Is volatility risk priced in the securities market? Evidence from S&P 500 index options

The authors examine whether volatility risk is a priced risk factor in securities returns. Zero‐beta at‐the‐money straddle returns of the S&P 500 index are used to measure volatility risk. It is demonstrated that volatility risk captures time variation in the stochastic discount factor. The results suggest that straddle returns are important conditioning variables in asset pricing, and investors use straddle returns when forming their expectations about securities returns. One interesting finding is that different classes of firms react differently to volatility risk. For example, small firms and value firms have negative and significant volatility coefficients, whereas big firms and growth firms have positive and significant volatility coefficients during high‐volatility periods, indicating that investors see these latter firms as hedges against volatile states of the economy. Overall, these findings have important implications for portfolio formation, risk management, and hedging strategies. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:617–642, 2007     

Market Timing With Moving Averages

I present evidence that a moving average (MA) trading strategy has a greater average return and skewness as well as a lower variance compared to buying and holding the underlying asset using monthly returns of value‐weighted US decile portfolios sorted by market size, book‐to‐market, and momentum, and seven international markets as well as 18,000 individual US stocks. The MA strategy generates risk‐adjusted returns of 3–7% per year after transaction costs. The performance of the MA strategy is driven largely by the volatility of stock returns and resembles the payoffs of an at‐the‐money protective put on the underlying buy‐and‐hold return. Conditional factor models with macroeconomic variables, especially the default premium, can explain some of the abnormal returns. Standard market timing tests reveal ample evidence regarding the timing ability of the MA strategy.     

Timing the Market with a Combination of Moving Averages

A combination of simple moving average trading strategies with several window lengths delivers a greater average return and skewness as well as a lower variance and kurtosis compared with buying and holding the underlying asset using daily returns of value‐weighted US decile portfolios sorted by market size, book‐to‐market, momentum, and standard deviation as well as more than 1000 individual US stocks. The combination moving average (CMA) strategy generates risk‐adjusted returns of 2% to 16% per year before transaction costs. The performance of the CMA strategy is driven largely by the volatility of stock returns and resembles the payoffs of an at‐the‐money protective put on the underlying buy‐and‐hold return. Conditional factor models with macroeconomic variables, especially the market dividend yield, short‐term interest rates, and market conditions, can explain some of the abnormal returns. Standard market timing tests reveal ample evidence regarding the timing ability of the CMA strategy.     

Fama–French in China: Size and Value Factors in Chinese Stock Returns

We investigate the size and value factors in the cross‐section of returns for the Chinese stock market. We find a significant size effect but no robust value effect. A zero‐cost small‐minus‐big (SMB) portfolio earns an average premium of 0.61% per month, which is statistically significant with a t‐value of 2.89 and economically important. In contrast, neither the market portfolio nor the zero‐cost high‐minus‐low (HML) portfolio has average premiums that are statistically different from zero. In both time‐series regressions and Fama–MacBeth cross‐sectional tests, SMB represents the strongest factor in explaining the cross‐section of Chinese stock returns. Our results contradict several existing studies which document a value effect. We show that this difference comes from the extreme values in a few months in the early years of the market with a small number of stocks and high volatility. Their impact becomes insignificant with a longer sample and proper volatility adjustment.     

Disentangling Beta and Value Premium Using Macroeconomic Risk Factors

In this paper, we study the time-varying total risk of value and growth stocks. The objective is to investigate the contention that the market factor's ability to explain the value premium is limited. Inspired by Ferson and Harvey [1999], we revisit the role of the market beta in the presence of aggregate economic factors. We discuss the incorporation of aggregate economic conditions in the context of multifactor risk models and provide cross-sectional evidence on the relationship between average returns and postranking betas for book-to-market (BE/ME) sorted portfolios. We show that the ineffective role of the market beta can be altered by incorporating aggregate economic risk factors in the cross-sectional asset pricing tests of size and BE/ME sorted portfolios. No previous study provides such a decomposition of the cross-sectional role of the market beta in the presence of macroeconomic risk factors.     

