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.*