Monday, 28 March 2011

The alchemical goose still lays golden eggs

I'm going to describe a a class of pure trend following system and look at the logical consequences.  This class may be a caricature of reality or perhaps it encompasses some real trend following models out there.   I don't need to commit to an opinion on this to make the point I want to make.  So let us assume, for the sake of argument, that there could exist pure (I call them 'fundamentalist' in the religious sense), robust trend following systems.  They are pure insofar as they make no reference to so-called fundamental data (company valuations, index valuations, commodity mechanisms of supply and demand, macro-economic circumstances, etc..)  They are robust insofar as the system can work across a range of markets and asset classes.

This must be nirvana for some purist trend-followers.  A universal golden egg machine.  One capable of becoming profitable in Eurodollar futures markets, currency markets, credit markets, volatility markets, equity markets.  It also satisfies the philosophical position of the putative evangelists for pure trend following.  These people have become convinced that no amount of fundamental data can improve trading returns.  In fact, some of them reckon even trying to include this information would result in poorer performance of their trading results.  To them, you can't time the market based on economic or valuation based research.  No matter how much of an expert you become in valuing banks, or tracking the availability of credit in the market, or deciphering the Fed, it is impossible to produce a system which can lead to trading signals which help you to time going long or short any market.

If such a class of system existed, which markets would you run them on, and when?  Well, I guess there's going to be some kind of diversification benefit, so you'd likely calculate the inter-market correlations and run the system in all available markets, sized up as a function of their correlation (i.e. a function of their diversification benefit).  And when?  Why not all they time.  Traders would then control their overall risk by a global risk appetite function, which results in individual positions being sized up or down across the whole set of markets.

So this system is 'always on', in all markets.  Of course, assuming you're a purist, it wouldn't make sense for you to increase the weight of any one market more than its diversification benefit would suggest.  In other words, if you thought we were in a potentially increasing inflationary environment, you would make no change.  Since trying to prejudice your weighting in the Eurodollar or the equity market is just delusional.  Likewise after a major natural disaster, there would be no increased weighting to the volatility markets.  And if you just discovered a major accounting black hole in an international conglomerate's balance sheet, it wouldn't be any use trying to weight this into your trading system.

Being this purist about the trading system requires you to admit that there's no better or worse time than any other time in the market.  And there's no reason to shift weightings between all the markets you're trading in.  You just sit there, making money out of the momentum effect.  If you need to make a better return, you can lever up.  If you want to be more cautious, you lever down.

You, the system writer, have no idea when or in which market the next profitable trend will develop.  Nor, for that matter, in which direction it'll develop.  That is, to all intents and purposes, purely random.  So if you had to switch the system off for a day, say for maintenance, or because you're going on holiday, there surely could be no compelling reason why to pick one day over the other, in the face of such a radically uncertain phenomenon as the timing and development of trends.

I am ignoring, for simplicity, other price action phenomena such as the January effect, the Weekend effect, and other such anomalies.  These do exist, but let us assume that all such effects have in time been arbitraged away, leaving only the momentum effect to support our trend following systems.

I may want to turn my system off as an alternative risk management strategy, deciding to trade only on 3 days per week.   Or I might be seriously ill and require Friday chemotherapy treatment.  Clearly I'm leaving some money on the table by doing this, but I might be happy to do this.  Indeed any period of time would a priori look just as good or just as bad a time to have the system running, in search of nascent trends.  In the long run, if I only turned the machine on one trading day out of five, then it wouldn't matter a jot how I chose that single trading day.  I could toss a coin.  It just needs to be on long enough to identify and exploit trends at whatever level (minute to year granularity) it sees fit.  So it perhaps couldn't be switched on and off instantaneously, since this would disrupt the exploitation of  trends, which last longer than an instant.  So let us add that as a constraint.

But another way of saying all this is that, regardless of any algorithm you use to determine when to switch the machine on and off (subject to the 'longer than an instant' constraint), no extra harm will be done to your profitability.  In other words, lets say you produce a random process which on average switches the machine off 10% of the time.  Now, all other ON/OFF algorithms which also power down for 10% of the time are just as good as each other; in fact can never be any worse than, the random switching algorithm.  Examples could be switching off based on some fundamentalist, economic, valuation based criterion.  Even if your fundamentalist criterion turned out to be illusory, then you could not make the system any worse when you compare it to a system which switched off randomly 10% of the time.

So you can't ruin the profitability of a 90% ON system by developing macro-economic or valuation switching rules.  Likewise with an N% ON system.  

In a world where the only arbitrage-resistant market anomaly is presumed to be the momentum effect, if you think you need the option to be out of the market for a period of time for a fundamentals-based reason, then provided you're happy to pay the the cost of the option to be out of the market for (100-N)% of the time, feel free to use that option for fundamentals based reasons.  The worst you can do is delude yourself. 

In a similar way, I could ignore any diversification benefit and assume my system could only run in one market  at a time, again chosen randomly.  With this baseline level of profitability (1 of M markets at a time), then you again have a free hand in selecting which market to go into based on fundamentals, and are guaranteed no worse profitability than the random 1 of M algorithm, providing you can 'correct' for differing inter-market volatility/beta levels to achieve a stable leverage target.

Penultimately, I could run a similar line of reasoning over whether to make my algorithm long biased or short biased.  We don't need further to assume that there an equal number of long vs short opportunities, by the way.  Just that we are switched ON only to the long side, or switched ON only to the short side,.  If this happens to result in us being switched OFF say 50% of the time (while, say, putative long opportunities are created and pass us by) and we remain ON for the remaining 50% of the time (to exploit the short opportunities), then provided we're happy to be off that fraction of the time, you have a free choice to interpolate fundamentalist reasoning safe in the knowledge you can't make it perform any worse.

Finally, for any given 'budget' as expressed as a percentage of the 'fully on' uptime, you can spend that budget   in any way that suits be it identifying which market to be in, which direction to be (long or short), and when to be on the sidelines completely.  

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