Turnover and return in global stock markets

I study how growth affects liquidity of global stock exchanges and how liquidity determines cross-sectional returns on those stock exchange index portfolios. I measure portfolio liquidity by turnover ratio computed as value of shares traded over the market capitalization. I obtain data from FIBV, an association of global stock exchanges. In a multiple regression model for turnover ratio, I find age, size, type of exchange, competition for order flow, and growth rate to be significant determinants of portfolio liquidity; however, exchange- and time-specific effects are more appropriate for modeling portfolio liquidity. The time effects yield to three distinct regimes, while the exchange-specific effects are surrogates for the legal systems, English common law, and Civil laws of the countries. I estimate the parameters of a multiple regression model in a two-stage GLS framework in which index return is a function of turnover. The GLS method is preferable since a turnover ratio may have a non-stationary, random component. The significant determinants of index return are turnover and volatility, although some of the volatility effect may be a spillover from a January effect. Investors expect higher return from high turnover markets. However, the positive turnover expected return relation is true only in emerging markets; in developed markets expected return is a function of volatility. This result confirms existing empirical evidence that high turnover stock portfolios generate superior returns and further the sources and pricing of risk in emerging and developed markets are different.     

Asymmetric pricing of implied systematic volatility in the cross‐section of expected returns

Assuming a symmetric relation between returns and innovations in implied market volatility, Ang, A., Hodrick, R., Xing, Y., and Zhang, X. (2006) find that sensitivities to changes in implied market volatility have a cross‐sectional effect on firm returns. Dennis, P., Mayhew, S., and Stivers, C. (2006), however, find an asymmetric relation between firm‐level returns and implied market volatility innovations. We incorporate this asymmetry into the cross‐sectional relation between sensitivity to volatility innovations and returns. Using both portfolio sorting and firm‐level regressions, we find that sensitivity to VIX innovations is negatively related to returns when volatility is rising, but is unrelated when it is falling. The negative relation is robust to controls for other variables, suggesting only the increase in implied market volatility is a priced risk factor. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:34–54, 2011     

Volatility and jump risk in option returns

We examine the importance of volatility and jump risk in the time-series prediction of S&P 500 index option returns. The empirical analysis provides a different result between call and put option returns. Both volatility and jump risk are important predictors of put option returns. In contrast, only volatility risk is consistently significant in the prediction of call option returns over the sample period. The empirical results support the theory that there is option risk premium associated with volatility and jump risk, and reflect the asymmetry property of S&P 500 index distribution.     

Time‐varying jump risk premia in stock index futures returns

This study tests the presence of time‐varying risk premia associated with extreme news events or jumps in stock index futures return. The model allows for a dynamic jump component with autoregressive jump intensity, long‐range dependence in volatility dynamics, and a volatility in mean structure separately for the normal and extreme news events. The results show significant jump risk premia in four stock market index futures returns including the DAX, FTSE, Nikkei, and S&P500 indices. Our results are robust to various specifications of conditional variance including the plain GARCH, component GARCH, and Fractionally Integrated GARCH models. We also find the time‐varying risk premium associated with normal news events is not significant across all indices. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:639–659, 2012     

Is there information in the volatility skew?

Since the 1987 crash, option prices have exhibited a strong negative skew, implying higher implied volatility for out‐of‐the‐money puts than at‐ and in‐the‐money puts. This has resulted in incorporating multiple jumps and stochastic volatility within the data generating process to improve the Black–Scholes model in an attempt to capture negative skewness and a highly leptokurtic distribution. The general conclusion is that there is a large jump premium in the short term, which best explains the significant negative skew for short maturity options. Alternative explanations for the negative skew are related to market liquidity driven by demand shocks and supply shortages. Regardless of the explanation for the negative skew, we assess the information content in the shape of the skew to infer if the option market can accurately forecast stock market crashes and/or spikes upward. We demonstrate, using all options on the S&P 100 from 1984–2006, that the shape of the skew can reveal with significant probability when the market will crash or spike. However, we find the magnitude of the spike prediction is not economically significant. Our findings are strongest for the short‐term out‐of‐the money puts, consistent with the notion of investors' aversion to large negative movements. We also find that the power of the crash/spike prediction decreases with an increase in the time to option maturity. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:921–959, 2007     

