Economics and similar, for the sleep-deprived

Wednesday, February 18, 2009

 
Capital Decimation Partners: slight return

OK, wife and kids are off at the seaside, a couple of gin and tonics in the back of the neck … let's talk three thousand words of medium to high-end financial economics. General interest readers are excused this one, although I don't intend to bring out the "Math Cock" (a mythical organ possessed by graduates of Warwick University and Imperial College, which is ritually drawn out and slapped on the table whenever they appear to be losing an argument about economics) too much and it ought to be possible to follow along with a bit of help from google. Read the footnotes last rather than as you go along, since most of them are tangentially related rants on personal hobby horses of modern finance.

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Basically, hedge fund performance measurement, and specifically the question of how to distinguish between genuine investment talent[1] on the one hand, and put-writing strategies (the familiar "Capital Decimation Partners") on the other. How would I go about choosing a hedge fund (specifically, let's make this concrete and say a long/short equities fund; presume that all references to "hedge fund" in this post are so), if I were rich enough to be in the position to choose? Difficult question; let's start with a few building blocks.

Building block 1: Capital Decimation Partners. Basically, Andrew Lo suggested, in a couple of papers and in his book on hedge funds, that one could match up a few of the stylised facts about hedge fund performance over the last ten years, to an unsophisticated strategy of writing puts on the SP500 index, thus showing that in short runs of data which did not contain a major market crash, it was impossible to distinguish between genuine talent, and simply being structurally short volatility and creating a position that earned seemingly abnormal returns in low-volatility periods, which were merely the reward for bearing the risk of crashes. This view got picked up by the Taleb fans and index fund cultists, who are always on the lookout for another way of arguing that people richer than themselves are charlatans and dupes, without necessarily much understanding of Lo's actual point (as discussed in the linked post above). One thing that's in Lo's book which people don't talk about anything like as much is the fact that he also gave the example of "Capital Decimation Partners II", which didn't simply write puts; it carried out a trading strategy in cash equities which replicated the payoffs from a written put, using the Black-Scholes equation to act as if it were delta-hedging a long put position. This brings me on to:

Building block 2: Options are financial services. Another thing falling into the category "jolly useful things I learned at London Business School". Anthony Neuberger's options & futures class drummed this into you - the derivatives market is essentially a financial services market, where you hire someone else to carry out a trading strategy on your behalf, on the assumption that they have economies of scale in doing so. This is most obvious in the case of portfolio insurance, where one literally hires a trading firm to execute what amounts to a massive stop-loss order, but it's of utterly general application; every derivatives payoff structure defines a trading strategy. Often if you're confused by a security, it's worth thinking about what kind of trades you would execute if you were replicating it.

So, as I said, if you think about the trades you'd execute if you were replicating a call option, it's easy to see what you're doing - you're selling securities for cash as the price falls (eventually going to 100% cash as time goes on if the option is out of the money), and buying securities as the price rises. In other words, what you're doing is similar to the execution of a stop-loss - you are "cutting your losses and letting your winnings ride". On the other hand, if you think about how you'd replicate a written put (or the Capital Decimation Partners II trading strategy, same thing), you would sell securities as the price rose, and buy when the price fell. You would be "buying dips and selling rallies".

The beginnings of a clue: If we think about the options in payoff terms, a long call option is equivalent to buying insurance, and a written put is equivalent to selling insurance. If we think about them in trading terms, however, a long call is like a stop-loss, while a short put is like … well, who in the market is a structural buyer when the world is selling, and a structural seller when the world is buying? Answer - among other people, the market-maker, specialist or equivalent liquidity provider. Someone who's providing liquidity to the market more or less has to do this, or they're not providing liquidity. And this gives the first hint of a clue, because it does suggest that not all "Capital Decimation Partners" are mugs, no matter what Nassim Nicholas Taleb thinks[2]. As anyone with even a passing knowledge of the market knows, specialists tend to make a ton. Which implies that if you have even quite a small information advantage (say, a specialist's knowledge of the order book), investment strategies which can be seen as having a high-level similarity to structural synthetic written puts, can be very good news indeed.

But, but but … a specialist doesn't just sit tight and provide liquidity! He uses his information! Yes, just a second, I need to do a little model first.

