Markets: The Rise of The Vol Tourists

Since the Great Financial Crisis, the volatility market has undergone some significant changes. One major driver was an increased awareness about tail risk hedging. This was further aided by increasing acceptance of volatility as an asset class. Following the correlation one period during the crisis, the trend among asset managers has been risk factors based investment, moving away from traditional asset class diversification. This, along with the rising popularity of exchange traded funds and exchange traded notes, has given rise to a whole new set of demands for volatility products as an asset class.

Another impact came via the central bank reaction function route. The profound changes and the new normal condition following the crisis brought in a new set of players ready to supply (short) volatility - including those so called "vol tourists". But the appeal of systematic short volatility strategy has been strong following the crisis. As the unprecedented monetary stimulus created a huge yield chasing pressure, shorting volatility has become an important source. I have written about this quite a while back from rates perspective, but this is generally applicable to any asset class.

The left hand side chart below shows why shorting volatility systematically has been so popular. This tracks performance of a strategy that shorts the nearest IMM VIX futures and rolls just before expiry. The size is determined to match a margin of 10% of the invested capital (the approximate worst case loss). After the crisis, apart from a few hiccups (notably during the 2011 US debt ceiling crisis), the performance has been quite impressive. 

The result has been a discernible dynamics in the VIX futures market. The right hand side chart above shows the typical nature of VIX positioning that we have seen in recent time.

On one hand we have the asset managers managing the various ETNs linked to VIX. The left hand chart below shows the flows in to such ETNs (the short VIX ones are added with sign, reflecting net flow in to equivalent long VIX funds). These flows have typically been negatively correlated with VIX level itself. And the positions of these asset managers in the futures market have pretty much followed these flows - as shown in the right hand chart.

This has led to a situation where dominant players are the swap dealers (large banks) and leveraged money managers - the hedge funds - either discretionary or systematic short vol players. In fact, given the fact that after the introduction of tighter regulations since the crisis, most of the swap dealers positioning will be driven by hedges. So this leaves the leveraged managers as the only discretionary players in the VIX markets. 

This particular development in volatility markets - fundamentally driven by ZIRP policy of central banks, new regulations and the paradigm of risk factor investing - has resulted in an overall low volatility and high contago environment, even over and above what one can expect with a central bank puts. Apart from the China fear back in Aug 2015, the VIX level has remained remarkably tamed - below 25 almost always. Also the spread between front month VIX futures and the VIX levels itself has widened significantly since the crisis, as the most discretionary players have been systematically short in futures. The futures curve has been so steep that it is now very costly for long players to systematically roll macro hedges in VIX futures. In a normal market in a mean-reverting asset class like volatility, you would expect just the reverse.

The second impact, arguably, has been the feedback loop to S&P itself. As we have seen above, the VIX funds are flow driven. This means the leveraged managers are short against the large banks. The fact that most banks will have a hedged position, especially after the new regulations, make this positioning quite asymmetric. For the short VIX players, it is a linear position in volatility. However for the swap dealers - the opposite long VIX position will also mean a short option position as hedge. It is not important whether the short option position is the trade and long VIX is the hedge or vice versa. What is important that, a long VIX positioning will also mean a short gamma position. And the act of delta hedging will feed this into the underlying, i.e. S&P. If most hedgers are short gamma, as the underlying moves and the hedgers buy or sell to re-balance delta, they will tend to amplify the move. On the other hand, if most of the hedgers are long gamma, their delta hedging will introduce a stabilizing effect on the underlying. And this is captured in the following chart.

The chart shows the 20 day correlation (kernel-smoothed to capture the trend) of S&P 500 opening moves vs trading hours moves. This can be treated as a measure of the gamma effect above. We can treat the opening move as an impulse from overnight news. If the day move tends to counter that systematically, it is highly probable that the long gamma dealers are introducing a stabilizing effect. This means you would expect to show this up as an accompanying short VIX position for the swap dealers under such condition. Whereas if the day move amplify the open, this points to a short gamma position of the street (long VIX). So this correlation measure should move in steps with swap dealers positioning if we are right. And as we can see this is indeed the case, especially since 2014.

