you, hf-trading

There seems to be a developing meme out there suggesting that algorithmic-, and in particular high-frequency, trading is some kind of gold-rush route to easy money which brings to mind…

…this revision of a paper I’d read previously: “Statistical Arbitrage in the US Equities Market” by Avellaneda and Lee.   It’s a detailed and thoroughly worked (and now re-worked) paper illustrating the development and analysis of a US equity stat-arb strategy based on Principal Component Analysis (PCA) and then revised to use ETFs.

I came across this paper as I have still never used PCA in any of my own strategy development work and read Carol Alexander’s excellent Market Models over my summer vacation with an eye towards giving a PCA hedging model a spin in the near-term. Thus, I wanted another look at this paper as a reference point.  Although it’s an excellent paper, I’m not going to urge you to go out and read it immediately unless you have a reasonably pressing practical interest.  Instead, I find it interesting largely because of one of its authors – Professor Avellaneda – and its conclusions in the form of its strategies’ performance.

I’ve seen Prof Avellaneda speak a number of times at a variety of quant meetups organized by the relevant Columbia/NYU financial engineering depts.  His paper reminds me that at least once during my noisome adolescent years, my father intoned darkly that:

the streets are littered with brilliant minds

Implying that any wits I may believe myself to possess wouldn’t by themselves be worth much in life and that I’d need to bring actual tools to the task of solving problems if I wanted to address interesting ones.  Having seen Mr Avellaneda speak, I’m confident that at my peak, my “processor” was never as fast as his.  Much worse, there is no comparison between the tools he can level at a problem compared to me – he’s on an entirely different playing field so far as concrete mathematical/analytical capabilities go.  That’s why I go see him speak and read his papers.

Thus, the results of Avellaneda and Lee’s work are particularly interesting to me as they’re really pretty dull: something like a Sharpe of .9 and degrading briskly.  Now, you don’t expect people to be providing detailed recipes to wildly profitable strategies, and this result isn’t bad, particularly given that they’re describing strategies which likely have significant capacity.  Still, it illustrates that very smart people working with sophisticated mathematical tools even over extended periods are still operating under noteworthy constraints.  Perhaps also: ideas are relatively easy – examining them in the requisite detail is difficult and time consuming, even for (particularly for?) people with the most finely honed toolsets…

I frequently have friends or colleagues who will observe that if you “just write a strategy that foos when bar but yaddas when baz… you should surely make money.”  Maybe.  But the reality is that just putting together the strategy and working through it takes significant time for anything but the simplest strategies.  Once you add genuine complexity to a strategy, you can spend enormous time tuning it.

This, in turn, poses a dilemma I encounter frequently and honestly don’t have a great answer for:

how to find the balance between continuing development on a known good strategy and initiating the development and analysis of unrelated and novel strategies?

the back of the envelope as canvas

This next (de-)reference isn’t directly pertinent to algo trading, but the lessons learned by building BIG distributed systems can surely be applied elsewhere.  And they’re just plain fascinating.

Google’s Jeff Dean gave a recent talk entitled “Designs, Lessons and Advice from Building Large Distributed Systems” at the Large Scale Distributed Systems and Middleware (somehow “LADIS”) workshop and the slides are here.   Go read them.

If bald exhortation doesn’t convince you maybe slide 24 will:

or perhaps what he does with these baseline numbers in slide 27 will pique your interest:

back of the envelope as art form

One that made me (a serial prototype-builder) cringe:

Important skill: ability to estimate performance of a system design
– without actually having to build it!

Ouch.

maybe it is easy after all

Of course, if you’ve studied Avellaneda & Lee’s paper and it held no challenges or surprises and you’ve reviewed Mr Dean’s presentation and it’s old hat to you, too…

During some recent travels, I read William Poundstone’s ramblingly entertaining Fortune’s Formula.  It had been sitting on my shelf after I’d originally gotten it, perused it and offhandedly discarded it as yet another of these science-is-fun-and-full-of-wacky-characters books for the butch humanities student.  My initial impression was a bit harsh as the book proved entertaining and covered a lot of ground including significant coverage of Ed Thorp and his stat arb alchemy (see here for his own papers on the topic).

One of the more compelling segments of the book relates Claude Shannon’s demon which is a nice thought-experiment / trading-strategy which illustrates the tractability of the problem of trading on a random walk market with fixed properties.  I wrote the above applet to explore the impacts of applying friction and otherwise modifying the behaviors of the market and the demon.

The original demon posited a world with no friction in which the market contains one instrument which doubled or halved in value each day.  Shannon’s demon looks to take advantage of this volatility by maintaining a portfolio which was rebalanced each day to ensure a 50/50 split between cash and the market.  The applet implements a very simple monte-carlo test-bed for Shannon’s Demon.  You can configure the demon and the marketplace along a variety of parameters, and then run many instances of the demon, each on its own self-contained random-walk market.

