Time-varying risk The case of the American computer industry

A bivariate GARCH-in-mean model for individual stock returns and the market portfolio is designed to model volatility and to test the conditional Capital Asset Pricing Model versus the conditional Residual Risk Model. We find that a univariate model of volatility for individual stock returns is misspecified. A joint modelling of the market return and the individual stock return shows that a major force driving the conditional variances of individual stocks is the history contained in the market return variance. We find that a conditional residual risk model, where the variance of the individual stock return is used to explain expected returns, is preferred to a conditional CAPM. We propose a partial ordering of securities according to their market risk using first and second order dominance criteria.     

The Conditional CAPM and the Cross-Section of Expected Returns

Most empirical studies of the static CAPM assume that betas remain constant over time and that the return on the value-weighted portfolio of all stocks is a proxy for the return on aggregate wealth. The general consensus is that the static CAPM is unable to explain satisfactorily the cross-section of average returns on stocks. We assume that the CAPM holds in a conditional sense, i.e., betas and the market risk premium vary over time. We include the return on human capital when measuring the return on aggregate wealth. Our specification performs well in explaining the cross-section of average returns.     

On the characteristics and performance of long-short, market-neutral and bear mutual funds

We evaluate the return performance of long-short, market-neutral and bear mutual funds using multi-factor models and a conditional CAPM that allows for time-varying risk. Differences in the bearish posture of these mutual funds result in different performance characteristics. Returns to long-short mutual funds vary with the market, returns to market-neutral mutual funds are uncorrelated with the market and returns to bear mutual funds are negatively correlated. Using the conditional CAPM we document significant changes in the market-risk exposure of the most bearish of these funds during different economic climates. We then assess the flow-performance relationship for up to 60 months following up and down markets and find that investors direct flows towards market-neutral and bearish funds for several months after down markets. Market-neutral funds provide a down market hedge, but bear funds do not generate the returns that investors hope for.     

Exchange risk and universal returns: A test of international arbitrage pricing theory

According to the international arbitrage pricing theory (IAPT) posited by Solnik (1983), currency movements affect assets' factor loadings and associated risk premiums. Based on a novel universal return decomposition, we propose an empirical model to test this proposition and perform tests using U.S. stock returns in the period 1975–2008. Our results confirm that currency movements significantly affect the market betas of a large proportion of stocks. Further cross-sectional tests indicate that currency movements affecting the market factor are significantly priced in stock returns. Based on these and other findings, we conclude that Solnik's IAPT is supported. An important implication of our findings is that exchange rate risk can broadly affect stock returns through both factor loading and residual factor channels.     

Examination of Conditional Asset Pricing in UK Stock Returns

I examine the empirical performance of various specifications of the capital asset pricing model (CAPM) in UK stock returns, using the stochastic discount framework. When the proxy for the market portfolio includes a proxy for labor income growth in addition to the stock market index, the performance of the CAPM improves. The improvement in performance shows in the magnitude and significance of the pricing errors and in the reduced impact of asset characteristics and other factors in the pricing of assets. There is further improvement when I use conditional versions of the models.     

Are the gains from international portfolio diversification exaggerated? The influence of downside risk in bear markets

The fundamental rationale for international portfolio diversification is that it expands the opportunities for gains from portfolio diversification beyond those that are available through domestic securities. However, if international stock market correlations are higher than normal in bear markets, then international diversification will fail to yield the promised gains just when they are needed most. We evaluate the extent to which observed correlations to monthly returns in bear, calm and bull markets are captured by three popular bivariate distributions: (1) the normal, (2) the restricted GARCH(1,1) of J. P. Morgan’s RiskMetrics, and (3) the Student-t with four degrees of freedom. Observed correlations during calm and bull markets are unexceptional compared to these models. In contrast, observed correlations during bear markets are significantly higher than predicted. Higher-than-normal correlations during extreme market downturns result in monthly returns to equal-weighted portfolios of domestic and international stocks that are, on average, more than two percent lower than those predicted by the normal distribution. If the extent of non-normality during bear markets persists over time, then a US investor allocating assets into foreign markets might want to allocate more assets into foreign markets with near-normal correlation profiles and avoid markets with higher-than-normal bear market co-movements.     

