How Many Dependencies did you Declare?

Correlation is a statement of historical fact.  The measurement of correlation does not necessarily give any indication of future tendencies unless there is a clear interdependency or lack thereof.  That is especially true when we seek to calculate losses at probability levels that are far outside the size of the historical data set.  (If you want to calculate a 1/200 loss and have 50 years of data, you have 25% of 1 observation)

Using historical correlations in the absence of understand the actual interdependencies could possibly result in drastic problems.

An example is the sub primes.  One of the key differences between what actually happened and the models used prior to the collapse of these markets is that historical correlations were used to drive the models for sub primes.  The correlations were between regions.  Historically, there had been low correlations between mortgage default rates in different regions of the US.  Unfortunately, those correlations were an artifact of regional unemployment driven defaults and unemployment is not the only factor that affects defaults.   The mortgage market had changed drastically from the period over which the defaults were measured.  Mortgage lending practices changed in most of the larger markets.  The prevalence of modified payment mortgages meant that the relationship between mortgages and income was changing as the payments shifted.  In addition, the amount of mortgage granted compared to income also shifted drastically.

So the long term low regional correlations were no longer applicable to the new mortgage market, because the market had changed.  The historical correlation was still a true fact, but is did not have much predictive power.

And it makes some sense to talk about interdependency rising in extreme events.  Just like in the subprime situation, there are drivers of risks that shift into new patterns because systems exceed their carrying capacity.

Everything that is dependent on confidence in the market may not correlate in most times, but that interdependency will show through when confidence is shaken.  In addition to confidence, financial market instruments may also be dependent on the level of liquidity in the markets.  Is confidence in the market a stochastic variable in the risk models?  It should be – it is one of the main drivers of levels of correlation of otherwise unrelated activities.

So before jumping to using correlations, we must seek to understand dependencies.

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Explore posts in the same categories: Assumptions, Correlation, Enterprise Risk Management, ERM, Financial Crisis, Modeling, Risk, risk assessment, Risk Management, Statistics, Sub prime, Tail Risk

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