Markets | VIX - Waiting For Godot

By now everyone and their cats are aware that volatility across markets and asset classes are low, been so for a long time, and shows no signs of reversal. VIX, the US market benchmark vol index is around it's historic lows. The MOVE Index - the bond markets benchmark from BofA/ML - is no better. CVIX - an FX benchmark from Deutsche - is doing a bit better but nothing assuring. People have punted, hoped and feared a come back of volatility, but so far we have not seen any sustained sign of it.

The reasons and the expectations from analysts come under mainly two flavours. The first narrative is that volatility is artificially suppressed by big league volatility sellers (speculators, but more importantly those ETFs folks and systematic risk factors people). The second narrative is market in general is going through a hopeful optimistic patch supported by central bank puts. Both groups believe volatility is going to explode sooner or later. According to the first narrative, a potential driver is a random shock, that will force re-balance in ETFs and risk factors strategies and will amplify the move. The second version is we are just a few bad economic prints or some geo-political mis-steps away from a runaway volatility.

While both of these narratives have some merits, none of them is either sufficient or complete. Or even useful for any practical purpose. There are different opinions, but I tend to side with the arguments from risk factors people (like AQR) that this line of arguments vastly over-estimates the impact of risk factors portfolios. And it is hardly fair to blame some folks for selling vols in a steep roll-down scenario as we have these days (we have written about it before). On top there is certainly some influence from street positioning. As we have written about before, for a long time now, the dominant positions of the big hedgers (read big banks and market making houses) in the markets have been long gamma, putting a stabilizing effect and pinning the vol down. The second "complacency" narrative appears less plausible, but of course cannot be ruled out.

But irrespective of which one (or may be even both) you believe in, none is useful to take a position in volatility. Essentially the argument is: volatility is trading in a distorted way and we need an external event to set it right. It is cheap since such an event will surely come some time in future. Unfortunately, by definition, we cannot predict much about the timing of an unexpected external event. And presumably you do not have the luxury of an infinite stop-loss on the bleeding you will have while you wait for that vol exploding event to materialize.

In fact the only predictable statement to make about the direction of volatility is: when the rates go up, VIX will follow. And here is why.

To start, note that although the VIX is near historical lows, it is not cheap. The realized has been lower. And the second fundamental thing to note that in the post-crisis world, the volatility has transcended its status as just a "fear gauge" and has become an asset class in its own right. And in this world of unconventional monetary policy and low rates, volatility has become intrinsically tied to the level of rates. The chart below captures this point.

We talked about this point way back in 2012 (from bonds markets point of view). When you treat volatility as an asset class (where selling volatility is a surrogate carry strategy) it becomes clear to see the connection. Consider an asset allocator who has an option to either sell volatility and collect the premiums, or buy some equivalently risky carry product, e.g. a high yield corporate bonds portfolio.

To make apple-to-apple comparison, we can think of a hypothetical "volatility bond". Given the existing spread of risky (BBB) bonds to treasury, we can deduce the probability of default of such an investment. From this, we can hypothesize a volatility bond, which consists of selling an out-of-the-money (OTM) call spread and put spread on S&P 500, each 100 point wide. The strike of the short options are such that the probability (implied from volatility) of them ending up in the money is equal to the probability of default of the high yield portfolio above (worth 100 in notional). In both cases the maximum we can lose is $100 (note in the case of short vol strategy, only one of the call or put spread can be in the money and exercised against us). So the yield from the high yield portfolio, and the premium collected (let's call that volatility yield) are comparable returns from portfolios with comparable risks. The chart above shows the yields from these two roughly equivalent portfolios. As we can see, in this rough approximation, the vol yield has in fact been higher than comparable BBB yield through out the post-crisis period, and moved in steps. The relative value before the crisis was unbalanced. It would have paid to buy OTM options spreads, funded by a high yield portfolio (anecdotally, there was an equivalent popular trade there during that time, but in the wrong market - the infamous Japanese widow maker). But at present the markets are pretty much in sync with each other and appear efficient. Far from the "distortion" argument in the narratives above.

The only way the vol can rationally go up from here is if the general risk portfolio yields also go up. That can happen in two ways. Either spread to risk-less rates (like treasury) increases (signifying a risk-off event like in the narratives above). Or through a secular rise in rates - which basically takes us back to Fed and inflation. As argued in the last post, pretty much everything we can expect now hangs on future inflation path.

The results are outcome of an approximate analysis. We obviously ignored some important issues (like skew and convexity of these deep OTM strikes) and made some shortcuts (a digital set-up is more appropriate than a options spreads as in here). We also missed a bit more fundamental point here, which is correlation. S&P 500 is a much broader index than the high yield universe, and the comparison above is more appropriate as the market-wide correlation goes up. As the correlation goes lower, we can afford to sale closer to the money options spread in S&P to retain the same riskiness in the portfolio, thus making the volatility yield even higher. And as we have it, the correlation (again see the last post) is down off late. But the main point remains unchanged - Vol is low but NOT cheap (although last few points in recent time in 2017 points to some relative cheapness).

