Thursday, December 28, 2017

Markets | Bitcoin - The Hidden Optionality

A lot of things about Bitcoin defy conventional logic. For example, valuation of bitcoin can be treacherous and common sense ranges are a tad too wide for traditional economists or investors1. "Exceptionally ambiguous", so to speak. Then we have confusions as captured in the tweet below.

The attitude of the crypto-currency enthusiasts is best understood in terms of Keynesian beauty contest. It is not important to have a specific valuation in mind to HODL Bitcoin. All you need is your estimates of what others might value it at. It is not important to start using Bitcoin to pay for your morning coffee to realize the dream of replacing fiat currencies. All you need is to believe that enough of other people believe in doing so. The entire thing is a second order guessing game.

Theoretically, this set-up makes for an interesting characteristics of Bitcoin price. Since there is hardly any well-accepted valuation, a sudden rally or sell-off will not see the typical stabilizing intervention we see from value investors in other asset classes. Also since most (if not entire) valuation depends on the collective average of investors' expectation, a rally will see further buying and vice versa. This means the time series of price will show intrinsic characteristics of a momentum strategy.

The chart below captures this feature. The chart on the left shows the empirical distribution of MA(1) coefficients for daily returns for Bitcoin (black) and S&P 500 (red). The MA(1) coefficients can be interpreted as the response to a random shock in price. A series showing momentum nature will tend to magnify these moves, i.e. will have higher response coefficient. As shown in the chart, the Bitcoin response is highly skewed towards the right compared to S&P. The chart on the right similarly shows the response to a previous trends (AR(1) coefficients here). Here again the Bitcoin distribution is skewed towards the right. It even crosses the 1.0 mark, the upper limit of stationarity - turning in to what is called explosive process occasionally2!

The second characteristics of Bitcoin is its fat tails. The chart on the left below shows standardized returns across different asset classes (Bitcoin - thick red, equities - black, FX - blues, gold - gold, commodities - purple, rates - green, inflation - brown, VIX - orange, credits - grey). The peaked value and fat tails for Bitcoin far exceeds other asset classes (closest is the option adjusted spreads of AA credit). The right hand chart shows an easy to understand metric for fatness of tails. This displays the ratios of mean absolute deviation to standard deviation. Since standard deviation is a square root of square measure, it is more sensitive to large tail values than mean absolute deviation. The ratio of them shows the fatness of tails. A lower ratio means fatter tails. As the distribution approaches normal distribution (no excess kurtosis), this ratio approaches 0.8. Here we see by far, the ratio for Bitcoin is the smallest. It also shows strong positive skew.

The above two observation makes Bitcoin quite a bit of unique asset class. Nevertheless, we tried to explore which asset class comes close to it, in terms of time series characteristics. Here is the outcome - where Bitcoin stands among different asset classes based on a few measures:

There are multiple ways of clustering time series. One is "shape-based" - e.g. measuring a geometric distance like Euclidean distance. The top left chart shows the asset class hierarchy based on this measure. Bitcoins in this respect behaves similar to gold - very distinct from the carry assets block (VIX and credits), FX, rates, equities and commodities block. On "structural" measure (bottom left), like based on time series correlation, Bitcoin teams up with the commodities block. Finally, based on complexity or information based models (top right and bottom right), Bitcoin reflects the distribution and fat tails characteristics discussed above and behaves more like AA spread or VIX. On the whole, Bitcoin does not appear to be either digital gold, or a currency at all. It is more like a commodity showing fat tails similar to credit spreads and volatility.

In fact this fatness of tails, along with the momentum characteristics discussed above makes Bitcoin less like an asset class, and more like a derivative. Momentum strategies are comparable to options. Most  momentum trading strategies display two characteristics - many small losing trades and a few big winners. The big winners give rise to fat tails (with positive skew). And those small losing trades can be compared to carry cost of an option (theta cost or time value). This interpretation can be readily extended to Bitcoin as well. The good thing about Bitcoin is, given the upwards trends till date, the so-called carry cost has been positive!

Beyond the economists and valuation experts communities, I suspect most traders understand this optionality of Bitcoin by instinct. You invest an amount you are happy to lose, with a possibility of large upside - this is the optionality of Bitcoin without all these technical details. This says nothing about Bitcoin being a bubble or not. But a long position in Bitcoin in a positive trend (or a short position in a negative trend) is going to act like a long option position. A proper valuation of the Bitcoin, therefore, must include this embedded optionality.

1. For example here is a rather ridiculous attempt. And a rather commonsensical overview.
2. Notice how the S&P AR(1) coefficients distribution gets truncated at 1.0, as it should be for stationary processes

Saturday, October 21, 2017

Systematic Trading | Using Autoencoder for Momentum Trading

In a previous post, we discussed the basic nature of various technical indicators and noted some observations. One of the ideas was: at a basic level, most indicators captures the concept of momentum vs mean-reversion. Most do so in the price returns space, but some in a non-linear transformation of the returns space, like signed returns or time since new high/ low. We presented the idea of a PCA approach to extract the momentum signals embedded in these indicators. From there to a trading model, the steps will be to collate this momentum signal (1st PCA component or higher if required) along with other input variables (like returns volatility and/ or other fundamental indicators) to train a separate regression/ classification model (like a random forest or a deep NN).

