## Thursday, August 18, 2016

### Systematic Trading: Getting Technical with Technical Indicators

There are few investors and traders who have never used a technical indicator. Some use them as part of their core trading strategies, others as confirmation or as a timing tool. I am reasonably certain even the most ardent value investors perhaps look at them in time of trials and tribulations. The set of these indicators are large (and ever increasing) as different ones developed over course of time, often from different markets and asset classes1. This is usually not a problem, as most practioner will settle down with one or two favorites.

However, most indicators have a lot in common among them. They are usually a function of past and present market data. They can be usually expressed as a function of returns of the underlying, and they tend to move in a range (though not always statistically stationary2).

Taking the example of a simple one - the moving average cross-over indicator. This is expressed as a difference of two moving averages (a short and a long ones). Mathematically, this can be represented as $mom=\sum_{i=0}^{n_1} a_i.P_i - \sum_{i=0}^{n_2} b_i.P_i$, where $n_1$ and $n_2$ are the short and long moving average periods, $a_i$s and $b_i$s are the weights (for simple moving average $a_i=1/n_1$ etc.) and $P_i$s are the prices. It can be shown that this can be converted from this price space to returns space, as $mom=\sum_{i=0}^{n} w_i.r_i$. Here $r_i=P_i - P_{i-1}$ (returns assuming log prices) and $n=n_2$ from above.

Similar treatment can be applied to other common indicators to convert them as a function of returns $r_i$s. A few example 3 below:
• Momentum cross-over = $\sum_{i=0}^{n} w_i.r_i$
• MACD Histogram = MACD line - signal line = $\sum_{i=0}^{n1} w_i^1.r_i$ - $\sum_{i=0}^{n2} w_i^2.r_i$ $\Rightarrow$ $\sum_{i=0}^{n} w_i.\Delta{r_i}$, Here $\Delta{r_i}=r_i - r_{i-1}$. This follows from logic similar to the momentum crossover above, and noting the difference of sum is in returns terms instead of prices.
• CCI = (Price - Average Price)/(0.15 x Mean Deviation) = $\frac{1}{\sigma}\sum (P_i - \bar P)$ $\Rightarrow$ $\frac{1}{n.\sigma}\sum (r^{n}+r^{n-1}+..+r)$ $\Rightarrow$ $\sum w_i.r_i$, where $r^k = r_i - r_{i-k}$
• Know Sure Thing = (RCMA1 x 0.1) + (RCMA2 x 0.2) + (RCMA3 x 0.3) + (RCMA4 x 0.4) = $a1.\sum w_1.r^{n_1} + a2.\sum w_2.r^{n_2} + a3.\sum w_3.r^{n_3} + a4.\sum w_3.r^{n_3}$ $\Rightarrow$ $\sum w_i.r_i$

Similarly most others can be expressed as a function of returns, although not all of them as linear (or even polynomial) as above. Broadly, we can divide all common technical indicators that can be expressed as function of returns in three different classes 4
• Indicators that are linear (or polynomial) combination of past returns in returns space ($f(r)$). Examples - the ones above. Under certain condition (stationarity) they can be modeled as Gaussian distribution
• Indicators that are functions of sign of the returns in signed returns space ($f(r^+, r^-)$). Examples - like RSI or Chande Momentum Oscillator. They can be analyzed using folded normal distribution
• Indicators that are function of returns in time space ($f(t(r))$). An examples is the Aroon indicator

One objective of analyzing commonality of technical indicators can be to choose the one that is best suited to a particular purpose (depending on the time series characteristics of the underlying and the trading strategy). Another, and perhaps more common, can be dimensionality reduction as part of inputs to advanced machine learning based trading systems.

Following figure shows the outcome of principal component analysis of different technical indicators run on different equity indices5 - showing the first two principal components. Interestingly, for most cases (both in real market data and simulations6) the first two components will explain close to 85% or more variance in the indicators. As we can see all indicators load similarly on the first component. This is the underlying momentum component. This component typically explain around 70% variance, and will probably be the choice of inputs in a support vector machine or neural network system incorporating technical indicators.