Exchange rate jumps and exports: Evidence from China

We apply the autoregressive conditional jump intensity (ARJI ) model to monthly exchange rate returns of China against 81 countries and investigate the impact of exchange rate volatility on exports over the period of 1995–2004. We decompose bilateral exchange rate volatility into continuous and discrete components and find that only the discrete part of exchange rate volatility, that is, the exchange rate jumps, has a significantly negative effect on exports, which to some extent reconciles the old yet unsettled debate in previous literature on the role of exchange rate volatility in international trade. There is also some evidence suggesting that the development of domestic financial market will boost international trade, but it does not help attenuate the negative effect of bilateral exchange rate jump risk on exports.     

Unveiling Contemporaneous Relations Between Jump Risk and Cross Section of Stock Returns

This study analyzes the impact of time varying jump risk on aggregate returns. We, in particular, examine the pricing of jump size and intensity components in the cross section of stock returns for four Asian markets. We use stochastic volatility model with jumps to estimate jump size and intensity. Fama–MacBeth regression results indicate that both jump size and intensity have statistically significant effect on expected returns. A one standard deviation increase in jump intensity beta lowers the expected annual returns by 1% for Japan, 2% for China, 5% for India, and 7% for South Korea. The results are consistent even after controlling for the Fama and French three factors, firm size, and liquidity proxies.     

EQUILIBRIUM ASSET AND OPTION PRICING UNDER JUMP DIFFUSION

This paper develops an equilibrium asset and option pricing model in a production economy under jump diffusion. The model provides analytical formulas for an equity premium and a more general pricing kernel that links the physical and risk‐neutral densities. The model explains the two empirical phenomena of the negative variance risk premium and implied volatility smirk if market crashes are expected. Model estimation with the S&P 500 index from 1985 to 2005 shows that jump size is indeed negative and the risk aversion coefficient has a reasonable value when taking the jump into account.     

MCMC ESTIMATION OF LÉVY JUMP MODELS USING STOCK AND OPTION PRICES

We examine the performances of several popular Lévy jump models and some of the most sophisticated affine jump‐diffusion models in capturing the joint dynamics of stock and option prices. We develop efficient Markov chain Monte Carlo methods for estimating parameters and latent volatility/jump variables of the Lévy jump models using stock and option prices. We show that models with infinite‐activity Lévy jumps in returns significantly outperform affine jump‐diffusion models with compound Poisson jumps in returns and volatility in capturing both the physical and risk‐neutral dynamics of the S&P 500 index. We also find that the variance gamma model of Madan, Carr, and Chang with stochastic volatility has the best performance among all the models we consider.     

Machine learning portfolios with equal risk contributions: Evidence from the Brazilian market

We investigate the use of machine learning (ML) to forecast stock returns in the Brazilian market using a rich proprietary dataset. While ML portfolios can easily outperform the local market, the performance of long-short strategies using ML is hampered by the high volatility of the short portfolios. We show that an Equal Risk Contribution (ERC) approach significantly improves risk-adjusted returns. We further develop an ERC approach that combines multiple long-short strategies obtained with ML models, equalizing risk contributions across ML models, which outperforms, on a risk-adjusted basis, all individual ML long-short strategies, as well as alternative combinations of ML strategies.     

