by Thomson Reuters.
This article was authored by: Paul Jackson, Joel Sebold and Jack Sarkissian.
Traditional measures of volatility do not address a key concern of traders and risk managers needing to make proactive decisions: what is market volatility now? Realized volatility is typically calculated as standard deviation of backward looking historical daily price moves over some past period such as three months. As such, this measure is not appropriate or reactive enough to use for intraday volatility which can fluctuate widely. Realized volatility lags and is slow to adjust to dynamic changes in volatility on a time scale of minutes during which traders need to make decisions. On the other hand implied measures of volatility such as that used to calculate the CBOE Volatility Index (VIX), are derived from expectations of volatility in options market 30 days into the future. This measure suffers from lack of transparency and direct interpretability for current conditions. Neither answer the trader’s main concern adequately.
Ever since its introduction in 1986 VIX was a subject of debate. Originally designed to provide “effective tools for hedging against changes in volatility”1 it became a matter of speculation and betting. Involving complex mathematical analysis of option pricing mechanisms, the authors of VIX intended for it to reflect the level of volatility. Today, disregarding many of these complexities, traders, analysts and risk managers started referring to VIX as simply a predictor of future market volatility.
This approach received substantial criticism in recent years. The famous icon trader and scholar Nassim Taleb raises the subject in his paper “We Don’t Quite Know What We are Talking About When We Talk About Volatility”. Another legendary Wall-Street quant Emanuel Derman, author of “My Life as a Quant” warns in his twitter account: “VIX does not average implied vols from Black-Scholes. It averages market prices of options with diff strikes — that’s its charm”. Other authors argue that VIX just tracks the reverse S&P 500 movements and lost value of its own.
These authors and practitioners keep reminding investors that models are always based on numerous assumptions, and shouldn’t be used in a simplistic way to make critical decisions about investment management.
1 Brenner, Menachem, Fand Galai, Dan. “New Financial Instruments for Hedging Changes in Volatility,” Financial Analysts Journal, July/August 1989.
VIX cannot be traded itself since it is not a security. Instead, VIX futures and options are available for trading. These futures are then repackaged into ETNs that are more accessible to the public than plain futures. Issuers of these ETNs called their products all kinds of names that contained VIX, to which the public reacted again by simplifying, creating a confusing array of overlapping poorly defined products. There are known cases when seasoned traders and C-level executives bought the VXX (Barclays Bank Plc iPath S&P 500 VIX Short-Term Futures ETN) – the volatility of the VIX – thinking that they are buying the VIX itself and thus protecting their portfolios against volatility spikes.
The VXX (the volatility of the VIX) is Very Different Than the VIX
Source: Eikon from Refinitiv – Click to Request a Free Trial
This approach backfired when the investors realized that the performance of these VIX based ETNs was quite different from VIX plots. It took years to realize that instead of just reading security names on a trading screen, the investors should carefully read the official documentation called the prospectus or investment declaration.
With volatility levels decreasing after the huge spike in 2008 crisis, we saw the birth of a bunch of ETNs that tracked inverse volatility. These products were supposed to give investors ability to make money on volatility while it was decreasing. Some of them were designed to do it even faster – with x2 leverage! And again, the trading community’s simplistic approach led them to find out that when a direct ETN dropped 10%, their ETN “mysteriously” made only 2% return.
The VIX Surges and the XIV Collapses
Source: Eikon from Refinitiv – Click to Request a Free Trial
The last blow came after the flash crash of Feb 5, 2018 when the DJI lost and recovered more than 800 points in just 20 minutes shortly before the market close. After closing on Feb 5 at 99.0 the VelocityShares Daily Inverse VIX Short-Term ETN (ticker XIV) opened the next day at only 10.49. As a result, the ETN’s issuer, Credit Suisse, was forced to liquidate the entire ETN on the 15th – one of the largest by assets and trading volume at the time.
These developments confirm that the classics of volatility were right: “we don’t quite know what we are talking about when we talk about volatility”. As we are looking for answers to important questions sometimes we are ready to accept just about anything for an answer. In the meantime, having accurate and transparent measures of volatility is important for timely reaction to changing market conditions.
Refinitiv is actively engaged to bring to the market innovative tools addressing the trader’s need for accurate, fast measurements of current volatility and risk metrics without the burden of collecting a long history of data or projecting well into the unknown future. These new tools are completely transparent in terms of exactly known inputs and direct, straightforward interpretation. We are inspired by the work “Express Measurement of Market Volatility using Ergodic Concept” by Jack Sarkissian of Algostox Trading. In this work he provides the idea and develops it into computational-ready process.
According to Sarkissian, “As market practitioners, we are concerned with the immediate volatility, while the traditional measures provide us only with distant proxies of it. That is why we are developing these new indices. They let us take proactive rather than reactive approach to trading. Approaching the markets as physicists, we are able to extract objective information, not corrupted by opinions and guesses”.