The second component is where the indicators differ a lot. This component captures the signature of the filtering carried out by the indicator. This signature has two parts, one is the intrinsic method of the filter computation. For example from the above formulate, we see MACD is a function of difference of returns and hence will tend to behave more like over-differenced series (assuming the returns are stationary). In contrast, KST will have a large component which is simply sum of returns, and hence will behave more like a non-stationary series in the limit. Indeed, for common parameters for these indicators (representing a look back of 20 days), the time series characteristics of these signals can be captured in the following (inverse) unit root circle plot (here roughly speaking, closer the plotted points, i.e. roots, towards the center of the circle, more mean-reverting is the series)

We can see from the PCA plot there are four major groups of indicators based on their time series characteristics - MACD, which is very much mean-reverting (i.e. suitable for short term trends), KST (which is quite the opposite) and then we have two groups - one consisting the first type of indicators noted above (function of returns) and the other group consists of the second and third types (function of signed returns and returns in time space). This is validated in the unit root plot as well, we see MACD has roots much closer to the center, KST almost on the circle perimeter, RSI quite close to it, and Bollinger bands closer to the center relatively.

Another way to appreciate how different indicators impact the momentum signal differently, is to look at how they filter the components of the underlying (returns in this case) at different frequencies - as seen in the AR spectral analysis chart below. Click on the indicators on the right hand side legend to turn them off or on.

A spectrum that has higher values towards zero frequency (like KST) means they will tend to filter out higher frequency in the data,whereas the ones that has a peak away from zero, or drop off slowly from peak at zero will tend to pick up faster components (in the extreme resembling high negative correlation of a over-differenced signal). Of course as we increase look back period, an indicator will tend to move away from the second kind and towards the first kind.

Using this insight, one can design an appropriate set of indicators to extract an "average" momentum signal, to be used in other strategy or as inputs to a neural networks or similar system.

For this purpose, the first PCA component is the one we seek to use as input as momentum signal, straight and simple. The usefulness of the second component is that it allows us to fine-tune the momentum signal for our purpose. A momentum signal depends on our time frame - a short period momentum can look like mean-reversion in longer time frame. To extract a consistent signal we need to tune the choice of the indicators and parameters. If we are looking to extract momentum signals averaged over different filtering methods, but not over time, we need to ensure all factor loadings on the second component are within acceptable limits. Whereas if we want to span as much frequency spectrum as possible we want the loadings to span much larger space. Depending on out choice we extract the kind of signal we want from the first component7.

Note, while I mention the first component as momentum signal, it is NOT same as what is known as the time series momentum factor. However, it can easily computed by back-testing trading PnL based on this momentum signal. As we have seen in general these signals can be expressed as $\sum w.r$, the PnL will be (using a linear sizing function) $\sum (w_i.r_i).r_j$, or (using a sign function) $sign(\sum (w_i.r_i)).r_j$. Of course we can approximate the signum function, and then in general, the PnL becomes a polynomial of auto-covariances of the underlying returns.

1. This is a useful place with good introductory materials on different indicators
2. In general an indicators will tend to become non-stationary at a given periodic frequency (e.g. daily) as we increase the look-back parameter
3. There is no guarantee the sum of weights adds up to one. Please feel free to notify me in comments if you spot any error.
4. Here we ignore the indicators that take volume as an input as well
5. All data from Yahoo Finance
6. Based on simulations assuming expected market behaviours, i.e. AR or ARMA type return characteristics.
7. One can design an algorithm for this purpose, that will maximize the explained variance by the first component of the PCA, by optimizing over the parameter space of the indicators within a pre-defined set.

## Tuesday, August 9, 2016

### Off Topic: Olympic Gymnastics Medal Table Dynamics

Being the month of summer Olympics, here are some stats from past games while we wait for the tally from Rio (since Barcelona 92). The major highlights are
• The spectacular rise of China, especially after Athens 2004
• The emphatic decline of Eastern European countries in medal tally, especially after 2004
• The great decline of Russia (includes Ukraine tally, for ease of historical data handling only) and what appears to be a recent comeback
Click the play button in below chart to see how the dynamics evolved. Select the little boxes on the right to track a particular bubble.

The change that happened was a complete revision of the point system following a judging controversy in Athens summer Olympics in 2004. This includes abolishing the "perfect 10" and introduction of "difficulty level" in scoring.