Memory in returns and volatilities of futures' contracts

Various authors claim to have found evidence of stochastic long‐memory behavior in futures’ contract returns using the Hurst statistic. This paper reexamines futures’ returns for evidence of persistent behavior using a biased‐corrected version of the Hurst statistic, a nonparametric spectral test, and a spectral‐regression estimate of the long‐memory parameter. Results based on these new methods provide no evidence for persistent behavior in futures’ returns. However, they provide overwhelming evidence of long‐memory behavior for the volatility of futures’ returns. This finding adds to the emerging literature on persistent volatility in financial markets and suggests the use of new methods of forecasting volatility, assessing risk, and optimizing portfolios in futures’ markets. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:525–543, 2000     

The information content in implied idiosyncratic volatility and the cross‐section of stock returns: Evidence from the option markets

Current literature is inconclusive as to whether idiosyncratic risk influences future stock returns and the direction of the impact. Earlier studies are based on historical realized volatility. Implied volatilities from option prices represent the market's assessment of future risk and are likely a superior measure to historical realized volatility. Implied idiosyncratic volatilities on firms with traded options are used to examine the relationship between idiosyncratic volatility and future returns. A strong positive link was found between implied idiosyncratic risk and future returns. After considering the impact of implied idiosyncratic volatility, historical realized idiosyncratic volatility is unimportant. This performance is strongly tied to small size and high book‐to‐market equity firms. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28: 1013–1039, 2008     

基于跳跃、好坏波动率的混频已实现EGARCH模型的波动率预测与风险度量

为探究资产价格的跳跃行为和收益波动的非对称效应对波动率预测的影响,以高频数据建模为视角,基于跳跃、好坏波动率将Realized EGARCH-MIDAS模型进行拓展,以提升模型的波动率预测能力与风险度量效果。运用拓展后的模型,以沪深300指数价格高频数据为样本进行实证分析,探究中国股票市场的波动性规律,并采用似然函数、信息准则和基于损失函数的DM与MCS等检验方法,综合比较了改进前后的模型对波动率及风险值的预测效果。实证结果显示：(1)沪深300指数收益的长期波动主要来源于连续波动而非跳跃波动,且受正连续波动影响更大,而负跳跃对波动具有明显的负向冲击;(2)文章提出的拓展模型均能更好地捕捉波动率的长记忆性,在样本内估计和样本外预测上也都有更好的表现,其中同时考虑跳跃与非对称影响的Realized EGARCH-MIDAS-RSJ拓展模型拥有最优的估计及预测效果。     

The impact of parallel market exchange rate volatility and oil exports on real GDP in Syria: Evidence from the ARDL approach

This paper investigates the impact of parallel market exchange rate volatility and trade on real GDP and real GDP growth in the Syrian economy over the period of 1990Q1–2010Q4. To this end, we first construct a parallel market exchange rate volatility indicator. Second, we estimate an autoregressive distributed lag (ARDL) model where we include our indicator of volatility among the main determinants of real GDP. Our findings imply that real GDP can be explained by three main variables: parallel market exchange rate, money supply, and oil exports. The long-run equilibrium reveals that parallel market exchange rate volatility has a negative impact on real GDP compared to the positive impact of money supply and oil exports. In contrast, the short-run impact of parallel market exchange rate volatility on real GDP growth is positive and very small counter to the long-run impact. Furthermore, the coefficient of the error correction term of the estimated ARDL model indicates that real GDP deviation from the equilibrium level will be corrected by about 10% after each quarter.     

The performance of alternative futures buy‐write strategies

This study compares the performance of a conventional buy‐write (or covered call writing) and a dynamic buy‐write strategy. The conventional strategy generally enhances portfolio returns in low volatility conditions but underperforms the underlying cash asset in sharply rising markets. The dynamic strategy adjusts the moneyness of the option according to market conditions. The study extends Hill, J. M., Balasubramanian, V., Gregory, K., and Tierens, I. ( 2006 ) and tests how and to what extent market volatility and market direction affect the performance of these two strategies. The study finds that both strategies offer significant positive α, higher returns and lower standard deviations than the market. Consistent with prior research, the abnormal returns of the buy‐write strategies can be attributed to a volatility premium embedded in the options prices. The buy‐write returns from the Hong Kong market appear to be lower than those found in the U.S. and U.K. markets. The conventional buy‐write outperforms the dynamic strategy in both high and low volatility environments, and in sharply falling markets. However, by targeting exercise probability, the dynamic strategy provides a greater upside in sharply rising markets. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark