### Of tail risk

##### March 12, 2016

###### Suppose one cares about tail risk, what is the best way to estimate it? There are two, not mutually exclusive, ways; statistical and structural. Which is right?

Suppose one cares about tail risk, what is the best way to estimate it? There are two, not mutually exclusive, ways; *statistical* and *structural*. Which is right?

Start with the question of what tail risk is. A quick and dirty definition may be:

Tail risk is the risk of a very infrequent and very serious event that materially affects ones financial well-being

Perhaps, the worst market outcome in 20 years or equivalently, the chance the market drops by 20%. Tail risk is certainly not remotely connected to the 99% or 97.5% daily risk of Basel or the the systemic risk measures like SES, MES, CoVaR, SRISK or Sharpley.

Tail risk is often used synonymously with systemic risk, sometimes justified, but usually not. For at least two reasons. First, tail risk is often idiosyncratic, so I can suffer from significant tail risk while no one else does. Secondly, the risk of systemic events, every 42 years on average, will be higher or lower than any tail risk most users will care about.

So how can one estimate tail risk? There are two ways, statistical and structural.

### The statistical approach

All one does is to take one of the friendly risk forecast methods, usually one of these, along with a chunk of history of the same asset, and use that to forecast the risk of tail events. If it is really tail risk one is interested in, the only method that really works is EVT.

I don't think the statistical approach to tail risk works all that well — apologies to my EVT friends — because tail events are caused by specific economic events that cannot be predicted by the historical observations of the assets in question. In other words, the asset history does not contain the necessary information.

### The structural approach

This argues that extreme outcomes in financial markets are caused by particular economic circumstances that can only be understood and forecasted in the context of the financial market in question. For example, for the Swiss FX shock, was quite likely given the ownership of the central bank and the increasing loss on the trade.

Therefore, the only way to understand tail risk is to understand the structural issues. Economic, political and legal analyses are much better in capturing tail risk than running statistical methods on past returns.

##### Models and risk

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