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Guest Post: Playing with Tails: The Fundamental Problem of Tails
Submitted by JM
Playing with Tails: The Fundamental Problem of Tails
Does it generate higher returns to buy an equal weight mix of HiVol and XOver or to buy an equal weight mix of AA (and better) and distressed debt assuming equal roll and execution costs?
This is what I call “true barbells versus center bets”. This kind of questioning is relevant to just about any financial setting. Some examples:
Assume that yields of all maturities lie precisely on your interpolated yield curve. Does it generate higher returns to buy the mid-curve or reasonably equal weight positions in the wings?
Assuming equal thickness, does it generate higher returns to buy a mezzanine tranche or reasonably equal weight positions in senior and junior tranches?
I’m not sure that there is a correct answer here, but the question itself is the fundamental problem of playing with tails.
A capital structure barbell can be constructed using senior debt and equity versus mezzanine debt. An index barbell construction comes from large and small cap stocks versus a center bet of midcaps. One can argue that this one gives a clue to a possible global answer: over decades-long time lines, midcaps outperform large caps. The problem is that small caps haven’t been around that long at least in total return calculations.
For cross-asset trades like the latter it needs to be established that the different probability measures can be combined in such a way that they have a finite limit. To do this, formulate the problem as one of two probability measures P and Q on the state space (X,?). Let Pn be an increasing family of measurable finite partitions of X, i.e Pn = {A1, . . . ,An} with X = disjoint Aj ’s from 
and Pn+1 a finer partition than Pn. The Radon Nikodym derivative on Pn is defined by
Since P and Q are absolutely continuous with respect to P + Q, fn(x) has an almost sure limit with respect P and Q.
These questions are not easy to answer for several reasons. One is due to the idiosyncracies of different asset classes. Bond indexes have roll issues that make weight balancing costly, and securitizations have those “thickness” properties (among other factors). Another reason is that the future is unknown and we can only speak of expected return until they are realized by future marks.
Another relates to the statistical properties of the returns themselves. If the return distribution is i.i.d. and has no skew, then it would seem that moves in the extremes in excess of what is gained by the center position will cancel each other: the gains at one tail are equal and opposite to the losses of the other tail. We know if the returns are i.i.d. distributed, then a sample of sufficient size from either tail is normally distributed. But then again, that little tidbit from extreme value theory depends on statistical independence, which is not given in finance at all. Observed skewness ensures that one tail will not dominate the other, but returns are then contingent on picking the correct tail bet. It depends on the extent of skewness and the correctness of your positions whether you make more (or lose less) with a center bet.
Skewness
Tail risk thinking is often unhistorical thinking, trying to grasp potentialities that fall outside of past reference points. Sometimes it is very historical thinking but on such a timeline that you play the role of Cassandra. One may ultimately win big, but lose even more in the waiting. This asymmetry, or skewness, can kill because it is unstable. As evidence, I look at one of the bedrock financial spreads in the modern financial economy: the TED spread. TED is the spread of 3 month Eurodollars over 3 month treasury bills. I’ve never calculated a 90-day rolling skewness statistic for these purposes, so I am open different interpretations of the data presented.
There are a lot of reasons why the wait can be long. I prefer to fall back on the fact that life, the universe, and even bedrock measures of stability aren’t governed by an unchanging mechanism. It is always in motion.
Rethinking Tail Risk Funds
So I don’t have a good answer for the fundamental problem of tails. But there is an observed regularity in life reflected in the sayings “it is always darkest before dawn” and “where the danger grows, so grows the saving power” to quote Holderlin. And when no one can know the future, and the mechanism governing the future is unstable, anticipation of heightened risk premia warrants a barbell. In financial markets, extreme meltdowns are met by extreme policy reactions. Practically stated, it seems best to play center bets when others do not, and the tails when others do not. After markets price in heightened risk, actively manage the position by lowering exposure to the big gain leg. Move the proceeds to the center or double down on the other tail.
Perhaps this is how one should manage tails. Given that the known categories of human experience do not provide adequate predictions, luck dominates control. Nobody has it all figured out. Even when you think you have it all figured out, everything blows up in your face again. We'll never figure it all out. Nobody can predict the future, and we don't have good enough imaginations to dream up every contingency.
Such management is neglected. We do think about tails a lot—a whole zoology of black, grey, and paisley swans abound in financial thinking. But each one of these birds carries an unfortunate negative connotation that dwells solely on negative events and the negative tails. Black Swan has come to mean only bad stuff. And there is a whole mentality that developed with it.
At its worst, it becomes apocalyptic thinking, a kind of deterministic—bordering on fatalist—view that the future has been settled long ago according to some inexorable rules. History becomes the simple product of some unfolding plan, firmly determined since the beginning of time. Since history is just an observed mechanism set in motion, the desirable end point became no longer the triumph of good (reason, compassion, and courage) over evil (ignorance, inhumanity, and fear). Instead, this is replaced by a view of the world and everything in it as so hopelessly evil it all requires total replacement. There is no place for compassion, because nothing about immutable fate can be averted.