A little model. Say there's a security which has the true value V, and you (because you're that good) have a private and wholly reliable signal which tells you V with certainty. For the time being (and this is important), V is a constant. Say also that V trades in a market which is "efficient" in the Fisher Black sense - the price P fluctuates widely, but is always between 50% and 200% of the true value. You've got the job of trading V for Capital Augmentation Partners. And you're managing my money, so get it bloody right. What is any model of your optimal trading strategy going to be like?

Well, let's put the math cock back in the math pants, and just think about qualitatively how you're going to use your signal. Obviously you're going to be long when P/V <1 and short when P/V>1. And similarly, because you want to profit from volatility and deploy your capital optimally, your maximum long position will be achieved when P/V ~=0.5 and your maximum short position will be when P/V ~=2.

In other words, for an informed trader in a market where the true value of the security is reasonably stable, "buying dips and selling rallies" is almost always going to be the right thing to do. And this is the strategy which is bound to show up on any statistical test (including Lo's own proposed measure) as being equivalent to a put-writing strategy, or Capital Decimation Partners. The point that I want to make here is that if you've got a good actuarial estimate of the risks, writing insurance is the right thing to do - a good trader will very likely give a false positive on any measure which is meant to distinguish "genuine" talent from "mere" put-writing.

So what happens if fair value is variable. The thing that will sort the sheep from the goats, however, is what happens when V changes. Say there's a sudden stepwise change in V, so that it moves to a tenth of its previous value. On reasonable assumptions about the stochastic process for P, P is going to start moving downwards. But this time, you really don't want to be buying this dip, because it's not a "dip", it's a shift down to V'=0.1V, and if you follow your old strategy of going all in at 0.5V, then you're going to lose your shirt. And now I can cash the cheque I wrote a couple of paragraphs ago in talking about market-makers - the skill of running a specialist book is entirely in realising when "normal" provision of liquidity has become a dangerous game, and when the price needs to be marked up or down to a new level.

In fact, this isn't just the skill of being a market-maker - it's a hell of a lot of the whole skill of investing. The technical analysts will tell you, if you stop sneering and making hilarious jokes about astrology long enough to let them, that securities tend to spend about two-thirds of their time in trading ranges and one-third of their time in trends. Which would be consistent with a wide variety of sensible market microstructure models under which true value changed slowly, and as a result to specific and infrequent events (say, because it was determined by economic processes which shifted regimes as a result of historic, nonergodic processes). Investment talent of the sort that you want to look for in a hedge fund manager, resides in being able to know, ahead of the rest of the market, when underlying value is going to change, and to adapt trading structure accordingly.

A somewhat overcomplicated estimator for talent. So basically, a really excellent fund manager would have the characteristic that changes in his trading strategy anticipated changes in V. Investment in this view is a problem of forecasting structural breaks or regime changes. So if I had unlimited resources of data and mathematical ability, I would take data on securities prices, and on the trading positions of the fund under analysis. I would use a STOPBREAK (stochastic permanent breaks) model to identify regime changes in both, giving me a vector of dated regime-changes in the equity returns series, and a vector of dated regime-changes in the trading strategy series. I'd then use the normal toolkit to estimate the lead-lag relationship between the two series. Obviously a lead of the trading strategy series over the returns breaks series would be ideal, but a short lag would also be worth knowing about - while the man who can tell you when a big change is coming is a gem of great price to be treasured, the man who can spot when something's going wrong and stop losing, is also a highly useful lad to have around, and perhaps a bit more realistic to hope for[3]. So that's what I'd do if I were in the manager research game.

A less complicated and perhaps more sensible estimator: This is a bit of a sledgehammer to crack a nut approach though. I would guess (and could probably prove if I had three weeks spare time and masochism to devote to relearning a load of stochastic processes again) that a reasonably good robust non-parametric estimator for the lead-lag based talent measure suggested above, would be the number of >10% drawdowns, which is a statistic that lots of funds will put in their risk disclosures anyway. I'd specifically divide the average return per year, by the average number of drawdowns per year, and give myself a measure of how much return these guys made per "mistake". I'd then take a look at >20% drawdowns and see whether they were prone to making big mistakes. [5]

So there you go. I almost feel like a disquisition on David Hume's theory of causation now (in that the skill I'm talking about is that of identifying when a past regularity is no longer reliable), but this is almost certainly the gin talking. Be careful out there people - whether you're trading stocks or fighting land wars in Asia, the race may be to the swift, the battle to the strong, but long term survival goes to he who identifies stop loss points ahead of time and sticks to them.