One of the issues with using simple PCA is that it is linear and hence may not be appropriate to summarize different measures captured across all these indicators. Here we discuss the next logical improvement - a nonlinear dimensional reduction approach using autoencoder.

As discussed here, the new Keras R interface has now made it very easy to develop deep learning models in R using the TensorFlow framework. Here we use this interface to train an autoencoder to fit the same set of technical indicators on NSE Nifty 50 Index as before. The steps involved are relatively straight-forward. First we generate and standardize the inputs (technical indicators levels). Then we build the computation graph.

To do so, first we define the encoding layers (2 hidden layers, the latent coded unit size is 3, to match the first 3 components of the PCA we use for comparison), and two different decoding layers. The two different decoding layers are to  enable us to train the auto-encoder as well as compute only decoding independently.

Next we combine these layers to create the computational graph. One for the encoder only, another for the decoder, and a third one for the end-to-end autoencoder, that we will actually train.

The rest of it is standard. We define a loss function to map the input to the output, measuring mean squared losses, and train the model. The training is done on data till 2013, and test set is since 2014 till present. Once the training is done, we can use the encoder and decoder separately to generate a dimensionality reduction of the input space and vice-versa.

The output of the dimensionality reduction is compared with the PCA. As it appears from the correlations, the PCAs are almost one-to-one mapped to the three latent dimensions in the hidden layer generating the encoding. So the encoded layers are orthogonal in our case, although this need not be true always.


The scatter plot below captures the same, but also highlights the some non-linearity, especially the first component of PCA vs the first latent dimension from the autoencoder.

From here the next step is obvious, replace the PCA factors inputs in the momentum trading model in the first paragraph with these latent dimensions from the autoencoder and re-evaluate. This will capture a richer set of inputs that can handle non-linearity and hopefully performs better than linear PCA. Here are some results what other reported (opens PDF). Here are some more (opens PDF) on the using autoencoder for cross-sectional momentum trading. The entire code is available here.

Friday, September 22, 2017

Macro | A Paradigm Shift For India's Retail Investors?

The Indian economy is at an interesting point. We had two large scale policy moves in recent time - the much controversial Demonetization in November last year, and the implementation of (a somewhat rundown version) of Goods and Services Tax regime this year. Early this month, we had the first GDP print following these two major steps. The headline prints came in lower than consensus - 5.7 percentage for Q2 vs. 6.5 (and 6.1 last quarter). This was followed by equally weak Industrial Production release. A stronger than expected headline CPI prints did not help, as this squeezes the room for any rate cuts from the RBI.

A closer look at the GDP data (see component break-down in the chart below) shows some serious weakness. The private consumption part (C) has weakened significantly following the demonetization (the vertical red dashed line). The investment component (I) has been weak for a while (although staged a comeback in the last quarter). Exports growth was not helped by a strong rupee. In last few quarters, government expenditure helped the headline a lot. But the sustainability of this is questionable. We will have the fiscal deficit data out later this month. But the street does not expect anything great.

The story of the IIP paints a similar picture (see chart below, overall IIP, manufacturing, base materials, consumer durable, consumer non-durable, capital goods, electricity, intermediate goods and mining respectively). While demonetization appears to have caused a negative shock, in general most of them peaked out before that, around early 2016 to be fair. The capital goods, which staged a minor comeback since bottoming out in 2014, again resumed the downward trend, along with most (except consumer durable, and to some extend mining).

This is all in a relatively benign global macro scenario. In spite of the Fed taper 2.0 announcement, we have little jitters in the markets. Rates, both global and local, are relatively low and volatility remains subdued. Oil prices remain range-bound. A rally in oil along with a weakening INR following Fed and expected ECB taper later this year can worsen the scope of fiscal stimulus. Most in the business sectors does not expect private investments to turn around before end of this year at the earliest. The investment exuberance back in 2004-06 left many corporates laden with unmanageable debt burden and bank balance sheets with NPA.

In this background of weakening macro story, the Indian equity markets is in a tear. The flagship NSE Nifty Index posted a YTD 21%+ gain, among the best globally and compared to it's own history. The trailing 12-month PE ratio is looking worryingly high. High valuation remains a big concern among investors in this, and most other traditional metrics (a bit better in terms of price to book).

However, comparing the PE ratio to its historical average is not very good way to capture everything that goes on to determine fair price. In the most basic approach, the price of equity is a function of market risk free rates (say the local sovereign bond) and equity risk premium. Following the approach in this paper from AQR, I modeled the BSE SENSEX P/E based on the risk factors - the bond yields as well as the equity and bond volatilities (as in the original paper) along with current account balance as a percentage of GDP (reflecting the fiscal risk of the economy) and spread of bond yields to US Treasury (captures the flow risks). The last two are more relevant for an emerging market economy like India. The time-series shows a marked shift in relationship between pre- and post-crisis era. I fitted the model only on (monthly) data from 2010 onward to capture the recent dynamics. As it turns out, the bond vol has little contribution to market risk premia for India. The bond yield and equity vol shows significant but low correlation, whereas the CA deficit and spread to treasury captures a significant portion of the variance. The chart below shows the fit on this model (adjusted R-squared ~0.72).
According to this model, the PE ratio is only slightly on the over-valuation side - not a cause of great alarm. According to this model, the market was highly over-valued around late 2011, and early 2015. We saw corrections in both cases. Also the under-valued period, early this year, was followed by upward corrections as well. This model does not forecast a large correction anytime soon unless we rally up a lot quickly from here (obvious caveat: these are in-sample results).

But what is most interesting, and perhaps most significant is the recent flows that we have seen in Indian equity markets. Traditionally, the equity markets in India has been shunned by a large portion of retail investors. The experience of scams in 1990s and the melt-downs, once during dot-com busts and another in 2008, did not helped. The foreign portfolio investors dwarfed the domestic flows in cash equities for a long time (although it is a different story in F&O). But since 2014, something changed. The extra-ordinary flows in to the equities markets, led by domestic mutual funds (presumably on the back on retail savings channeled to equities) completely outpaced the foreign flows.
Is this a mass optimism following the 2014 election outcome and equity rally? Or are we witnessing a major shift in the savings behaviour of retail investors in India. The retail money has missed the initial come-back equity rally following the 2008 crash, and a part of the early 2014 rally as well, where the foreign investors made out handsomely. But much of the late rally in Indian equities has gone to the retail pockets. Is this dumb money chasing recent gains? We do not know for sure, but as we argued above, we are some distance away from any valuation melt-down in Indian equities. And the flow signifies the loss tolerance of the retails - who are sitting on some comfortable profits - has quite a bit room before panic. And finally, the weakening property markets and demonetization may have incentivized a permanent change in retail behaviour.

We do not know for sure. But what is the implication if it is indeed a fundamental shift in savings behaviour? As argued above, the macro in India is down, but with policies properly executed, the turn-around can be sharp. If oil remains range-bound and the Fed and ECB do not stray afar from the implied forward curves, we will have little in terms of global shock to upset the local economy. On the other hand, the efforts to put banking sector NPA in shape, along with the full kick-back of the GST regime should significantly improve the badly needed private investments. Add to this mixture this retail savings paradigm shift, and we are looking at the very beginning of a multi-year rally in Indian equity markets.

Wednesday, August 23, 2017

Off Topic | How Not To Discourage Banks from Short Term Trading

Lately we have had a lot of talks about Volcker repeal or replace. Does Volcker rule do what it is supposed to? Is it good or bad, and for whom? There are many issues, lobbying and conversations going on right now. Here is the latest proposal from Harvard Law School:
To achieve the objectives of the Volcker rule, we propose that banks be prohibited from basing compensation on trading-based profits. Our prohibition would encompass both ex ante compensation on trading-based profits (such as contracts or non-legally binding representations that the individual’s pay will be tied to their trading profits) and ex post compensation (such as discretionary bonuses the amount of which set based on a trader’s trading profits). Violations of this rule would result in a fine to the entity, claw-back of the individual’s impermissible incentive pay, and potential criminal liability for intentional violations.
The essence  of the argument from the authors are:
  1. Banks compete in the securities market with other banks and firms to make short term trading profit (the target of the rule). Since this is a zero-sum game, only those banks who are able to attract top traders are able to turn in a positive profit, while others will be discouraged (by potential losses).
  2. Since banks also compete in the labour market - i.e. to attract trading talent, banning profit-linked compensation will force talented traders to hedge funds.

Wham! together, the end result is banks getting second-tier trading talents who must compete against the first-tier traders from hedge funds and will lose money in the zero sum game that short term trading is. Hence banks in general will be discouraged to trade short term at all.

There are some serious issues with this proposals and authors' understanding how short term trading, compensation and banks work in general.

Firstly the way banks and hedge funds make money can be significantly different. A top-tier trader in a bank will not necessarily be a top-tier in a hedge funds. In short term trading, there are three ways to make money - 1) You have superior information of who owns what and who wants to trade which way 2) have a balance sheet advantage - to overwhelm markets or to hold your ground or 3) have superior analytical capabilities (better guts, models AI, whatever for short term price prediction) and/or pure trading skill.

Banks usually excel in #1 and #2 because of their dealing role (may be not #2 much anymore, but also they do not have to cross the bid-ask spread). Hedge funds have limited access to these information and balance sheet advantages, but are supposed to have an edge in #3. Many top traders from a banking set-up fail in a hedge fund environment because of this. The trading and making money work differently.

