There are no irrelevant alternatives
To a Bayesian, almost everything is informative and therefore relevant. This means that the Independence of Irrelevant Alternatives axiom is rarely applicable.
A good illustration is provided by the Joint Staff Report on “The U.S. Treasury Market on October 15, 2014”. On that day, in the narrow window between 9:33 and 9:45 a.m. ET, the benchmark 10-year US Treasury yield experienced a 16-basis-point drop and then rebounded to return to its previous level. The impact of apparently irrelevant alternatives is described in the Staff Report as follows:
Around 9:39 ET, the sudden visibility of certain sell limit orders in the futures market seemed to have coincided with the reversal in prices. Recall that only 10 levels of order prices above and below the best bid and ask price are visible to futures market participants. Around 9:39 ET, with prices still moving higher, a number of previously posted large sell orders suddenly became visible in the order book above the current 30-year futures price (as well as in smaller size in 10-year futures). The sudden visibility of these sell orders significantly shifted the visible order imbalance in that contract, and it coincided with the beginning of the reversal of its price (the top of the price spike). Most of these limit orders were not executed, as the price did not rise to their levels.
In other words, traders (and trading algorithms) saw some sell orders which were apparently irrelevant (nobody bought from these sellers at those prices), but this irrelevant alternative caused the traders to change their choice between two other alternatives. Consider a purely illustrative example: just before 9:39 am, traders faced the choice between buying a modest quantity at a price of say 130.05 and selling a modest quantity at a price of 129.95. They were choosing to buy at 130.05. At 9:39, they find that there is a new alternative: they can buy a larger quantity at a price of say 130.25. They do not choose this new alternative, but they change their earlier choice from buying at 130.05 to selling at 129.95. This is the behaviour that is ruled out by the axiom of the Independence of Irrelevant Alternatives.
But if one thinks about the matter carefully, there is nothing irrational about this behaviour at all. At 8:30 am, the market had seen the release of somewhat weaker-than-expected US retail sales data. Many traders interpreted this as a memo that the US economy was weak and needed low interest rates for a longer period. Since low interest rates imply higher bond prices, traders started buying bonds. At 9:39, they see large sell orders for the first time. They realize that many large investors did not receive this memo, or may be received a different memo. They think that their interpretation of the retail sales data might have been wrong and that they had possibly over reacted. They reverse the buying that they had done in the last few minutes.
In fact,the behaviour of the US Treasury markets on October 15 appears to me to be an instance of reasonably rational behaviour. Much of the action in those critical minutes was driven by algorithms which appear to have behaved rationally. With no adrenalin and testosterone flowing through their silicon brains, they could evaluate the new information in a rational Bayesian manner and quickly reverse course. The Staff Report says that human market makers stopped making markets, but the algorithms continued to provide liquidity and maintained an orderly market.
I expected the Staff Report to recommend that in the futures markets, the entire order book (and not just the best 10 levels) should be visible to all participants at all times. Given current computing power and communication bandwidth, there is no justification for sticking to this anachronistic practice of providing only limited information to the market. Surprisingly, the US authorities do not make this sensible recommendation because they fail to see the highly rational market response to newly visible orders. Perhaps their minds have been so conditioned by the Independence of Irrelevant Alternatives axiom, that they are blind to any other interpretation of the data. Axioms of rationality are very powerful even when they are wrong.
Posted at 5:55 pm IST on Sat, 25 Jul 2015 permanent link
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