Variance Risk Premium Research Articles

Tactical Target Date Funds

We propose target date funds modified to exploit stock return predictability driven by the variance risk premium. The portfolio rule of these tactical target date funds (TTDFs) is extremely simplified relative to the optimal one, making it easy to implement and to communicate to investors. We show that saving for retirement in TTDFs generates economically large welfare gains, even after we introduce turnover restrictions and transaction costs, and after taking into account parameter uncertainty. This predictability also appears to be uncorrelated with individual household risk, suggesting that households are in a prime position to exploit it. This paper was accepted by Tomasz Piskorski, finance.

Realized bipower variation, jump components, and option valuation

AbstractWe develop a new option pricing model that captures the jump dynamics and allows for the different roles of positive and negative return variances. Based on the proposed model, we derive a closed‐form solution for option pricing under the condition of a nonmonotonic pricing kernel. Our results indicate that the new model has superior option pricing performance to its nested models, including the jump model of Christoffersen et al. (2015) and affine realized semivariance model of Feunou and Okou (2019). The models accommodating jumps, high‐frequency information, and accounting for variance risk premium perform well compared with traditional benchmark models.

Nonparametric Tests of Conditional Independence for Time Series

We propose consistent nonparametric tests of conditional independence for time series data. Our methods are motivated from the difference between joint conditional cumulative distribution function (CDF) and the product of conditional CDFs. The difference is transformed into a proper conditional moment restriction (CMR), which forms the basis for our testing procedure. Our test statistics are then constructed using the integrated moment restrictions that are equivalent to the CMR. We establish the asymptotic behavior of the test statistics under the null, the alternative, and the sequence of local alternatives converging to conditional independence at the parametric rate. Our tests are implemented with the assistance of a multiplier bootstrap. Monte Carlo simulations are conducted to evaluate the finite sample performance of the proposed tests. We apply our tests to examine the predictability of equity risk premium using variance risk premium for different horizons and find that there exist various degrees of nonlinear predictability at mid-run and long-run horizons.

The Time Variation in Risk Appetite and Uncertainty

We formulate a dynamic no-arbitrage asset pricing model for equities and corporate bonds, featuring time variation in both risk aversion and economic uncertainty. The joint dynamics among cash flows, macroeconomic fundamentals, and risk aversion accommodate both heteroskedasticity and non-Gaussianity. The model delivers measures of risk aversion and uncertainty at the daily frequency. We verify that equity variance risk premiums are very informative about risk aversion, whereas credit spreads and corporate bond volatility are highly correlated with economic uncertainty. Our model-implied risk premiums outperform standard instruments for predicting asset excess returns. Risk aversion is substantially correlated with consumer confidence measures and in early 2020 reacted more strongly to new COVID cases than did an uncertainty proxy. This paper was accepted by Haoxiang Zhu, finance.

Can the Implied Information of Options Predict the Liquidity of Stock Market? A Data-Driven Research Based on SSE 50ETF Options

Liquidity reflects the quality of the market. When the market is short of liquidity, it often causes investors’ trading difficulties and stock price volatility, expanding the investment risk. As a risk management tool, options attract more informed investors to trade because of their flexible design. To explore whether the implied information based on the formation of option price can predict the liquidity of stock market, we take SSE 50ETF options from February 9, 2015, to December 31, 2020, as the research sample. Based on the idea of data-driven approach, we extract the implied information contained in option price, including implied volatility, implied volatility spread, and variance risk premium. Through the regression analysis method, we examine the ability to predict the liquidity of the stock market. The results show that implied volatility spread has the strongest ability to predict the liquidity of the stock market, and it is more significant within 270 days. Implied volatility contains the information about the short-term (120 days) liquidity of the stock market in the future. It shows that implied volatility and implied volatility spread are good indicators to predict stock market liquidity. In contrast, variance risk premium cannot predict the liquidity of stock market. The research conclusion verifies the role of option-implied information in predicting the stock market’s liquidity. By extracting the information of options price, investors and financial regulators can scientifically participate in the financial market under data guidance.