For a few days prior-to UK referendum, you must have noticed this phenomenon in practice. Taking a cue from the European markets, the S&P would open down more often than not, only to recover and more almost with statistical consistency during the trading hours. 

The rise of the vol tourists (and the short vol players in general) means watching VIX positioning and tallying it with the underlying moves has now become an important input for investors, even if you have nothing to do with VIX itself.

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all data from CFTC reports and Bloomberg

Markets : Brexit - Positioning Under Uncertainities

There are plenty of research notes and opinions around the possible outcome of and how best to position for Britain's upcoming EU referendum on Thursday. They vary from quite pessimistic to quite bullish on Sterling Pound and other risks assets. This piece does not intend to add to that crowd. I do not posses any special knowledge or skills to prognosticate a voting outcome. However, with that in mind, here are few points to note.

Firstly, positioning for the referendum is much less of an issue if it is for hedging. You really do not need to worry about picking a direction. It is about taking the position that reduces risk exposure of existing portfolio. The decision is then to design hedges that are cheap. I have written about some options a while back.

However, for a speculator, positioning for the referendum necessarily means picking a direction and hence having an opinion on the outcome of the vote - which is inherently uncertain. (This is also applicable for volatility trading, or anything else - here the direction is on the second order than underlying for vol trading). But even if you do not have a strong opinion on the possible result on Friday, a few consideration can help to form ideas about potentially profitable positioning.

And that mean picking trades based on 1) subjective probability (or expectation) 2) market prices (implied or average market expectation) and 3) opportunity costs. 

The first two are pretty intuitive and commonly practiced - basically compares what an investor expects the price distribution to be based on different outcomes, vs. the actual priced-in distribution. This is essentially a relative value analysis in a broad sense (which usually means a pair strategy in the narrow sense).

The third one, i.e. opportunity costs is arguably the most important consideration for decision under uncertainties. In the context of the referendum, let us assume that we have happened to choose to position of short risks. If the outcome is Brexit, our position will be profitable. But if it is not, we will lose on our short positioning. Worse still, if you assume that given the recent rally in risk assets, the upside is limited, then before we square off and initiate a long position, it is already too late. The upside from Bremain is a relief rally for status quo. The market will adjust upwards quickly and find a stable level. 

Now consider the reverse. If you are long and it is a Bremain outcome, again we are in luck. However, the opposite outcome is not same as before. A Brexit outcome will cost us initially. However, a Brexit outcome is far more uncertain than a Bremain outcome, and it is very difficult for risk markets to quickly price in all the consequences and find a proper and stable equilibrium very soon. We will have initial drag from our long position, but plenty of time to reverse that and catch the down-drift. 

The explicit assumption here is that from current levels, upside in risks assets are not great and market is more likely to find a stable levels on the upside than on the downside relatively quickly. If this assumption is correct, an analysis of opportunity cost tells us we should have a bias for long positioning.

In addition, the outcome of Thursday's vote will surely have a binary impact. I have written previously about how one should think about distribution when facing a binary outcome. If we believe in the assumption on the market dynamics above, along with the assumption of a binary outcome, we should base our estimates of the first point, i.e. subjective probability, on these assumptions to be consistent. These two assumptions gives rise to an asymmetric bi-modal distribution. Such a distribution will imply a thinner tail for upside outcome along with a heavy-tailed downside. Statistically this means on the upside we will have single jump probability, but multiple jumps allowed on the downside.

Practically this means we cannot use a single volatility model to price across the strikes on both sides of the at-the-money level. This also implies there is no realistic meaning of skew or vol-of-vol parameters as under these assumptions. The volatility dynamics are very different on the two sides and a single group of parameters valid across strikes on both sides does not make much sense. We essentially have to think about two sides as two parallel realities and combine them to arrive at a subjective price and then compare this to what the market is quoting.