Everything is in flux and the future is not set in stone. What stands in contrast to Black Swan thinking is the mobility and fluidity of history. Luck, time and chance, dominates control. And luck can be both good and bad. Tail risk management is not about exclusively about preparing for ill times.
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Sarkozy, the warmonger :
http://www.guardian.co.uk/business/video/2011/dec/08/europe-risk-sarkozy...
Europe has never faced bigger risk of exploding, says SarkozyStinking bankster puppet, GO TO HELL.
Complacency abounds. Many of the same people who hate regulations, big government and politicians interfering with the markets are betting the same bureaucrats will save the day, come to the right decisions and execute the plan competently. Many of the current perma bulls are delusional hypocrites.
It's not an issue of complacency as much as agnosticism.
No state will fail to act to avert a banking crisis... they are in effect acting to avert a potential mortgage and/or business crisis.
Why do you think banks fail? They absorb the risk embedded in an economy.
So fucking what, they know who's in control. Get groped slave.
I love that the CIA is fomenting revolution with he drum beating free shit army OWS through the techniques developed by Optor! and co-opted the Pentagon to do the bidding of a banking cartel. It's as if Apollo himself is fucking us all in the ass.
You lost me at "For cross asset trades..."
Try reading from the end to the beginning. It's a favorite strategy of mine, and works here too. You can stop once you get to the 'Paisley Swans'.
::1/2 SARC::
In a casino, house always wins.
You started with, "I don't know". That is the beginning and key. Cause you don't.
Rather refreshing, I thought.
Agreed, most definitely.
It is alway darkest just before it goes all black.
So, taking a position on known unknowns carries an inordinate amount of risk.
Got it!
Think about it this way. You may have a good notion about the general idea of the shape of things, but nobody knows what the future brings. So how do you protect capital?
You can typically play it safe in something like IG credit and equities, or you can hold a barbell in gold and long bonds to get exposure to really wild extremes. I don't know which works better, but I think that after a market prices in the real possiblility of civilizational collapse, then positions that provide returns on these contingencies really have no place to go but down. So book some gains and invest more in the other tail, which is much, much cheaper now. Lots of variations on this, like selling gold and buying cocoa. Or selling treasuries into a "center position" like IG corporates and spoos.
More examples. You can take a kind of dispersion trade. Everybody hates Japanese equities, so look for something that really has value that is beaten down. Or look at one of the largest banks in Asia that has 10% core tier 1 capital ratio and trades at 4X earnings while everyone avoids banks.
What you need in a civilizational collapse isn't gold. Such a scenario negates both the need and use of investing. Income and cashflow from employment is what matters here as investment mean nothing. So there is no point in worrying about it.
Playing the long tail is hard. Amazon did it and suceeded but others did not. If there is a collapse ... long cigarettes and booze.
Thanks for the response. I did enjoy it, despite my snark.
"What you need in a civilizational collapse isn't gold. Such a scenario negates both the need and use of investing."
I don't believe we will have a civilizational collapse...monetary yes, the civilized world no. The thing that holds it together is trust & faith. Both are MIA. There's no sense (for me) in trading in things based on this when "it" is missing...the very foundation.
Gold and land and all things of value certain, did not destroy faith & trust. Evil people did. And all people are not evil.
So, no, civilization won't perish or collapse.
But the good among us need to do a little weeding, with all that entails ;-)
Please, stop thinking the markets are predictable with Pseudo mathematical BS crap. In other word this article is about... I dont really know anything and cant predict anything but will try anyway using math stuff i may or may not have learned in uni , that was made to explain nature and then i will devise a great trading system that will ultimately blowup because human nature is not reductible to an equation.
Tinker toys are in the corner. Enjoy!!
Good piece as usual from jm. Like the skew and rethinking tail risk parts especially.
Some traders have been playing the SPX smile vs VIX as a divergence-convergence play. Very recently the smile has been steep although still implying people aren't buying OTM options (as per the skew) nor ATM options (as per the VIX). This is the same divergence that was evident in July, and we all know what happened after...
Cassandra syndrome. Well put.
Awesome comment. Thx.
I have to agree with him about the apocalyptic thing. See a lot of that on here.
Remember, this is a trade. A bet that a few small to medium countries will default on their debt, leading to a recession and credit contraction.
But try not to be Herold Camping about it. I saw this in 1999 when I couldn't get my PM to take risk with great companies like DOW at $7. When he said "this could be the next Great Depression", that was the start of a 100% move in the market (500% for DOW).
To borrow from the article, miss the 1st and last 20% of a cycle. Be in cash and make your money betting with conviction in the 40%-80% range.
To give an example, no one called 1,600 to 666. But it wasn't too hard to see the upside go out of the market at 1,350-1,400 and go to cash. And when we recrossed that point on the way down it was pretty easy to ride to 900-1,000. At 666 it was pretty clear things were under priced again going to cash around 1,200.
But I'll gladly miss 900 to 700 to buy stuff again at 650.
Sounds like a Jack of all Trades? but King of None??
1. Buy Silver.. and sit on it.. 2. Buy Gold.. and sit on it as well. 3. Relax, its the Holidays!
or?? Buy more! its the Holidays!!
