Life always has a fat tail, according to American economist Eugene F. Fama. When the hedge fund Amaranth lost more than $6 billion due to natural gas bets, it was reported that their risk models had not predicted such a loss. More recently, the Bank of Montreal also reported losses of $680 million from its natural gas trading.
Once again, it appeared that the value at risk models were out of step with reality. According to a report in The Globe and Mail(April 28, 2007), the bank’s models pegged the maximum loss of its trading activities at $17 million per day. In simple terms, this would imply that the bank had racked up maximum losses for the proverbial 40 days in a row before unwinding its trading positions.(One wonders at what point the “suits” in the mahogany offices would have instructed the derivative traders to cease and desist if this had been the case).
Setting aside the possibility of improper behaviour or unauthorized trading, one can safely assume that this was not what happened. The value at risk forecasted loss would have been at the 95th percentile confidence level, and the outcome was clearly outside this range. Furthermore, there are many possible reasons, or combinations of reasons, for derivative trading to cause such an outcome: extreme market movements, lack of liquidity, changing volatility, excess of hubris, or in the extreme case, a virtual conspiracy to sabotage the known market positions of a competitor(as was experienced in the Long-Term Capital debacle).
What is often puzzling though, is when the risk managers express themselves surprised that their models didn’t forecast the outcome. It’s not clear whether this is due to the “quants” living in ignorance as to how markets and market participants actually behave, or whether they convince themselves that their models are invincible.
Using a normal distribution to assess the probability of market events leads to some interesting comparisons:
• the equity crash of 1987 would have the same chance of occurring as finding a particular hydrogen atom in the universe;
• the Russian bond defaults of August 1998 should only occur once in the entire history of the earth.
Risk models can be helpful as indicators of relative risk levels or trends. But risk, by its very nature, does not follow well-behaved patterns and needs to be considered across the full range of outcomes. The insurance industry, where risk is assumed but not accepted indiscriminately, tests its risks at the 99th percentile level and stress tests for worst case scenarios beyond that.
As pension funds explore new risk territory through the more extensive use of derivatives or hedge funds, they would be well advised to start out by defining their risk tolerance very carefully.
It can be said that a manager may assume three levels of risk: The first level is the risk of such a loss that the portfolio manager will be embarrassed and forego some of their incentive compensation for the year. The second level is the risk of such a loss that the portfolio manager will be mortified and will be relieved of their duties. The third level is the risk of such a loss that the portfolio manager will be approached to publish their story as to how they managed to bankrupt the fund and totally impair the security of the benefits. Unfortunately for trustees and other fiduciaries, the manager may be indifferent between the second and the third outcomes(and may even have a bias towards the latter!)So the governance model needs to ensure alignment of interests between all parties when risk is being assumed with other people’s money.
Comments
You wrote an important article well.
-Gordon Ross, CFA
Well said Josephine. Life always has a fat tail or several fat tails.
I am not sure what “normal” is anymore.
Expect the unexpected.
-Terri Troy