Perhaps it is a good time to stop complaining about low VIX prints and watch those HY spreads and inflation development carefully instead.

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All data from CBOE website/ Yahoo Finance/ Bloomberg

Markets | The Most Peculiar Positioning Build Up Since US Election

Last week's S&P sell-off was apparently a big news. We had some serious analyses why it happened like here and of course the usual noise about end of Trump trade and reflation trade. Also the indomitable cottage industry of the permabears quickly felt a sense of vindication. However, the real surprise was why it took so long for S&P 500 to suffer a 1% down day. If we have only one 1% down day since October (roughly say 100 trading days), it is equivalent to an approx 7% annualized vol. VIX has been near record low, but at the 12-13 handle, looks quite rich given this 7% realized (or a bit over 8% if the standard deviation of daily returns is used to calculate the annualized vol). In fact the realized volatilities are very very timid and just barely off the historical lows.

In this light one the most interesting development that I suspect few has noticed is the curious build up of S&P option positioning. CFTC publishes the participant-wise positioning data at both futures and combined levels. The combined data is calculated by adding the futures equivalent option positioning (delta equivalent) to the futures data. So the difference between these two shows us the net option positions in delta equivalent terms. And as the chart below shows, it has never been more peculiar.

Among the major categories in CFTC reports, asset managers at present have a historically large short positions in options, against the dealers and the CTA/ leveraged  money managers. This is a remarkable build-up of positions since the US presidential election. It is interesting to note the usual trading incentives of these major players. The dealers are mostly market makers and their positions are in general reflective of other players' views. Leveraged/ CTA funds, to a large extent, are momentum driven. The asset managers on the other hands perhaps represent the most discretionary part, although most of them will be long-only players. In fact they as a group have built up a combined long position after the US election results - no surprise there. Along with this particularly interesting short build up in options space - quite unexpectedly.

The large short delta equivalent option positions from asset managers can be built in two ways. Buying puts - which is a common hedging strategy for the asset managers, or selling (covered) call - which is again a very standard income strategy. But their impact on the market dynamics are quite different. We do not have enough information above to see which one is more dominant. So to do that we look at what the behavior of S&P 500 price itself tells us.

From the chart above, we see the dealers positioning mirrors that of the asset managers. If the asset managers are mostly long puts, that will mean dealers are short puts and hence short gamma. On the other hands if the asset managers are net short delta equivalent in options through short calls, the dealers will be net long gamma (long calls). And since the dealers, as market makers, will tend to run a hedged book - this will lead to some expected gamma signature in the market dynamics. When the dealers are net long gamma, they will tend to sell in a rally and buy in a sell-off (sticky gamma). This will have a stabilizing effect on S&P. The reverse is true when they are net short gamma (slippery gamma), a move reinforcing itself away from stability. We compute an approximate measures of this relationship. First we see the how much the open to low move is reversed by low to close move for each day in a given time period (20 days) for S&P 500. Then we use least square regression to estimate a beta between these two moves. This beta signifies how likely in a given day, a down move will witness opposing flows to reverse it completely or partially. A high beta signifies a large pressure of opposing flow (beta = 1 means all downside move reversed by day end). The major drivers in this reversal will be the dealers long gamma hedging activities and potentially the buy-the-dip or momentum flows from other players (apart from other flows which we assume to have a zero net effect on the balance over a time periods). We call this beta (kernel-smoothed to capture the trend) downside gamma. The chart below shows this juxtaposed with the above positioning data, as well as S&P 500.

The interesting thing to note that during the last large short delta equivalent option positioning build up by asset managers (following Brexit), the downside gamma measure actually dipped, signifying a net short gamma for the dealers, and hence long put positioning from the asset managers. The current positioning, following the same logic, points to a large short call positioning from the asset managers. In fact there were some noises around this in February as well. As a result of this, the recent moves in S&P has been remarkably resilient. However as of last Tuesday's (21st March) data, it seems this long gamma positioning is coming off from the peak. Which has also coincided with a reduction in net short delta positioning of the asset managers in the option space. Theoretically, this means we can now expect a pick up in realized volatility in S&P. And it is time to shelve the buying-the-dip intraday strategy till the next opportunity comes.

Markets: Volatility Ahead

Finally we had a little bit of excitement back in the markets, and a vindication of sort for the numerous bears. Analysts from Citi confirm the macro drivers to blame. Indeed the cross market correlation has been on the rise. Below table shows the current cross market correlation¹. As it shows, rates and inflation still remain the major drivers, along with a very high level of correlation between commodities and currencies.

The chart below shows average correlation across asset classes. The recent spike is still far away from the levels around August 2015, but clearly captures the market sentiment.

