Tuesday, 1 August 2006

Mathematical Finance as a Historical Subject

Reading papers outside your discipline is good, and I've just found a corker, The Big, Bad Wolf and the Rational Market: Portfolio Insurance, the 1987 Crash and the Performativity of Economics by Donald MacKenzie in the Sociology Department at Edinburgh. He makes several interesting points.

Firstly he suggests treating finance as (a) historically variable in its verisimilitude; (b) dependent for its verisimilitude on institutional and technological conditions; and (c) implicitly a historical project, incorporated into efforts to transform its object of study, the financial markets. No surprises so far, but rather nicely put. MacKenzie then introduces the term 'performative' for utterances that make themselves true, giving as examples the naming of a ship or the Black Scholes theory of option pricing. (Of course before Black Scholes, the warrant markets traded rather far from Black Scholes prices, a fact that cost Black, Scholes and Merton rather a lot of money. It was only once their theory became established that the markets came in line, modulo the smile.)

Then MacKenzie goes on to point out that the 1989 crash fits rather poorly within any of the standard Brownian motion based models of asset price dynamics, but it does mirror somewhat startlingly the initial falls of the Dow Crash of 1929.

Personally I think MacKenzie over emphasises the potential role of portfolio insurance in the Black Monday crash. He suggests that once markets were close to or beyond the protection bounds of CPPI strategies being executed by market participants, further falls were inevitable. While this is clearly true, it remains unclear if there was sufficient activity in this area to explain much of the Black Monday fall, at least compared with the activities of the large stock funds, investment managers (many of whom were aware of the comparison between the run up to Black Monday and the run up to the 1929 events before the fact), and indeed anyone else with a stop loss.

MacKenzie quotes Leland, one of the fathers of portfolio insurance, on the topic of information. Leland contents that if investors had known how much of the Black Monday selling was caused by programme selling, that is automatic selling under CPPI or options hedging, market participants would have been reassured and the fall would not have been so severe as 'judgement' investors would have been more willing to buy into the fall. This is an interesting claim: a devious experiment would be needed to test it, but the results would be fascinating.

Finally, MacKenzie comments on the market's performativity. To summarise a rather complex conclusion in a few sentences, he suggests that banks have an interest in making the markets as like the model as possible and that this process is dangerous in that it gives confidence in the stability of model applicability over time that may not be justified. It is almost as if we are saying 'the model works unless there are big jumps', then hedging so that big jumps are less likely but, if they happen, they will become bigger. Mathematical Finance is performative around the money, then, and antiperformative in the wings. Scarey.

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