We extend the ex-ante mean-variance (SVIX) asset pricing models of Martin (2017) and Martin-Wagner (2019) to a mean-variance-asymmetry (AVIX) framework by incorporating higher-moment and co-moment risk in asset pricing. Our proposed AVIX model is risk-neutral with left-tail asymmetries in returns to correct the SVIX approach's downside bias. We derive an option implied market beta of a stock as the weighted average of the betas of SVIX and AVIX. Empirically, the implied beta has significant predictability of risk/return relationship We develop an investible portfolio (MKT*) that mimics realized outcomes on the implied market index adjusted for volatility asymmetry.

Studies of the dynamics of bond risk premia that do not account for the corresponding dynamics of bond risk are hard to interpret. We propose a new approach to modeling bond risk and risk premia. For each of the US and China, we reduce the government bond market to its first two principal-component bond-factor portfolios. For each bond-factor portfolio, we estimate the joint dynamics of its volatility and Sharpe ratio as functions of yield curve variables, and of VIX in the US. We have three main findings.(1) There is an important second factor in bond risk premia. (2) Time variation in bond return volatility is as important as time variation in bond Sharpe ratios. (3) Bond risk premia are solely compensation for bond risk, as no-arbitrage theory predicts. Our approach also allows us to document interesting cyclical and secular time-variation in the term structure of bond risk premia in both the US and China.

VIX Exchange-traded Products (ETPs) provide tracking on the return of a constant-maturity VIX futures index, instead of the uninvestable VIX spot index. In this paper, we develop a comprehensive framework to analyze the behaviors and fundamental drivers of the tracking performance of regular and leveraged VIX ETPs. In this framework, naïve investors in VIX ETPs expect to achieve the ETP’s leverage ratio multiplied by the VIX return during their holding period, but the actual ETP return can deviate dramatically from this naïve expected return due to four components of return deviation. The index substitution deviation is shown to be the primary driver of the bull (inverse) VIX ETPs’ return erosion (enhancement), which can be explained by the negative roll-yield as a result of the contango term structure of VIX futures. For leveraged VIX ETPs over multiple holding days, the compounding deviation due to the “constant-leverage trap” can be sizable. In addition, the NAV deviation due to expense ratio and fund management issues is negative, and the inefficiency deviation doesn’t accumulate over long holding periods due to the creation/redemption feature. Our return deviation framework can be generalized to other ETPs tracking indices that are either uninvestable or unrealistic to replicate.

In this paper, we derive the corresponding implied VIX formulas under the locally riskneutral valuation relationship proposed by Duan (1995) when various forms of GARCH model are proposed for S&P 500 index. The empirical study shows that the GARCH implied VIX is consistently and significantly lower than the CBOE VIX for all kinds of GARCH model investigated. Moreover, the magnitude of the difference suggests that the GARCH option pricing model is not capable of capturing the variance premium, which indicates the incompleteness of the GARCH option pricing under the locally risk-neutral valuation relationship. The source of this kind of incompleteness is then theoretically analyzed. It is shown that the framework of GARCH option pricing model fails to incorporate the price of volatility risk or variance premium.