And this sentiment is what is reflected in the latest AAII release last week. The market neutrals and bears remain significantly above the historical average as we have during most of this post-crisis bull runs. The change to highlight is an increase in bears at the expense of mostly the neutrals. 

For a contrarian, this would signal a limited scope of continued sell-off. However the other factor is positioning on the derivatives side. I have written about this before, but you must have already observed the change in the intraday price patterns in S&P. During much of last few months, it showed a strong mean-reverting characteristics (opening price shocks reversed during the day). For last few session starting from the 9th sell off, it seems the intraday trends are self sustaining now. That is confirmed on more quantitative measures as well. The chart ² below shows two approximate indications of short gamma positioning of the dealers. The idea behind this is in a market where the dealers (i.e. the hedgers, as opposed to players who hold options positions unhedged) are short gamma (net sellers of options), the natural hedging activity will create price pressure that will tend to amplify a price move (a up move in to a sustained rally and vice versa). On the other hand, when the dealers are net long, this will tend to stabilize price moves. Much of the stability in S&P intraday move for past few months can, at least partially, be attributed to net long position from the dealers, which appears changing now, as the short term intraday trends get stronger and sustain longer.

On the valuation side, however, S&P is still not screaming over-valued. Below chart shows world equity markets valuation vs trends (past 1-year returns) in two measures. The left one is the regular P/E measure, on which S&P is quite in the red zone, along with India and only second to Mexico. However, just going by historical P/E in a world of zero rates can be highly misleading. In terms relative valuation to bonds, S&P is quite in the middle.

If you followed the trades from my last post, it would have been a good couple of weeks capturing most of the major moves in the markets in the right direction. Looking ahead, if you are a bear, the investor sentiments and the valuation is not at a very helpful support to go big short at current levels. On the other hand the change in the gamma signature of the markets tells us unless something changed after Friday's expiry, we will continue to see decent swings and volatility will pick up. Although vols are not particularly cheap (relative to realized, yet), and I think given the reasons discussed before, it still makes more sense to buy options than to buy VIX here.

A traders' market after a long time. Brace for the upcoming Fed, but more for the BoJ. Going beyond equities, the major moves in rates (one of the major driers across asset classes now) has been set in motion by BoJ arguably. The recent bout of steepening in fixed income started with a bout of sell-off in JPY rates markets. This transmitted to rest of the world following ECB, with sharp steepening across EUR, USD, and GBP. The built up to the month end BoJ is almost palpable, and if not FOMC, at least this is almost certain to be an interesting event.

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1. This is based on smoothed data (Gaussian kernel smoothed with 5-day bandwidth) to capture medium-term correlation.

2. The left chart is based on identifying trends quantitatively using change point techniques. The idea is as trends become more sustaining the ratio of max to median trends will increase, as shown in the chart. The right hand chart shows absolute value of beta in a simple regression of intraday price to time, capturing the strength of the trend (if any) irrespective of its direction (rally or sell-off).
3. Data from Bloomberg and Google Finance

Trade Ideas: Macro Trades - The Fall-Winter Collection

The speech from Fed Chair in the Jackson hole was quite uneventful. The far more interesting was this one. It was a while back the ever useful Michael Pettis hinted at how rate cuts can be deflationary - exactly the opposite of mainstream central bank thought process. This represents another argument, and how crucial fiscal participation is in delivering monetary objectives.

Talking of central banks, this month is another one for central bank focus. Starting with ECB next week, followed by BoE around middle of the month, and ending with Fed and BoJ towards the end, the mood of the market is expected to swing based on these policy outcomes. The general expectation is a hawkish Fed while the rest continues the dovish stance. Here are the top 5 trade to consider for the moment.

#1: Pay USD 10y swap spread: USD swap spread was hammered just after the last FOMC hike in December, but now on a slow yet firm upward trend. Theoretically, swap spread should be determined by the expected futures spread on GC rate vs libors. While empirically this had little influence for US treasury swap spreads in the past, still this is an important metrics. And if you have not been gone for long for the summers, it is hard to miss the sharp widening of the spot spread of GC vs libor - mainly influenced by the sharp increase in libor rate. There is a good reason for this, as the market regulations kicking in forced quite a few prime money market funds from bank-issued commercial papers to US treasuries, pushing up the borrowing cost for the banks. It appears so far this yet has to be passed through the swap spread prices in any form or substance. On top, a pay position in swap spread (pay swap, receive treasury) has been highly directional with general rates levels historically. Given this correlation and the current levels (near the bottom of the trend channel), this represents an efficient position for any FOMC hawkishness, especially unexpected ones. This also benefits from a positive roll-down. In addition, this position is empirically should be somewhat long volatility - quite an asymmetric position at current levels.

