How does the market variance risk premium vary over time? Evidence from S&P 500 variance swap investment returns

We explore whether the market variance risk premium (VRP) can be predicted. We measure VRP by distinguishing the investment horizon from the variance swap’s maturity. We extract VRP from actual S&P 500 variance swap quotes and we test four classes of predictive models. We find that the best performing model is the one that conditions on trading activity. This relation is also economically significant. Volatility trading strategies which condition on trading activity outperform popular benchmark strategies, even once we consider transaction costs. Our finding implies that broker dealers command a greater VRP to continue holding short positions in index options in the case where trading conditions deteriorate.     

Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets

We estimate a flexible affine model using an unbalanced panel containing S&P 500 and VIX index returns and option prices and analyze the contribution of VIX options to the model’s in- and out-of-sample performance. We find that they contain valuable information on the risk-neutral conditional distributions of volatility at different time horizons, which is not spanned by the S&P 500 market. This information allows enhanced estimation of the variance risk premium. We gain new insights on the term structure of the variance risk premium, present a trading strategy exploiting these insights, and show how to improve S&P 500 return forecasts.     

Time-Varying Variance Risk Premium and the Predictability of Chinese Stock Market Return

A number of studies have shown that the variance risk premium (VRP), defined as the difference between risk-neutral and physical expected variances, has strong predictive power for the excess stock market return, and this predictability peaks at 3- to 6-month prediction horizons. However, little research presents empirical evidences for Chinese stock market due to the absence of option market. Under general equilibrium asset pricing framework, this article estimates time-varying VRP using the Chinese stock market data. We find that the estimated VRP predicts the excess Chinese stock market return, and this forecasting power is stronger at 4- and 5-month horizons, which is consistent with the findings of existing literature.     

Do Newly Listed Derivatives Affect the Market Risk Premium in a Thin Stock Market?

This study examines the effects on the stock market unitary risk premium and volatility associated with the listing of stock and stock index derivatives in Switzerland. Based on a univariate GARCH (1,1) specification of the stock index variance and a time-varying unitary risk premium representation, we can reject the hypothesis that stock and stock index derivatives listings do not affect the total risk premium. Contrarily to previous empirical evidence, we find that derivatives listings affect both the conditional market returns' variance and the unitary risk premium through structural shocks. The gradual market completion hypothesis is further corroborated in that, cumulatively, the three stock and stock index options futures derivatives listings reduced the unitary risk premium while the marginal impact of each successive listing decayed.     

Do Newly Listed Derivatives Affect the Market Risk Premium in a Thin Stock Market?

This study examines the effects on the stock market unitaryrisk premium and volatility associated with the listing of stockand stock index derivatives in Switzerland. Based on a univariateGARCH (1,1) specification of the stock index variance and atime-varying unitary risk premium representation, we can rejectthe hypothesis that stock and stock index derivatives listingsdo not affect the total risk premium. Contrarily to previousempirical evidence, we find that derivatives listings affectboth the conditional market returns’ variance and theunitary risk premium through structural shocks. The gradualmarket completion hypothesis is further corroborated in that,cumulatively, the three stock and stock index options futuresderivatives listings reduced the unitary risk premium whilethe marginal impact of each successive listing decayed. JELClassification: G12, G14.     

The impact of political risk on the currencies of emerging markets

This study investigates the effects of political risk on the exchange rate returns of Brazil, Chile, Mexico, and Russia. The results indicate the presence of a risk premium for all currencies. Political risk was observed to negatively impact trade returns for only the Brazilian real, a result of depreciating the exchange rate. This effect was not observed for the other countries analyzed. In Brazil, transitory risk-premium volatility was positively associated with both the VIX index and political risk, indicating that greater global and local political risk increased volatility. Furthermore, local political risk had a more significant impact on risk-premium volatility than global risk.     

Components of Market Risk and Return

This article proposes a flexible but parsimonious specificationof the joint dynamics of market risk and return to produce forecastsof a time-varying market equity premium. Our parsimonious volatilitymodel allows components to decay at different rates, generatesmean-reverting forecasts, and allows variance targeting. Thesefeatures contribute to realistic equity premium forecasts forthe U.S. market over the 1840–2006 period. For example,the premium forecast was low in the mid-1990s but has recentlyincreased. Although the market's total conditional variancehas a positive effect on returns, the smooth long-run componentof volatility is more important for capturing the dynamics ofthe premium. This result is robust to univariate specificationsthat condition on either levels or logs of past realized volatility(RV), as well as to a new bivariate model of returns and RV.     