So even if banks lose out top trading talents to hedge funds, by no means they will lose their edges that they specialize in (more true for OTC-heavy asset classes like fixed income and less applicable for exchange-heavy asset classes like equities). The advantages belong more to the seat than the man (or woman as the case may be) occupying it.

And then the compensation scheme itself is weak. The easiest way to link trader's incentives to performance - where you cannot directly link it to trading profit - is to tie it to job security. Hire top talents with a very high fixed compensation. Prune the second-raters in next cycle. Rinse and repeat. The top talents will be attracted  - if they are indeed better, they will know they can perform. A compensation scheme linked to trading profits is a series of call option on trader's PnL. Tweaking this to high fixed compensation is similar, just a series of digital calls (instead of a vanilla calls), with a knock-out feature (based on trading profit).


Tuesday, August 8, 2017

Markets | Trading the "Bond Bubble"

One of the most confusing conundrum in recent time has been the curious case of stubbornly weak inflation and upbeat economy with low unemployment.

The US GDP number, while not spectacular, has been solid. Atlanta Fed GDP-Now picked up significantly in recent time. The consensus forecast for medium term GDP (2018) also improved from the start of the year and now stands at 2.3 percent. Unemployment rate remains near record lows, below pre-crisis number. According to JOLTS surveys, both quit rate and job opening rate matches or betters the pre-crisis cyclical highs. Even the relatively more pessimistic Fed labor market conditions index has improved significantly from the lows of early 2016. But both market and survey based inflation expectations are going the other way. The 5y treasury break-even inflation came-off ~40bps from highs of early this year and now stands at 1.65 percent. Similar is the story for break-even swaps markets. To match, the medium term consensus inflation forecast has come down from 2.4 percent early this year to 2.2 percent. The fall is even steeper for 2017 forecast, from 2.5 percent as recent as April, it is now at 2.10 handle. And this does not appear to be driven by oil or commodities. Both Brent and WTI have been range-bound since mid of last year. Even the set-back in general commodities prices (see Bloomberg Commodity or CRB index) early this year is now on the path of recovery. The Phillips curve is either flat, dead or was never there.

This conflicting development seemed to have a win-win impact on major asset markets. Instead of the fabled great rotation, we have seen strong money flows in both stocks and bonds - blame it on the re-balancing of portfolios, or general optimism.

The stock market benefited from solid economy and strong earnings, with valuation also supported by low rates. But the positioning remains cautious (with a correction in the gamma positioning as well).

A more interesting development is happening in the bonds markets. The bonds markets seem to have sided with the low inflation view - that no matter what the Fed does - inflation, and rates, are not going anywhere anytime soon. The over-all positioning remains solidly in the long territory. But the peculiarity is in the strong flattening bias build-up. Early this year we saw a massive swing in long maturity bonds positioning, from extreme shorts to moderate longs. This was presumably driven by the built-up and subsequent unwinds of the Trump Trade. As a side-effect, this has resulted in the extreme flattening positioning on the street. It appears everyone is positioned for a low pace of rate hikes from the Fed, and anchored low inflation expectation - resulting in a yield curve flattening. Last few times we had this kind of extremes (early 2010, mid 2012, around just before Taper tantrum and start of 2015) we had a very strong steepening that bloodied all these speculative position well and good.

Most of the players in the markets are already wary of overall bonds positioning. Some are calling out a bond bubbleSome are ready to take the opposite view. If you are in the markets to trade and not for punditry, it is hard to take a strong view. This extreme positioning in the curve provides a cheap (in terms of risk to reward ratio) way to position for a bonds sell-off. Or forget bursting the bubble, even a Fed balance sheet normalization can be the trigger. It is not at all certain balance sheet normalization will lead to increase in term premia and long term yields. But most theories say so. And if the Fed decides to hold short term policy rates during this normalization, this steepening can play out in both bull or bear scenario. And honestly, nobody has any clue how the Chinese are going to change their treasury buying patterns after the National Congress in the Autumn. If the current premier is able to stamp his authority, as generally expected, this may mark a definitive shift in policy from GDP growth target to economic stability. That, in turn, will have far reaching ripples for global asset markets.

At current level, the US curve is the flattest among all major currencies (except 5 year vs. 10 year area where JPY curve is flatter). A steepening in USD rates is a highly asymmetric trade - the trade to position for a bond bubble, whether you believe in it or not.

1. Data source: ICI for funds flow data, CFTC commitment of traders for positioning data (latest 1st August)
2. Steepening position is implied from short end (2 year and 5 year) and long end futures positioning, expressed in equivalent (approximate) duration at 10 year point.

Sunday, June 25, 2017

Off Topic| Wide and Deep Learning in R

R is an excellent environment for quick and dirty data science. I am a R user and obviously a bit biased, but between Python and R, R has always had the edge for data visualization and quick hypothesis testing. If you do not find the latest and greatest methods of bleeding edge analytics somewhere available already within the strong R package ecosystem, it is more or less safe to assume it does not exist anywhere else either. And forget Python, the IDE from R Studio is perhaps the best IDE across any development platform (although the Visual Studio perhaps has a better debugging interface). But one area where R has been weak is in machine learning, especially in the deep learning area. And with the explosion of interest (and fad?) in deep learning, this has become quite a glaring gap.

