The Hindu Business Line : Risk of ruin

All of you may be aware of how Amaranth Advisors, a US hedge fund, recently lost 65 per cent of its capital betting on the price movements in natural gas. Some experts contend that Amaranth ignored the "risk of ruin" and took large bets in natural gas. What is risk of ruin?

It is the chance that a series of losses will wipe out your capital. Suppose you want to bet Rs 100 on a game of tossing coins. Risk of ruin is essentially the chance of consecutive losses on each game leading to erosion of your capital.

Position sizing is important to reduce your risk of ruin. That is, you will have to decide on the amount you will bet on each game. If you bet Rs 100 in the first game and you lose, your entire capital is wiped out. Importantly, you are out of the game. This means your chances of winning are small. So, what do you do?

You have to find the maximum amount you can bet on each game so that you play for a long time. This increases your chances of winning.

Your objective then is to find out the probability of losing (getting tails consecutively) before you wipe out your capital. Suppose the probability of getting tails 10 times in a row is one in thousand. You will bet Rs 10 (Rs 100 capital divided by 10 consecutive losses) on each game. If you are conservative, you may consider the chance of losing 15 times in a row, which is one in 10,000. So, you bet Rs 7 (Rs 100 divided by 15) on each game. That is how quant traders use risk of ruin to position-size their trades.

(The author is based in Toronto, Canada)

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