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.     

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 intertemporal relationship between market return and variance: an Australian perspective

In this paper we investigate the intertemporal relationship between the market risk premium and its conditional variance in an Australian setting. Using a bivariate EGARCH‐M model combined with the dynamic conditional correlation (DCC) framework as proposed by Engle (2000), we find evidence of a positive relationship between the market risk premium and its variance and evidence of two distinct interest rate effects. Furthermore, while the bond market's own variance is not priced by investors, we find that the covariance between equity and bond markets is a significant risk factor that is priced in the market.     

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.     

Conditional Equity Premium and Aggregate Corporate Investment

We document a strong negative relation between aggregate corporate investment and conditional equity premium estimated from direct stock market risk measures. Consistent with the investment-based asset pricing model, the comovement with conditional equity premium fully accounts for aggregate investment's market return predictive power. Similarly, conditional equity premium is a significant determinant of classic Tobin's q measure, although q has much weaker explanatory power for aggregate investment possibly because of its measurement errors. Moreover, the positive relation between aggregate investment and investor sentiment documented in previous studies reflects the fact that both variables correlate closely with conditional equity premium.     

Does It Pay to Bet Against Beta? On the Conditional Performance of the Beta Anomaly

Prior studies find that a strategy that buys high‐beta stocks and sells low‐beta stocks has a significantly negative unconditional capital asset pricing model (CAPM) alpha, such that it appears to pay to “bet against beta.” We show, however, that the conditional beta for the high‐minus‐low beta portfolio covaries negatively with the equity premium and positively with market volatility. As a result, the unconditional alpha is a downward‐biased estimate of the true alpha. We model the conditional market risk for beta‐sorted portfolios using instrumental variables methods and find that the conditional CAPM resolves the beta anomaly.     

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.     

Time‐Varying Risk–Return Trade‐off in the Stock Market

We uncover a strong comovement of the stock market risk–return trade‐off with the consumption–wealth ratio (CAY). The finding reflects time‐varying investment opportunities rather than countercyclical aggregate relative risk aversion. Specifically, the partial risk–return trade‐off is positive and constant when we control for CAY as a proxy for investment opportunities. Moreover, conditional market variance scaled by CAY is negatively priced in the cross‐section of stock returns. Our results are consistent with a limited stock market participation model, in which shareholders require an illiquidity premium that increases with CAY, in addition to the risk premium that is proportional to conditional market variance.     

The intertemporal risk-Return relation,investor behavior,and technical trading profits: evidence from the G-7 countries

The intertemporal risk-return relation and investor behavior are both important pricing factors that jointly determine the expected market risk premium. Using the price adjustment process as a control variable, we find that the intertemporal risk-return relation is positive conditional on bad market news, but is non-positive conditional on good market news. This implies that good (bad) market news weakens (strengthens) the positive risk-return relation. The pattern in the distortion of the risk-return relation is consistent with short-term mispricing in which investors overvalue (undervalue) the stock market in reaction to good (bad) market news. We also show that ignoring the price adjustment process in the estimation of the risk-return relation leads to model misspecification and induces an upward (downward) bias in estimates of the relative risk aversion parameter conditional on good (bad) news. Our model of the asymmetric risk-return relation along with the price adjustment process is capable of generating the return dynamics that is attributable to technical trading profits. We suggest that the profitability of technical trading rules is not a violation of market efficiency, but a consequence of trading rules exploiting the asymmetric effect of price changes on the risk-return relation, along with the persistence property of price changes.     

How to Discount Cashflows with Time-Varying Expected Returns

While many studies document that the market risk premium is predictable and that betas are not constant, the dividend discount model ignores time‐varying risk premiums and betas. We develop a model to consistently value cashflows with changing risk‐free rates, predictable risk premiums, and conditional betas in the context of a conditional CAPM. Practical valuation is accomplished with an analytic term structure of discount rates, with different discount rates applied to expected cashflows at different horizons. Using constant discount rates can produce large misvaluations, which, in portfolio data, are mostly driven at short horizons by market risk premiums and at long horizons by time variation in risk‐free rates and factor loadings.     

Tests of the CAPM with Time-Varying Covariances: A Multivariate GARCH Approach

This paper examines an asset pricing model in which the Sharpe-Lintner CAPM and the zero-beta CAPM are special cases. The model allows the ratio of expected market risk premium to market variance, the conditional expected excess returns, and the risks to change over time. The results are found to be sensitive to the choice of the portfolio formation techniques. Significant time variability is shown in the conditional expected excess asset returns and risks and also in the reward-to-risk ratio.     

The impact of COVID-19 on the stock market crash risk in China

This study investigates the impact of the COVID-19 pandemic on the stock market crash risk in China. For this purpose, we first estimated the conditional skewness of the return distribution from a GARCH with skewness (GARCH-S) model as the proxy for the equity market crash risk of the Shanghai Stock Exchange. We then constructed a fear index for COVID-19 using data from the Baidu Index. Based on the findings, conditional skewness reacts negatively to daily growth in total confirmed cases, indicating that the pandemic increases stock market crash risk. Moreover, the fear sentiment exacerbates such risk, especially with regard to the impact of COVID-19. In other words, when the fear sentiment is high, the stock market crash risk is more strongly affected by the pandemic. Our evidence is robust for the number of daily deaths and global cases.     