But hopefully not anymore. We already have Google's TensorFlow available in R for a while. But to be honest, it did not have much feel of R in it and looked like a deprecated version of the Python release. However, very recently the R Studio folks released a R support for the excellent Keras high level API, with back-end of TensorFlow. This feels like R (with some quirk like in memory modification of objects) and works like a charm. Although it runs on top of a local python platform, the package exposes pretty much all the functionalities Keras support.

You will already find a list of examples in their site here. Here is to add a basic example of how to set up a wide and deep learning network. This involves creating two separate learning network. The wide one has only one layer (effectively a logistic regression of sort). The deep network is created separately. The output of two is combined (concatenated) in a final decision layer (this is slightly different architecture than the TensorFlow example). This is run on the usual Census Income data-set. The error rate for this set up is around 16 - comparable to other methods officially reported.

Tuesday, June 6, 2017

Markets | Positioning For The UK Election

UK goes in to elections this week. Since the surprise announcement in April, the polling has narrowed quite a bit between the two major parties. (See chart below - although note a large part of Labour gain has been at the expense of smaller parties, especially UKIP). However although the markets had a sharp initial reaction to the announcement, the moves subsequently have been more cautious. The outcome of the election is touted as determining the direction of Brexit negotiation. And markets appear to be waiting to assess the situations once the results are out. However, what the market will focus on in Thursday evening is not only the UK's divorce from the European Union.
Looking past the Brexit, the major differences between the Tories and Labour campaign is their respective stance on tax and government spending. If conservatives have their ways, it will basically continue the status quo, without any significant change in taxation or spending.
On the other hand, the labor plans to increase taxation (focused on corporates and top earners) as well as infrastructure spending. The National Transformation Fund with a corpus of £250b proposed by the Labour compares to a £23b National Productivity Investment Fund of the Tory government. The net effect is an increased need for borrowing, put at 45b estimates by the Tories. The other major campaign difference will perhaps add to this bill. The Labour maintains a so called "soft Brexit" approach, and a change in government in London may actually increase goodwill in Brussels. But Labour's negotiation aims also implies the UK may actually end up footing a substantial Brexit bill.
Put together, these means increased issuance of Gilts for a Labour government compared to the Tories. So in an unlikely scenario of a major Labour win, all the market forces and economics fall nicely in place. Gilts will sell-off on the back of fiscal plans - along with a steepening of the curve. Sterling pound will rally, supported by both the new Brexit stance and a rising yields. Equities will sell off, triggered by both taxation and a rallying pound and rising yields. For a strong conservative win, the impact is mostly in market sentiments than any dramatic departure in economics.
As we see from the charts above, the correlation in Tory polling vs. GBP and Gilts have mostly switched to negative off-late (and to rather positive territory for Labour). These correlations implies a Tory win will have some downside impact for GBP. But strong win may even see a small upside driven by a reduced political uncertainty before the economics kicks in. Gilts have little scope to respond vigorously, facing the inflation pressure on one hand and a more than expected Dovish BoE on the other - marginally positive for Gilts (yields go down). Equities will perhaps shrug off all of it.
That leaves us with the scenario of a Labour-led coalition government. This will in general hurt the market sentiments, with a higher chance of a addled up Brexit negotiation and potentially another election around the corner. This will be a sort of risk-off moment for UK, with sell-off in pounds and equities and a rally in gilts. This will also be a shock event - as at present the betting markets prices in a 90+ % probability of a Conservative majority. Assigning some reasonable probabilities to various outcome, the pay-off matrix looks like below. And it suggests a short GBP position before the election.
Position-wise we have seen a large reversal of positions in futures (as per CFTC reports) after the election announcement - a large decrease in net speculative shorts in Sterling pound. On the other hand, the currency options market shows a significant increase in negative skew pricing (demand to protect from a sterling crash). In fact the GBP 1 week 10 delta risk reversals is near the highs around the Scottish referendum in 2014 (although much less than the highs reached around Brexit referendum). So it appears we have some options positioning (or at least demands) - indicating a position switch from futures to options. Assuming most dealers in the FX markets will have the opposite position, this adds to a negative bias on Sterling.

Saturday, May 6, 2017

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.

All data from CBOE website/ Yahoo Finance/ Bloomberg

Monday, May 1, 2017

Macro | Cross Asset Correlation Update

The markets seem to slowly leave behind the massive focus on fiscal impulse following the US presidential election, and the inordinate amount of stress and optimism about the US dollar rally. This is already reflected at least in terms of asset price behaviours, if not media and analysts focus yet.