Markets: Sucker Punch - Trading Events Based on Standard Vol Parameters

The high expectation before the Thursday ECB has made the smile in both rates and equities very acute (I have not checked the FX, but that should be no different). For example DAX and Euro Stoxx 50 is priced for a crash with skewed and convex smile favoring the puts. However, you still hear many market participants talking about how the vol of vol or skew is still cheaper - probably under the impression that these skews and vol of vol is still not enough to capture the fat tails that can result from such an event.

Which is a bit surprising, given the expected outcome. It is generally agreed that whatever ECB does, we will have a significant move in either side and then the level will settle down. If this is the case, what we are talking about is a classical case of bimodal outcome. And compared to that, the vol of vols and skews - i.e. in general the tails are quite over-priced. To see why, read on.

It is not very clear to everyone when someone talks about cheap vol of vol or skew (or whatever parameters), what exactly is being expressed by that view. Technically this should mean different things to different styles of trading. For a speculator (no delta hedging), this means the underlying distribution with the implied parameters is different than what she expects to realized. In particular, if one thinks vol of vol is cheap, the expected realized distribution has wider tails than the implied one. For a market maker (delta hedger), the relevant distribution is the PnL distribution after delta-hedge, which is quite different (and a bit more complex - a gamma weighted function of above) than the case of a speculator.

Nevertheless, let's examine the case of the speculator in a situation like Thursday - a bimodal outcome. One simple way to capture a bimodal distribution is what is known as skew bimodal normal (opens PDF, a bit technical). This distribution can be described as below

$$\Psi(x) = \Phi(x) - a(x)\phi(x)$$

Here $\Psi(x)$ is the cumulative distribution function (CDF) for the bimodal distribution, $\Phi(x)$ is the CDF of a normal distribution, and $\phi(x)$ is the PDF of the same. Here $a(x)$ is a linear function of x. Using a normal distribution with mean $\mu$ and variance $\sigma^2=1/\psi$, it is useful to express $a(x)$ as 

$$a(x)= \frac{(x+\mu-2\beta)}{1+2\psi [\delta+(\beta-\mu)^2]}$$

This allows us to parameterize the bimodal distribution in terms of $\beta$ and $\mu$ as the location parameters (mean), $\psi$ as the scale parameter (inverse of variance approximately) and $\delta$ as the bimodality parameter.

With this framework, we pick-up a 1 month option with ATM forward at 100 and ATM vol at 25% (annualized), and tweak the $\delta$ parameters to generate a range of bimodal distribution of the underlying (matching the forward and variance to above values, i.e. the first and second moments). Compare these with the normal distribution.

Next step is to use these distributions to price the entire smile for each case, inverting the price to get BS vol. We get the following results:
Yes! This is what a typical smile under bimodal distribution looks like. This is counter-intuitive. The fair tail vols are actually lower than ATM for a bimodal outcome - typical of what could happen in ECB (or in June during Brexit). This is of course extreme and idealized version. But the point is measuring the vol of vol (or skew) in the conventional ways through fitted parameters or through price of a fly is not a very useful way to trade options around such events. We are trying to fit a log-normal like distribution to a one that is completely different. It is not a case of wrong pricing parameters, it is wrong a bit more fundamentally! Bimodal has thinner tails.

We are better off to try to pick the strikes near ATM (or biased towards one of the peaks depending on your view - but before the intersections)  - this will be cheaper than what is priced in if this distribution is realized  And cheapen that with a spread by selling the tail strikes (which is costlier according to our assumptions, even go 2x if you want). That is the correct way to play an event with bimodal outcome.

Note, this is the fair smile only for speculators. For market makers, even for a clear bimodal outcome, the smile will never be like this - as she cannot control some one picking her off to some tail strikes and not trading the the entire smile.