Economics and similar, for the sleep-deprived

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Update: seemingly not

Update: Oh yeah!

Friday, October 16, 2009

In Which, I disagree with Professor Krugman, but not about anything important

Warning: contains extensive digressive footnote

Via, I would submit that this is not really an awesome takedown - it's a pretty good polemic and thoroughly researched, but it's actually promoting what I consider to be a common but fairly unrealistic and naive view of the purpose of what forecasts are for.

In summary, my argument can be taken from the text of my Easter Sermon on the subject of hedge fund performance measurement:

"Obviously [evidence of genuine forecasting ability -dd] 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"[1]

I think we can all agree that it's useful to know whether the economy is currently in an expansion or a recession. There are different forms of economic behaviour appropriate to the two cases. We should also be able to agree that it's actually rather difficult to know whether the economy is currently in an expansion or a recession. Or rather (because even the dullest person can spot the way the wind's blowing at the height of a speculative mania or the depth of a slump) it's powerfully difficult to spot the moment when the economy moves from expansion to recession. The NBER Business Cycle Dating Committee will only tell you when it's much too late to save your money or your reputation (ask Donald Luskin).

Central banks, for whom this is basically the be-all and end-all (because monetary policy is one of those areas where different action is appropriate during recessions and expansions), spend a hell of a lot of time and effort on this question - the Bank of England used to have a large and well-staffed department of "Conjunctural Analysis", even tolerating the somewhat dubious word "Conjunctural" for the purpose (of or pertaining to the current conjuncture, allegedly, although don't mention it during tea at a lexicographer's). Forecasting the recent past is an honourable and sensible profession. Nigel Lawson, in his autobiography, suggested that it should be the main goal of the economics profession and there is a lot to what he says.

If you look at it in that context, the forecasting service described doesn't seem to me to have done all that badly at all. Shortly after the recession began, and well before the NBER spoke up, they made their recession call. They didn't call it too early (they aren't permabears who hang around making undated predictions of doom for years and then claim vindication, naming no names) and they didn't hang on to a "not necessarily a recession" call when it went wrong. That's about the best you can reasonably expect from an economic forecasting service. It is a bit of a shame that for purposes of marketing material, all these commercial forecasters have to pretend to be the Oracles of Delphi, but this is the world we live in.

[1] Related to this, a great big massive digression on the fascinating subject of correct use of forecast information, which has been taking up a percentage of my time this last month - People tend to hugely underestimate how small an informational "edge" can be, and still be amazingly useful. If, for example, you have a trader who every day has a 55% chance of making a 1% profit and a 45% change of making a 1% loss, then at the end of a year (250 trading days), he will on average make a return of around 28% with a standard deviation of 20% (Sharpe ratio 1.3), and will show a positive return over the year 93% of the time. That would be pretty amazing performance from a hedge fund - this guy would be very solidly top quintile on any measure you care to name. I have dressed this one up a bit by abusing the miracle of compound interest (the 'edge' in this example is made to look clearer by effectively compounding it 250 times), but the principle illustrated is a real one - important real-world applications can make use of forecasting edges much smaller than this guy's 5%[2].

And to return to my subject - "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". In order to explain what I mean by this, we need to think a bit more about the nature of interesting real-world forecasting problems. Consider what would happen if I took my imaginary trader above and imposed a 10% stop-loss discipline on him (ie, if at any point his total returns ytd were worse than -10%, I closed him down). Would this make the expected returns better, or worse?

The answer is, "worse" - in this case. It's worse because I set the example up so that a 10% loss isn't informative - every day the guy comes in and he either makes 1% or loses it. There's a drift over time because of his edge, but every day is a brand new draw from the probability distribution, and the fact that in some runs of history, the guy's portfolio has gone down from 100 to 90 half way through the year is not informative about whether it's going to go up or down from there (Markov process, yes, that's the phrase I'm looking for, christ dementia is clearly setting in this week)[2]. That's how I set the example up. If I had set it up differently, I could have made it the case that there was a lot of persistency in the returns series, in which case a stop-loss order would have been a very sensible thing to do indeed (imagine, say, a "Groundhog Day" version of the same spreadsheet, where the guy's daily trading returns from the first week are repeated again and again for the rest of the year - in that case, if he's had a bad first week, you obviously need to sack him right away). In general, this is a special case of the Kelly Criterion; the extent to which you should use stop-losses or similar discipline depends on the extent to which you believe that returns to date are informative about your betting edge.

Which case is relevant? Depends on what your forecasting problem is. Some things are like Markov processes and some things aren't. Is the stock market? Dunno. Anyway, what is this, a stock tips newsletter? I thought we were talking at a slightly higher level than that. This isn't about investment returns; it's just that, inevitably when you're talking about information theory or probability, you end up coming back to examples about betting or stock trading, because that's the clearest context in which to demonstrate that it matters not just whether you were right but by how much you were right.

[2] Alternative illustration - go to Las Vegas and see the kind of things you can build with the cash flow from a house edge of about 2%. This is also using the high-frequency compounding trick.

[3] Actually I knew it was a Markov process all along and in fac wrote and deleted a rather pissy digression about distinctions between "random walk", "Markov process", "unit root process" and other forecasting terms of art, mainly about the annoying tendency of financial economists to use the phrase "random walk" as if it meant "impossible to predict" (the definition of a Wiener process is that the increments are independent of each other, not that they're independent of everything else, you bastards[4]). This bit put in in order to avoid scaring off laymen by excessively aggressive wielding of the math cock.

[5] Oh god, I'm annoyed all over again. Look, consider the series X, which is a random walk. Consider the series Y such that Y(t) = X(t-1). Y is a random walk too isn't it? Isn't it? It is, isn't it? And X(t) is a perfect forecast of Y(t+1), isn't it? So "random walk" doesn't mean "unforecastable", does it? Why is this so fucking hard to understand???? Sorry, it's been a very long week.
5 comments this item posted by the management 10/16/2009 12:10:00 AM

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