Buyers can purchase volatility hedges on the inventory market utilizing variance swaps or VIX futures. One motivation for hedging volatility is its detrimental relationship with the inventory market. When volatility will increase, inventory returns have a tendency to say no contemporaneously, a end result often called the leverage effect. On this put up, we measure the price of volatility hedging by decomposing the costs of variance swaps and VIX futures into volatility forecasts and estimates of anticipated returns (“fairness volatility time period premia”) from January 1996 to June 2020.
VIX futures permit traders to hedge towards implied volatility shocks over completely different horizons. The payoff to a VIX futures contract is the distinction between the futures worth and the Chicago Board Choices Trade Volatility Index (VIX index) at maturity. From its definition, the VIX index upon which VIX futures are based mostly is the same as the sq. root of a one-month artificial variance swap price. The swap price is “artificial” as a result of it’s computed from a portfolio of S&P 500 index choices following the no-arbitrage formula for pricing variance swaps.
Variance swaps and VIX futures present perception into fairness market expectations for future dangers and returns. Traditionally, promoting volatility by receiving the fastened price in one-month variance swaps on the S&P 500 index has earned a large and important common return. As well as, the realized variance risk premium and associated measures just like the SVIX have been discovered to foretell inventory market returns. In distinction, the common returns from selling implied volatility haven’t been as important as these for promoting realized volatility, counter to the predictions from a few of the main consumption-based asset pricing fashions.
This put up contributes to our understanding of the risk-return tradeoff in monetary markets by offering time-varying estimates of realized variance and implied volatility time period premia (“fairness volatility time period premia”) from a brand new term-structure mannequin that’s developed in a current New York Fed Staff Report. The time period premia estimates signify the price of volatility insurance coverage or the anticipated return from receiving the fastened price in variance swaps and from promoting VIX futures of various maturities.
Realized Variance Time period Premia
Realized variance time period premia (RVTP) measure the anticipated return from receiving the fastened price in variance swaps. For instance, if the one-month variance swap price and realized variance forecast are 20 p.c and 15 p.c in volatility items, the one-month RVTP is .202 – .152 = .0175, or 1.75 p.c, in annualized variance items. This sizable risk premium is much like the historic common return from receiving the fastened price in one-month variance swaps. After all, as variance swap charges and volatility forecasts range over time, RVTP range as nicely.
The chart beneath plots estimates of RVTP for receiving the fastened price in one-month and six-month variance swaps from January 1996 to June 2020. Because the plot signifies, RVTP are constructive and countercyclical. In periods of monetary misery, such because the monetary disaster and COVID-19 pandemic, RVTP have a tendency to extend and may attain ranges as excessive as 5-15 p.c versus the unconditional common nearer to 2 p.c. As well as, the plot highlights that there’s a term-structure part to anticipated variance swap returns. After a detrimental shock, short-dated time period premia spike and revert to the imply extra shortly than long-dated time period premia that enhance and stay elevated. Lastly, the plot reveals that the time period construction of RVTP has modified for the reason that monetary disaster, with lengthy‑dated time period premia rising relative to short-dated time period premia, on common.
Implied Volatility Time period Premia
Implied volatility time period premia (IVTP) measure the anticipated return from promoting VIX futures. The chart beneath studies IVTP estimates for one‑month and six-month horizons. The IVTP estimates are giant in magnitude and swap between being constructive and detrimental. For instance, following the monetary disaster, IVTP attain ranges as excessive as 1-3 p.c per thirty days, however had been detrimental earlier than the monetary disaster and in recent times. The detrimental estimates of IVTP and downward spikes when systematic danger will increase are stunning. Equilibrium models predict that traders ought to earn a constructive danger premium for bearing publicity to realized and implied volatility shocks that’s rising, not lowering, in systematic danger.
Fairness Volatility Time period Premia and Danger
The charts beneath present additional evaluation on the connection between fairness volatility time period premia and systematic danger. The plots report impulse response capabilities (IRFs) for one‑month RVTP and IVTP in response to a one‑standard-deviation enhance within the VIX index from a bivariate vector autoregression (VAR). The rise within the VIX proxies for a shock to systematic danger. The IRFs point out how the time period premia estimates evolve within the VAR in response to a VIX shock over completely different horizons within the absence of different shocks. The purple line represents the common response, with the grey shaded area reflecting a 95 p.c confidence interval.