#2: Pay GBP 10s30s steepener: Following Brexit, the long end sterling curve steepened sharply, followed by an equally sharp flattening after the early August BoE. This is presumably a reaction from the QE announcement, but it is not entirely intuitive. While we had similar sharp flattening move in Euro after ECB QE in early 2015, the large difference in size between this two perhaps points towards a bit over-reaction (ECB's initial €60b per month, later €80b, compared to BoE's £10b per month, i.e. £60b over 6 months). Not only in terms of absolute size, the ECB QE is also larger in comparison with the supply - for example at the ECB capital key, Germany amounts to approx €20b per month currently, compared to a gross supply of around €16b per month (as per Bundesbank projection figures for this years). For the UK, this compares to £10b per monthly to £11b of monthly supply (as per UK DMO projections). This does not correct for the German securities trading at an yield lower than ECB depo rate (and hence not eligible for QE), and also the fact that ECB QE will extend beyond the BoE one, hence the actual difference in supply pressure is much more acute. The second interesting point to note is the maturity distribution (see chart below). UK has a squeeze in the middle segment (belly, i.e. 7 year to 15 year remaining maturities) of the curve, whereas the squeeze for ECB is mostly in the long end, putting a relative rally pressure in the belly UK Gilts curve. Add to this the facts that the market price of expected inflation spread between UK and Euro area (breakeven inflation swap) has actually widened following Brexit. This is presumably influenced by the sharp decline in GBP vs USD, but this inflation premium somehow has to be priced in the nominal rates which in general should exert a steepening pressure. This combination makes a steepening position for GBP 10s30s attractive. One of the possible reason for such a sharp flattening can be the expressed intention of the BoE governor to steer clear of negative rates and that remains a risk (somewhat mitigated by a still 25bps to go). Other risk is a sudden strong recovery in UK economy, which will weaken the case for steepening.

#3:  Equity bearish protection: For all those bears out there, shorting the all time highs have been as appealing as it has been money loosing since June. The equity markets around the world has been quite oblivious to shocks. FTSE 100 had one of the best runs in Europe. European equities have been less spectacular, but nonetheless not in correction territory. Nikkei 225 handled strengthening yen better than expected. Even EM had a decent run. The key has been the amazing resilience of S&P 500 - and appears everything is now pending on a breakdown in the US equity market. As a result, S&P is now trading at tad lower from all time high, and tad higher than all time low realized volatility. On top, last print from CFTC traders positioning shows the highest ever short positioning in VIX. But there are potential issues on the horizon to be cautious, FOMC in September is the obvious one, South African political situation may be a trigger, or sometimes things just happen. Fortunately, we also have the S&P calendar vol spreads around the highs. This present a good cautious positioning of buying the near term puts vs long term (e.g. 3m/6m) - relatively less damning long gamma position. A large downside move in the US equity market will almost certainly have repercussion across the globe, and if triggered by FOMC, especially across the emerging markets.

#4: Pay Cross-currency basis widener in EUR: One for the long-ish term - this is a reversal of Euro savings glut trade. Since the start of the financial crisis, the cross currency basis widened as everyone panicked after dollar funding. Subsequently during the period of European sovereign crisis, this basis remained under stress, and only started normalizing after the whatever it takes promise from ECB's Draghi. However, after peaking at around mid 2014, this basis (not only in Euro, but across major currencies like GBP and JPY), started widening again. My theory is: this time it has less to do with financial market panic and shortage of dollar funding from the liability side, and more with the savings glut on the asset side. In such a scenario, asset managers willing to invest in higher yielding assets (like US treasuries or equities) will swap their euro funding with a euro vs dollar cross currency swap (effectively a dollar loan against euro) and paying dollar interest vs receiving euro interest. As more and more money chase this trade, there will be a receiving pressure on the euro leg, pushing the basis down. The fact that this is asset driven and not liability driven is corroborated by a flattish slope in the basis for different maturities. During the panic days, it was a strictly inverted slope (e.g. 1y tenor wider than 5y), which is now reversed or almost flat. Given this, any recovery in the euro area (and indeed globally) consumer and investment spending will set the direction in a reverse trend. Currently the levels are near short term support. Also given the slope as mentioned above, this benefits from a positive roll-down. This is a relatively low risk and low cost of carry trade for global economic recovery. The alternative is of course that long-dated forward trade in euro. But I like this one better at the moment: the long dated forward can remain stuck even after normalization (i.e. end of savings glut), but the basis will surely feel the pressure. Plus the once juicy carry in those long-dated forwards are mostly gone. Reportedly, there is currently a dollar funding shortage, on account of the money market regulation change mentioned above. But also reportedly a large part of the switch from CP to treasury is done.

#5: The ECB Trade: ECB is not BoJ and Euro area is not yet Japan. The question is if you see them converging or diverging. The chart below shows market reactions in rates and FX for recent major central bank decisions in Euro area and Japan. Note how in recent time, ECB meetings followed a rally in Euro and a flattening in the curve. Also note how the similar the reaction was in BoJ. And finally, how the last one from BoJ in July end, which underwhelmed the market, reversed the flattening trend, with less pronounced effect and in fact a net steepening. The story of QE is perhaps running out of steam.