Dividend predictability and higher moment risk premia

I use model-free methods to estimate the term structures of the variance risk premium (VRP) and the skewness risk premium (SRP) derived from dividend futures and options. I find that VRP is on average negative, whereas SRP is on average positive. They have unique characteristics and can hardly be explained by equity risk factors and equity moment risk premia. I present evidence that both dividend moment risk premia contain significant forecasting power for dividend futures returns in- and out-of-sample. Dividend futures returns are predicted by the VRP (SRP) in almost all setups with a negative (positive) sign.

Cross-stock market spillovers through variance risk premiums and equity flows

We estimate variance risk premiums (VRPs) in stock markets of selected major advanced economies (AEs) and emerging market economies (EMEs) over 2007–2015, and decompose the VRP into variance-diffusive risk premium (DRP) and variance-jump risk premium (JRP). Daily VAR analysis reveals significant spillovers from US and developed Eurozone’s VRPs to the other economies’ VRPs, especially during the post-Global Financial Crisis (GFC) period. We also find that during the post-GFC period, shocks on the DRPs of the United States and the developed Eurozone have relatively strong and long-lived positive effects on other economies’ VRPs, whereas shocks on their JRPs have relatively weak and short-lived positive effects. In addition, we show that increases in the size of US VRP, DRP and JRP tend to significantly reduce weekly equity fund flows to all other AEs and some EMEs during the post-GFC period, while the impacts are limited during the GFC period. Finally, US DRP plays a more important role than US JRP in the determination of equity fund flows to other AEs during the post-GFC period. Such results indicate the possibility of equity fund flows working as a channel of cross-stock market VRP spillovers.

Practical Applications of The Bitcoin VIX and Its Variance Risk Premium

In The Bitcoin VIX and Its Variance Risk Premium, published in the Spring 2021 issue of The Journal of Alternative Investments, Carol Alexander and Arben Imeraj (both of the University of Sussex) introduce the bitcoin volatility index. CryptoCompare now streams this index every 15 seconds, under the ticker BVIN. Alexander and Imeraj are the first to investigate the bitcoin variance risk premiums and the behavior of the term structure of fair-value variance swap rates. The authors collect price data on bitcoin derivatives traded on the Deribit exchange via its application programming interface. They construct a family of indexes for different maturities using the same methodology used by CBOE’s equity volatility index, the VIX. They describe the methodology, noting that it accounts for information in volatility skews but assumes no jumps in prices. They also compare the indexes with those created with an alternative technique that does not rely on the no-jump assumption. In addition, they explore the diversification potential of bitcoin variance through correlation matrixes with other assets’ volatility indexes, realized volatilities, and other variance risk premiums. TOPICS:Currency, mutual funds/passive investing/indexing, statistical methods, performance measurement

Practical Applications of The Bitcoin VIX and Its Variance Risk Premium

In <b>The Bitcoin VIX and Its Variance Risk Premium</b>, published in the Spring 2021 issue of <b><i>The Journal of Alternative Investments</i></b>, <b>Carol Alexander</b> and <b>Arben Imeraj</b> (both of the <b>University of Sussex</b>) introduce the bitcoin volatility index. CryptoCompare now streams this index every 15 seconds, under the ticker BVIN. Alexander and Imeraj are the first to investigate the bitcoin variance risk premiums and the behavior of the term structure of fair-value variance swap rates. The authors collect price data on bitcoin derivatives traded on the Deribit exchange via its application programming interface. They construct a family of indexes for different maturities using the same methodology used by CBOE’s equity volatility index, the VIX. They describe the methodology, noting that it accounts for information in volatility skews but assumes no jumps in prices. They also compare the indexes with those created with an alternative technique that does not rely on the no-jump assumption. In addition, they explore the diversification potential of bitcoin variance through correlation matrixes with other assets’ volatility indexes, realized volatilities, and other variance risk premiums. <b>TOPICS:</b>Currency, mutual funds/passive investing/indexing, statistical methods, performance measurement

Time-varying uncertainty and variance risk premium

This paper extends the AK production model in Pindyck and Wang (2013) into a more general setting in which the volatility of capital stock is stochastic and driven by shocks. After solving the equilibrium, the fundamental shocks are embedded into the stock price and the leverage effect is contributed from three distinct channels. As an application, we employ our extended AK production model to match well the negative variance risk premium.

