Subtle is the Lord,but malicious He is not: the calculation of abnormal stock returns in applied research

We use the expected logarithmic returns formula for the Geometric Brownian Motion (GBM) in conjunction with the expected logarithmic returns formula for the Feller diffusion to illustrate the nature and magnitude of errors which arise in computed abnormal returns when one applies an expected logarithmic returns formula which is incompatible with the stochastic process that generates a stock’s returns. Empirical analysis based on FTSE 100 stock price data for the five year period ending in 2017 shows that the scale of the errors in computed abnormal returns will hinge on the volatility of the returns generating process but will be particularly pronounced for relatively low stock prices. Although our principal focus is with comparing abnormal returns on the GBM and Feller diffusion, we also simulate logarithmic returns for the Uhlenbeck and Ornstein (1930) process, several interpretations of the Constant Elasticity of Variance (CEV) process and the scaled ‘t’ process of Praetz (1972) and Blattberg and Gonedes (1974). Taken in conjunction with the GBM and the Feller diffusion, these processes underpin virtually every equilibrium based asset pricing model which appears in the literature. However, computing abnormal returns for any of these processes using the expected logarithmic returns formula for the GBM inevitably leads to errors in the abnormal returns. Hence, an important principle which emerges from our analysis is that it is crucially important for researchers and others to test the compatibility of empirically observed returns with the distributional assumptions on which the empirical analysis is based if the complications arising from mis-specified modelling procedures are to be avoided.     

Information diffusion and the predictability of New Zealand stock market returns

This paper examines the impact of international predictors from liquid markets on the predictability of excess returns in the New Zealand stock market using data from May 1992 to February 2011. We find that US stock market return and VIX contribute significantly to the out‐of‐sample forecasts at short horizons even after controlling for the effect of local predictors, while the contribution by Australian stock market return is not significant. We further demonstrate that the predictability of New Zealand stock market returns using US market predictors could be explained by the information diffusion between these two countries.     

The current account and stock returns

In this paper, I use stock return data to test an intertemporal model of the current account. I find that the model performs well in three countries: the U.K., Canada, and Japan. Hall [Hall, R.E., 1978. Stochastic implication of the life cycle-permanent income hypothesis: theory and evidence. J. Polit. Econ. 86 (6), 971–987] points out that because stock price predicts the future state of the economy, it predicts consumption. Assuming that consumption depends on permanent income, my empirical finding indicates that a representative agent smoothes consumption based on stock market information. In other words, stock market returns yield information about permanent income.     

The relationship between stock returns and volatility in international stock markets

This study examines the relationship between expected stock returns and volatility in the 12 largest international stock markets during January 1980 to December 2001. Consistent with most previous studies, we find a positive but insignificant relationship during the sample period for the majority of the markets based on parametric EGARCH-M models. However, using a flexible semiparametric specification of conditional variance, we find evidence of a significant negative relationship between expected returns and volatility in 6 out of the 12 markets. The results lend some support to the recent claim [Bekaert, G., Wu, G., 2000. Asymmetric volatility and risk in equity markets. Review of Financial Studies 13, 1–42; Whitelaw, R., 2000. Stock market risk and return: an empirical equilibrium approach. Review of Financial Studies 13, 521–547] that stock market returns are negatively correlated with stock market volatility.     

Terrorism,country attributes,and the volatility of stock returns

This study investigates the interplay between terrorism and finance, focusing on the stock return volatility of American firms targeted by terrorist attacks. We find terrorism risk is an important factor in explaining the volatility of stock returns, which should be taken into account when modelling volatility. Using a volatility event-study approach and a new bootstrapping technique, we find volatility increases on the day of the attack and remain significant for at least fifteen days following the day of the attack. Cross-sectional analysis of the abnormal volatility indicates that the impact of terrorist attacks differs according to the country characteristics in which the incident occurred. We find that firms operating in wealthier, or more democratic countries, face greater volatility in stock returns relative to firms operating in developing countries. Firm exposure varies with the nature of country location, with country wealth and level of democracy playing an important role in explaining the likelihood of a terrorist attack. Our results show that despite significant terrorist events this past decade, stock markets in developed countries have not taken terrorist risk into sufficient consideration.     