I expect similar reaction for ECB even if they announce a QE extension beyond September 2017. The standard trade will be fading the move, which is as of today expected to be a steepener. However, a rally in Euro may be more difficult in the short term as the focus shifts immediately to Fed.

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All data from respective treasury offices, and Bloomberg.

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.

Trade Idea: Top Thematic Trades For June

Trade #1: Positioning for Fed: Pay 2s5s in swaps (pay 5y point).

Rationale: After the latest minutes release from FOMC last week, we have seen a huge positioning for a rate normalization (we discussed this before). But in some sense, normalization in dollar rates already started a while back. Although the policy rate is still stuck at very low level, the shadow rate (Wu Xia shadow rate), a representation of effective policy rate has tightened a lot since late 2014. Also in nominal space, although the rates levels are historically low, we have seen considerable normalization in slopes and curvature.

As the charts show (the left: range since 2000; right chart: range of average rates through different rates cycle - hike, cut and neutral, red triangles mark the current values; data from FRED and Bloomberg), in most measures of higher orders, the current yield curve is not far from normal. There is little scope for a further significant flattening of the curve to price in further rate hikes expectation. Add to this, there has been a large increase in short euro dollar positioning lately for FOMC. Given this, the best way forward is not to position for the next hike, but rather the ones that may follow. The next round of normalization (if at all) will be in rates levels and especially in long term equilibrium rates (terminal rate). The ideal way to position for this to take advantage of the historically tight 2s5s. The spread difference prices roughly only one rate hike between 2 year and 5 year. This levels are usually seen around recession time - or a scenario of "few and done" as some may argue. If you do not believe we have a recession around the corner, this is arguably mis-priced. On top this can benefit asymmetrically for a much more dovish Fed than expected, as the front end positioning unwinds.

Trade #2: ECB on Thursday : Long Euro vs GBP in FX

Rationale: The latest balance of payments data (released end of May for March 2016) from ECB points to continued net outflow from Euro area fixed income markets (chart below; data from ECB database). This flow is massive. The Euro area has seen a net outflow of almost €580B since 2015 in debt instruments. This is roughly at $40B per month, a pace higher than the FX reserve depletion of PBoC of China. This, from pure flow point of view, puts upward pressure on long end yields. However, the QE from ECB has been more than effective to counter that. But on one hand, as this exports the downward pressure on yields to international bond market (similar to Japan), it also makes the long end yields vulnerable to technical sell-off from time to time. However, with FOMC around the corner and the negatively carry, it may not be the perfect timing now to position for such a move.

On Thursday, ECB is little expected to surprise the market. Euro area inflation print continues to print in the negative territory. However, given the recent recovery in commodities, with all probabilities the ECB economic forecasts on Thursday will not paint a dire picture requiring immediate further policy measure. This should put technical pressure on Euro for a tactical leg upwards. This is best expressed against GBP whose recent strength and technicals make it poised for a corrective move. Alternative positioning is on the long end of the Euro rates as discussed above.

Trade #3: Brexit hedge: Buy EUR/USD calendar vol spread in straddle

Rationale: The basic idea for this hedge is to avoid directionality and buy gamma instead. Since the cross-asset vol spiked early this year, we have witnessed most vols across asset classes getting cheaper (the chart shows 3m rolling average of number of 2σ moves in each asset class for one-to-one comparison; data from Bloomberg). Also, rates and equities vols are much cheaper than FX and commodities in general. Still it makes sense to express this hedge in FX. The relative performance of FTSE (compared to DAX, Euro Stoxx or even S&P) has been quite impervious to Brexit hopes and fears, and there are few reasons to assume we will see an effective hedge in the equity space.

However, in FX space, there appears to be a mis-pricing: Given a Brexit outcome, it is hard to believe we see a large move in the cable, without any commensurate move in EUR/USD. And EUR/USD vol, especially the calendar spread at flat log-normal vol points, is a much cheaper option to position for a hedge.

Trade #4: Brexit upside: USD 5s10s steepener vs GBP 

Rationale: The spread between USD and GBP swap curve slopes, e.g. 5s10s, is at historical low. 5s10s in dollar rates flattened a lot since last year pricing in an expectation of rates normalization (as discussed above). But what is still quite a bit away from "normal" (apart from the rates levels of course) is the level of curve risk premia - for example the ACM term premium - at historical low. Yield curve slope (adjusted for the level of rates) captures a large component of this term premeia. And it appears even conditional on the much lower term premium, we have some parts of the yield curve relatively flatter, like 5s10s vs 10s30s in dollar rates.