Cross‐sectional Tests of Conditional Asset Pricing Models: Evidence from the German Stock Market

We study the performance of conditional asset pricing models and multifactor models in explaining the German cross‐section of stock returns. We focus on several variables, which (according to previous research) are associated with market expectations on future market excess returns or business cycle conditions. Our results suggest that the empirical performance of the Capital Asset Pricing Model (CAPM) can be improved when allowing for time‐varying parameters of the stochastic discount factor. A conditional CAPM using the term spread explains the returns on our size and book‐to‐market sorted portfolios about as well as the Fama‐French three‐factor model and performs best in terms of the Hansen‐Jagannathan distance. Structural break tests do not necessarily indicate parameter instability of conditional model specifications. Another major finding of the paper is that the Fama‐French model – despite its generally good cross‐sectional performance – is subject to model instability. Unconditional models, however, do a better job than conditional ones at capturing time‐series predictability of the test portfolio returns.     

On the exclusion of assets from tests of the two-parameter model: A sensitivity analysis

This study investigates the sensitivity of tests of the CAPM to different sets of asset returns. Tests are conducted with market portfolios that include returns for bonds, real estate, and consumer durables in addition to common stocks. Even when stocks represent only 10% of the portfolio's value, inferences about the CAPM are virtually identical to those obtained with a stocks-only portfolio. In contrast, inferences are sensitive to the set of assets used in the tests.     

Conditional coskewness and asset pricing

We explore the empirical usefulness of conditional coskewness to explain the cross-section of equity returns. We find that coskewness is an important determinant of the returns to equity, and that the pricing relationship varies through time. In particular we find that when the conditional market skewness is positive investors are willing to sacrifice 7.87% annually per unit of gamma (a standardized measure of coskewness risk) while they only demand a premium of 1.80% when the market is negatively skewed. A similar picture emerges from the coskewness factor of Harvey and Siddique (Harvey, C., Siddique, A., 2000a. Conditional skewness in asset pricing models tests. Journal of Finance 65, 1263–1295.) (a portfolio that is long stocks with small coskewness with the market and short high coskewness stocks) which earns 5.00% annually when the market is positively skewed but only 2.81% when the market is negatively skewed. The conditional two-moment CAPM and a conditional Fama and French (Fama, E., French, K., 1992. The cross-section of expected returns. Journal of Finance 47,427465.) three-factor model are rejected, but a model which includes coskewness is not rejected by the data. The model also passes a structural break test which many existing asset pricing models fail.     

Delayed Reaction to Good News and the Cross-Autocorrelation of Portfolio Returns

We document a directional asymmetry in the small stock concurrent and lagged response to large stock movements. When returns on large stocks are negative, the concurrent beta for small stocks is high, but the lagged beta is insignificant. When returns on large stocks are positive, small stocks have small concurrent betas and very significant lagged betas. That is, the cross-autocorrelation puzzle documented by Lo and MacKinlay (1990a) is associated with a slow response by some small stocks to good, but not to bad, common news. Time series portfolio tests and cross-sectional tests of the delay for individual securities suggest that existing explanations of the cross-autocorrelation puzzle based on data mismeasurement, minor market imperfections, or time-varying risk premiums fail to capture the directional asymmetry in the data.     

Investor preferences and portfolio selection: is diversification an appropriate strategy?

This paper analyzes the relationship between diversification and several distributional characteristics that have risk implications for stock returns. We develop a flexible three-parameter distribution to model the stock returns. Using data on the current 30 DJIA stocks, we show that an investor's strategy on diversification depends on the measures of risk for particular concerns. For example, investors who desire to increase positive skewness would hold a less diversified portfolio, while those who care more about extreme losses would hold a more diversified portfolio. Experimenting with a more general pool of stocks yields the same conclusions.     

The Effectiveness of Price Limits and Stock Characteristics: Evidence from the Shanghai and Shenzhen Stock Exchanges

We examine the effectiveness of price limits on Chinese A shares and investigate the characteristics of those stocks that hit their price limits more frequently. We find that the effect of price limits is asymmetric for the A shares in upward and downward price movements and different for bullish and bearish sample periods. During a bullish period price limits effectively reduce stock volatility for downward price movements, but not for upward price movements; while during a bearish period price limits effectively reduce stock volatility for upward price movements, but not for downward price movements. Second, price limits delay efficient price discovery for upward price movements, but not for downward price movements. However, we do not find evidence to suggest that price limits harmfully interfere with the stock trading processes in the Chinese A share markets. Finally, we find that actively traded stocks hit their price limits more often and tend to hit the lower limit more frequently when overall market conditions are bearish. Stocks with high book-to-market values of equity hit their upper price limits more frequently, while stocks with a high ratio of tradable shares tend to hit their price limits less frequently.JEL Classification: G10, G14, G15     