Cross asset macro drivers for 2017 YTD (based on first factors extracted from principle component analysis for each asset class) looks much like H1 of 2016, which saw a cautious rally in risk assets following the early stress period - albeit now it comes with reduced influence of oil prices and volatility on risk asset prices. This stands markedly different from the H2 of either 2015 or 2016 - which saw a pick up cross asset correlation (with very different outcome, a risk-off move in H2 2015 and a risk-on rally in H2 2016). The MST charts below captures this dynamics pictorially.

Among the risk assets, DM equity factor shows increased positive sentiments to rates (i.e. increased yields leading to rally). Inflation has become more important for DM equities as well, while FX has virtually no influence. For EM equities, the latest trends has been a slight de-sensitization to rates and FX movement, although they remain significant. The credit factor also picked up its correlation to rates (and FX, which is mostly influenced by EM credits part), while retaining correlation to inflation.

This makes the rates and inflation path the most important determinants for risk assets at present - at least from Developed Markets equity investors' point of view. Markets will always react (or over-react) to tax cuts expectations and presidential elections. But we are now, it appears, back to the basics.

On this fundamental note, we have seen some recent encouragement in global inflation space. The left chart below shows GDP weighted CPI inflation (global top 20 economies as well as Developed Markets within that). Since the recent bottoming out at start of 2016, we have seen a secular rise in inflation, which is more pronounced for the DM case. However, the core inflation scenario (not presented here) is far from running hot. Core inflation in the US and China have improved from 2015 lows, but much less dramatically. Only in the case of Euro area this has been solid (from very low levels). One the other hand, global credit growth (right chart below) appears to have topped out in a secular manner. On the positive sides, the wage growth in the US (not shown here) has been encouraging and sustained.

If we consider these points, in the context of extraordinary monetary accommodation that exists across the globe today, we should be more hesitant to conclude we are heading towards a definite normalization anytime soon, in spite of strong sentiments. The rates market seems to agree. We have seen inflation recoveries in 2011 (remember the ECB hike mistakes) and also in early 2014. It was a misfire in both cases. A weakening credit impulse and barely normal inflation in the face of extraordinary monetary stimulus represents a global demand which is far from recovered. This makes the case for removal of these extraordinary monetary measures very difficult - most policy makers are still biased to err on the upside inflation naturally. That is unless we see the whites in the eyes of inflation - in which case, it either may be too late, or have to be too harsh and steep. For now, the forward looking inflation measures (both market based like break-even inflation and model based like Cleveland Fed now-cast) remain stable without any sign of worrisome upward pressure. This means the risk assets will largely avoid negative reaction by a possible June Fed hike (market probability of 67% as of date priced in). The key risk in this regard remains any (mis-)communication or premature taper on the central bank balance sheets.

All data from St Louis Fred Database

Saturday, March 25, 2017

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.

Wednesday, March 22, 2017

Off Topic: A Package to Send Text Messages From R

If you often run long processes in R and want to get the results notified to you once finished, but not always around to check it on the terminal, this is a very useful package. 

Of course one option is to send a mail from R (there are quite a few packages for that). However, this may not be a very safe option if you are running the R process on a remote machine (on the cloud). Most mail packages in R will require you to enter your mail password in clean text. While this is okay for your local machine, on the cloud it is a little bit unsafe. Another difficulty is your R process will have to sign in to your mail account (Gmail for example) to be able to send the message. However, your mail provider can refuse - like Google will, citing an unidentified app access. To bypass that you have to considerably reduce your security option in your mail account - which is not ideal.

Texting the message using a third party service like Twilio is a great alternative. They offer a free-tier account (with no expiry as they claim). If you are not a heavy user, my best guess is that will be sufficient in most cases. This package simply wraps the REST API interface from Twilio for the simple text messaging service inside an R package for convenience. All that is needed is signing up for the service and obtain the assigned mobile number, and authentication details and you are good to go. I am not sure about the restrictions on international texts, but this works fine for me for local texts. Results direct to my mobile with insignificant time delay.

You can download the package from here. The installation and usage (pretty straightforward) are in the readme file in the repository.

Friday, February 24, 2017

FOMC | The Ides of March

We have quite a bit of built up anticipation for the March FOMC. The Fedspeak analysis of "Fairly Soon" has been interpreted by most as leaning towards a March hike. Some are even claiming the rates markets are underestimating the probability of a March hike.
The chart above shows implied 3-month treasury forward curve term structure since the 2014 (after the highs from 2013 Taper Tantrum). In early 2014 the market estimates of long run equilibrium rates were just about 4 percent. Since then we have come a long way. As we see we have three major clustering of market estimates - one at around sub 2 percent (during Brexit rally), another just above 2 percent (early 2016) and the most common level at just about 3 percent. The sell-off after the US presidential election has just brought us back to this 3 percent level. Coincidentally, after disagreeing with the markets on this long run terminal rate for a long time (erring consistently on the upper side), the FOMC also now more or less agrees with this level. So after quite a while markets and the FOMC seem to have converged in outlook. 