The evolution of risk premium as a measure for intra-regional equity market integration

We estimate and test the conditional version of an international capital asset pricing model using a parsimonious multivariate GARCH process and the multivariate nonlinear least squares method. Since our approaches are fully parametric, we can recover any quantity that is a function of the first two conditional moments. Our findings strongly support using a model that includes both regional market and foreign exchange risk. However, both sources of risk are detected only when their prices are allowed to change over time. Our empirical results show clear evidence of market integration to varying degrees, explained by the US term premium and the level of market openness. Though it reaches high values during turmoil periods and exhibits an upward trend toward the end of the estimation period, the Indonesian stock market remains partially integrated into the ASEAN-5 regional market. These results suggest that diversification into Indonesian market assets continues to produce substantial profits and that asset pricing rules should reflect a state of partial integration.     

Resolving the Puzzling Intertemporal Relation between the Market Risk Premium and Conditional Market Variance: A Two-Factor Approach

The existing empirical literature fails to agree on the nature of the intertemporal relation between risk and return. This paper attempts to resolve the issue by estimating a conditional two-factor model motivated by Merton's intertemporal capital asset pricing model. When long-term government bond returns are included as a second factor, the partial relation between the market risk premium and conditional market variance is found to be positive and significant. The paper also helps explain the convoluted empirical relation between the market risk premium, conditional market variance, and the nominal risk-free rate previously reported in the literature.     

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.     

Conditional risk and performance evaluation: Volatility timing, overconditioning, and new estimates of momentum alphas

Unconditional alphas are biased when conditional beta covaries with the market risk premium (market timing) or volatility (volatility timing). We demonstrate an additional bias (overconditioning) that can occur any time an empiricist estimates risk using information, such as a realized beta, that is not available to investors ex ante. Calibrating to U.S. equity returns, volatility timing and overconditioning can plausibly impact alphas more than market timing, which has been the focus of prior literature. To correct market- and volatility-timing biases without overconditioning, we show that incorporating realized betas into instrumental variables estimators is effective. Empirically, instrumentation reduces momentum alphas by 20-40%. Overconditioned alphas overstate performance by up to 2.5 times. We explain the sources of both the volatility-timing and overconditioning biases in momentum portfolios.     

International asset pricing under segmentation and PPP deviations

We analyze the impact of both purchasing power parity (PPP) deviations and market segmentation on asset pricing and investor's portfolio holdings. The freely traded securities command a world market risk premium and an inflation risk premium. The securities that can be held by only a subset of investors command two additional premiums: a conditional market risk premium and a segflation risk premium. Our model is empirically supported with important implications for tests of international asset pricing.     

Are conditional illiquidity risks priced in China? A cross-sectional test

In this study, we theoretically derive conditional illiquidity risks from the conditional liquidity-adjusted capital asset pricing model (CLCAPM) that we propose by incorporating funding illiquidity into the LCAPM, and we examine whether they are priced empirically in China's A-share market. We provide new evidence of the positive premiums of conditional illiquidity risks even after controlling for mispricing signals and sentiment. The finding suggests that conditional illiquidity risk could be an alternative channel to explain the cross-section of stock returns. Moreover, investors could obtain higher premiums as compensation for their tolerance of more highly conditional illiquidity risks during high market volatility (low market returns) periods.     

There is a risk-return trade-off after all

This paper studies the intertemporal relation between the conditional mean and the conditional variance of the aggregate stock market return. We introduce a new estimator that forecasts monthly variance with past daily squared returns, the mixed data sampling (or MIDAS) approach. Using MIDAS, we find a significantly positive relation between risk and return in the stock market. This finding is robust in subsamples, to asymmetric specifications of the variance process and to controlling for variables associated with the business cycle. We compare the MIDAS results with tests of the intertemporal capital asset pricing model based on alternative conditional variance specifications and explain the conflicting results in the literature. Finally, we offer new insights about the dynamics of conditional variance.     

An Intertemporal International Asset Pricing Model: Theory and Empirical Evidence

We extend Campbell's (1993) model to develop an intertemporal international asset pricing model (IAPM). We show that the expected international asset return is determined by a weighted average of market risk, market hedging risk, exchange rate risk and exchange rate hedging risk. These weights sum up to one. Our model explicitly separates hedging against changes in the investment opportunity set from hedging against exchange rate changes as well as exchange rate risk from intertemporal hedging risk. A test of the conditional version of our intertemporal IAPM using a multivariate GARCH process supports the asset pricing model. We find that the exchange rate risk is important for pricing international equity returns and it is much more important than intertemporal hedging risk.