Markets | The Trump Trade?

Keynesian beauty contest is an interesting concept that shows a group of perfectly rational agents trying to predict the outcome of an event may not converge on the most expected case, provided their risk and reward depends on what most others think. I think something similar happens in the markets around a big event. Rarely it is clear what are the implications of different possible outcomes of such events. In such a scenario, a trader's immediate pay-off depends on how good he is at predicting market reaction (as opposed to the actual implications). As a result collectively the market ends up reacting in some ways that very few people may actually believe.

Next week's presidential election is such an event. There are strong evidences that economy has significant impact on election outcomes. however the reverse result is very weak if any. Performance of a large globally connected economy depends on more things beyond the control of the Oval Office than we give credit for. However the markets seem to have already formed an opinion and trading according to the poll results in recent week. This is not only the US market but across the globe. The common denominator is an expectation of underperformance with a republican win.

The consensus is more or less a status quo with a democratic victory and large uncertain changes with the republic candidate in office. Honestly, I think it is too early to say what will be the policy changes as we hardly have any clue on specific policies apart from election promises. For example it is usually considered republican victory will be good for defense stocks. However if Mr Trump carries out his promise on cutting down on NATO, will that necessarily be the case? He promised to unwind trade agreements. But sure there will be something to replace it, will that be very different than the existing one, and will that have really any significant impact on trades, prices and job? Or may be you should buy Apple? - he is sure to threaten EU to withdraw the taxation case and make America great again! My personal take is Mr Trump promised things, but post election (if he wins) it will be hard to deliver on many of them except in a much run-down version. Hence in the base case, sooner than later, we focus back on things like earnings and economy and inflation once the initial reaction is over.

However, the market is close to pricing in a crash scenario for an outcome favoring the republican candidate. The VIX (and volatility of VIX) are tad shy of last August peaks. The implied skew and (near-month) implied correlation in S&P 500 are racing sky-wards (and interestingly with a quite flat vol convexity, i.e. high skew and very low smile). There is a high amount of uncertainty. 

And if you are planning to take decision (being flat is one of them), I have already written about how to generally think about positioning under uncertainties before. If you are a hedger, you know what you need to do - that's quite it. And if you are a speculator, after all the analyses and mumbo-jumbo, basically you have to choose a side (rally or sell-off) and stick to it. And the only things that matter are:

1. what is your expectation and how that looks from risk-reward already priced in the markets and 
2. How to optimize your responses in case you are wrong.

The first one is commonly understood. At present the markets are definitely pricing a large sell-off. This is in the background of decent economic news and improving global PMIs. Technically most markets across the globe has or on the verge of confirming a bearish signal (see chart above). The asymmetric pricing in the downside suggests there are large price move expected, but at the same time it makes the risk-reward unattractive compared to the upside. And based on the past history in S&P which has breached a technical support recently, the distribution of near term returns favors the upside statistically (albeit with a rather large uncertainty spread around that). The chart shows the historical price distribution after such technical breaches (categorized in to three types of technical formation - megaphone, triangle and channel, and whether the existing trend was ascending or descending, and also if the breach is of resistance (up) or support (down))¹. We are in a down breach within an ascending megaphone (see the figure above).

As far as the second point is concerned, if you are positioning for downside and it turns out wrong, your responses are limited if you assume it will be a relief rally, (not a sustained one). Alternatively, if you are positioning for the upside and if you are wrong, you will have plenty of opportunities to react. We will sure enter a period of high volatility and there will be plenty of trading opportunities.

So it appears purely based on the second criteria, a long risk positioning is preferred². Of course this assumes the outcomes are fairly priced from criteria one and you do not have any strong view on either outcome.

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Note: 1) This is based on systematic technical analysis, for details see here, for code page go here. You can select or de-select series on this interactive chart
2) this is not an investment or trading advice, do your own due diligence, form your own opinion. See the disclaimer page.

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.

Brexit: Getting the Probabilities Right

Brexit is the next big known unknown macro event this year. And probably you have already heard enough about it from a multitude of different sources.

And if you have, one thing you must have noticed. While the opinion polls are neck to neck mostly, the betting market pricing is quite different. For example the latest from Telegraph poll tracker puts it at 51% for "stay" and 49% for "exit". The best current offer for "stay" from the bookies is at $4/11$ - which prices a 73% probability of stay.

This has (and continues to) caused quite a bit of confusions among economists and strategists - cursory glances at the estimates and research notes doing the rounds will give you the idea. It seems the opinion polls and the betting market are not consistent with each other. And it seems most sell-sides (and some buy sides too) are siding with the tight calls from opinion poll.

