahead relationships between the market volatility and portfolio returns.

     

Long-term U.S. infrastructure returns and portfolio selection

Our understanding of the long-term return behavior and portfolio characteristics of public infrastructure investments is limited by a relatively short history of empirical data. We re-construct U.S. listed infrastructure index returns by mapping their monthly performance to received systematic and industry risk factors from 1927 through 2010. Our findings reveal that the infrastructure returns in recent years may understate the tail-risk that investors could experience over the long-term, however, this tail-risk is commensurate with holding a broad portfolio of U.S. stocks. For mean-variance and mean-CVaR investors, we report the benefits of holding public infrastructure assets in investment portfolios.     

Optimal Estimation of the Risk Premium for the Long Run and Asset Allocation: A Case of Compounded Estimation Risk

It is well known that an unbiased forecast of the terminal valueof a portfolio requires compounding at the arithmetic mean returnover the investment horizon. However, the maximum-likelihoodpractice, common with academics, of compounding at the estimatorof mean return results in upward biased and highly inefficientestimates of long-term expected returns. We derive analyticallyboth an unbiased and a small-sample efficient estimator of long-termexpected returns for a given sample size and horizon. Both estimatorsentail penalties that reduce the annual compounding rate asthe investment horizon increases. The unbiased estimator, whichis far lower than the compounded arithmetic average, is stillvery inefficient, often more so than a simple geometric estimatorknown to practitioners. Our small-sample efficient estimatoris even lower. These results compound the sobering evidencein recent work that the equity risk premium is lower than suggestedby post-1926 data. Our methodology and results are robust toextensions such as predictable returns. We also confirm analyticallythat parameter uncertainty, properly incorporated, producesoptimal asset allocations, in stark contrast to conventionalwisdom. Longer investment horizons require lower, not higher,allocations to risky assets.     

Online learning of time-varying stochastic factor structure by variational sequential Bayesian factor analysis

Investment tasks include forecasting volatilities and correlations of assets and portfolios. One of the tools widely utilized is stochastic factor analysis on a set of correlated time-series (e.g. asset returns). Published time-series factor models require either sufficiently wide time windows of observed data or numeric solutions by simulations. We developed a ‘variational sequential Bayesian factor analysis’ (VSBFA) algorithm to make online learning of time-varying stochastic factor structure. The VSBFA is an analytic filter to estimate unknown factor scores, factor loadings and residual variances. The covariance matrix of the time-series predicted by the VSBFA can be decomposed into loadings-based covariance and specific variances, and the former can be expressed by ‘explanatory factors’ such as systematic components of various financial market indices. We compared the VSBFA with the most practiced factor model relying on wide data windows, the rolling PCA (principal components analysis), by applying them to 9-year daily returns of 200 simulated stocks with the ‘true’ daily data-generating model completely known, and by using them to forecast volatilities of long-only and long/short global stock portfolios with 25-year monthly returns of more than 800 stocks worldwide. Accuracy of the forecast covariance matrices is measured by a (symmetrized) Kullback–Leibler distance, and accuracy of the forecast portfolio volatilities is measured by bias statistic, log-likelihood, Q-statistic, and portfolio volatility minimization. The factor-based covariance and specific variances predicted by the best VSBFA are significantly more accurate than those by the best rolling PCA.     

Investment Horizon Effects

Abstract:   Boudry and Gray (2003) have documented that the optimal buy‐and‐hold demand for Australian stocks is not necessarily increasing in the investment horizon when returns are predictable. Such finding is in contrast with Barberis (2000) who shows that positive monotonic horizon effects predominate for US stocks. Using a closed‐form approximation to the asset allocation problem, this paper relates the return dynamics to the investor's portfolio choice for different investment horizons. In the special case of a single risky asset, it is shown that return predictability under stationarity may induce both positive and negative horizon effects in the optimal allocation to the risky asset. The paper extends previous empirical results by solving for the optimal portfolio when two risky assets with predictable returns are available for investment.     

A dynamic model of active portfolio management with benchmark orientation

This paper studies optimal dynamic portfolios for investors concerned with the performance of their portfolios relative to a benchmark. Assuming that asset returns follow a multi-linear factor model similar to the structure of Ross (1976) [Ross, S., 1976. The arbitrage theory of the capital asset pricing model. Journal of Economic Theory, 13, 342–360] and that portfolio managers adopt a mean tracking error analysis similar to that of Roll (1992) [Roll, R., 1992. A mean/variance analysis of tracking error. Journal of Portfolio Management, 18, 13–22], we develop a dynamic model of active portfolio management maximizing risk adjusted excess return over a selected benchmark. Unlike the case of constant proportional portfolios for standard utility maximization, our optimal portfolio policy is state dependent, being a function of time to investment horizon, the return on the benchmark portfolio, and the return on the investment portfolio. We define a dynamic performance measure which relates portfolio’s return to its risk sensitivity. Abnormal returns at each point in time are quantified as the difference between the realized and the model-fitted returns. Risk sensitivity is estimated through a dynamic matching that minimizes the total fitted error of portfolio returns. For illustration, we analyze eight representative mutual funds in the U.S. market and show how this model can be used in practice.     

The Predictive Ability of Dividend and Earnings Yields for Long-Term Stock Returns

We use empirical models to examine the predictive ability of dividend and earnings yields for long‐term stock returns. Results show that dividend and earnings yields share a similar predictive power for future stock returns and growth. We find that the predictive power of dividend yields increases with the return horizon, but that yields forecast future returns and growth over a much longer horizon. Finally, dividend and earnings yields exhibit high autocorrelation and strong contemporaneous relations.     