Given this background, I think whether the FOMC hikes in March or not is now a far less important question than what it used to be a couple of years or even a year back. Before March FOMC, we have a round of PCE (Fed's favored measure of inflation) as well as employment and GDP data release scheduled. Unless we have a major upward surprise, March probably will be a no-hike meeting. And more importantly, given the improving economy, markets are in a much better position to absorb a hike anyways. The US and global inflation are improving, but it is much tamed than the "reflation trades" coverage makes it sound. Inflation was a worry (on the downside) before, now slowly it is ceasing to be so. There are few signs the FOMC is behind the curve as of now.

What can really take the market off-guard, is however, the question of Fed balance sheet. If and when FOMC plans to reduce its QE-bloated balance sheet, and how they communicate this point. Hiking is a way of tightening. But a controlled balance sheet reduction is also another way. While the former affect the short term rates more (a bear flattening), the later should be more prone to affect the long end rates (bear steepening). A reason why FOMC may actually opt this is to address the historically compressed risk premia - see the left chart below. Even with the recent sell-off, the risk premia remain at a depressed levels. The short end pressure felt on the back of FOMC moves more or less leaned towards a flattening of the curve than any significant correction of risk premia. While the European and Japanese bonds are trading at super-depressed levels, perhaps it is not entirely to the Fed to correct this. But adjusting balance sheet is definitely a direct way to address this.

The most important reason NOT to do this it the unpredictable potential impact. This has the strongest potential to send confusing signal to the market, perhaps resembling a taper tantrum version 2.0. The right-hand chart above shows a quick check to identify the pain points based on the current Fed holdings vis-a-vis supply. The vulnerability is concentrated in the long end, especially if this is adjusted for the duration risk (not shown here). The primary reason this may create unwanted responses is that it is not at all well understood. Balance sheet reduction after a massive QE is a completely new thing for both the Fed and the market. The last FOMC minutes (published last week) discussed this issue explicitly for the first time, if I remember correctly. So it is fair to expect this will definitely come up in the March discussion as well. At present FOMC expects re-investing to continue "until normalization of the level of the federal funds rate is well under way". The most important event for the markets from the March FOMC will be any potential change on this view. 

Realistically, this can be the trigger that can bring us back to the 4-handle level of long term equilibrium rates we had at the end of 2013. Trump fiscal push blow ups and run-away inflation seems pretty far-fetched at present. The asymmetric positioning here is bear steepening.

Similarly on the equity and risk assets side, this can have the most unexpected and damaging impact than a regular FOMC hike. Possibly more than even an adverse French elections. The National Front candidate Marine Le Pen, even if elected as the President against all odds, will find it hard to muster enough support in the parliament to call for a national referendum to leave the Euro area. And even if the referendum is held and a majority votes to leave, it is not clear that will actually be followed through - going by the outcome of the 2005 referendum.

all data from Federal Reserve and US Treasury.

Saturday, January 14, 2017

Markets | Quick Take on Presidential Inauguration

Next week's Presidential Inauguration is a much awaited phenomenon - for general public as well as for the financial markets across the globe. Dow 20K is mostly an arbitrary mark for a market index designed for pre-computer era (and some equally arbitrary Theoretical Dow has already crossed the benchmark). But it appears the entire market is somewhat directionless at present. Since the election, it has made certain assumptions on the policies of the upcoming government and has shown some very strong move across asset classes (see here, here and here). However, we still have very little in terms of concrete policy direction to rely upon. The latest press conference did not quite live up to the expectation of details on policies. A strong guidelines on future policy in the inauguration can provide a new direction to the market one way or the other. And this can kick start the next phase in the market.

The charts below show the market impact of Presidential inauguration since the post-war era (excluding first term of Barack Obama, which was in many ways an outlier). The X-axis is the number of business days from the inauguration day. The chart on the right shows normalized moves of the S&P 500 Index from 3 month before to 3 month after for each inauguration. The chart on the left shows the median line and the uncertainty around it. It appears more often than not, the markets usually rallies in to the inauguration, experiences a slight correction going in to the exact date, and tops out  around 1 or 2 weeks after the actual date before picking up its own course. (Note we have not corrected for the usually positive trends for the markets in general and hence we should not focus much on the trends here but change in the direction of the trends instead.) However we have quite an amount of uncertainties around this. Looking closely at the right hand side chart we see this pattern was more or less followed by around 10 or 11 times out of last 17 cases. (The legends on the right chart are initials of the presidents followed by a digit signifying the term, if required)

Overall positioning-wise, we have nothing extreme in either way. Post elections the leveraged funds (CTAs and hedge funds) and asset managers have increased their long (from CFTC reports). The dealers have become slightly short the markets - but all well within range. On VIX, however the dealers and asset managers remain long against the leveraged players.