Earnings seasonality,management earnings forecasts and stock returns

We examine whether management earnings forecasts (MEFs) help reduce the stock return seasonality associated with earnings seasonality around earnings announcements (EAs) in Chinese A-share markets. We find that firms in historically low earnings seasons outperform firms in high earnings seasons by 2.1% around MEFs. Firms in low earnings seasons also have higher trading volume and return volatility than their counterparts around EAs and MEFs. MEFs significantly reduce the ability of historical seasonal earnings rankings to negatively predict announcement returns, volume and volatility around EAs. The reduction effects are stronger when MEFs are voluntary or made closer to EAs. The evidence suggests that MEFs facilitate the correction of investors’ tendency to extrapolate earnings seasonality and its resulted stock mispricing.     

An examination of the relation between asymmetric risk measures,prior returns and expected daily stock returns

We use a sample of individual firm stock returns over the 1988–2009 time period to determine whether: (1) expected daily returns are related to asymmetric risk measures, (2) expected daily returns are related to the directional change of the prior day's price, and (3) our results are robust to the addition of firm size, book-to-market equity and liquidity. We find that investors are compensated for asymmetric risk; however, the positive risk–return relation is present only for our smallest firm quintile. We find a short-term return reversal present in all subgroups, except for the largest firms in our sample. We also document that the low volatility anomaly may be related to firm size and liquidity.     

Private placements of convertible securities: stock returns,operating performance and abnormal accruals

This study examines long‐run stock returns, operating performance and abnormal accruals of private placements of convertible securities. We investigate the effects surrounding private placements to test and differentiate the implications of several competing hypotheses. While the monitoring and certification hypotheses suggest positive effects, the managerial entrenchment, overvaluation and windows‐of‐opportunity hypotheses suggest the opposite. We find that placing firms generally experience positive effects in the pre‐periods and negative effects in the post‐periods. Our overall findings are more consistent with the predictions of the overvaluation and windows‐of‐opportunity hypotheses while our post‐placement evidence is also consistent with the predictions of the managerial entrenchment hypothesis.     

Size,value and momentum in stock returns: evidence from India

This paper examines the effects of size, value and momentum on the cross-sectional relation between expected returns and risk in the Indian stock market. We find that the conditional Carhart four-factor model empirically describes the variation of cross-section of return better than the unconditional model. When size, book-to-market and momentum effects are controlled in the conditional model, the positive relation of market beta, book-to-market and momentum with expected returns remains economically and statistically significant. However, this evidence is found to be subject to characteristics of test portfolios. The expected returns are sensitive to changes in predictive macroeconomic variables.     

The value premium,aggregate risk innovations,and average stock returns

We test whether innovations in aggregate risk, interpolated from a vector autoregressive system that contains the Chen et al. (1986) five factors as in Petkova (2006), are common factors in cross-sectional stock returns. We provide direct evidence that innovation in industrial production growth, a classical business-cycle variable that summarizes the state of the economy, is associated with the cross-sectional return predictability of individual stocks. We conclude that the role of innovation in aggregate risk is not random, and furthermore that it provides guidance concerning an important source of nonfinancial market-based risk in asset returns.     

An empirical analysis of the day-of-the-week effect in stock returns: The case of U.S. and Japan

This article employs daily closing index data to investigate the relationship between the U.S. and Japanese equity markets. It reassesses and extends the Becker et al. (1990) methodology over a longer sample space. The article then advances the analysis further by estimating structural equation models and by including the exchange rate as an additional explanatory variable. The resulting multivariate econometric design shows that the U.S. equity market strongly affects the Japanese equity market Monday through Friday while the Japanese market exerts a weaker influence on the U.S. market with the influence observed only on Mondays and Wednesdays.