Asymmetric information,volatility components and the volume–volatility relationship for the CAC40 stocks

This paper investigates the relationship between trading volume components and various realized volatility measures for the CAC40 index constituents. A mixture-of-distribution model is used to decompose trading volume into informed and liquidity components. Realized volatility is broken down into continuous volatility and jumps. Our findings confirm the strong positive contemporaneous relationship between total trading volume and volatility when realized volatility and its continuous component are considered. A limited evidence of the effect of total trading volume on discontinuous volatility is found. The positive volume–volatility relationship is mainly driven by the informed component of trading volume. Conversely, liquidity volume is negatively related to realized volatility lending some support to the view that liquidity trading dampens the volatility of stock returns. A stronger negative relationship between liquidity volume and volatility jump is uncovered.     

Realized volatility and transactions

This paper re-examines the impact of number of trades, trade size and order imbalance on daily stock returns volatility. In contrast to prior studies, we estimate daily volatility using realized volatility obtained by summing up intraday squared returns. Consistent with the theory of quadratic variation, realized volatility estimates are shown to be less noisy than standard volatility measures such as absolute returns used in previous studies. In general, our results confirm [Jones, C.M., Kaul, G., Lipson, M.L., 1994. Transactions, volume, and volatility. Review of Financial Studies 7, 631–651] that number of trades is the dominant factor behind the volume–volatility relation. Neither trade size nor order imbalance adds significantly more explanatory power to realized volatility beyond number of trades. This finding is robust to different time periods, firm sizes and regression specifications. The implications of our results for microstructure theory are discussed.     

ESTIMATING EXPECTED EXCESS RETURNS USING HISTORICAL AND OPTION‐IMPLIED VOLATILITY

We test the relation between expected and realized excess returns for the S&P 500 index from January 1994 through December 2003 using the proportional reward‐to‐risk measure to estimate expected returns. When risk is measured by historical volatility, we find no relation between expected and realized excess returns. In contrast, when risk is measured by option‐implied volatility, we find a positive and significant relation between expected and realized excess returns in the 1994–1998 subperiod. In the 1999–2003 subperiod, the option‐implied volatility risk measure yields a positive, but statistically insignificant, risk‐return relation. We attribute this performance difference to the fact that, in the 1994–1998 subperiod, return volatility was lower and the average return was much higher than in the 1999–2003 subperiod, thereby increasing the signal‐to‐noise ratio in the latter subperiod.     

Trading Activity and Price Volatility in the Municipal Bond Market

Utilizing a comprehensive database of transactions in municipal bonds, we investigate the volume–volatility relation in the municipal bond market. We find a positive relation between the number of transactions and a bond's price volatility. In contrast to previous studies, we find a negative relation between average deal size and price volatility. These results are found to be robust throughout the sample. Our results are inconsistent with current theoretical models of the volume–volatility relation. These inconsistencies may arise because current models fail to account for the effects of overall market liquidity on the costs of large transactions.     

When noise trading fades,volatility rises

We hypothesize and test an inverse relation between liquidity and price volatility derived from microstructure theory. Two important facets of liquidity trading are examined: volume and noisiness. As represented by the expected turnover rate (volume) and realized average commission cost per share (noisiness) of NYSE equity trading, both facets are found negatively associated with the ex post and ex ante return volatilities of the NYSE stock portfolios and the NYSE composite index futures. Furthermore, the inverse association between noisiness and volatility is amplified in times of market crisis. The negative noisiness–volatility relation is also supported by our analysis on the effects of trade size on price volatility. The overall results demonstrate that volatility increases as noise trading declines.     

The return impact of realized and expected idiosyncratic volatility

We show that the negative relation between realized idiosyncratic volatility, measured over the prior month, and returns is robust in non-January months. Controlling for realized idiosyncratic volatility, we show that the relation between returns and expected idiosyncratic volatility is positive and robust. Realized and expected idiosyncratic volatility are separate and important effects describing the cross-section of returns. We find the negative return on a zero-investment portfolio that is long high realized idiosyncratic volatility stocks and short low realized idiosyncratic volatility stocks is dependent on aggregate investor sentiment. In cross-sectional tests, we find the negative relation is weaker for stocks with a large analyst following and stronger for stocks with high dispersion of analyst forecasts. The positive relation between expected idiosyncratic volatility and returns is not due to mispricing.     

Expected Idiosyncratic Volatility Measures and Expected Returns

We find that idiosyncratic volatility forecasts using information available to traders at the time of the forecast are not related to expected returns. The positive relation documented in a number of other papers only exists when forward‐looking information is incorporated into the volatility estimate. That positive relation is driven by the realized idiosyncratic volatility component that cannot be forecasted by investors. Our findings are robust to several different empirical tests, volatility forecasting models and time periods.     

