Modeling the Conditional Covariance Between Stock and Bond Returns: A Multivariate GARCH Approach

To analyze the intertemporal interaction between the stock andbond market returns, we assume that the conditional covariancematrix follows a multivariate GARCH process. We allow for asymmetriceffects in conditional variances and covariances. Using dailydata, we find strong evidence of conditional heteroskedasticityin the covariance between stock and bond market returns. Theresults indicate that not only variances, but also covariancesrespond asymmetrically to return shocks. Bad news in the stockand bond market is typically followed by a higher conditionalcovariance than good news. Cross asymmetries, that is, asymmetriesfollowed from shocks of opposite signs, appear to be importantas well. Covariances between stock and bond returns tend tobe relatively low after bad news in the stock market and goodnews in the bond market. A financial application of our modelshows that optimal portfolio shares can be substantially affectedby asymmetries in covariances. Moreover, our results show sizablegains due to asymmetric volatility timing.     

Combining long memory and level shifts in modelling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons.     

Realizing stock market crashes: stochastic cusp catastrophe model of returns under time-varying volatility

This paper develops a two-step estimation methodology that allows us to apply catastrophe theory to stock market returns with time-varying volatility and to model stock market crashes. In the first step, we utilize high-frequency data to estimate daily realized volatility from returns. Then, we use stochastic cusp catastrophe theory on data normalized by the estimated volatility in the second step to study possible discontinuities in the markets. We support our methodology through simulations in which we discuss the importance of stochastic noise and volatility in a deterministic cusp catastrophe model. The methodology is empirically tested on nearly 27 years of US stock market returns covering several important recessions and crisis periods. While we find that the stock markets showed signs of bifurcation in the first half of the period, catastrophe theory was not able to confirm this behaviour in the second half. Translating the results, we find that the US stock market’s downturns were more likely to be driven by the endogenous market forces during the first half of the studied period, while during the second half of the period, exogenous forces seem to be driving the market’s instability. The results suggest that the proposed methodology provides an important shift in the application of catastrophe theory to stock markets.     

Forecasting financial market volatility: Sample frequency vis-à-vis forecast horizon

This paper explores the return volatility predictability inherent in high-frequency speculative returns. Our analysis focuses on a refinement of the more traditional volatility measures, the integrated volatility, which links the notion of volatility more directly to the return variance over the relevant horizon. In our empirical analysis of the foreign exchange market the integrated volatility is conveniently approximated by a cumulative sum of the squared intraday returns. Forecast horizons ranging from short intraday to 1-month intervals are investigated. We document that standard volatility models generally provide good forecasts of this economically relevant volatility measure. Moreover, the use of high-frequency returns significantly improves the longer run interdaily volatility forecasts, both in theory and practice. The results are thus directly relevant for general research methodology as well as industry applications.     

Shock and Volatility Transmission in the Futures and Spot Markets: Evidence from Turkish Markets

This paper examines the volatility transmission mechanism between the futures and corresponding underlying asset spot markets, focusing on Turkish currency and stock index futures traded on the lately established Turkish Derivatives Exchange (TURKDEX). Employing multivariate generalized autoregressive conditional heteroskedasticity modeling, which allows for potential spillovers and asymmetries in the variance-covariance structure for the market returns, the paper investigates the volatility interactions among each of the three futures-spot market systems. For all market systems under study, the volatility spillovers are found to be important and bidirectional. For the stock index market system, in line with the previous literature, volatility shows asymmetric behavior and strong asymmetric shock transmission. The main implication is that investors need to account for volatility spillovers and asymmetries among the futures and the spot markets to correctly build hedging strategies.     

Conditional Properties of Hedge Funds: Evidence from Daily Returns*

Using daily returns on a set of hedge fund indices, we study (i) the properties of the indices' conditional density functions and (ii) the presence of asymmetries in conditional correlations between hedge fund indices and other investments and between hedge fund indices themselves. We use the SNP approach to obtain estimates of conditional densities of hedge fund returns and then proceed to examine their properties. In general, a nonparametric GARCH(1,1) model appears to provide the best fit for all strategies. We find that the conditional third and fourth moments are significantly affected by changes in the current volatility of returns on hedge fund indices. We examine changes in the conditional probability of tail events and report significant changes in the probability of extreme events when the conditioning information changes. These results have important implications for models of hedge fund risk that rely on probability of tail events. We formally test for the presence of asymmetries in conditional correlations to determine if there is contagion between hedge funds and other investments and between various hedge fund indices in extreme down markets versus extreme up markets. We generally do not find strong evidence in support of asymmetric correlations.     

A High‐Frequency Investigation of the Interaction between Volatility and DAX Returns

One of the most noticeable stylised facts in finance is that stock index returns are negatively correlated with changes in volatility. The economic rationale for the effect is still controversial. The competing explanations have different implications for the origin of the relationship: Are volatility changes induced by index movements, or inversely, does volatility drive index returns? To differentiate between the alternative hypotheses, we analyse the lead‐lag relationship of option implied volatility and index return in Germany based on Granger causality tests and impulse‐response functions. Our dataset consists of all transactions in DAX options and futures over the time period from 1995 to 2005. Analyzing returns over 5‐minute intervals, we find that the relationship is return‐driven in the sense that index returns Granger cause volatility changes. This causal relationship is statistically and economically significant and can be clearly separated from the contemporaneous correlation. The largest part of the implied volatility response occurs immediately, but we also observe a smaller retarded reaction for up to one hour. A volatility feedback effect is not discernible. If it exists, the stock market appears to correctly anticipate its importance for index returns.     

Asymmetric volatility connectedness on the forex market

We show how bad and good volatility propagate through the forex market, i.e., we provide evidence for asymmetric volatility connectedness on the forex market. Using high-frequency, intra-day data of the most actively traded currencies over 2007–2015 we document the dominating asymmetries in spillovers that are due to bad, rather than good, volatility. We also show that negative spillovers are chiefly tied to the dragging sovereign debt crisis in Europe while positive spillovers are correlated with the subprime crisis, different monetary policies among key world central banks, and developments on commodities markets. It seems that a combination of monetary and real-economy events is behind the positive asymmetries in volatility spillovers, while fiscal factors are linked with negative spillovers.     

Stock and bond market interactions with level and asymmetry dynamics: An out-of-sample application

We model the dynamic interaction between stock and bond returns using a multivariate model with level effects and asymmetries in conditional volatility. We examine the out-of-sample performance using daily returns on the S&P 500 index and 10 year Treasury bond. We find evidence for significant (cross-) asymmetries in the conditional volatility and level effects in bond returns. The out-of-sample covariance matrix forecasts of the model imply that an investor is willing to pay between 129 and 820 basis points per year for using a dynamic trading strategy instead of a passive strategy.     

Empirical Analysis of Stock Returns and Volatility: Evidence from Seven Asian Stock Markets Based on TAR-GARCH Model

This paper investigates the time-series behavior of stock returns for seven Asian stock markets. In most cases, higher average returns appear to be associated with a higher level of volatility. Testing the relationship between stock returns and unexpected volatility, the evidence shows that four out of seven Asian stock markets have significant results. Further analyzing the relationship between stock returns and time-varying volatility by using Threshold Autoregressive GARCH(1,1)-in-mean specification indicates that the null hypothesis of no asymmetric effect on the conditional volatility is rejected for the daily data. However, the null cannot be rejected for the monthly data.     

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.     

Conditional Volatility of Equity Real Estate Investment Trust Returns: A Pre- and Post-1993 Comparison

We examine the dynamic behavior of Equity Real Estate Investment Trust (EREIT) volatility in a GARCH context 1972–2006 using monthly EREIT returns, and comparing volatility performance for “early” Equity REITs 1972–1992 with that of “modern” EREITs 1993–2006. Consistent with findings for conventional firms, we find that EREIT conditional volatility is time-varying, persistent, and predictable. There is a positive relationship between expected return and expected risk in EREIT stocks pre-1993, but the relationship disappears after 1993. We find no evidence that negative shocks affect EREIT volatility differently from positive ones in either time period. Different from reported results for conventional firms, we find that changes in the conditional volatility of fundamental macroeconomic variables have strong explanatory value for future changes in EREIT volatility. Finally, comparing EREIT volatility performance with volatility in the Russell 2000 Index, a proxy for small stocks, we find that EREIT volatility behaves differently from that of small stocks in many respects, indicating that risks in the small stock index cannot effectively proxy for risks in the EREIT market.

Asymmetric volatility and risk in equity markets

It appears that volatility in equity markets is asymmetric:returns and conditional volatility are negatively correlated.We provide a unified framework to simultaneously investigateasymmetric volatility at the firm and the market level and toexamine two potential explanations of the asymmetry: leverageeffects and volatility feedback. Our empirical application usesthe market portfolio and portfolios with different leverageconstructed from Nikkei 225 stocks. We reject the pure leveragemodel of Christie (1982) and find support for a volatility feedbackstory. Volatility feedback at the firm level is enhanced bystrong asymmetries in conditional covariances. Conditional betasdo not show significant asymmetries. We document the risk premiumimplications of these findings.     

Long-memory and heterogeneous components in high frequency Pacific-Basin exchange rate volatility

Recent research examining high-frequency financial data has suggested that volatility dynamics may be confounded by the existence of an intra-day periodic pattern and multiple sources of volatility. This paper examines whether these dynamics are present in the US Dollar exchange rates of five Pacific Basin economies. Using 30-min sampled returns, evidence of a ‘U’-shape intra-day pattern in volatility for regional markets is reported and controlled for using a Flexible Fourier transform. Supportive evidence for the existence of multiple volatility components is offered by semi-parametric fractional difference estimates of the long-memory properties of absolute exchange rate returns at various intra-day data sampling frequencies. Further parametric evidence of an explicit component structure in such high frequency exchange rate volatility is offered by the estimates of a component-GARCH model which comprises both a long-run volatility component exhibiting slow shock decay and a short-run volatility component exhibiting far more rapid decay, and provides a generally superior fit to the data. Further application of these C-GARCH models in the analysis of high frequency volatility spillovers between the currencies considered also reveals that such spillovers are predominantly transitory rather than highly persistent in nature, but that where volatility spillovers do impact on the long-run component of exchange rate volatility the Australian Dollar plays a pivotal role in the localised causality transmission mechanism.      

Empirical analysis of real and financial volatilities on stock excess returns: evidence from Taiwan industrial data

This paper tests the relation between stock excess returns and risk factors measured by volatility. The sources of the volatility are based on the volatility of macroeconomic factors and time-series volatility. To model the macroeconomic fundamentals, we divide the risk into real and financial volatilities pertinent to Taiwan's economic environment. By examining the data of indusry excess returns and market excess returns, we find evidence to reject the hypothesis that the stock excess returns are independent of the real and financial volatilities.     

Spot and forward volatility in foreign exchange

This paper investigates the empirical relation between spot and forward implied volatility in foreign exchange. We formulate and test the forward volatility unbiasedness hypothesis, which may be viewed as the volatility analogue to the extensively researched hypothesis of unbiasedness in forward exchange rates. Using a new dataset of spot implied volatility quoted on over-the-counter currency options, we compute the forward implied volatility that corresponds to the delivery price of a forward contract on future spot implied volatility. This contract is known as a forward volatility agreement. We find strong evidence that forward implied volatility is a systematically biased predictor that overestimates movements in future spot implied volatility. This bias in forward volatility generates high economic value to an investor exploiting predictability in the returns to volatility speculation and indicates the presence of predictable volatility term premiums in foreign exchange.     

Estimating daily volatility in financial markets utilizing intraday data

This study proposes a new approach to the estimation of daily realised volatility in financial markets from intraday data. Initially, an examination of intraday returns on S&P 500 Index Futures reveals that returns can be characterised by heteroscedasticity and time-varying autocorrelation. After reviewing a number of daily realised volatility estimators cited in the literature, it is concluded that these estimators are based upon a number of restrictive assumptions in regard to the data generating process for intraday returns. We use a weak set of assumptions about the data generating process for intraday returns, including transaction returns, given in den Haan and Levin [den Haan, W.J., Levin, A., 1996. Inferences from parametric and non-parametric covariance matrix estimation procedures, Working paper, NBER, 195.], which allows for heteroscedasticity and time-varying autocorrelation in intraday returns. These assumptions allow the VARHAC estimator to be employed in the estimation of daily realised volatility. An empirical analysis of the VARHAC daily volatility estimator employing intraday transaction returns concludes that this estimator performs well in comparison to other estimators cited in the literature.     

Long memory in volatility and trading volume

We use fractionally-integrated time-series models to investigate the joint dynamics of equity trading volume and volatility. Bollerslev and Jubinski (1999) show that volume and volatility have a similar degree of fractional integration, and they argue that this evidence supports a long-run view of the mixture-of-distributions hypothesis. We examine this issue using more precise volatility estimates obtained using high-frequency returns (i.e., realized volatilities). Our results indicate that volume and volatility both display long memory, but we can reject the hypothesis that the two series share a common order of fractional integration for a fifth of the firms in our sample. Moreover, we find a strong correlation between the innovations to volume and volatility, which suggests that trading volume can be used to obtain more precise estimates of daily volatility for cases in which high-frequency returns are unavailable.     

A note on the Wang and Wang measure of the quality of the compass rose

H. Wang and C. Wang [Visibility of the compass rose in financial asset returns: A quantitative study, J. Bank. Financ. 26 (2002), 1099–1111] derive a measure of the visibility of the radial patterns that appear in a plot of current and past returns, which are more commonly known as the compass rose. In theory, this measure should be positively related to the tick/volatility ratio. In practice however, we find that this relationship does not hold for higher tick/volatility ratios that are common to stock market data. Thus, the use of this measure is limited in real world applications. We propose a correction factor that improves the behaviour of the quality measure over higher tick/volatility ratios, however, further research is required to fully identify and correct the problem.     

Do fear indices help predict stock returns?

This study investigates the forecasting power of implied volatility indices on forward looking returns. Prior studies document that negative innovations to returns are associated with increasing implied volatility of the underlying indices; thus, suggesting a possible relationship between extremely high levels of implied volatility and positive short term returns. We investigate this issue by examining the predictive power of three implied volatility indices, VIX, VXN and VDAX, on the underlying index returns. We extend previous research by also focusing on characterised selected stocks and examine the relationship between implied volatility indices and future returns across different sectors and classified portfolios. Our findings suggest that implied volatility indices are good predictors of 20-days and 60-days forward looking returns and illustrate insignificant predictive power for very short term (1-day and 5-days) returns.