Variance risk premia under volatility models

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

Variance Risk in Aggregate Stock Returns and the Return Predictability

Equity risk premia and the pricing of foreign exchange risk

The intertemporal CAPM model of Merton (Econometrica, 41:867–887, 1973) demonstrates that the aggregate market risk premium is determined by the uncertainty of underlying returns, quantified by the return variance. When holding the market portfolio, however, an investor is also bearing the uncertainty of the variance itself. Just like that the equity premium demanded by investors is a result of fear to the uncertainty of future returns, the variance risk premium, defined as the difference between risk-neutral and physical expected variances, is also required to compensate for the risk of the uncertain variance. Several recent studies document the link between risk preference and variance risk premium. In particular, Bakshi and Madan (Manag Sci, 52:1945–1956, 2006) argue that the variance risk premium is approximately determined by the risk aversion parameter and the higher order moments of underlying returns. In a similar vein, Bollerslev et al. (J Econ, 160:102–118, 2011) assume an affine version of the stochastic volatility model in Heston (Rev Financ Stud, 6:327–343, 1993) and show that the variance risk premium is linearly related to the risk preference of individual agents. Other investigations in this area include Bekaert and Engstrom (Asset return dynamics under bad environment-good environment fundamentals. Working Paper, NBER, 2010), Todorov (Rev Financ Stud, 23:345–383, 2010), and Gabaix (Q J Econ, 127:645–700, 2012).

PurposeThe purpose of this paper is to study the variance risk premium in corn and soybean markets, where the variance risk premium is defined as the difference between the historical realized variance and the corresponding risk-neutral expected variance.Design/methodology/approachThe authors compute variance risk premiums using historical derivatives data. The authors use regression analysis and time series econometrics methods, including EGARCH and the Kalman filter, to analyze variance risk premiums.FindingsThere are moderate commonalities in variance within the agricultural sector, but fairly weak commonalities between the agricultural and the equity sectors. Corn and soybean variance risk premia in dollar terms are time-varying and correlated with the risk-neutral expected variance. In contrast, agricultural commodity variance risk premia in log return terms are more likely to be constant and less correlated with the log risk-neutral expected variance. Variance and price (return) risk premia in agricultural markets are weakly correlated, and the correlation depends on the sign of the returns in the underlying commodity.Practical implicationsCommodity variance (i.e. volatility) risk cannot be hedged using futures markets. The results have practical implications for US crop insurance programs because the implied volatilities from the relevant options markets are used to estimate the price volatility factors used to generate premia for revenue insurance products such as “Revenue Protection” and “Revenue Protection with Harvest Price Exclusion.” The variance risk premia found implies that revenue insurance premia are overpriced.Originality/valueThe empirical results suggest that the implied volatilities in corn and soybean futures market overestimate true expected volatility by approximately 15 percent. This has implications for derivative products, such as revenue insurance, that use these implied volatilities to calculate fair premia.

Nous decomposons la prime de risque de la variance en primes de risque a la hausse et a la baisse. Ces composantes refletent la remuneration, par le marche, des risques lies aux variations de la « bonne » et de la « mauvaise » incertitude. La difference entre les deux represente une mesure de la prime de risque d’asymetrie, laquelle rend compte de l’asymetrie des opinions au sujet des risques favorables ou defavorables.

This study aims to examine the return predictability of variance risk premium, which is defined as the difference between risk-neutral variance and expected realized variance, on KOSPI 200 index returns. Although extant literature shows that variance risk premium estimated from U.S. index options has a predictive power on underlying returns, little study has been conducted in KOSPI 200 index returns. In addition, there is no conclusion for the predictive power of variance risk premium in other financial markets. In this paper, we can find the predictive power of S&P500 variance risk premium on KOSPI200 index returns as well as on S&P500 index returns, but cannot find the predictive power of KOSPI200 variance risk premium on both indices. These results are consistent to Londono (2012) and Bollerslev et al. (2013). The poor performance of KOSPI200 variance risk premium is explained by the assumption that U.S. economy is a leader economy, while Korea economy is a follower economy. To support this conclusion, we conduct Vector Auto-Regression (VAR) using two variance risk premiums. Two premiums have bi-directional lead-lag relationship but S&P500 variance risk premium is informationally superior to KOSPI200 variance risk premium regarding return predictions.

We propose a new decomposition of the variance risk premium in terms of upside and downside variance risk premia. The difference between upside and downside variance risk premia is a measure of skewness risk premium. We establish that the downside variance risk premium is the main component of the variance risk premium, and that the skewness risk premium is a priced factor with significant prediction power for aggregate excess returns. Our empirical investigation highlights the positive and significant link between the downside variance risk premium and the equity premium, as well as a positive and significant relation between the skewness risk premium and the equity premium. Finally, we document the fact that the skewness risk premium fills the time gap between one quarter ahead predictability, delivered by the variance risk premium as a short term predictor of excess returns and traditional long term predictors such as price-dividend or price-earning ratios. Our results are supported by a simple equilibrium consumption-based asset pricing model.

Variance risk premiums in foreign exchange markets

Variance Risk Premium and Return Predictability: Evidence from the Chinese SSE 50 ETF Options

To expand and to abandon: Real options under asset variance risk premium

Same firm, two volatilities: How variance risk is priced in credit and equity markets

Firm Characteristics and Common Factors in the Variance Risk Premia

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.

Term Structure of Variance Risk Premium in Multi-Component GARCH Models