Variance risk and the idiosyncratic volatility puzzle

We decompose the CBOE's VIX index into the variance risk premium (to proxy for risk aversion) and conditional variance of stock returns (to proxy for economic uncertainty). We show that the variance risk premium has relatively strong predictive power for the return spread between high and low idiosyncratic volatility (IVOL) quintile portfolios. Thus, investors demand a premium for variance risk, which reflects the uncertainty of the asset's return variance itself. The findings also indicate that higher levels of risk aversion and tense economic conditions help minimize the IVOL-return puzzle. Our results are robust using value-weighted and equal-weighted returns.

Learning, slowly unfolding disasters, and asset prices

We develop a model that generates slowly unfolding disasters not only in the macroeconomy but also in financial markets. In our model, investors cannot exactly distinguish whether the economy is experiencing a mild/temporary downturn or is on the verge of a severe/prolonged disaster. Due to imperfect information, disaster periods are not fully identified by investors ex ante. Bayesian learning induces equity prices to gradually react to persistent consumption declines, which plays a critical role in explaining the VIX, variance risk premium, and put-protected portfolio returns. We show that our model can rationalize the market patterns of recent major crises, such as the dot-com bubble burst, Great Recession, and COVID-19 crisis, through investors' belief channel.

Central bank tone and currency risk premia

I analyze how the tone of central bank press conferences impacts risk premia in the currency market. Tone is measured as the difference between the number of hawkish and dovish phrases mafide during a press conference, as a fraction of total phrases. A one standard deviation increase in the hawkishness of a press conference is associated with a 1.5% decline in the variance risk premium, a 4.9% decline in the subsequent variance swap return, and a 0.2% increase in option implied risk aversion. The impact of tone comes primarily from the questions & answers, or the unscripted portion of the press conference.

Under-diversification and idiosyncratic risk externalities

We study the effects of idiosyncratic uncertainty on asset prices, investment, and welfare. We consider an economy with two main components: under-diversification and endogenous, countercyclical idiosyncratic risk. The equilibrium is subject to underinvestment and excessive aggregate risk-taking. Inefficiencies stem from an idiosyncratic risk externality, as firms do not internalize the effect of their investment decisions on the risk borne by others. Risk externalities depend on an idiosyncratic risk premium and a variance risk premium. We assess their magnitude empirically. The optimal allocation can be implemented through financial regulation using a tax benefit on debt and risk-weighted capital requirements.

The Global Determinants of International Equity Risk Premiums

&amp;amp;lt;ns2:p&amp;amp;gt;We examine the commonality in international equity risk premiums by linking empirical evidence for the international stock return predictability of US downside and upside variance risk premiums (DVP and UVP, respectively) with implications from an international asset pricing framework, which takes the perspective of a US/global investor and features asymmetric global macroeconomic, financial market, and risk aversion shocks. We find that DVP and UVP predict international stock returns through different global equity risk premium determinants: bad and good macroeconomic uncertainties, respectively. Across countries, US investors demand lower macroeconomic risk compensation but higher financial market risk compensation for more-integrated countries.&amp;amp;lt;/ns2:p&amp;amp;gt;

Does the risk aversion of crude oil market investors have directional predictability for the precious metal and agricultural markets?

