Saturday, January 31, 2009

The Nature of Risk - Ari Paul

What is risk? Is it the volatility of returns? The threat of a permanent loss of capital? Is risk the chance of a significant drawdown, and if so, what defines "significant"? In the past year, Volkswagen briefly became the biggest company in the world and much of Wall Street ceased to exist. According to sophisticated quantitative models, we witnessed once a millennium, 5 standard deviation moves and even the statistical equivalent of pigs flying and hell freezing over.

Where did the models and risk managers go wrong? The simplest explanation is that they were the unlucky victims of a rare "black swan" event, but there was no black swan. The collapse wasn't started by a natural disaster or terrorist attack. A speculative bubble and credit pyramid were built up over the last 7 years and are now being unwound. Like with most bubbles, traders and analysts examined data from the last few years and extrapolated the safe returns forward. It's like looking at last year's weather and concluding you won't need an umbrella this afternoon…even after it starts raining.
Let's take a closer look at the common risk metrics through the lens of two simple games. In the first game, we flip a twelve sided die. If it lands on an even number you get $3, if it lands on odd you owe me $1. In the second game we flip that same die; if it lands on a 12 you get $12, otherwise no money changes hands. Which game is riskier and which game would you rather play? Your expectation in both games is the same: you'll average a $1 profit for every roll. By most common investment metrics, the second game is riskier; it has more volatility and a lower sharpe ratio. Yet common sense tells us that the first game must be riskier because we are exposed to unlimited losses and a high likelihood of being down after a few rolls. In the second game we can sleep easily at night and just keep playing until we win. We can construct similar games to expose the faults of VAR and the Capital Asset Pricing Model as well.

As this example suggests, risk metrics can be irrational under the best of circumstances, and they can be downright devastating when correlations and volatility change as they have in the past year. What's the alternative? If not with complex metrics, how can we manage risk? I'll leave that for my next post.

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