Although Shannon’s demon is a highly “stylized” case in the sense that it operates on a very synthetic, unrealistic and favorable formulation of a random-walk marketplace, it has spawned a great deal of interest and serious research.

Most of all, it’s a revealing illustration of the kind of reasoning one must embrace in order to address stat arb strategy development.  Enjoy.

—
Updated: March 4th – made price axis logarithmic to better reveal mc paths.

I came across this gem of a quote in a comment on the big picture and it reminded me, somewhat circuitously, of another one of the things I view as axiomatic about algorithmic trading.

In The Alchemy of Finance, George Soros observed that one of his advantages as a trader was that while he held beliefs strongly, he was also capable of abandoning or even reversing them quickly as conditions evolved.  An algorithmic trader needs something like this but more so – an automated trader is best served free of opinions entirely.

I think this is why the sunken ship quote made me think of this.  While charts are an effective means of quickly communicating potentially a great deal of information to a human viewer, the cult of chart technicians and the endless supply of books, lecture series and training materials they actually make their money on might convince you that you can form your opinions based on chart patterns…

And so you can!  Whether this is a good way to trade is another matter entirely.  For the “mouse trader,” I suppose it might be, and I certainly won’t argue it one way or the other.

But for an algorithmic trader, the only kind of opinion that matters isn’t about a particular chart formation or even fundamental factors driving a particular market.  The only opinion that matters for an algo trader is the firm conviction in the deployed algorithm and the methodology employed to develop it.

A few years ago a study (discussed here, actual study here) revealed that brain damage which limited emotive function seemed to correlate positively with investment performance.  From the article:

“Antoine Bechara, an associate Professor of Neurology at Iowa, suggested that successful investors in the stock market might plausibly be called ‘functional psychopaths’.”

Charming, right?

We have an out: we don’t have to be the “functional psychopaths,” we just have to write them and then have the self-control to let them do their thing.  One of the big benefits of algorithmic trading is that fear and greed are taken right out of the equation.  Unless, of course, the person operating the algos loses her mettle mid-stream and shuts things off precipitously or starts ill-advisedly twisting at the knobs on the side of the box…

The only opinion relevant for us is the one that fortifies our belief in the system in the face of whatever the markets happen to throw at it.

I might have a view about, say, crude based on some sort of fundamental or geopolitical perspective, but it will affect my trading precisely as much as my opinions about Eli vs. Payton Manning – not at all!

]]> http://www.puppetmastertrading.com/blog/2008/11/12/every-sunken-ships-got-a-room-full-of-charts/feed/ 1 http://www.puppetmastertrading.com/blog/2008/10/06/entrepreneurs-inspiration/ http://www.puppetmastertrading.com/blog/2008/10/06/entrepreneurs-inspiration/#comments Mon, 06 Oct 2008 17:44:25 +0000 tito http://www.puppetmastertrading.com/blog-test/?p=95

I was looking for a couple of books on amazon today and came across this offering of a hoodie (pictured above) which reads: “I helped bailout the banking system and all I got was this lousy tee shirt!” which I’d (admittedly more rancorously) suggested only a few days ago…

Just as curious, the search that revealed this gem was meant to find books similar to one I’ve recently read by Dr. Andrew Lo, “Hedge Funds: an Analytic Perspective” (pictured left) and which, like all of his work, I found interesting and informative. I’m not sure exactly how Amazon matched these two products together, but it’s funny to imagine that the same people buying the one are also buying the other!

Professor DeLong points out that Emanuel Derman has begun posting lecture notes to classes he’s teaching as part of the Columbia Master’s of Financial Engineering. If you’re even remotely interested in financial engineering or algorithmic trading, then you should read Dr. Derman’s engrossing book “My Life as a Quant” as it gives a unique and personal perspective on the explosion of engineering as a discipline within finance. I haven’t studied his notes carefully yet but a cursory examination suggests they look very worthwhile.

I recently found in my inbox an invitation to study for a Certificate in Quantitative Finance which is, I’m sure, a great program. But it’s pretty pricey and any quant should be aware of costs! Laughing in the dark might be a reasonable alternative to shelling out for a more structured offering…

The best way to reason about a trading strategy’s performance, that is valuing it, is as an option.

Or perhaps as a collection or portfolio of them.

I have to assume that people reading this have a working idea of what an option is, so I’m not going to provide definitions that can be readily found elsewhere. I will note that my favorite book on the trading of options is by Allen Jan Baird.

Let’s consider the three illustrative trading strategies we’ve looked at up until now. The trend-following strategy suffered many little losses and then enjoyed a big win. Sounds like buying options. The mean-reverting strategy made lots of little profits and then risked getting clobbered with a big loss. Sounds like someone who’s writing options. And the first strategy we looked at, the morning range breakout, had a payoff which looked like a long straddle or strangle where the break-evens were near the observed high and lows for the session (where we set our entry stops).