On the sterling rates side, however, all these actions have been missing - partly because of softer economic data, and partly because of the risk of a Brexit. This has led to a historical level of the 5s10s spread in dollar vs sterling rates. The USD leg has little further room to flatten, while a remain outcome in Brexit may lead to some bear flattening of the sterling rates. This can further be supported by better than recent prints for UK economic data once the Brexit is over.

This is also an asymmetric positioning. Even if we have a Brexit outcome, there is a good chance of dollar spread sharply steepening in a risk-off mood, and sterling undergoes a panic bull flattening. The structure above will be benefit from that. 

The ideal structure is at least the GBP leg through swaptions, i.e. conditional bear flattener (sell the payer on 10s). Even though it is themed around Brexit, longer expiry is preferred. to take advantage of bull flattening in adverse outcome and better economic data in favorable outcome as discussed above.

Markets: The Yen and The Yang

A shaky market trying to forget the early Q1 blues just need another focus shift to scare itself in to another round of sell-offs. And the BoJ action today may as well be the catalyst.

BoJ has very few solid reasons not to act today: The inflation prints have been horrible, in the negative territories. Even the core inflation (ex fresh food, the measure BoJ prefers) registered negative. If I am not mistaken that will be lowest since BoJ expanded the QE in line with Abenomics in 2013. The market actions, either from the  breakeven inflation markets, or the recent rally in yen, does not support any case of enthusiasm there either. Negative rates so far is quite untested for jacking up inflation expectation. They have been successful for exchange rates policies in smaller European nations, but for Japan the market has given a clear thumbs down with yen rallying instead. And the Japanese banks have not been much amused with it either. That, and many other things (jump to first of Q&A), will possibly floor the use of negative rates in future.

There are three possible interpretation here. The first one is that BoJ gave it a pass to focus in June, by which time a Fed course of action will be clearer and probably priced in - this implies a question of time. Second, BoJ is really more optimistic than markets, which implies a question of further data. And lastly, BoJ is running out of options. This is the worst of course. In principle it is hard for a central bank to run out of options. But honestly, looking ahead for Japan, one can be hardly optimistic about the effectiveness of a monetary lever.

Whichever the case, if markets interprets things more in the line of the third, it is not going to be nice.

Off Topic: Changing Face of Global Terrorism

Terrorism is not a new thing for most of the existence of Human civilization. Wikipedia traces it back to 1st century AD. History is dotted with such atrocities, usually following a major epoch of change in the way of lives of a society(s). In modern times, the first organization to use modern terrorist techniques was arguably Irish Republican Brotherhood post WW-II. Since then we have an incessant series of them - with their eventual rise and fall.

But in recent time, the global terrorist activity has gone from a linear to exponential growth. And has some fundamental changes in characteristics. The chart shows the exponential growth of fatality attributed to terrorist attacks since 1970.

One of the most notable changes has been globalization of terrorism. Terror attacks evolved over time, moving from localized areas in South America and Asia during the cold war to engulf much of Eurasia and Africa now. This chart is in log scale.

The second characteristic of the change has been the changing ideology. We had an early peak of terrorist activities around the 70s dominated by localized communist movements. The first major peak came around the dismantling of the erstwhile USSR, driven by a much more wide spread, but still local, separatist movements. Since mid 2000s, and especially after the 2008 financial crisis, this has taken on a new never-before scale. This time dominated by a much more globalized Islamist version.

The third observation is the weapon used. While the separatist movements during the 90s was mostly focused on fire-arms as weapons of choice, the risk of Islamist violence has seen a specific shift towards use of explosives. Although very lately fire-arms have made a comeback and are used with almost equal deadliness.
Interestingly, in spite of this proliferation, it is not certain these terrorist attacks are in general getting more successful at scaling up in terms of individual impact. Below chart shows the fatality distribution in last decade (2004 to 2014) compared to the decade before (1994 to 2004). The extreme heavy tails are not that much different. What has accommodated this large increase in fatalities in the recent years, compared to past, is a higher number of relatively small intensity successful attacks.Note this distribution is plotted in log scale.

In fact, if we go back to the first chart and take a re-look, we see this is indeed the case, and the average fatality per attack is actually on a down trend (although there has been a relative reversal since 2012, around the Arab Spring).

Now this can be interpreted as more effective counter-terrorism measures to prevent large scale attacks, or a counter-counter-terrorism strategy to move away from large scale to low intensity multiple attacks.

Terrorism is sparked by ideologies, but as this video makes it amply clear, it is ultimately about the economics. The globalization in trade and finance has undoubtedly has helped the globalization of terrorism we see. In fact this globalization trend was first perhaps picked up by organized crime, even before terrorist organizations. This is why more than body search in Airports or x-ray scanner in departmental stores, a coordinated Anti-Money Laundering effort is perhaps the most effective weapon to fight this globalization of terrorism.