基于小波神经网络的高阶CAPM实证研究

本文在传统CAPM的基础上,引入了一个高阶的CAPM。借助小波神经网络在非线性函数逼近方面的优势,使用上海证券交易所股票数据分别对二阶至四阶CAPM进行了实证分析。最终的研究结果表明:就上海股市而言,12只大盘股组合已经能够有效分散非系统风险,而12只小盘股不能充分化解非系统风险,存在所谓的规模效应;训练后的网络预测显示,高阶CAPM无论是在预测精度还是预测稳定性上都要明显优于传统的CAPM,在一个非系统风险得到充分分散的证券组合中,加入三阶矩的CAPM已经能够比较准确地把握风险资产的市场定价。     

Return sign forecasts based on conditional risk: Evidence from the UK stock market index

Recent theoretical works have found a link between return sign forecastability and conditional volatility. This paper compares the predictive performance of the conditional country risk and the conditional residual risk in forecasting the direction of change in the return on the UK stock market index. The conditional country risk and the conditional residual risk are estimated using the bivariate BEKK-GARCH technique and the direction of change in the UK stock market index is modelled using the binary logit approach. Both the in-sample and the out-of-sample predictions suggest that, as a predictor, the conditional residual risk is superior to the conditional country risk. Our findings support the residual risk model while contradicting the traditional capital asset pricing model (CAPM). Moreover, our tactical asset allocation simulations show that when the conditional residual risk is used in conjunction with multiple-threshold trading strategies to guide the investment decisions, the actively managed portfolio achieves greater returns than the return on a buy and hold portfolio.     

Is the Market Portfolio a Dynamic Factor? Evidence from Individual Stock Returns

This paper uses a factor model to test whether the market portfolio is a dynamic factor in the sense that individual stock returns contain a premium linked to the conditional risk of the market portfolio. The market conditional risk is based on a decomposition of the market variance into a time-varying trend component and a transitory component. The evidence shows that the conditional market premium is rising when the permanent trend rises relative to the conditional variance. The evidence for individual stock returns supports the notion that the market portfolio is a dynamic factor. Individual stock return autocorrelations are fully explained by the time variation in the market premium. The risk premia attributed to static factors are statistically insignificant.     

Estimation of expected return: CAPM vs. Fama and French

Most practitioners favour a one-factor model (CAPM) when estimating expected return for an individual stock. For estimation of portfolio returns, academics recommend the Fama and French three-factor model. The main objective of this paper is to compare the performance of these two models for individual stocks. First, estimates for individual stock returns based on CAPM are obtained using different time frames, data frequencies, and indexes. It is found that 5 years of monthly data and an equal-weighted index, as opposed to the commonly recommended value-weighted index, provide the best estimate. However, performance of the model is very poor; it explains on average 3% of differences in returns. Then, estimates for individual stock returns are obtained based on the Fama and French model using 5 years of monthly data. This model, however, does not do much better; independent of the index used, it explains on average 5% of differences in returns. These results therefore bring into question the use of either model for estimation of individual expected stock returns.     

Institutional investors and the limits of arbitrage

The returns and stock holdings of institutional investors from 1980 to 2007 provide little evidence of stock-picking skill. Institutions as a whole closely mimic the market portfolio, with pre-cost returns that have nearly perfect correlation with the value-weighted index and an insignificant CAPM alpha of 0.08% quarterly. Institutions also show little tendency to bet on any of the main characteristics known to predict stock returns, such as book-to-market, momentum, or accruals. While particular groups of institutions have modest stock-picking skill relative to the CAPM, their performance is almost entirely explained by the book-to-market and momentum effects in returns. Further, no group holds a portfolio that deviates efficiently from the market portfolio.     

Cashflow news,the value premium and an asset pricing view on European stock market integration

The decomposition of national CAPM market betas of European countries’ value and growth portfolio returns into cashflow and discount rate news driven components reveals that i) high average returns on value portfolios are associated with disproportionately high sensitivity to national cashflow news which corroborates recent evidence for the U.S. and ii) two-beta variants of national CAPMs capture the cross-sectional dispersion in European stock returns. The latter finding is suggestive of relatively well integrated stock markets among the core European countries and reflects basic asset pricing theory. One (national) discount factor should price any (international) asset.     

The Random Walk Hypothesis in the Emerging Indian Stock Market

This paper examines the random walk hypothesis in the emerging Indian stock market using daily data on individual stocks. The statistical evidence in this paper rejects the random walk hypothesis. The results suggest that daily returns earned by individual stocks and by an equally weighted portfolio show significant non–linear dependence and persistent volatility effects. The non–linear dependence takes the form of ARCH–type conditional heteroskedasticity and does not appear to be caused by nonstationarity of underlying economic variables. Though conditional volatility is time varying, it does not explain expected returns.