PurposeRisk aversion is considered as an important factor in predicting asset prices. Many studies have proved that there exists important price information spillover among crude oil, precious metals and agricultural markets. Then there naturally follows the question: Is the risk aversion of investors in crude oil market predictable for the returns of precious metals and agricultural products? The purpose of this paper is to answer this question. For this reason, the authors explore the directional predictability and the cross-quantile dependence between risk aversion of crude oil market investors and returns of precious metals and agricultural products.Design/methodology/approachTo better describe the risk aversion of investors, this paper uses high-frequency data and model-free calculation method to obtain variance risk premium of crude oil. Then, this paper uses the cross-quantilogram method to investigate the directional predictability and cross-quantile dependence between risk aversion of crude oil market investors and returns of precious metals and agricultural products. Meanwhile, it employs the partial cross-quantilogram (PCQ) method to test the impact of control variables on the empirical results.FindingsFirstly, risk aversion of crude oil market investors has directional predictability for returns of precious metals and agricultural products. Secondly, different degrees of risk aversion of crude oil market investors have different impacts on returns of precious metals and agricultural products. A low (high) degree of crude oil market investors' risk aversion has negative (positive) predictability for returns of precious metals and agricultural products. Finally, during the sample period, the returns of precious metals are more affected by risk aversion of crude oil market investors than returns of agricultural products.Originality/valueFirst of all, this paper studies the impact of risk aversion of crude oil market investors on returns of precious metals and agricultural products. It updates previous relevant studies on the factors influencing the prices of precious metals and agricultural products, and provides a new idea for the forecast of those commodity returns. Secondly, this paper provides the evidence that different degrees of risk aversion of investors have different effects on the returns of commodities, and expands the research on the topic of commodity returns prediction. Finally, high-frequency data are employed in this paper to better capture the risk aversion of investors than commonly used daily data.

The Informational Content of High-Frequency Option Prices

We propose the option realized variance as an observable variable to summarize the information from high-frequency option data. This variable aggregates intraday option returns from midquote prices to compute an option’s total variability for a given day, providing additional information about the jump activity in the data generating process. Using the S&amp;P 500 index time series and options data, this paper documents the performance of this realized measure in predicting the index realized variance as well as the equity and variance risk premiums. We estimate an option pricing model and analyze its parameter estimates. Our results show that excluding high-frequency option information produces significant differences in variance jump parameters, estimated risk premiums, and option pricing errors.This paper was accepted by Tyler Shumway, finance.

Stock Return Extrapolation, Option Prices, and Variance Risk Premium

Abstract This paper presents a tractable dynamic equilibrium model of stock return extrapolation in the presence of stochastic volatility. In the model, consistent with survey evidence, investors expect future returns to be higher (lower) but also less (more) volatile following positive (negative) stock returns. The biased volatility expectation introduces a new channel through which past returns and investor sentiment affect derivative prices. In particular, through this novel channel, the model reconciles the otherwise puzzling evidence of past returns affecting option prices and the evidence of variance risk premium predicting future stock market returns even after controlling for the realized variance.

Economic Uncertainty and Bank Lending

AbstractThis paper shows that economic uncertainty proxied by the variance risk premium (VRP) has an important explanatory power for bank credit supply and demand. Higher VRP exerts a negative influence on both loan demand and supply, increases loan spreads, reduces loan size and maturity, and increases the proportion of collateralized loans. These effects are substantive in the syndicated loan market and are worse off during economic recessions. Upon isolating the effect of uncertainty on bank credit supply from loan demand, we find that VRP dominates credit supply, which suggests that bank credit shortages can potentially aggravate economic downturn during recessions.

Financial Uncertainty with Ambiguity and Learning

We examine a production-based asset pricing model with regime-switching productivity growth, learning, and ambiguity. Both the mean and volatility of the growth rate of productivity are assumed to follow a Markov chain with an unobservable state. The agent’s preferences are characterized by the generalized recursive smooth ambiguity utility function. Our calibrated benchmark model with modest risk aversion can match moments of the variance risk premium in the data and reconcile empirical relations between the risk-neutral variance and macroeconomic quantities and their respective volatilities. We show that the interplay between productivity volatility risk and ambiguity aversion is important for pricing variance risk in returns. This paper was accepted by Tomasz Piskorski, finance.