This concept takes the ergodic principle seriously as a way to measure market volatility – namely that time averaging over long times can be replaced by ensemble averaging over short times. We refer to measures calculated this way as “e-measures” for ensemble or ergodic. It is based on very well established mathematical and physical premise.
In this picture, each stock is to be considered as representing one possible microstate of the entire system of stocks. The ergodic principle says that by considering an ensemble of stocks, we will reproduce the distribution of returns in a short time that we would observe on a single instance over a long time.
Ergodic measures of volatility are intended for fast intraday trading and risk assessments since prices at only two close time points across index constituents are utilized. The principle is illustrated in Figures 1(a) and 1(b) using 1-minute intervals. Each member’s capitalization contribution to the total index are the weights used to form the distribution by returns. At , all capitalization is centered on 0% return and at capitalization disperses to a distribution which – by ergodic hypothesis – represents what the entire market would reproduce if observed for a long time.
We define 2 e-measures of risk:
In other words, e-Vol measures dispersion of returns, e-VaR measures loss probability. Let’s look at the minute by minute time series of e-measures on a ‘normal’ day during low volatility period (July 18, 2017) and compare it to an unusual day (Feb 5, 2018) when a ‘Flash Crash’ occurred. The natural comparison for these is VIX and the S&P 500 and we include time series for them as well.
As usual, VIX is moving in an inverted way relative to S&P 500 level… except for a surge around minute 310. Careful examination of the index itself offers no obvious reason for such a surge. Ergodic measures do not display this feature. You can also observe the fast reaction of e-measures to volatility jumps in the returns of the S&P500 around minute 80 which rapidly decays.
Unlike VIX, our new metrics captures the very typical J-shaped profile of intraday volatility. Their more stochastic behavior than VIX is a natural consequence of being more reflective of the current condition of volatility rather than expectations over 30 days into the future.
In figure 2(b) a flash crash occurred for Feb 5, 2018. The S&P500 level starts dropping early in the day – VIX is rising as in a mirror image. e-Vol is consistently 6-8 bp reflecting relatively high market volatility in the hours leading up to the crash. The key feature occurs around minute 340 of trading. Both e-measures spike rapidly then enter in recovery period with elevated levels. Within a few minutes after the crash, as the index recovered, e-Vol reacts by decaying to about 12-13 bp which persisted out to end of day. VIX on the other hand shows little recovery reaction and remained highly elevated afterward.
How might a Trader interpret these new measures?
The plots are suggestive that a typical baseline of e-Vol during periods of low volatility would be 3 bp – this may be considered an acceptable level of risk by many traders. This tells them a security could move by 3 bp in 1 minute. For a $30 stock that is after all only 1 cent move. Higher levels of e-Vol fluctuations that persists in a range of 5-10 bp may be a warning sign. Similarly a 10 bp of 95% e-VaR tells trader that only 5% of total market capitalization can shift downward by more than 10 bp per minute.
As evident from the plots, these new indices capture very well the typical pattern of volatility during the day. It starts high and drops to usual intraday values, then increases again at market close.
Considering the extreme flash crash depicted in figure 2(b), both e-measures spike at the crash point, then quickly decay in the recovery period to levels somewhat higher than before crash. Within 10 minutes or so after the crash, e-Vol decayed substantially from 90 bp peak to about 12-13 bp which persisted out to end of day – this reflects the recovery phase. VIX on the other hand shows little recovery and remain highly elevated afterward. One might observe how VIX is overestimating volatility post the dramatic market drop.
There is an intense demand in both professional trading and risk management communities for fast, accurate measures of volatility to support more proactive intraday decision making. Traditional measures are either backward looking and lack sufficient time resolution (realized) or forward looking (implied) and do not tell us anything reliable about current volatility conditions. VIX has become a popularly used measure for volatility, but suffers from well known transparency issues, strange uninterpretable moves and speculative distortions.
Refinitiv is actively developing these new measures for risk (called e-measures) based on ergodic principle which allows us to quickly calculate market wide (or large portfolios) volatility (e-Vol) and value at risk (eVaR) in a completely transparent way using constituent price moves of the index across two close time points. These measures are fast reacting and reliably reproducing intraday dynamics of volatility in the S&P500 on a scale of minutes under both normal and extreme flash crash conditions. They are meaningful and easily interpretable for traders and risk managers.
We think these new measures will be a great addition to the volatility toolkit for traders and brokers to stay on their toes in competition for the best prices. Traders can use it to react quickly to changing volatility conditions. Liquidity providers and brokers would be interested to use it to manage risk or adjust execution of orders when volatility rises.
This article was authored by: Paul Jackson, Joel Sebold and Jack Sarkissian