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[1] I am using "investment talent" here in contexts where lots of people say "alpha". "Alpha" is a technical financial term for "I don't know what I'm talking about, even if I do have a CFA after my name". People who believe in the literal truth of the one-period CAPM can convince themselves that investment outperformance of a risk-adjusted index is generated by a linear factor which enters into the securities market equation as a simple premium to the market-beta rate of return. This is a false belief which is frighteningly resistant to evidence. Alpha doesn't work as a measure of market-timing ability, for example - someone whose portfolio has a beta of 1 when the market's going up and 0 when it's going down, can in some circumstances be estimated as having negative alpha (basically if he uses his magical abilities to achieve a market rate of return with lower volatility, which is quite plausible, he will show up as having subpar alpha because of his seemingly high correlation with the market - he only makes money when everyone is making money, and the typical CAPM equation won't give him enough credit for not losing money when everyone else does). The use of "alpha" to mean "outperformance", like the use of "tail events to mean "crashes", is a piece of jargon in the most pernicious sense possible - it gives the impression of understanding things at a deeper level, while actually committing you to a theory which is badly misleading about important cases. "Beta" as a measure of market factor risk is not on much better ground.

[2] Taleb tends to get cross with people who point out that in general, buyers of options lose money and sellers of options make money. At various points in "Fooled By Randomness" (less so in "The Black Swan"), he gets quite close to arguing that in sufficiently long runs of data, the opposite will be the case (and as I noted in my first CDP post, this is trivially true as a statement of actuarial science, because if long call/short put is equivalent to buyer/writer of insurance, and it is, then since the probability of ruin for an insurer with finite capital is 1, in finite time, there is a sense in which in the long run, all the capital has to go from the sellers to the buyers of insurance. But this is self-evidently not an economically interesting sense). In the real world, though, a specialist on the NYSE, particularly under the old regulations, was a structural writer of put options with a small but significant information advantage, and the position of NYSE specialist was a notoriously lucrative one, handed down from father to son like a taxi badge.

[3] Perhaps at this point one might wonder if there is a short way here - to gain the advantages of the synthetic put strategy, while building in a rigorous discipline of using stop-loss orders. An attractive thought, but I think no dice. A "buy dips and sell rallies" strategy combined with a stop-loss discipline - well, convert it back into options language. Here you'd have a written put, combined with a bought put at a lower strike price. In other words, what I would call a "collar" and Bernard Madoff apparently called "a split-strike conversion strategy"[4]. What you've got here is a strategy with the intrinsic leverage of the put-writing strategy, but limited downside in the event of a real crash, and in exchange for that downside protection, you've effectively paid a fixed cost element equal to the call premium. So you've got financial leverage and a fixed cost, which suggests that if you're doing this, you had better be really sure that you're right in your estimate of V, and in your estimate of the volatility of P (which would determine the level of P/V at which you placed your stop loss). If you get this last parameter right, you've achieved what you wanted to, but if you get it wrong, then you're going to get repeatedly stopped out, which will kill your overall returns.

[4] Oh yes indeed. As I note above, trading collars really does separate the men from the boys - it's probably more or less equivalent to the actual behaviour of a skilled specialist, and notoriously it's a very leveraged market; yet another way to look at it is that you're trading calls, which is intrinsically leveraged, but doing so for less premium because of the options you're writing, which allows you to achieve even more leverage. If you've got talent trading collars, you're going to make a hell of a lot of money, but if you haven't, you're gonna find out really fast. This, by the way, is how Harry Markopolos really spotted that Madoff was a con artist from the returns series - it's a bit unclear in his SEC testimony but basically the Madoff fund returns looked nothing like a collars-trading set of returns - you can make good money trading collars, but you can't make it in the smooth way that Madoff claimed.

[5] I would then, having done this, give up on the temptation to create single indicators. The approach I've outlined here would, I think, do pretty well in measuring the performance of long/short, high turnover funds. But it would keep you out of more or less every biotech fund in the world, for example - people who are shooting for ten-baggers in smallcap tech stocks are going to have to tolerate lots of drawdowns on the way up of the sort that I would view as a "mistake" if it happened in the context of an active trading strategy. And although I haven't checked, I would guess that people who did in fact generate their outperformance through something similar to Sharpe's alpha (picking securities with a single, constant, small premium to the market return), would show up as having so-so performance on this screen. There is, basically, no substitute for understanding what you're talking about in both a statistical and a fundamental sense, which was the subject of my Christmas address.
49 comments this item posted by the management 2/18/2009 03:56:00 PM