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Cambridge University Science Magazine
The work highlights the effect that widespread use of a particular type of averaging technique is having on risk calculation. The ensemble average works by averaging out possible scenarios running in parallel from the same starting position. Peters suggests that because financial transactions are embedded in real time, our risk calculations should instead use time averages.

The difference between the two approaches can be illustrated with a simple example. Consider an initial investment of £1000 in a market where shares first rise by 15% and then fall by 14%. Using an ensemble average, we would suggest that there was a profit to be made, with the mean of 1000 + 15% (1150) and 1000 - 14% (860) giving us a figure of £1005.

However if we consider that the 14% drop comes only after we have seen a 15% rise in the prices of the shares, a different picture emerges. Using a time average we would calculate the shares rising to a price of 1000 + 15% (1150) and then subsequently falling to 1150 - 14% (989). This loss of £11 (enough to buy at least a basic maths textbook) would not have been anticipated if we had analysed the risk using ensemble averages.

Whilst in the real world financial transactions are a lot more complicated, this example highlights a fundamental problem with current practices which may be leading us to substantially underestimate risk. It is hoped that this insight will help regulators to set better guidelines for financial institutions in the future.

Written by Helen Gaffney