THE SCHWANTZ! THE SCHWANTZ!
What if the problem isn't just the tail...but the monster that is connected to it? Here...have a look:
http://www.youtube.com/watch?v=o7gFlSGXt_k&feature=player_detailpage
i mean talk about tail risk!
Forget about the tails and the phoney math. Just stay clear of the rigged casino. Oh wait... you can't because you play with other people's money -- got it. Stay away from them too. They're all just leaching off you and the math is there to baffle you with bullshit.
Forensic way of saying "not sure what to do here." The excerpted section below is where the insight is needed:
Bond indexes have roll issues that make weight balancing costly, and securitizations have those “thickness” properties (among other factors). Another reason is that the future is unknown and we can only speak of expected return until they are realized by future marks. Another relates to the statistical properties of the returns themselves. If the return distribution is i.i.d. and has no skew, then it would seem that moves in the extremes in excess of what is gained by the center position will cancel each other: the gains at one tail are equal and opposite to the losses of the other tail.
So it's costly to change positions (transaction fees, to over-simplify) which puts a premium on getting good bet placement to start with (nothing different than with other investment choices). Problem is, probability distributions are only really useful if the observations are produced from a space of consistent conditions (that is, the parameters are not so prone to arbitrary "dislocations" by outside events that the marginal changes are obscured).
For the long stretch of time when we trusted the markets, "events" that dislocate the space were relatively infrequent and transparent (so we could explain and/or control for them). The constant manipulation of the so-called "markets" is such that there is no longer enough integrity to trust the distributions, particularly at the tails where the responses are magnified. I'm generalizing, of course, but its very difficult now to filter out the residual effects of dislocation events - in no small part because manipulation/fraud purposefully binds supposed external "events" to an illusion of a "parametric response." So the math seems to give reasonable answers for ex ante decisions until the "returns are realized."
My cryptic two cents.
wavefront set singularities + wave function collapse
JM,
Not following you here. Are you offering how you account for interference in the state vector(s)? If so, I'm interested (genuinely) to understand how successful you've been ex ante.
Sorry, it's tough to know who is technically averse and who is not. My point is that people make investment decisions based on "fundamentals"-- balanace sheets, and also based on price action--what other people are doing. The act of observing what others are doing creates turbulence or something like quantum effects where dynamical laws (the wave function) collapses into something else. Intuitively, this is like the market seeing a hedge fund outperform and then spending time and effort in investing in the same positions. Once leverage gets involved, instability is inevitable.
My success? Well, I have an allocation for tails, but I think a lot of people are playing tails right now. Thus the market has overpriced tails. Practically speaking, I've had some good success and solid failure in the past. It's really just the old adage of buy cheap (who cares what it is) and sell rich (no emotions about it). Biggest practical difficulty is that being a knifecatcher isn't easy and I have fallen for some value traps. Also, leverage/liqudity issues create problems: the payoff has to wildly asymetric upside with clear limited downside to make it worth the effort.
Thanks, most helpful.
Get'n all mathematical and stuff is all fine and dandy, but the problem is the math can not be used to model the hidden criminal behavior, the sudden stampeed, nor the government intervention.
Even complex modeling for something practicle, like rocket science, needs careful control. Sure the equations can be created, tested, and used to design and operate a very complex and expensive machine, but the a-hole managers who know nothing of the limitations and do not care push the use of such models/machines outside the intended operating conditions - like the SST Challenger explosion.
So, why does Wall Streed pay rocket scientists to produce such complex mathematical models for finance? Exactly, simply to hide the fraud, that's all.
You can dream up all the financial equations your heart desires and it won't make any difference. It's what I call Non Computable trading, and the major problem is that you cannot control or know all the risks because nobody really knows what the "fundamentals" are. You may think you know some of them, but you will never know all of them. And there's the rub.
http://vegasxau.blogspot,com
"Move the proceeds to the center or double down on the other tail." Is this the Anti-Hope trading strategy? Great article.
You have a problem of classification on Mid-Cap, smallcaps and largecap. That is a falacy of grouping. The definition is erroneous and teh result will be too. Example: A small company has 50% of the world production of say cork stopper with a very vast array of clients, and limited debt. Is it a midcap, a small cap. Its economics are closer to one large cap even if it is a micro-cap. Why? Its end demand has littel variation, it dominates its industry, its clients have little bargaining power. It has economics more similar to a large cap than a micro-cap.
Thanks for the good insight.
An analogous example: in 1939, Dow Jones booted IBM from the large-cap Industrial Average and replaced it with AT&T -- a hugely popular stock for its high and stable dividend ... but in fact, a UTILITY, not an industrial issue. Indeed, AT&T was pulled OUT of the Dow Utility Average to make the substitution.
So for 45 more years until the AT&T divestiture, its stock was fundamentally misclassified by Dow Jones, depriving the Utility Average of what would have been its largest-cap member, while polluting the Industrials with a utility that had limited capital appreciation potential compared its other 29 industrial members.
Ultimately you have to apply your own judgment. Similar mislabeling and misclassifications are rampant today. They're just harder to spot in real time.