Volatility as an Asset Class: European Evidence

Abstract

Volatility movements are known to be negatively correlated with stock index returns. Hence, investing in volatility appears to be attractive for investors seeking risk diversification. The most common instruments for investing in pure volatility are variance swaps, which now enjoy an active over-the-counter (OTC) market. This paper investigates the risk-return tradeoff of variance swaps on the Deutscher Aktienindex and Euro STOXX 50 index over the time period from 1995 to 2004. We synthetically derive variance swap rates from the smile in option prices. Using quotes from two large investment banks over two months, we validate that the synthetic values are close to OTC market prices. We find that variance swap returns exhibit an option-like profile compared to returns of the underlying index. Given this pattern, it is crucial to account for the non-normality of returns in measuring the performance of variance swap investments. As in the US, the average returns of selling variance swaps are found to be strongly positive and too large to be compatible with standard equilibrium models. The magnitude of the estimated risk premium is related to variance uncertainty and past index returns. This indicates that the variance swap rate does not seem to incorporate all past information relevant for forecasting future realized variance.     

Predicting the equity market with option-implied variables

We comprehensively analyze the predictive power of several option-implied variables for monthly S&P 500 excess returns and realized variance. The correlation risk premium (CRP) and the variance risk premium (VRP) emerge as strong predictors of both excess returns and realized variance. This is true both in- and out-of-sample. Our results also reveal that statistical evidence of predictability does not necessarily lead to economic gains. However, a timing strategy based on the CRP leads to utility gains of more than 5.03% per annum. Forecast combinations provide stable forecasts for both excess returns and realized variance, and add economic value.     

Limited information-processing capacity and asymmetric stock correlations

Through an orthogonalized impulse-response analysis, I studied the relationship between the variance risk premium, market variance and stock correlations in the French stock market from September 2002 through September 2006, using high-frequency data-based measures. Variance risk premium is estimated using realized variances and index options-implied variances and used as a state vector to proxy investors perceived uncertainty. I found that a shock to variance risk premium causes long-lasting increases in the market variance pointing to the limitedness of investors information-processing capacity. At the same time, the shock generates consecutive increases in realized correlations between individual stocks and the market portfolio. I propose this as a possible explanation for the asymmetric/counter-cyclic behaviour of stock correlations.     

Rare disaster risk and the expected equity risk premium

Consistent with the predictions of rare disaster models, we find that a proxy for the time‐varying probability of rare disasters helps to explain fluctuations in expectations of the equity risk premium. Our proxy for disaster risk is a recently developed measure of global political instability, and the expected market risk premium is from Value Line analysts' expected stock returns. Consistent with long‐run risk models, uncertainty about expected GDP growth and expected consumption growth is also significantly positively related to the expected market risk premium. We obtain similar results when we use the earnings–price ratio and the dividend–price ratio as proxies for the expected market risk premium.     

偏度风险溢酬及其预测能力研究——基于人民币对外汇期权的实证分析

基于无模型方法,利用在岸人民币对美元期权的市场价格数据,通过提取风险中性三阶矩和已实现三阶矩估算偏度风险溢酬,并考察其时变特征、与波动率风险溢酬的关系和对汇率尾部风险的预测能力。结果表明,外汇期权市场上存在显著为负的时变偏度风险溢酬;偏度风险溢酬与波动率风险溢酬存在共同的驱动因子。此外,偏度风险溢酬在短期内对汇率暴涨的尾部风险事件具备一定的预测能力。当偏度风险溢酬增加时,投资者对偏度风险的厌恶加剧,预期未来人民币大幅贬值的概率上升。     

Variance risk premiums in foreign exchange markets

Based on the theory of static replication of variance swaps we assess the sign and magnitude of variance risk premiums in foreign exchange markets. We find significantly negative risk premiums when realized variance is computed from intraday data with low frequency. As a likely consequence of microstructure effects however, the evidence is ambiguous when realized variance is based on high-frequency data. Common to all estimates, variance risk premiums are highly time-varying and inversely related to the risk-neutral expectation of future variance.When we test whether variance risk premiums can be attributed to classic risk factors or fear of jump risk, we find that conditional premiums remain significantly negative. However, we observe a strong relationship between the size of log variance risk premiums and the VIX, the TED spread and the general shape of the implied volatility function of the corresponding currency pair. Overall, we conclude that there is a separately priced variance risk factor which commands a highly time-varying premium.     