This confusion is utterly wrong and in all likelihood, both results are right and support each other.

No fault of the economists and the strategists of course. There are many cases where we humans have a good intrinsic sense of chance - like sensing the movement in our peripheral vision to determine the probabilities if it is friend or foe, and converting that to a swift "stay calm" or a "fight-or-flight" decision. Unfortunately, we are not naturally evolved to understand how the probability works in opinion polls!

The opinion polls and the betting market present two connected, yet different, measures. The poll figures shows how many will, if the referendum is held right now, choose "stay" - for example. The betting market odds indirectly gives a probability of "stay". The connection between these two measures is subtle. To understand that, assume an extreme case where we have no undecided voters in the opinion polls. Also the voters are absolutely certain and will not change their mind come what may. If we have 51 to 49 in favor of "stay", what is the probability of a "stay" outcome?

It is 100%! An absolute certainty. We will have 51% in favor votes and 49% against. Since this outcome is guaranteed and $51 > 49$, the resulting win for the "stay" choice is guaranteed as well. This hold true for a 50.5 to 49.5 split. We can go even further. This apparent 50-50 results are actually far from 50-50.

Of course, in real life, there are three deviations from this scenario. Firstly, we are not polling the entire population, hence that 51-49 split is just an estimate from a smaller sample. Secondly, opinions can change on the actual day of voting. Thirdly we do have undecided voters who will eventually vote one way or the other, and decided voters who will end up missing it.

We have statistics as our tool to do our best with the first observation. The entire thing called opinion poll is asking some $n$ number of people about a binary choice ("stay" or "exit"). This is much like a bi-nomial trial. Let's assume the true fraction in the entire population that supports "stay" is $\Pi$. What we are trying to estimate is $Pr(\Pi > 0.5| \pi )$. Here $\pi = X/n$ is our estimate of the fraction that support the "stay" outcome, $X$ being the number votes in favor.

The rest is straightforward, although a bit mathematically involved. We assume prior probability distribution of $\Pi$ as $f_\Pi(\pi')$, carry out the opinion polls, and from the results compute the posterior probability distribution $f_\Pi(\pi)$, using Bayes theorem. Doing just that, we plot the probability of a "stay" outcome against the percentage point difference in the opinion polls.

As you can see, the probability of "stay" quickly converges to $0$ or $1$ as the lead diverges from $0$ on either side. Around $0$, it is highly non-linear. In fact for our extreme case above, it would just jump from impossible (probability = $0$), just below lead $0$ to probability of $1$ (complete certainty) slightly above that - a step function.

The current spread between "stay" and "exit" vote (51 to 49) reflects a probability of "stay" at $0.80$. Inversely, the betting market probability of $0.73$ indicates a lead of $+1.55$ priced in. So obviously both the betting markets and the opinion poll results are not very different. Also another very good crowd-based event forecasting source with expert-beating results projects the odds at 75%.

All of these are quite comparable. And is nowhere near the 40% to 50% odds thrown in most research notes. Take a note before you put your position.

What still can change from here? Well we still have the observations two and three from above - a change in mind for the voters, and swing of the undecided. They add to the uncertainties. On the other hand, we have assumed an unbiased prior - but most likely the people of the United Kingdom has a certain bias to stay to start with. That will add support to a "stay" outcome.

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Technical details: Here we have taken the YouGov January survey results - with a sample size of $n=1735$. Also we have assumed the prior distribution as conjugate beta (which leads to posterior beta distribution as well), with unbiased (non-informative) prior - beta distribution shape parameters as $\alpha=\beta=0.5$. The upper and lower bound is computed based on the standard error $\pm\frac{1}{\sqrt{n}}$. For more technical details, you can see here.

Lucky by Randomness: The Sage of Omaha

So Warrent Buffet says "Lucky to be American" in the latest Berkshire annual meet.

Indeed. Wonder what would value investing mean if he was born across the other pond, in Japan around the same time.

Systematic Strategies: HIgh Probability Trading Under Uncertainities

Stop-loss and take profit orders are powerful tools to manage an underlying trading view. And there are some misconceptions about them. Many people believe take-profit and stop-loss limits define the risk-reward ratio of a strategy. Far from it.

If a strategy has 100 on the upside as take-profit and 50 on the downside as stop-loss it is preposterous to estimate the risk-reward as 2:1. The most important input missing here are the probabilities of hitting the take-profit and stop-loss limits. For example if the probability of hitting the take profit in the trading horizon is 20% and hitting the stop-loss is 50% (i.e. the underlying can be within the range with a probability of 100% - 20% - 50% = 30%), then expected upside is 20%*100 = 20 and downside is 25. And the real risk-reward is 20:25 i.e. 4:5, far from the 2:1 before.