Small caps in international equity portfolios: the effects of variance risk

We show that predictable covariances between means and variances of stock returns may have a first order effect on portfolio composition. In an international asset menu that includes both European and North American small capitalization equity indices, we find that a three-state, heteroskedastic regime switching VAR model is required to provide a good fit to weekly return data and to accurately predict the dynamics in the joint density of returns. As a result of the non-linear dynamic features revealed by the data, small cap portfolios become riskier in bear markets, i.e., display negative co-skewness with other stock indices. Because of this property, a power utility investor ought to hold a well-diversified portfolio, despite the high risk premium and Sharpe ratios offered by small capitalization stocks. On the contrary, small caps command large optimal weights when the investor ignores variance risk, by incorrectly assuming joint normality of returns.      

Asymmetric reverting behavior of short-horizon stock returns: An evidence of stock market overreaction

This paper investigates the uneven mean reverting pattern of monthly return indexes of the NYSE, AMEX and NASDAQ, using asymmetric non-linear smooth-transition (ANST) GARCH models. It also evaluates the extent to which time-varying volatility in the index returns support the stock market overreaction hypothesis. The models illuminate patterns of asymmetric mean reversion and risk decimation. Between 1926:01 and l997:12, not only did negative returns reverse to positive returns quicker than positive returns reverted to negative ones, but negative returns, in fact, reduced risk premiums from predictable high volatility. The findings support the market overreaction hypotheses. The asymmetry is due to the mispricing behavior on the part of investors who overreact to certain market news. The findings also corroborate arguments for the “contrarian” portfolio strategy.     

Mean-variance optimization using forward-looking return estimates

Despite its theoretical appeal, Markowitz mean-variance portfolio optimization is plagued by practical issues. It is especially difficult to obtain reliable estimates of a stock’s expected return. Recent research has therefore focused on minimum volatility portfolio optimization, which implicitly assumes that expected returns for all assets are equal. We argue that investors are better off using the implied cost of capital based on analysts’ earnings forecasts as a forward-looking return estimate. Correcting for predictable analyst forecast errors, we demonstrate that mean-variance optimized portfolios based on these estimates outperform on both an absolute and a risk-adjusted basis the minimum volatility portfolio as well as naive benchmarks, such as the value-weighted and equally-weighted market portfolio. The results continue to hold when extending the sample to international markets, using different methods for estimating the forward-looking return, including transaction costs, and using different optimization constraints.

     

Targeting market neutrality

Neutralizing portfolios from overall market risk is an important part of investment management, particularly for hedge funds. In this paper we show an economically significant improvement in the accuracy of targeting market neutrality for equity portfolios. Key features of the approach are the relatively short forecast horizon of one week and forecasting with realized beta estimators computed using high quality, error corrected, intraday returns. We also find that too long and too short estimation windows result in poor beta forecasts and that the optimal length of estimation window depends on the frequency of return observations.     

Distinguishing Between Rationales for Short‐Horizon Predictability of Stock Returns

In this paper, we shed light on short‐horizon return reversals. We show theoretically that a risk‐based rationale for reversals implies a relation between returns and past order flow, whereas a reversion in beliefs of biased agents does not do so. The empirical results indicate that returns are more strongly related to own‐return lags than to lagged order imbalances. Thus, the evidence suggests that monthly reversals are not completely captured by inventory effects and may be driven, in part, by belief reversion. We do find that returns are cross‐sectionally related to lagged imbalance innovations at horizons longer than a month.     

A behavioral explanation of the value anomaly based on time-varying return reversals

We investigate the dynamics of the value anomaly in order to identify the driving forces of the anomaly. We show that the large positive value-minus-growth portfolio returns are explained by an over-reaction (under-reaction) to the positive (negative) market movements in short, specific time periods, during which the average returns of value-minus-growth portfolios are more than 2% a month. We propose an explanation based on behavioral biases: the dynamics of the value anomaly reflect the increased speed of return reversals subsequent to overreaction. Two conditions that increase the return reversals are proposed: when investors respond to public signals asymmetrically or when public signals become noisy. Our empirical results reveal that the value anomaly is explained by either one of these two channels.     

Short-term predictability of equity returns along two style dimensions

This study uses daily return data on 20 portfolios split along two dimensions, growth/value and market size, over the period of four decades and employs over 12,000 trading rules to investigate the short-term predictability of portfolio returns. It shows that, historically, portfolios of small stocks and value stocks have been more suitable for active trading strategies since returns on value portfolios exhibit more predictability than returns on growth portfolios and returns on portfolios of large stocks appear to be less predictive than returns on portfolios of small stocks. The predictive ability of trading rules is all but gone during the 2000s. Popularization of exchange-traded funds and the introduction of quote decimalization on the exchanges are the most likely reasons behind the lack of predictability.     

Predictability and diversification benefits of investing in commodity and currency futures

We re-examine diversification benefits of investing in commodities and currencies by considering a risk-averse investor with mean-variance preferences who exploits the possibility of predictable time variation in asset return means, variances, and covariances. We implement unconditional and conditional efficient portfolio strategies designed to exploit this predictability, together with more traditional and/or ad hoc ones yet hitherto relatively unexplored in this context (including the equally weighted, fixed weight, volatility timing, and reward-to-risk timing strategies). We find that, for all portfolio strategies, commodities and currencies do not improve the investment opportunity set of the investor with an existing portfolio of stocks, bonds and T-bills, and an investment horizon of one month. Our findings, which reverse the conclusions of previous studies that focus on static portfolio strategies, are robust across several performance metrics.