by Tyler Durden
A fascinating insight from Graham Giller of Statistical Trader Blog, who
analyzes over 55 years of Treasury data to point to what is the crux of the
problems of monetary policy since Greenspan took over the Fed. The
Greenspan [and Bernanke] era monetary policy has altered the
distribution of changes in interest rates in a way that exchanges a reduction in
day-to-day 'normal' variability for a considerably higher (perhaps
catastrophically higher as we are finding out this week) likelihood of extreme
shocks.
I first made the attached chart in 2004 after attending a lecture by
Benoit Mandelbrot, and reading his "Fractals and Scaling in
Finance." Mandelbrot's argument based on his early research (in the 60's) on
financial price data was that the variance of speculative prices was undefined
(i.e. infinite). This has profound implications for quantitative
finance as a venture since the error on the mean is proportional to the
square root of the variance, and for a distribution with an infinite variance
the law of large numbers does not apply ---- i.e. you cannot make
precise measurements of the mean as there is no convergence of the sample mean
towards the population mean. Mandelbrot's research was done before
ideas such as stochastic volatility were created, and in a modern context we do
find evidence of stable variance.
However, one of the interesting aspects of his work was to pose the question:
how does one measure an infinite statistical moment from a finite data sample,
since that finite sample will always give a finite answer? Mandelbrot
suggested in his early papers looking at the time series of the cumulative
sample moments of the data --- i.e. to measure using all data
up to some time and to plot that value as a function of each and every time. If
the true parameters of the distribution of the data being measured are unbounded
(infinite) then this plot will show no signs of convergence --- the measured
datum will march steadily away from zero as each additional data point is
added.
Mandelbrot's ideas also apply to higher moments: the sampling error of the
variance is determined by the kurtosis (degree of "fat tails") and so on.
My plot illustrates the cumulative kurtosis,
computed after Mandelbrot, of the daily change in US three month
treasury bills. Ever since the arrival of Alan Greenspan's post
'87 crash crisis management regime, this plot shows a systematic and steady
march upwards in the kurtosis of changes in US interest rates. I find
this chilling. This means that, if the truth is as the evidence
suggests, that it is not possible to accurately determine the risk of a
portfolio of bonds because it is not possible to make reliable
measurements of the variance of interest rates. i.e. The whole
enterprise of bond portfolio risk management is intrinsically unreliable.
The data also tells another story. Also plotted is
the cumulative standard deviation of daily changes in rates. This shows a
systematic (but slow) decline in the measured value. This indicates
that the true value is below the current value of the cumulative measure and
that the cumulative measure is slowly decaying towards that value.
So a narrative for what the Greenspan era monetary policy has done
to the distribution of changes in rates is to exchange a decreased daily
variability for a higher (perhaps catastrophically higher as we have found out)
likelihood for extreme shocks.
As you can see the Bernanke era has done little to modify the general trend.
In 2006 I sent the chart to Jim Grant together with my prediction that something
nasty was lurking in the future. I decided to revisit the analysis today and
find nothing has changed. Discussions of the long-term consequences of
interventionist monetary policy are increasing (though still not in the
mainstream) and this plot shows the fingerprints of such policy writ large.
It is this constant papering-over of the day-to-day cracks (and business
cycle) that is supposedly so beneficial for our society (and central planners)
as a whole that creates a building tension as the underlying causes grow larger
and larger and are never purged until in one fell swoop, the market mechanism
finds a way.
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