History shows most form of terrorism driven by ideologies comes to its eventual fall, either by acceptance or rejection by the main stream. I am hopeful this recent waves will not defy history. But the question is at what price. Financially, markets have not been very sensitive to individual incidents. However beyond that, terrorism has a huge cost on economics, by changing the behavior of the economic agents, and increasing the economic costs. And the human cost involved is incalculable.

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All data from National Consortium for the Study of Terrorism and Responses to Terrorism (START). (2015). Global Terrorism Database [Data file]. Retrieved from http://www.start.umd.edu/gtd. The data span till 2014, the next release for 2015 is expected in August this year. The charts are based on this data and own calculation. The ideologies map is not provided in GTD itself, but is carried out based on association of terrorist organization and stated ideologies/ objectives based on public information, mostly Wikipedia.

Macro: FOMC Dot Plots, The Secular Stagnation Illusion

One of the major surprises in the March FOMC meeting was the re-marking of the long term rates as expressed by the Fed dot plot.

While most speculators were cutting their short bets on the 10-year treasury (as per CFTC commitment of traders reports) and were actively going bullish on the long-end, the short end short positioning was mostly maintained. This was especially supported by the up-tick in the inflation data in core and headlines before the FOMC (as well as inflation now-casting from the Cleveland Fed).

There are conspiracy theories about the Fed's worry and motivation for a weaker dollars in response to the bold liquidity enhancement actions from other major central banks. However, if we really take a deeper look in to it, a different story emerges⁽¹⁾.

FOMC started publishing the dot plot in 2012, between the QE2 and the QE3 phase. Looking at the evolution of the dot plot implied fed fund term structure, there have been two major changes since. First one happened just before the start of the QE tapering. That was the beginning of a steady upward shift for the fed funds rate in the near horizon (~3 year), where they stabilized. The second set of changes came in later half of 2014, which resulted in another gradual move. This time it was a downward shift of the long term rate forecast. From the peak of 2014, the FOMC estimate of long term fed fund rate is down by 75 bps. (Note I have projected the long term rates from the dot plots to 5-year maturity bucket.) Some suggests the Fed is slowly embracing the secular stagnation theory.

There are certain amount of merit in that hypothesis. The current projection implies, assuming Fed's target inflation of 2 percent is realized, a long run real rate of 1.25 percent. And irrespective of your view on the r-g model, a lower r does signify a lower level of long run real GDP growth. For the balanced case of r=g, this implies a growth rate of 1.25 percent.

This seems pretty pessimistic from the recent trends in real GDP. Figure⁽²⁾ below shows the trend in real GDP (normalized at 100 at the beginning).  The post crisis slope (since 2013) is definitely flatter than early 2000, but not by a huge margin (except Euro area). Add expected inflation to this numbers to get the long run nominal rates. Depending upon your preferred choice (10-year and 5-year swap market breakevens at 1.8 and 1.6 percent respectively, 5y5y TIPS breakeven at 1.66), this seems to imply a long-run rate in the range of 4.1 to 4.3 percent. Almost a full percentage point above FOMC dot plot.
The market seems to be even more pessimistic. The chart⁽³⁾ shows the spread of 1 month USD Libor (implied from the euro-dollar futures and swap curves) vs the FOMC dot plot. The 2013 taper tantrum was the only time when the market got spooked with a rate hike and over-estimated the future path of rates. Since then, it has steadily become more and more pessimistic to the FOMC prediction. The largest disagreement is in 3 years and beyond.
This level of suppressed nominal rates means either the market is pricing a marked departure in the growth trend from what we have seen even post-crisis so far. Alternatively it means a near term recession and/ or more liquidity measures from the central bank. Or at least it is pricing in the Fed's inability to hike rates substantially given the situation in China and Europe and Japan. So far the Fed has been doing the catch-up to the markets pricing.

The first possibility is what secular stagnation is all about. So far most of the evidences have been important and potentially even supportive, but at the same time inconclusive. It is not certain the impact attributed to secular stagnation is really a not cyclical effect attributed to a long run structural change. In fact Larry Summers, who revived this idea of secular stagnation in 2013, is himself very much aware of this. See the disclaimer in the last paragraph here. There has been many different views on this, for example see here for the counter-view from former Fed Chairman Bernanke. Real-time economics is hard. It will be much easier to settle this debate after a decade or two. But right now, I think the biggest argument against secular stagnation is the prior probabilities. The long run world growth rate data (for example see here) shows a staggered improvement, with last great bottom around just before the Industrial Revolution.  All recent variation in world GDP since post war seems more or less cyclical phenomenon in this scale.

And the other possibilities to justify such depressed nominal rates are definitely cyclical. In fact the FOMC statement and general stance so far, downplaying secular stagnation and emphasizing inflation, clearly shows the Fed is eager to keep its options open. Secular stagnation is a rather long-term commitment to a particular view around equilibrium rates, GDP and inflation. It does not come handy to set appropriate monetary policy expectation and maintain credibility at the same time in real-time economics.