This offers a positive skew to the participants. Choosing a high difficulty level enables one to achieve a much better chance to win a medal (and probably on the higher side - i.e. gold or silver). Although that means the execution will be difficult, and on an average they should balance out each other. However, if you aim for high difficulty levels and in rare cases manage to hit the execution, you will be sure to win a medal. This positive skew should theoretically motivate gymnasts to choose higher difficulty levels. This also means a higher variance in performance outcome.

This also should mean a higher rate of injuries for gymnasts. Unfortunately, data that I could get on this are too little to say anything statistically.

## Wednesday, August 3, 2016

### Macro: The End of QE-topia

Negative rate is much more than what it says on the label. One of the cornerstones of modern finance is what is called present value (PV). PV is used to evaluate real projects, value financial investments or price derivatives, you name it. Surprisingly, based on my personal experience, it appears many practitioners and investors are unaware of the fundamental assumption on which this all encompassing concept of PV is delicately balanced - an assumption of a properly functional lending and borrowing market. Without that, there is no mean to transfer values across time back and forth, and PV loses its real meaning. Negative rates makes one question the validity of this assumption.

Central banks, it appears, are having a hard time. Last week's BoJ's underwhelming policy outcome was scorned off by the markets with an emphatic rally in Yen and sell-off in JGBs. This week BoE is widely expected to kick-in with some Brexit easing, and the markets so far has greeted the possibility with a renewed sell-off in FTSE 100. ECB is also expected to up the ante with another QE extension sometime later this year, and the European equities do not seem overjoyed about it. To contrast, S&P 500 seems pretty much nonchalant about a plausible Fed hike. The usual QE-led risk rally, it appears, are drawing to an end. In fact a few are already calling out for a regime change - from QE to deflation dominance (or lack of demand).

In the wake of the Great Financial Crisis, most central bank carried out a massive amount of monetary stimulus. One way to track the global monetary stimulus beyond policy rates is to track the combined balance sheet of major central banks1, as we see below.

Few would argue against the unprecedented monetary stimulus led mostly by the Fed which served a crucial purpose during and after the crisis to restore confidence, liquidity and growth conditions. However, the effectiveness of QEs from other central banks have arguably been much weaker. ECB QE is so far hardly "successful".

Also, over time, the impact to real economy has grown visibly less dramatic. Below chart (left one) shows the growth in global major central bank balance sheet  vis-à-vis growth in M2 money supply as well as bank lending across major economies2. Since the abatement of the European Sovereign Crisis in Q3 2012, all the measures have started moving in lock-step. What is more, the magnitude of global M2 growth has been lower than central bank balance sheet growth, meaning less bang for the QE bucks. The bank lending growth has been even lower than that. It is hardly a surprise we started to have quite a bit of noise around the effectiveness of QE and monetary stimulus around that time and since.

It is not hard to see why. As the right hand chart3 shows, irrespective of what the central banks have been doing, the global private sector still continues with deleveraging (with some exception, like US corporates). The excess savings - especially for Euro area (and a large contraction in dis-savings in the US as well) clearly underscores the problem. This arguably is an expected outcome of a balance sheet recession - wherein the private sector, afflicted with too much debt and in a process to repair their balance sheet, will try to increase savings and desist from borrowing no matter how low the lending rates are pushed down by QE. This is less a question about pricing and more about the capacity and willingness to borrow. On top, the increased regulatory burdens and negative interest rates certainly did not help the banking sector much to upsize their loan books. The combined effect - anemic global demand and as a result, stunted global investments (not helped by pre-crisis built-up over-capacity in certain sectors) - was given a new moniker, secular stagnation.

Economies can be stimulated using many forms and jargon. But in any case, to boost demand it must work to enable the demand side to afford it. And this increase demand must be paid for by either increased debt (i.e. borrowing) or equity (like increased transfer or wage). Monetary policy, in practice, mostly tend to fund this increased demand through debt in its standard transmission channel through banks. In a scenario where many are focused on reducing leverage, it is no surprise that this will have a less-than-expected impact. Monetary policy can enhanced equity based spending as well, like through wealth effect or inducing an increase in wage through increased inflation expectation. While this has worked in the US, for the rest of the world, especially in Euro Area and in Japan, this has hardly been the case. The dis-inflation remains very much alive.