Now, there’s obvious differences between the trading strategies’ payoff structures as compared to the similar options strategies. There’s no premium, for instance, and that’s clearly significant. The morning range breakout seems to exhibit a sort of knockout effect when a position has been entered but then the market reverses and you’re “knocked-out” of your position. You just take a loss and do not collect even if the market turns back in your direction. With a straddle you don’t have this behavior. There are differences and they are worth keeping in mind. But the reasons for viewing trading strategies as options portfolios are many and compelling.

The superficial reason, as I mentioned, is that the basic payout structures are potentially similar. The deep reason is that ultimately the problems are the same – how to value complex instruments with engineered payouts. And the pragmatic reason is that many many very smart people have applied their considerable brains and diverse skill-sets to advancing options pricing techniques. There’s also a great deal of high quality software available out there which can be used to adapt these time-proven techniques to your own algorithmic trading strategy valuations.

The techniques which we’ve seen up until now, back-testing and parameter optimization, are sort of weak cousins of a family of techniques long used for options pricing: Monte-Carlo (MC) methods. MC simulation can clearly be used to assess a trading strategy’s performance.

In subsequent posts, we’ll talk about some of the details of each of these techniques and about some of their respective trade-offs. That should keep my pump primed for a bit, but in the meanwhile I leave you with a parting inquiry: what other options pricing techniques might we apply to our algorithmic trading practices?

This is each of the individual *executions* which the strategies made. On average, including fees & commissions, they lost 7-odd dollars per round-turn. Not good, and this was the best of the group. Pretty conclusive to me.

(This problem which I’ve tried to illustrate here – the data mining problem – is nicely discussed in chapter six of David Aronson’s “Evidence-Based Technical Analysis.”)

The next pair of strategies are inspired by a number of papers written by Prof Peter Stone in which he discusses market-making strategies. In his usage, a strategy is a market maker if it always maintains a bid and an ask in the market. We’re going to take this idea and create two very simple strategies: one which is a market maker which hopes to profit on reversion and one which will instead look to profit on trends.

Non-predictive mean-reverting market maker

This strategy is roughly based on this paper; it will always maintain a limit bid and a limit ask below and above the market respectively. The spread is adjusted by an optimizable parameter set by a user or perhaps an optimizer or other program. In the version I’m considering, we have three parameters to consider: what to trade (contract), minimum spread in ticks (integer) and an opaque adjustment factor which is a double. The adjustment factor will basically skew the spread away from the market based on my position in order to limit my inventory. For example, if the market is trading at $100 and I place my bid at 99 and my ask at 101 and my bid gets filled, my subsequent bid might be 2 dollars away from the market. Presumably the market will be more likely to hit my ask and reduce my inventory. As my position grows, the adjuster will continue to move me further away from the market. So, if the market bounces around this strategy will do well. If instead, the market shoots off in one direction or the other, then this strategy will get hurt badly.

Non-predictive trend follower

This strategy is essentially the inverse of the mean-reverting market maker. At all times it maintains a buy-stop above the market and a sell-stop below the market. Its behavior is not surprisingly roughly the mirror image of the other strategy – if the market shoots off in some direction, we profit and if it bounces aimlessly then we get hurt.

Oddments

A few final observations about these strategies before I conclude this post.. The first is their non-predictive nature. They are non-predictive in the sense that there is no predictive model underlying their “decision-making” such as it is. All the same, as we’ll see, they both exhibit noteworthy behavior in spite of their relatively dumb modus operandi.

Another thing worth noting is that in order to simulate the execution of these strategies, we need to have an exchange simulator which will support limit and stop orders. We do, so it’s not an issue, but there are reasonable concerns one should have when looking at the simulated results of such strategies. I’ll leave it at that for now, and in some later post I’ll discuss some of the implementation details of an exchange simulator and how a strategy developer can avoid pitfalls associated with simulated conditional orders.

Next time, we’ll look at some concrete results of these two strategies.

The rationale behind this strategy is based on the premise that the first n minutes of a trading session will frequently see the entire movement for the session and that thus breakouts from this range will prove to be decisive for the day. One can take this basic idea and create a bewildering array of strategies by adding pre-trade filters and all sorts of exits.

They all have the same basic feature: they’re losers.

We’ll stay simple and assume that our strategy will set stops at the observed max & min of the session after n minutes of the session have passed. At the end of the day, we’ll exit any position the strategy has
initiated. And for maximal simplicity (and perhaps some psychological sense of “safety”) we’ll allow the stops to stay in the market all day so they act as stop-losses for each other when positions are entered.

Thus our strategy has two optimizable parameters: what to trade and when to set the stops. The first is of type contract and the second is an integer. Finally, we have some fixed parameters (i.e., it doesn’t make sense to try to optimize them) denoting when the session starts and how much money to risk or how many shares or contracts to trade.

If we do a parameter optimization on this strategy using, say, the s&p 500 components as values for the first parameter and setting the n breakout range to values { 20, 40, 60, 80 } we end up with 500 X 4 distinct strategies which each get back-tested to produce our results.

In the next post, we’ll review the results and consider how to reason about them.