Leverage vs. feedback: Which Effect drives the oil market?

This article brings new insights on the role played by (implied) volatility on the WTI crude oil price. An increase in the volatility subsequent to an increase in the oil price (i.e. inverse leverage effect) remains the dominant effect as it might reflect the fear of oil consumers to face rising oil prices. However, this effect is amplified by an increase in the oil price subsequent to an increase in the volatility (i.e. inverse feedback effect) with a two-day delayed effect. This lead-lag relation between the oil price and its volatility is central to any type of trading strategy based on futures and options on the OVX implied volatility index. It is of interest to traders, risk- and fund-managers.     

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.     

The asymmetric relationship between returns and implied volatility: Evidence from global stock markets

We investigate the asymmetric relationship between returns and implied volatility for 20 developed and emerging international markets. In particular we examine how the sign and size of return innovations affect the expectations of daily changes in volatility. Our empirical findings indicate that the conditional contemporaneous return-volatility relationship varies not only based on the sign of the expected returns but also upon their magnitude, according to recent results from the behavioral finance literature. We find evidence of an asymmetric and reverse return-volatility relationship in many advanced, Asian, Latin-American, European and South African markets. We show that the US market displays the highest reaction to price falls, Asian markets present the lowest sensitivity to volatility expectations, while the Euro area is characterized by a homogeneous response both in terms of direction and impact. These results may be safely attributed to cultural and societal characteristics. An extensive quantile regression analysis demonstrates that the detected asymmetric pattern varies particularly across the extreme distribution tails i.e., in the highest/lowest quantile ranges. Indeed, the classical feedback and leverage hypotheses appear not plausible, whilst behavioral theories emerge as the new paradigm in real-world applications.     

Modelling the joint dynamics of oil prices and investor fear gauge

This paper investigates the interdependent relationship between WTI returns and the newly published crude oil volatility index (OVX), combining a cross-correlation function approach, a time-varying parameter (TVP) GARCH model, and a multivariate regression analysis, by which the direction, dynamics, magnitude and asymmetry of their relationship are modelled. At the same time, the implied volatility indexes in the stock market and the gold market are considered for comparison. It is found that there is a significant unidirectional causality-in-mean from WTI returns to the OVX changes, while causality-in-variance from the OVX changes to WTI returns is also significant. The contemporaneous relationship between the OVX changes and WTI returns is significantly negative, and their asymmetric relationship implies that OVX has played a greater role as a gauge of investor fear than as risk preference. The time-varying results indicate that the relationship between the changes in OVX and WTI returns is not always negative.     

A behavioral explanation for the negative asymmetric return–volatility relation

We examine the short-term dynamic relation between the S&P 500 (Nasdaq 100) index return and changes in implied volatility at both the daily and intraday level. Neither the leverage hypothesis nor the volatility feedback hypothesis adequately explains the results. Alternatively, we propose that the behavior of traders (from the representativeness, affect, and extrapolation bias concepts of behavioral finance) is consistent with our empirical results of a strong daily and intraday negative return–implied volatility relation. Moreover, both the presence and magnitude of the negative relation and the asymmetry between return and implied volatility are most closely associated with extreme changes in the index returns. We also show that the strength of the relation is consistent with the implied volatility skew.     

The leverage effect puzzle: Disentangling sources of bias at high frequency

The leverage effect refers to the generally negative correlation between an asset return and its changes of volatility. A natural estimate consists in using the empirical correlation between the daily returns and the changes of daily volatility estimated from high frequency data. The puzzle lies in the fact that such an intuitively natural estimate yields nearly zero correlation for most assets tested, despite the many economic reasons for expecting the estimated correlation to be negative. To better understand the sources of the puzzle, we analyze the different asymptotic biases that are involved in high frequency estimation of the leverage effect, including biases due to discretization errors, to smoothing errors in estimating spot volatilities, to estimation error, and to market microstructure noise. This decomposition enables us to propose novel bias correction methods for estimating the leverage effect.     

The information content of ETF options

We examine the information content of China's Shanghai Stock Exchange (SSE) 50 ETF options introduced in 2015. Trading volume and implied volatilities of calls versus puts differ markedly: trading volume is consistently higher for calls, and implied volatility is higher for puts. Put-call volume and implied volatility ratios are not good predictors of future SSE 50 returns. Implied volatility follows a right-skewed smirk across strike prices, indicating a tendency among option traders to turn bullish and expect the stock market to recover from the June 2015 market crash. The options market dominates the price discovery process, with an average information leadership share of 67%. Our price discovery results persist during the COVID outbreak.     