There are some recent trends, however, that is slowly becoming a theme - and it involves the other side of the stimulus coin. 2015 has been the first year after the extra-ordinary time during the crisis, that major global economies have experienced a reversal of a combined fiscal tightening (see below4 on the left). We are past the fiascoes like sales tax hike in Japan and the excessive focus on balanced budget in Europe. And a few countries like Canada and Japan have already stated fiscal stimulus as their explicit policy tools. US may see similar moves after the election. Of course the downside of the government playing the role of "consumer of the last resort" is that this comes at a cost of debt concentration at government sector.

We are on a cusp right now. Global consumption, despite all the allegation, has shown considerable resilience (although much away from their pre-crisis period, see chart5 above on the right). What we want now, more than ever, is avoiding any policy mistake. Given the fragile nature and very low margin of error on the policy side, it will be hard to recover from one. We are past the days of equity rallies with every new round of monetary easing. Markets will focus more and more on the underlying growth. This growth will of course have some costs - the key policy issue will be how to allocate that in a balanced manner between the fiscal and monetary side of this. One-sided efforts from central banks - increasingly larger asset purchase from a rather finite pool in a world characterized by negative interest rates and safe asset shortage - is perhaps past its used-by date.

1. source: national central banks
2. source: national central banks, IMF, Bloomberg

3. source: national statistics offices, IMF
4. source: national statistics offices, national central banks

5. source: national statistics offices, Bloomberg

## Saturday, July 23, 2016

### Macro | The Aerodynamics of Helicopter Money

As a former rotor-craft specialist I do have some experience with helicopters and its dynamics. It is a machine not supposed to fly, but somehow it does. And for some missions it is immensely more useful than the traditional stuff - fixed wing aircraft.

The next best thing to QE is already in town. Ever since former Fed chairman Ben Bernanke had a discussion with Japanese leaders last week, this has captured the attention of mainstream media. Although the BoJ Gov. Kuroda has effectively ruled out "helicopter money" (HM) on Monday, nobody missed the phrase "at this stage" in his statement. With increasing market frustration with the now-standard QEs, HM appears a real possibility in future policy adventure should things get much worse.

As is famously known, the term was originally described by the famous monetarist economics Milton Friedman to describe a permanent money creation and direct distribution to general population by central bank. In recent context, the meaning has changed more to monetary financing of fiscal stimulus. Nonetheless, it is interesting to see how this policy compares to other central bank tools like policy rates or QE.

There are two ways to look at, one from the accounting perspective and the other from economic perspective. From accounting point of view, HM is markedly different than other tools like policy rates or QEs that goes through what is known as open market operation (OMO). A central bank balance sheet, very roughly, can be thought as below.

In traditional policy operation, the central bank announces a target rate and use standard OMO to adjust the level of treasury holding (asset side) to affect corresponding changes in commercial bank reserves (liability side). Tight monetary policy reduces the available reserves and hence put pressure on the fed fund rate (the rate at which commercial banks lend reserves to each other). QE in operation is similar to this, only the central bank buys a much larger quantity (and longer maturity) of treasuries (with a corresponding large increase in bank reserves). While the operations are similar, the channels through which they impact the economy are quite different. In case of regular OMO, the channel is mostly interest rate channel, where the long term interest rates are assumed to be affected by short term rates. In case of QE however, there are multiple channels, with the most important ones being inflation expectation, interest rate (portfolio re-balancing) and wealth effect. See here for a more detailed view.

HM is quite different than either of these. In the original scenario propose by Milton Friedman, the central bank simply prints money and distributes to the public. From accounting angle, this means an increase in currency in circulation (liability). It is clear the only change that can balance this is a corresponding decrease in capital of the central bank. Technically a central bank can run a negative capital indefinitely, as it can print money to fund it. However, in practice this may be limited due to legal rules (if any) and public and political perception among other things.

The current avatar of HM is different. The proposed method is government issuing perpetual zero coupon bond (appearing on the asset side of the central bank against a balancing liability entry for government account) and then using the proceeds to fund tax cuts or pay for infrastructure programs (ultimately money in government account from the last step disappearing in to accumulating commercial bank reserves). Prima facie the net effect has the appearance of a QE process as outlined above (treasury holding goes up, reserves goes up), But the dynamics is quite different. In QE, the money created will hit the commercial bank reserves directly. Now it is up to the lending intention of the commercial banks (and of course the ability and willingness of the general public to borrow) if this will just sit at the reserve or will actually enter the real economy. However, for HM, it is the other way around. The money created first goes to (via government) the general public and finds its way back to the banking system and reserves as the public either spend or save it. In this sense this monetary financing of fiscal expenditure is closer to the original HM concept in spirit.