For RVTP, a rise in danger corresponds to a rise in anticipated returns that declines over time. This response is much like the qualitative response of risk premia to detrimental shocks in consumption-based asset pricing fashions. For IVTP, there’s a detrimental or insignificant response over quick horizons, which poses a puzzle. Over longer horizons, the IVTP response is constructive after which declines.
IVTP and the VIX Premium
Whereas stunning from an equilibrium perspective, the discovering that IVTP are lowering in danger over quick horizons is much like the habits of the VIX premium. The VIX premium is outlined because the VIX futures worth minus a statistical forecast of the VIX index at maturity scaled to a one‑month horizon. The chart beneath plots the one-month IVTP towards the VIX premium. Regardless of the completely different modeling approaches, the time sequence of the IVTP and VIX premium are considerably positively correlated for the reason that begin of VIX futures buying and selling on March 26, 2004. The IVTP estimates lengthen additional again in time as a result of they’re derived from artificial variance swap and realized variance information, not VIX futures information.
The numerous relationship between the IVTP and VIX premium is efficacious as a result of it questions the mechanism driving the implied volatility danger premium. One speculation for explaining the detrimental response to danger is that demand for volatility hedging falls when danger will increase. This rationalization is supported by the remark that vendor web positions (long-short) in VIX futures are inclined to fall when danger will increase as measured by the Commodity Futures Buying and selling Fee’s Commitments of Traders Report. Whereas demand stress could influence the VIX premium via VIX futures costs, the IVTP estimate is obtained with out utilizing VIX futures information. The constructive correlation thus suggests {that a} part of the implied volatility danger premium could also be pushed by the pricing of danger as captured by the term-structure mannequin.
Fairness Volatility Time period Premia throughout Maturities: Compensation for Danger or Darkish Matter?
Past the time-series dynamics, what position do fairness volatility time period premia play throughout maturities? The desk beneath studies a variance decomposition for the proportion contribution of time period premia and volatility forecasts in driving the variation in costs of variance swaps and VIX futures. For instance, at a one-month maturity, the RVTP accounts for round 40 p.c of the variation in variance swap charges whereas the realized variance forecast accounts for round 60 p.c of the variation in variance swap charges. Additional out on the curve, time period premia account for a bigger share of the variation in variance swap charges. The outcomes are qualitatively comparable and much more pronounced for VIX futures.
The discovering that time period premia play a dominant position on the lengthy finish of the time period construction has completely different interpretations. On the one hand, the Employees Report finds that RVTP forecast the returns from promoting variance swaps and index choices and that IVTP forecast the returns from promoting VIX futures. Time period premia may then be interpreted because the risk-based compensation for bearing publicity to volatility shocks over completely different horizons. Then again, current papers analyzing term-structure fashions in fixed income and across asset classes have discovered that lengthy‑maturity claims exhibit extra volatility relative to short-maturity claims. Understanding whether or not time period premia, the darkish matter of no‑arbitrage fashions, signify compensation for danger, market frictions, inefficiencies, or some mixture of explanations stays a fruitful space for analysis.
Conclusion
In abstract, this put up estimates the time period construction of volatility danger premia for the inventory market. Realized variance time period premia are rising in systematic danger and predict variance swap returns. Implied volatility time period premia are lowering in danger initially, however then enhance at a lag, predicting VIX futures returns. Time period premia account for a big fraction of the variation in long-maturity claims.
Peter Van Tassel is an economist within the Federal Reserve Financial institution of New York’s Analysis and Statistics Group.
Charles Smith is a senior analysis analyst within the Financial institution’s Analysis and Statistics Group.
cite this put up:
Peter Van Tassel and Charles Smith, “Fairness Volatility Time period Premia,” Federal Reserve Financial institution of New York Liberty Avenue Economics, February 3, 2021, https://libertystreeteconomics.newyorkfed.org/2021/02/equity-volatility-term-premia.html.
Disclaimer
The views expressed on this put up are these of the authors and don’t essentially replicate the place of the Federal Reserve Financial institution of New York or the Federal Reserve System. Any errors or omissions are the duty of the authors.