Option prices and stock market momentum: evidence from China

Option prices tend to be correlated to past stock market returns due to market imperfections. We unprecedentedly examine this issue on the SSE 50 ETF option in the Chinese derivatives market. To measure the price pressure in the options market, we construct an implied volatility spread based on pairs of the SSE 50 ETF option with identical expiration dates and strike prices. By regressing the implied volatility spread on past stock returns, we find that past stock returns exert a strong influence on the pricing of index options. Specifically, we find that SSE 50 ETF calls are significantly overvalued relative to SSE 50 ETF puts after stock price increases and the reverse is also true after the stock price decreases. Moreover, we validate the momentum effects in the underlying stock market to be responsible for the price pressure. These findings are both economically and statistically significant and have important implications.     

Idiosyncratic risk and the cross-section of expected stock returns

Theories such as Merton [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510] predict a positive relation between idiosyncratic risk and expected return when investors do not diversify their portfolio. Ang, Hodrick, Xing, and Zhang [2006. The cross-section of volatility and expected returns. Journal of Finance 61, 259–299], however, find that monthly stock returns are negatively related to the one-month lagged idiosyncratic volatilities. I show that idiosyncratic volatilities are time-varying and thus, their findings should not be used to imply the relation between idiosyncratic risk and expected return. Using the exponential GARCH models to estimate expected idiosyncratic volatilities, I find a significantly positive relation between the estimated conditional idiosyncratic volatilities and expected returns. Further evidence suggests that Ang et al.'s findings are largely explained by the return reversal of a subset of small stocks with high idiosyncratic volatilities.     

Volatility components, leverage effects, and the return-volatility relations

This paper investigates the risk-return trade-off by taking into account the model specification problem. Market volatility is modeled to have two components, one due to the diffusion risk and the other due to the jump risk. The model implies Merton’s ICAPM in the absence of leverage effects, whereas the return-volatility relations are determined by interactions between risk premia and leverage effects in the presence of leverage effects. Empirically, I find a robust negative relationship between the expected excess return and the jump volatility and a robust negative relationship between the expected excess return and the unexpected diffusion volatility. The latter provides an indirect evidence of the positive relationship between the expected excess return and the diffusion volatility.     

Causality in quantiles and dynamic stock return–volume relations

This paper investigates the causal relations between stock return and volume based on quantile regressions. We first define Granger non-causality in all quantiles and propose testing non-causality by a sup-Wald test. Such a test is consistent against any deviation from non-causality in distribution, as opposed to the existing tests that check only non-causality in certain moment. This test is readily extended to test non-causality in different quantile ranges. In the empirical studies of three major stock market indices, we find that the causal effects of volume on return are usually heterogeneous across quantiles and those of return on volume are more stable. In particular, the quantile causal effects of volume on return exhibit a spectrum of (symmetric) V-shape relations so that the dispersion of return distribution increases with lagged volume. This is an alternative evidence that volume has a positive effect on return volatility. Moreover, the inclusion of the squares of lagged returns in the model may weaken the quantile causal effects of volume on return but does not affect the causality per se.     

State‐preference pricing and volatility indices

This study uses a state‐preference pricing approach to develop a state‐price volatility index (SVX), as a forecast for market future realised volatility. We show that SVX is a more efficient forecaster than CBOE VIX for 30‐day realised volatility of SPX returns, using both in‐the‐sample and out‐of‐the‐sample tests. This result is robust to different measures of realised market volatilities. We also show that SVX provides a better volatility forecast than other alternative measures, including the at‐the‐money implied volatilities and GARCH (1, 1) volatility. Our results provide a foundation for forecasting higher risk‐neutral moments using the same state prices.     

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.     

The jump component of S&P 500 volatility and the VIX index

Much research has investigated the differences between option implied volatilities and econometric model-based forecasts. Implied volatility is a market determined forecast, in contrast to model-based forecasts that employ some degree of smoothing of past volatility to generate forecasts. Implied volatility has the potential to reflect information that a model-based forecast could not. This paper considers two issues relating to the informational content of the S&P 500 VIX implied volatility index. First, whether it subsumes information on how historical jump activity contributed to the price volatility, followed by whether the VIX reflects any incremental information pertaining to future jump activity relative to model-based forecasts. It is found that the VIX index both subsumes information relating to past jump contributions to total volatility and reflects incremental information pertaining to future jump activity. This issue has not been examined previously and expands our understanding of how option markets form their volatility forecasts.     

