Wednesday, December 30, 2009

The real problem with the Fed's Exit

Assume the fincance market makes Kelly trades. The formula:

W(p) is maximum when p * log(b) - H(p) is minimum, the betting proportion has maximum entropy.

The p is the proportion of wealth, W, to bet, b the probability that the Fed will exit in the next trade. H(p) is the entropy of the bets.

Right now the Fed is making noises about an exit strategy. The effect of the noises is reduce our knowledge of b, hence to slow down the Kelly Trades, which are, I think, just the way we do Carry Trades. A Carry trade is a bet that one can use cheap money and hold decorrelated assets during the betting period.

So Betters bet a proportion of wealth on the probability that one year rates rise, they bet every quarter. But information theory says that b will rapidly converge to .5. QM say b will converge to within an snr quanta of .5

The mechanism of this convergence is the growing economies of scale for the carry trade. The carry trade subdivides the problem into a bet that rates hold for four quarters, that is it begins to bet Kelly trades farther into the future, and an efficient, multi-stage market emerges, the production network. The Fed is facing a more precise market and discovers its inability to quantify its own future. b goes to .5 on the noise. The result is a return to the nominal aggregate noise floor.

Summary:

The Fed is competing against a Carry structure in the process of computing a more accurate future for the Carry trade. When the Fed loses control when it is less accurate than the Carry Trade market.

How to test this theory? Well, the TIPs market represents the closest we have to a retail inflation futures. Look to see how responsive is TIPS to Fed announcements. If TIPS is the more stable, then the Fed has lost control?


Kelly, A New Interpretation of Information Rate

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