Leverage and Fat Tails – Nassim Taleb

June 15, 2012 § 1 Comment

English: This is a photograph from the assortm...

English: This is a photograph from the assortment of freely available pictures at Nassim Nicholas Taleb’s web site. (Photo credit: Wikipedia)

The post is direct quote from Nicholas Nassim Taleb‘s writings at Fooled By Randomness

141 Why does leverage in an economy generate (or exacerbate)  fat tails? A purified proof

There is no need to write a complicated model (precise but stupid, the kind of stuff complexity idiots write to get academic credit), simple rigorous arguments can prove with minimal words and no mathematics how fat tails emerge from some attributes of complex systems. This argument is a  Dynamic Hedging-style (Taleb, 1997) argument.

A- Why fat tails emerge from leverage and feedback loops, single agent simplified case.
A1 [leverage]- If an agent with some leverage L buys securities in response to increase in his wealth (from the increase of the value of these securities held), and sells them in response to decrease in their value, in an attempt to maintain a certain level of leverage L, 
and
A2 [feedback effects]- If securities rise in value in response to purchasers and decline in value in response to sales, 
then, by the violation of the independence between the variations of securities, CLT [the central limit theorem] no longer holds (no convergence to the Gaussian basin). So fat tails are an immediate result of feedback and leverage, exacerbated by the level of leverage L.
A3 – If feedback effects are convex to size (it costs more per unit to sell 10 than to sell 1), then negative skewness of the security and the wealth process will emerge. (Simply, like the “negative gamma” of portfolio insurance, the agent has an option in buying, but no option in selling, hence negative skewness. The forced selling is like a short option.)
Note on Path dependence exacerbating skewness: More specifically, if wealth increases first, this causes more risk and skew. Squeezes and forced selling on the way down: the market drops more (but less frequently) than it rises on the way up.

B- Multi-agents: if, furthermore, more than one agent are involved, then the effect is compounded by the dynamic adjustment (hedging) of one agent causing the adjustment of another.

C- One can generalize to anything, such as home prices rising in response to home purchases from the Greenspan liquidity, etc.

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