The key difference is that QE or other OMOs are essentially asset swaps, swapping treasury for bank reserves - a swap between the two sides of the balance sheet. While HM is essentially swapping central bank capital for base money (currencies in circulation or bank reserves). In the above example, technically we recognized the zero coupon perpetual bonds issued by the government on the asset side at acquisition cost. But clearly such a bond has zero value, and a fair value treatment will create a hole in the capital, exactly like the original HM. The other key point to observe is that while QE is an increase of monetary base, its permanence is a function of central bank's credibility. Some may legitimately believe the central bank will withdraw this (sell QE assets) once the situation normalizes and hence factor that in into today's decision. However, HM is fundamentally an irrevocable permanent increase in base money. There is no way to reverse it unless central bank destroys currencies in circulation (reverse HM?) or forces the government to redeem those zero coupon perpetual bonds. Both seems highly unlikely under most scenarios conceivable.

Now on the impact of this policy on the broader economy - well since economics is not an exact science (and many assumptions are not even falsifiable), you can pretty much successfully argue for whatever you believe in. An HM operation can cause the interest rates to go down, as this means a large money supply in the economy. It can make things even worse if more people choose to save the money they get than to spend it, fearing an even lower interest rate and trying to keep interest income constant (think of retirees). You can argue for an increase in interest rates as well, as an injection of money in such a manner may increase inflation expectation. You can postulate that HM will cause GDP to increase - as a result of the direct fiscal expenditure and also through the fiscal multiplier. Or you can invoke the crowding out (and with some labor even the Ricardian equivalence) to assume no change at all.You can follow the thread of a heated argument here. However to give some method to the madness, we can arrange our thoughts in the IS-MP framework.

HM can be explained in this framework (see the figure below). The story is, in the beginning the aggregate demand is such that the output (GDP) is at y, below natural rate (y*). This causes inflation to fall. The central bank responds with a rate cut, to reduce the real rate, and pushes MP to right (expansionary policy), but hit the nominal zero lower bound. Then HM comes along and jacks up the inflation expectation (assuming that is the dominant dynamics, see above). This pushes the MP curve further to the right to MP1, beyond the possibility of zero lower bound. Then the fiscal stimulus component kicks in and moves the IS to the right at IS1 as well, bringing the output back to potential level of y*. Note the model suggests a final (real) interest rate levels higher than a pure play monetary policy response (only MP shifting to the right).

Theories apart, from market perspective a few things are more certain than others. Firstly, unless there is a crisis of confidence (or potential), fiscal stimulus is usually good for an economy, especially so at a zero rates environment when traditional monetary policy faces serious constraints, and at a time when economy can do with a booster dose or two. The fiscal stimulus component of HM therefore should be positive for markets and economy. One can argue why monetary financing is necessary when the government can borrow at such low rates. This is an excellent argument which the BoJ governor seems to like, at least for the time being. Nonetheless this part is positive for equities and risk assets. For FX markets, note the possibility of both the rates going down and up as noted earlier. Interestingly, this affects different parts of the curve differently. The part that will tend to go down will be short dated rates and long end will tend to push up. As a result FX (which is mostly influenced by the shorter end of the curve) will go down. And as for rates, assuming the market perception of HM is positive, this will mean 1) a re-pricing of the terminal rate upward as well as 2) increase in inflation expectation pricing. This will mean a bear steepening of the curve (increase in rates led by the long end on the balance).

The other aspect is of course the political risks of monetary finance. Some central banks absolutely abhor monetary financing (Bundesbank!), and many are potentially legally unable to do so. But leaving aside the muddled politics and economics, the key takeaway here is that in case of the next Lehman Brother scenario or a China bust, this talk about HM should assuage investors' collective concern that central banks are running out of options.

## Wednesday, July 20, 2016

### Off Topic | If you Read Only One Book From Every Country

This is a mighty interesting list. Appears here more as a bookmark for myself and a target before setting out on the final journey to the monosyllabic perdition.

## Saturday, July 2, 2016

### 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.

all data from CFTC reports and Bloomberg

## Tuesday, June 21, 2016

### 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.