We can use this powerful tools and this concept of probabilities to devise profitable strategies under uncertainties. For example, suppose the underlying view is long an asset. Let's assume the asset follows a (geometric) Brownian motion (in real world) as below

dS/S = drift*dt + vol*dW

Where dt is differential of time, and dW is the standard Brownian Motion. So according to our view, here the drift is a positive value (the underlying view is long). One way to position for this is to go long and unwind at the end of the trading time horizon (let's say 1 day). The probability of our position being in profit can simply be calculated from a Black-Scholes like digital call option price.

However, another way is to put a take-profit order. This order gets executed whenever the underlying breaches the target from below. The probability of this execution is the probability of the underlying Brownian motion breaching the barrier any time up to our trading horizon. There are standard approximate solutions to this problem. For example, see here (opens PDF). As an example I have plotted the ratio of this probability to the original Digital probability (i.e. being in the money at the end of trading horizon, irrespective of what happens in between) for a range of volatility and Sharpe ratios (ratio of the drift term above to volatility) in the chart below.

As you can see, the probabilities of hitting our profit target intraday is much higher than being in the money end of the day. Additionally, higher the uncertainties about the underlying trend (lower the Sharpe) this ratio works better in out favor. This shows clearly that if your view is not with high conviction, it is better to use a take-profit target than a buy-and-hold approach.

This gives rise to an interesting way to implement a short-dated view using options. The strategy is to buy an option (say a ATM call option to implement a long view on the underlying) and put a close take-profit target, and a wide stop-loss. The worst-case loss is the option premium. And we will hit out target with 1.2x to 2x more frequently, depending on the strength of the trend. By design it may appear we have a skewed risk to reward ratio here. But given the concept of probabilities (than just the width of the stops and targets) and the convexity of a long option position this is much less risky than it appears. None-the-less it is a skewed strategy, with high probabilities of hitting our profit targets regularly, and occasional large losses.

The chart above shows the expected profit ranges for such a strategy on the NIFTY index (the flagship index of National Stock Exchange, India). The Spot level assumed to be 8500. The profit-target is 1x the daily vol move and the stops are 2x of that. (Note this is approximated, i.e. I ignored the order of stop-loss and target hitting, which is valid for large enough stops). As you can see if you are somewhat certain about the direction of the underlying trend, this is quite profitable (the break-even here is daily trend is 40% or more of the daily vol) under high vol. The profit distribution as below (click to enlarge)

This ignores two realities -1) the convexity of the option position, which goes in our favor and 2) the jumps in stock moves (price moves are rarely Brownian), which goes against us (the probabilities should get affected symmetrically, but the size of loss makes it asymmetric).

Those interested in the underlying codes (in R) can find it here.

Probability Zombie Hunting: Mark Gilbert Edition

There are many ways to prognosticate what will the markets do

Getting the maths wrong is one of them. A bit lacking in intellectual support, but in any case as good as any other ways if you believe you cannot forecast the markets in the first place!

Here is an example. BTW, I have already written more on the underlying issue here

Unfortunately, Scotland has no bonds (or currency) of its own by which we might more clearly gauge the attitude of investors to the outlook for the country itself. Perhaps, then, the best guide is to be found among the bookmakers, still unanimous in backing the view that Scotland will reject autonomy, despite the recent YouGov poll that put the Yes campaign ahead for the first time. Betting five pounds on Scotland saying "no" will win you just two pounds plus your stake returned; a "yes" vote offers a potential profit of 9.38 pounds.

So on the basis that the house never loses, you'd back Scotland to stay in the union -- and you might also be tempted to buy pounds.

Well. Yes, the house never loses. That means they win if you get it wrong. Or if you get it right. And that is precisely why it gives no indication what so ever which outcome you should bet on! So you CANNOT ever bet on the "basis of the house never loses"!

Just to refresh your maths in case you need it (the author does, definitely!), The above odds means a (5/7) 71% probability of "no" and (5/14.38) 35% probability of "yes". The house always wins because the probability adds up to 106%, instead of fair 100%. So the house have a 6% advantage

All he probably meant that stick with "no", as "no" is priced in with a higher probability. In fact, that is also quite a useless investment thesis. It may have a higher probability, but it is compensated by a lower pay off as well. So your expected win (probability times the winning amount) should be same if the odds are fair (i.e. they add up to 100%). And since they are not in this case, actually the expected win is higher for betting on "yes"

And that is exactly the opposite of what the Mr Gilbert suggests!