Leverage effect breakdowns and flight from risky assets

Though part of ‘market lore’, in 1976 Black first reported the inverse relationship between price and volatility, calling it the ‘leverage effect’. Without providing evidence, in 1988 Black claimed that in the months leading up to the October 1987 crash the relationship changed: price and volatility both rose. Using daily data for the Old VIX, derived from S&P 100 Index option market prices, to estimate intra-quarterly regressions of implied volatility against price from Q2 1986 to Q1 2012, the author verifies Black’s claim for the October 1987 crash, and interestingly, for subsequent periods of crisis. He then analyses several constant-elasticity-of-variance optimal portfolio rules, which include the leverage effect, to show the elasticity sign switch implies that investors reduce their risky asset holdings to zero.     

The Joint Cross Section of Stocks and Options

Stocks with large increases in call (put) implied volatilities over the previous month tend to have high (low) future returns. Sorting stocks ranked into decile portfolios by past call implied volatilities produces spreads in average returns of approximately 1% per month, and the return differences persist up to six months. The cross section of stock returns also predicts option implied volatilities, with stocks with high past returns tending to have call and put option contracts that exhibit increases in implied volatility over the next month, but with decreasing realized volatility. These predictability patterns are consistent with rational models of informed trading.     

Modelling S&P 100 volatility: The information content of stock returns

Theoretical models that relate volatility to the quantity of information are extended to a multi-asset setting and it is deduced that stock returns may or may not have incremental information when modelling index volatility, depending on the sources of information that move stock prices. The first empirical study that can help resolve this theoretical uncertainty is presented. A detailed analysis of the daily volatility of the S&P 100 index from 1984 to 1998 shows there is some incremental volatility information in the returns from the 100 shares that define the index. This evidence is obtained from ARCH models that incorporate leverage effects, dummy variables for the 1987 crash and aggregate measures of stock return volatility. Significant differences between estimated volatilities are found for various stock measures and sub-periods.     

The information content of implied volatilities and model-free volatility expectations: Evidence from options written on individual stocks

We measure the volatility information content of stock options for individual firms using option prices for 149 US firms and the S&P 100 index. We use ARCH and regression models to compare volatility forecasts defined by historical stock returns, at-the-money implied volatilities and model-free volatility expectations for every firm. For 1-day-ahead estimation, a historical ARCH model outperforms both of the volatility estimates extracted from option prices for 36% of the firms, but the option forecasts are nearly always more informative for those firms that have the more actively traded options. When the prediction horizon extends until the expiry date of the options, the option forecasts are more informative than the historical volatility for 85% of the firms. However, at-the-money implied volatilities generally outperform the model-free volatility expectations.     

Oil prices implied volatility or direction: Which matters more to financial markets?

We examine the impact of oil price uncertainty on US stock returns by industry using the US Oil Fund options implied volatility OVX index and a GJR-GARCH model. We test the effect of the implied volatility of oil on a wide array of domestic industries’ returns using daily data from 2007 to 2016, controlling for a variety of variables such as aggregate market returns, market volatility, exchange rates, interest rates, and inflation expectations. Our main finding is that the implied volatility of oil prices has a consistent and statistically significant negative impact on nine out of the ten industries defined in the Fama and French (J Financ Econ 43:153–193, 1997) 10-industry classification. Oil prices, on the other hand, yield mixed results, with only three industries showing a positive and significant effect, and two industries exhibiting a negative and significant effect. These findings are an indication that the volatility of oil has now surpassed oil prices themselves in terms of influence on financial markets. Furthermore, we show that both oil prices and their volatility have a positive and significant effect on corporate bond credit spreads. Overall, our results indicate that oil price uncertainty increases the risk of future cash flows for goods and services, resulting in negative stock market returns and higher corporate bond credit spreads.     

On the relation between expected returns and implied cost of capital

We examine the relation between implied cost of capital and expected returns under an assumption that expected returns are stochastic, a property supported by theory and empirical evidence. We demonstrate that implied cost of capital differs from expected return, on average, by a function encompassing volatilities of, as well as correlation between, expected returns and cash flows, growth in cash flows, and leverage. These results provide alternative explanations for findings from empirical studies employing implied cost of capital on the magnitude of the market risk premium; predictability of future returns; and the relations between cost of capital and a host of firm characteristics, such as growth, leverage, idiosyncratic risk and the firm’s information environment.