This, and trend analysis of the recent intraday movement of S&P 500 suggests the street (i.e. the players who hedge) is mostly long gamma at this point. See the chart below (and see here for interpretation). This means a large sell-off is quite unlikely in the short term. On top of this, we have the asymmetric scenario on the policy clarity. If President-elect Trump does announce clear guidelines on his policies, this will likely confirm the market assumptions (very low chance of a major negative surprise) and market can have the next leg of rally. On the other hands, impact of rhetorics and vagueness will most likely be muted as there is always the next time. This suggests a long positioning for the equities. However the case of dollar is quite different. We have a very strong long dollar positioning from the leveraged players and any disappointment can be felt quite hard in the dollars.

Finally, while you can't miss the obvious market reaction to Trump's win, it is fairly easy to miss - what I think the most dramatic - real economy reaction. The NFIB small business optimism and outlook went over the top following the election, much more than the overall business outlook and optimism measures. The charts shows the standardized measure and the spread. 

I think in itself, this is quite significant. Historically, we have only two similar situations when the business indicators were significantly positive and small business optimism outperformed overall measures. Once was during the recovery of early 90s and secondly during the recovery of early 2000s. While we have too few data points to draw any statistical conclusion, in both cases we had sustained economic improvement and overall positive market performance. Of course small business optimism does not necessarily mean it will be realized, nor what is good for small businesses is also necessarily good for overall markets. But perhaps we have too many people bracing for a crash now?

Wednesday, January 4, 2017

Systematic Trading: Back-testing Classical Technical Patterns

Following up from my last post on systematic pattern identification in time series, here is the part on identifying and back-testing classical technical analysis patterns. This is based on the classic paper by Lo, Mamaysky and Wang (2000). The major improvement added here lies in defining local extrema in terms of perceptually important points (as opposed to the kernel regression based slope change technique proposed in the paper). In my view, the kernel method can be too noisy and much less robust with real data.

The R package techchart has two functions for identifying classical technical patterns. The function find.tpattern will sweep through the entire time series and find all pattern matches. It takes in the time series as the first parameter (an xts object), a pattern definition to search for, and a couple of tolerance parameters. The first one is used for matching the pattern itself. The second one pip.tolerance is used for finding the highs and the lows (perceptually important points) on which the pattern matching is based. These tolerance numbers are in terms of multiple of standard deviation. Below is an example:

x <- getSymbols("^GSPC", auto.assign = F)
tpattern <- find.tpattern(x["2015"], tolerance = 0.5, pip.tolerance = 1.5)

add_TA(tpattern$matches[[1]]$data, on=1, col = alpha("yellow",0.4), lwd=5)

Apart from returning the pattern matches, it also returns some descriptions and characteristics of the match. As below:

## ------pattern matched on: 2015-06-23 --------
## name: Head and shoulder
## type: complete
## move: 1.49 (percentage annualized)
## threshold: 2079.52
## duration: 57 (days)

While this is useful, you already must have spotted the catch. As this function looks at all available data at once to find a pattern, future prices influences past patterns. While this is useful for looking at a time series we need another function for rigorous back-testing. The second function available, find.pattern is to be used for this purpose. This function takes in similar arguments. It returns matched patterns. The match is based on either a completed pattern, or a forming one. A forming pattern is extracted by bumping the last closing price up or down by 1 standard deviation in the next bar and checking if it completes the pattern.

The process of identification of pattern is decoupled from the process of extracting patterns from the data - as proposed in the Lo et al (2000). The pattern defining function in the package is pattern.db.  This follows a similar implementation as here by Systematic Investor Blog, with some added features. The implementation of pattern.db in the package techchart contains some basic patterns - head and shoulder (HS), inverse head and shoulder (IHS), broadening top (BTOP) and broadening bottom (BBOT) - the default in the above functions being HS. However it is trivial to define any pattern (as long as it can be expressed in terms of local highs and lows) and customize this pattern library.

With this framework, it becomes quite straightforward to test and analyze pattern performance, run back-test on pattern based strategies and/ or combine patterns along with other indicators to devise trading strategies at any given frequency. 

Here is a straightforward implementation of such a back-test, using the quantstrat package. The strategy is quite straightforward. For a given underlying, we scan data for a head-and-should (or inverse head-and-shoulder) match. Once we find a match, we enter a short (long) position if a short term moving average is below (above) a long term one. Once we enter in to a short (long) position, we hold it for at least 5 days, and exit on or after that if a short term moving average is above (below) a long term one. We apply this strategy across S&P500, DAX, Nikkei 225 and KOSPI. The chart below shows the strategy performance.

The thick transparent purple line is the average performance across these underlying indices.  The performance metrics are as below. It also has (not shown here) a strong positive skew characteristics. 

Performance metrics
Annualized Return
Annualized Std Dev
Annualized Sharpe (Rf=0%)

Not spectacular, but nonetheless interesting. The R code for this back-test is here. Apart from techchart, you would need to install quantmod and quantstrat (and associated packages) to run this. Please note, running this pattern finding algorithm can take considerable time depending on the length of the time series and system characteristics.