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Doomed to repeat it?
 
 PUBLISHER                  RiskMetrics Group, Christopher C Finger     PUBLISHED       01/11/08
 
 CONTACT DETAILS      chris.finger@riskmetrics.com
 
 VIEW PAPER                Click here

Paper Objective 

 

This is an interesting article from the CreditRisk metrics group that looks how volatile equity markets have become over the history the Dow Jones.  It aims to answer the following questions:

 

  » How volatile have markets become?

  » How long do we have to wait for crisis volatility to abate?

 

If you aren't worried about the credit crisis, you might be after reading this paper.

 

How massive was this shock?

18% loss was a 3.4 standard deviation drop; the last week of February 2008 produced a 4.2 standard deviation fall.  No other week in the last two years has been as much as a three standard deviation surprise.  The last five standard deviation (weekly for what its worth) surprise came in 1946.

 

In the run-up in volatility in the Great Depression, the volatility stayed elevated for about sixteen months above 35% during which time the index fell by 50%.

 

When this document was published there were 29 consecutive trading days over 35% and 21 days over 50%. 

 

There has never been in history runs as long or has high in volatility as the current crisis.

 

   Key Points 
 

Three tenets of risk models

1 » Volatility is relevant

2 » Volatility changes 

3 » Changes in volatility are somewhat predicatable

 

The framework for the model is that the return to come is the product of the volatility and the residual which we do not know but which comes from a defined statistical distribution.

 

The Volatility Measure Technique 

Each days return can be thought of as an n-sigma event, where sigma is the standard deviation, or volatility, that we have forecast, and n is the size of the residual.

 

The approach is to work with a volatility forecast that is simple weighted average of prior days squared returns, with the weighting scheme from one of our standard risk models.

 

The residual is assumed to be the t-distribution where each days residual is distributed independent of whether volatility is high or low, of whether we are in the early or latter stages of history.    The historical residuals are calculated by dividing each days return by the volatility.