Predicting and Dating the Financial Crisis from the Treasury Bill Kurtosis

by Graham Giller September 11, 2009 12:47

On 10th. February, 2006, I performed the analysis repeated in this post, and also on an earlier post on this blog, looking at the cumulative kurtosis of the daily changes in interest rates. Not knowing what to do with the analysis, but concerned about it's possible implications, I considered writing a letter to the Director of Research at the Federal Reserve but, in the end, I sent a fax to James Grant, editor of Grant's Interest Rate Observer, and a noted skeptic of the glory of centrally planned monetary policy.

In my letter I wrote:

“During the last 20 years the Fed has made everybody happy by bringing down the volatility of interest rates but we appear to have paid for this by obtaining a distribution of daily changes substantially more prone to extreme variation; or, to put this a little more colourfully, that the animal spirits of interest rates have not been tamed but have undergone a metamorphosis from prowling tom cat to sleepy tiger.” Graham Giller, 02/10/2006.

Mr. Grant liked my ‘tom cat/tiger,’ imagery, but I feel I didn't fully convince him of my main point — that, by supressing the standard deviation in exchange for a badly controlled kurtosis, policy was running towards an extreme event that would be truly off-the-charts. However, the purpose of this post is not to claim some magical ex-ante call for the decline of western finance as we knew it. It is to re-examine these metrics and see, in the same manner as before, what story they're telling us.

Cumulative Kurtosis of Daily Changes in US Treasury Bills

So let us examine the tail end of the kurtosis curve in the above chart. This shows how the cumulative sample kurtosis of the one day change in the yield of U.S. three month treasury bills has been accumulating as each day of the Ben Bernanke tenure as Chairman of the Board of Governors of the Federal Reserve System.

The malfunction of the U.S. financial markets, as indicated by the momentary pause in the upward ascent of the cumulative kurtosis, appears to have started after the kurtosis peaked at 30.06 on 08/08/2007 and ended after it had drawn down to 28.50 on 10/30/2008. The dates we have estimated for the crisis in the performance of hedge funds, based on our monthly data series of the returns due to the dynamic trading risk factor (which is extracted from the returns of hedge funds, are 10/2007 to 11/2008. Since then it has been steadily marching upwards again, although it has not yet breached that peak level.

It remains to be seen whether this is indicating that the true population kurtosis is merely higher than the currently observed value, or whether it is entirely unbounded above. But this trend is consistent with the hypothesis that, as far as activity in the interest rate markets is concerned, game is back on!

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About the Author

Graham Giller - Headshot GRAHAM GILLER
Dr. Giller holds a doctorate from Oxford University in experimental elementary particle physics. His field of research was statistical astronomy using high energy cosmic rays. After leaving Oxford, he worked in the Process Driven Trading Group at Morgan Stanley, as a strategy researcher and portfolio manager. He then ran a CTA/CPO firm which concentrated on trading eurodollar futures using statistical models. From 2004, he has managed a private family investment office. In 2009, he joined a California based hedge fund startup, concentrating on high frequency alpha and volatility forecasting. A detailed resume is available.

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