Fear and the Fama‐French Factors

Investors’ expectations of market volatility, captured by the VIX (the Chicago Board Options Exchange's volatility index, also known as the “investor fear gauge”), affects the expected returns of US equities. Changes in the VIX drive variations in the expected returns of the factors included in the Fama and French three‐factor model augmented with a momentum factor. The market risk premium (R_m– R_f) and the value premium (HML) are especially sensitive to changes in the VIX. An increase in expected volatility is associated with flights to quality and increases in estimated required returns.     

A new approach to measuring riskiness in the equity market: Implications for the risk premium

We introduce a new approach to measuring riskiness in the equity market. We propose option implied and physical measures of riskiness and investigate their performance in predicting future market returns. The predictive regressions indicate a positive and significant relation between time-varying riskiness and expected market returns. The significantly positive link between aggregate riskiness and market risk premium remains intact after controlling for the S&P 500 index option implied volatility (VIX), aggregate idiosyncratic volatility, and a large set of macroeconomic variables. We also provide alternative explanations for the positive relation by showing that aggregate riskiness is higher during economic downturns characterized by high aggregate risk aversion and high expected returns.     

News sentiment and sovereign credit risk

We explore the impact of media content on sovereign credit risk. Our measure of media tone is extracted from the Thomson Reuters News Analytics database. As a proxy for sovereign credit risk we consider credit default swap (CDS) spreads, which are decomposed into their risk premium and default risk components. We find that media tone explains and predicts CDS returns and is a mixture of noise and information. Its effect on risk premium induces a temporary change in investors’ appetite for credit risk exposure, whereas its impact on the default component leads to reassessments of the fundamentals of sovereign economies.     

Multivariate continuous-time modeling of wind indexes and hedging of wind risk

With the introduction of the exchange-traded German wind power futures, opportunities for German wind power producers to hedge their volumetric risk are present. We propose two continuous-time multivariate models for wind power utilization at different wind sites, and discuss the properties and estimation procedures for the models. Applying the models to wind index data for wind sites in Germany and the underlying wind index of exchange-traded wind power futures contracts, the estimation results of both models suggest that they capture key statistical features of the data. We show how these models can be used to find optimal hedging strategies using exchange-traded wind power futures for the owner of a portfolio of so-called tailor-made wind power futures. Both in-sample and out-of-sample hedging scenarios are considered, and, in both cases, significant variance reductions are achieved. Additionally, the risk premium of the German wind power futures is analysed, leading to an indication of the risk premium of tailor-made wind power futures.     

The price of variance risk

Between 1996 and 2014, it was costless on average to hedge news about future variance at horizons ranging from 1 quarter to 14 years. Only unexpected, transitory realized variance was significantly priced. These results present a challenge to many structural models of the variance risk premium, such as the intertemporal CAPM and recent models with Epstein–Zin preferences and long-run risks. The results are also difficult to reconcile with macro models in which volatility affects investment decisions. At the same time, the data allows us to distinguish between different disaster models; a model in which the stock market has a time-varying exposure to disasters and investors have power utility fits the major features of the variance term structure.     

Does liquidity drive stock market returns? The role of investor risk aversion

In this paper, we explore the relations between liquidity, stock returns, and investor risk aversion as captured by the variance risk premium (VRP). This is motivated by theoretical and empirical evidence in the literature which suggests that investor risk aversion negatively correlates with asset liquidity, and ample empirical evidence documenting liquidity risk premium. We use monthly US data from January 1999 to December 2018 and show that innovations in the VRP Granger-cause stock returns, which in turn drive liquidity. Our findings are consistent with predictions of prior theories and highlight the predictability of the VRP. They also contribute to the on-going debate on the causal relation between stock returns and liquidity. Finally, we explore the channels through which the VRP impacts liquidity and find that the VRP influences market and momentum factors, and that movements in these factors lead to changes in liquidity.