Order book characteristics and the volume–volatility relation: Empirical evidence from a limit order market

Using unique data, we address the issue of price formation in a limit order market. A standard volume–volatility relation is documented with the number of trades acting as the important component of volume. The main contribution of the paper is to identify strong evidence that volume, volatility, and the volume–volatility relation are negatively related to the order book slope. These results are robust to the inclusion of several liquidity measures. A significant empirical relationship between the order book slope and the coefficient of variation in earnings forecasts by financial analysts suggests that the slope is proxying for disagreement among investors. Hence, our results support models where investor heterogeneity intensifies the volume–volatility relation.     

Credit default swaps,the leverage effect,and cross-sectional predictability of equity and firm asset volatility

Leverage represents both a fundamental component of equity volatility and a long-run selection variable. Based on this premise, we investigate the influence of leverage on the long-run cross-sectional predictability of future realized equity volatility. Leverage makes equity volatility significantly less predictable than underlying firm asset volatility, a result that is robust to different predictors of future realized volatility: credit default swap implied, historical, and option implied volatility. A simple model of optimal capital structure, wherein companies maximize tax benefits subject to a common maximum default probability (minimum credit rating) target, helps explain this finding.     

Firm age and realized idiosyncratic return volatility in China: The role of short-sales constraints

This paper investigates how realized idiosyncratic return volatility changes with firm age in the Chinese stock market. By employing a sample of 26,676 firm-year observations of 2798 A-share listed Chinese firms from 2001 to 2019, we find that realized idiosyncratic return volatility is negatively associated with firm age. Further, we find that loosening short-sales constraints strengthens this negative association, and that heterogeneity of investor beliefs is the most likely mechanism driving the negative relation, rather than the alternative explanations of cash flow volatility and growth options. Our results are fairly consistent under two different measures of firm age, and are robust to a choice of two multiple-factor models (the Fama-French three-factor and five-factor models) as well as two data frequencies (daily and monthly) used to estimate realized idiosyncratic return volatility.     

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.     

The determinants of the model-free positive and negative volatilities

In this paper we analyze the role of macroeconomic and financial determinants in explaining stock market volatilities in the U.S. market. Both implied and realized volatility are computed model-free and decomposed into positive and negative components, thereby allowing us to compute directional volatility risk premia. We capture the behaviour of each component of implied volatility and risk premium in relation to their different determinants. The negative implied volatility appears to be linked more towards financial conditions variables such as uncertainty and geopolitical risk indexes, whereas positive implied volatility is driven more by macro variables such as inflation and GDP. There is a clear shift in importance from macro towards financial determinants moving from the pre towards the post financial crisis. A mixed frequency Granger causality approach uncovers causality relationships between volatilities and risk premia and macro variables and vice versa, a finding which is not detected with a conventional low frequency VAR model.     

Asymmetric volatility in the foreign exchange markets

We examine the presence or absence of asymmetric volatility in the exchange rates of Australian dollar (AUD), Euro (EUR), British pound (GBP) and Japanese yen (JPY), all against US dollar. Our investigation is based on a variant of the heterogeneous autoregressive realized volatility model, using daily realized variance and return series from 1996 to 2004. We find that a depreciation against USD leads to significantly greater volatility than an appreciation for AUD and GBP, whereas the opposite is true for JPY. Relative to volatility on days following a positive one-standard-deviation return, volatility on days following a negative one-standard-deviation return is higher by 6.6% for AUD, 6.1% for GBP, and 21.2% for JPY. The realized volatility of EUR appears to be symmetric. These results are robust to the removal of jump component from realized volatility and the sub-samplings defined by structural-changes. The asymmetry in AUD, GBP and JPY appears to be embedded in the continuous component of realized volatility rather than the jump component.     

Forecasting volatility of the U.S. oil market

We examine the information content of the CBOE Crude Oil Volatility Index (OVX) when forecasting realized volatility in the WTI futures market. Additionally, we study whether other market variables, such as volume, open interest, daily returns, bid-ask spread and the slope of the futures curve, contain predictive power beyond what is embedded in the implied volatility. In out-of-sample forecasting we find that econometric models based on realized volatility can be improved by including implied volatility and other variables. Our results show that including implied volatility significantly improves daily and weekly volatility forecasts; however, including other market variables significantly improves daily, weekly and monthly volatility forecasts.     

Power and Bipower Variation with Stochastic Volatility and Jumps

This article shows that realized power variation and its extension,realized bipower variation, which we introduce here, are somewhatrobust to rare jumps. We demonstrate that in special cases,realized bipower variation estimates integrated variance instochastic volatility models, thus providing a model-free andconsistent alternative to realized variance. Its robustnessproperty means that if we have a stochastic volatility plusinfrequent jumps process, then the difference between realizedvariance and realized bipower variation estimates the quadraticvariation of the jump component. This seems to be the firstmethod that can separate quadratic variation into its continuousand jump components. Various extensions are given, togetherwith proofs of special cases of these results. Detailed mathematicalresults are reported in Barndorff-Nielsen and Shephard (2003a).     

Dynamic Relationship among Intraday Realized Volatility,Volume and Number of Trades

In this paper, the vector autoregressive model is fitted to find out the causal relationship among realized volatility, the number of transactions and volume with the intraday time intervals of 10, 20 and 30 min. To understand the impact of shock to the market on specific variables, a multivariate Impulse Response Function analysis is also introduced to visualize the causal relationship among the variables. From the analysis of a stock listed on the Stock Exchange of Hong Kong, we find that realized volatility reacts positively to the lagged average trade size. However, the realized volatility forms a negative relationship with the first few lagged number of trades. As a result, the intraday causal relationship among realized volatility, volume and the number of trades is quite different from that obtained on a daily basis. The findings of this paper can enhance the understanding of how the number of trades and the average trade size per transaction affect the risk evolution of financial securities and thus improve the risk management of day trading strategies.     

The high returns to low volatility stocks are actually a premium on high quality firms

Recent empirical research shows that low volatility stocks outperform high volatility stocks around the world. This study documents that the volatility effect is associated with the quality of the firm using a large sample of international stocks. First, adding a quality factor to the Fama–French model contributes to the explanation of the volatility effect. Furthermore, the negative volatility–return relation is shown to be stronger and significant only among high quality firms which are profitable and have stable cash flows. Second, a fundamental investment strategy that goes long high quality firms and short low quality firms performs like a volatility strategy and cannot be explained by common asset pricing models. However, a low–high volatility factor adds to the explanation of the return difference between high and low quality stocks as volatility and quality strategies have a common component.     

Implications of market microstructure for realized variance measurement

Volatility measuring and estimation based on intra-day high-frequency data has grown in popularity during the last few years. A significant part of the research uses volatility and variance measures based on the sum of squared high-frequency returns. These volatility measures, introduced and mathematically justified in a series of papers by Andersen et al. [1999. (Understanding, optimizing, using and forecasting) realized volatility and correlation. Leonard N. Stern School Finance Department Working Paper Series, 99-061, New York University; 2000a. The distribution of realized exchange rate volatility. Journal of the American Statistical Association 96, no. 453: 42–55; 2000b. Exchange rate returns standardized by realized volatility are (nearly) Gaussian. Multinational Finance Journal 4, no. 3/4: 159–179; 2003. Modeling and forecasting realized volatility. NBER Working Paper Series 8160.] and Andersen et al. 2001a. Modeling and forecasting realized volatility. NBER Working Paper Series 8160., are referred to as ‘realized variance’. From the theory of quadratic variations of diffusions, it is possible to show that realized variance measures, based on sufficiently frequently sampled returns, are error-free volatility estimates. Our objective here is to examine realized variance measures, where well-documented market microstructure effects, such as return autocorrelation and volatility clustering, are included in the return generating process. Our findings are that the use of squared returns as a measure for realized variance will lead to estimation errors on sampling frequencies adopted in the literature. In the case of return autocorrelation, there will be systematic biases. Further, we establish increased standard deviation in the error between measured and real variance as sampling frequency decreases and when volatility is non-constant.     

The effects of Federal funds rate surprises on S&P 500 volatility and volatility risk premium

In this paper, we examine the effects of expected and surprise components in Federal funds target rate changes on realized and implied volatility. We find that surprise changes in the target rate significantly increase volatility. Consistent with the efficient market hypothesis, our analysis suggests that the expected component of a target rate change as well as the target rate change itself, do not significantly affect volatility. We also show that larger than expected decreases in the Federal funds target rate tend to lower the volatility risk premium.     

A nonparametric test of the mixture-of-distributions model

Abstract

Intertemporal implications of the mixture-of-distributions hypothesis (MDH) are derived based on the concept of time reversibility in statistical mechanics. The restrictions are tested using simple nonparametric tests that do not impose auxiliary assumptions on the stochastic process for trading volume, price volatility or information arrivals. The tests reject the standard MDH with one latent factor. In particular, shocks to volatility and volume are temporally asymmetric, contrary to the predictions of the MDH. The results indicate that multifactor models are needed to explain the dynamics of the volume–volatility relation.