And in that scenario, near to medium term growth and inflation outlooks are much more critical. This also means a higher volatility and data dependency as the markets as well as the Fed react to data. The recent inflation uptick has been feeble, but definite. The fear of Yuan devaluation has subsided significantly. Given Fed's stance, it is perilous to believe the only move for the long term rate for the dot plots are down.

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(1) data from Federal Reserve
(2) data from BEA, Office for National Statistics, Eurostat
(3) data from Federal Reserve, Bloomberg

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.

Macro: Revisting The Dog That Did Not Bark

Very recently we have seen some rising voices on the upside inflation possibilities from various corners.  Soberlook covered it the other day. Deutsche has recently had a rather strong publication. Even the St Louis Fed has something to say on this. I am not so sure that inflation is just around the corner, but I have also covered it before (See here,here, here and here). The point is not to say we should worry about rising inflation now. The forecasting accuracy of economists are, well, not certain. And hence as market participants, investors should care about other possibilities than just their beliefs. Even when (and perhaps especially when) they tend to diverge. And these points are valid concerns to juxtapose against a general deflation concern, driven by Chinese and European economies.

The major points raised in favor of a more positive outlook on inflation are broadly 

• the recent rising inflation in the US
• the subdued wage inflation may be just a lagging indicator, and when corrected for productivity gain, unit labor cost inflation may be higher 
• inflation markets are too pessimistic about oil and finally 
• fighting deflation may be unproven, but fighting inflation is not easy either. 

Let's look at some charts to see where we stand on this. To start with, what is driving the recent pick up in inflation  in the US (click to enlarge)

Yes, it has been mostly driven by a recovery in the transport (read energy) component, and steady housing and healthcare components. The massive fall in oil price in late 2014 skewed the transport component and if oil steadies at these levels, this major effect will cancel out (as the Fed expects).

However, that is no cause of merriment, looking at a broader picture. As alleged, the wage rise has indeed been subdued, to historical standard. And as pointed out by numerous analysts, the traditional Philips curve has been much weaker (the chart on the right shows correlation to wage growth and inflation, with shaded area as US recession). Oil, and in general commodities have, in recent times, much stronger correlation to inflation that wage growth. Now this can be read as you like. One hand this means even an increase in wage may not reflect in a substantial increase in inflation (argued from the supply side, with so much excess capacity in the commodity sectors, which most analysts generally agree upon). On the other hand, notice the case of the early 90s recession and how the wage and inflation correlation picked up during the late stage of the recovery. As I have mentioned before, the current recovery is not entirely unlike that of this one.

The take-away here is wage growth or not, the supply side excesses will have to run its course before it can put pressure on commodity prices (perhaps not much downside from here, at the same time). What we really should try to figure out is what is the health of the demand side.

And here we see the mixed signals, especially if we consider the global point of view. Below charts shows GDP-weighted headline and core (ex-energy) inflation. While we have a strong recovery in the US, the rest of the world does not look that impressive at all. It is true we are not very much near a deflation scenario given the current levels, but not a fat lot of improvement in sight.

The point here is more nuanced than worrying about either deflation or inflation. On one hand we should remind ourselves not to write of return of inflation. On the other, we may not be near deflation, but that situation may change drastically if we face a sudden crisis. Given the current monetary and fiscal policy stance, it is very hard to see the wriggle room. And that is precisely the reason to worry for risk assets. Given status quo we should do fine. But in either case it is hard to see a fitting policy response that is credible and effective in either way. It is more like a short convexity trade. If you are in it, you better make sure you are getting paid for it.

Finally, yes, the oil market is indeed pricing the scenarios too pessimistically. But it is hardly fair to blame the traders. You may as well know the breakeven levels are likely wrong, but if you have stop losses it is hard to fight all in. Similar in rates markets. Understandably,  the Sterling markets, with all Brexit talks warming up, are not very optimistic compared to Euro. But given the inflation difference and fundamentals, this is likely a mis-pricing too. At the same time, how long the USD 10y can maintain a 100bps+ differential to Euro rates without attracting yield chasers. The table shows three month forward curves across markets and the policy action priced in.

Today	EUR	GBP	USD	JPY
Current	-0.34%	0.51%	0.49%	-0.03%
Max	1.49%	1.88%	2.42%	1.42%
Long-run average	0.98%	1.27%	2.22%	1.26%
Next Hike	Mar-19	Mar-19	Jun-16	Dec-21
Initial Hiking Pace	8.3	7.4	6.9	4.5
Peak Time	Mar-29	Mar-27	Mar-33	Mar-34

Eventually all these will correct, may be sooner than later. But rather than being directional, it is time to see how to position for the volatility when we edge towards either extreme and the market overreacts. I would rather like to sit on gun powder now than trying to cover later.

I think this entire arguments and counter arguments are nicely captured in this Galilean dialogues from Gavyn Davis on FT.

For title reference see this and this.