“Dynamic Hedging” by Nassim Taleb

Financial markets history is littered with stories of traders who bought an instrument and tried to reduce the risks by selling a “highly correlated one against it. only to discover that they doubled their risks. The trader after seeing on the screen the price of one of the two instruments go down (the one he is long, of course) and the other go up (the one he is short) will blame markets for not being well behaved.

A deeper analysis would show that, typically, some of the instruments that are easy to buy against easy-to-sell “correlated siblings” are invitations for trouble. They act as a trap that will attract many hedgers and arbitrage traders then force them into noisy liquidations. This effect can lead to disastrous results on gullible managers using such apparatus as the “value at risk.”

There is an application of a mathematical lemma called the Borel-Cantelli Lemma: If one puts an infinite number of monkeys in front of (strongly built) typewriters and lets them clap away (without destroying the machinery), there is a certainty that one of them will come out with an exact version of the Illiad. Once the hero among the monkeys is found, would any reader invest his life’s savings on a bet that the monkey would write the Odyssey next?

THe same applies to traders…

One of the key properties of probability laws is that they are counterintuitive. People look at a casino seeing how a small “edge” translates into virtually certain profits and infer that the same rules apply to a man rolling the die. The sums of random walks (net profits from the sum of roulette tables) act differently from the final sum of a random walk (a gambler’s net results at the end of one session on one roulette table). A modest advantage on a sum of random walks translates into certain profits. The same advantage of one roulette table is generally drowned by the volatility of the random walk itself. The reader could test the difference by generating a series of tosses on a spreadsheet using a random number generator and looking at the discrepancies in the results. Even with a small advantage, a counterintuitively high number of negative runs would mar the party. The only way to reduce the frequency of negative runs would be to increase the number of trades and make the bets smaller.

One could think of a roulette table and view the edge of a trader who has negative odds with a system that gives him a 45% chance of winning. What is the probability of the person betting $1 being in the black after 30 throws? Using the cumulative binomial distribution, he has at least a 35% chance of ending up profitable. If the gambler sliced the bet into pieces of $.10 and compensated with 10 times more bets, the final number of positive results would be 4.6%. This provides a vivid illustration of the reasons to use caution when considering the notions of “edge” and “skilled traders.”

When a security becomes perceived as expensive, there will be a rush of traders shorting it and buying a similar instrument. If the security stays so for a longer time owing to a specific buyer, the accumulation will turn too large for the arbitrage community to handle and traders will reach their limits. As the arbitrage community reaches its saturation level, pressure on the relationship between what is deemed expensive and what is deemed cheap will cause severe marks-to-market losses. Liquidation of the less capitalized arbitrageurs will ensue. “Inefficiencies in the market will last longer than traders can remain solvent.”