In the previous post I discussed a little history and a little theory about the consequences of a cartel of banks fixing the LIBOR fixes. Fortunately the data for LIBOR is readily available from the Federal Reserve Bank of St. Louis. Similarly, data for the discount rates of three month treasury bills is also available. Our hypothesis is that in a free market the transmission of risk free policy rates to risky market rates should essentially be linear, described by the equation

This says that each bank's individual cost of funds is linearly related to the risk-free-rate and as a consequence the market average of the banks' cost of funds is also linearly related to the risk free rate.

Thus, in an efficient market the stochastic process that is LIBOR should have the same autocovariance structure as that of US Treasury Bills. I'm not saying that bill rates have to be i.i.d. random, I'm just saying that *LIBOR should have the same dynamic*. So to find out if the LIBOR fixing process is efficient we should test to see if the processes are statistically similar or not.

I'm going to start with a simple model. Let's say that the changes in rate are a Markov chain with three states: up, unchanged, and down. (The actual change in rate is then the product of a direction variable and a size variable.) This state sequence possesses the advantages of being simple to compute and easy to understand. We can then ask whether the state sequences show evidence of the Markov property, that they are predictable from their prior instance, or whether they are independent of their own history. There is a nice test for this, called *Whittle's Test*, which is essentially about building a contingency table and appying a *χ² *analysis to the observed counts. It is simple and it is about counting, so there is no introduction of hypotheses of normal distributions or leptokurtocity or GARCH or any time-series sophistication.

This chart shows the result of applying this test independently to each full year for which we can get LIBOR quotes and to the Bill Rates for the same years. The shading indicates when the test rejects the null hypothesis of independent state sequences with a confidence of better than 99%. You can see that the LIBOR sequences are not independent from about 1996 onwards, whereas the Treasury Bill sequences mostly are.

Furthermore, without any statistical tests, I think it is plain to the eye that the LIBOR series is unnaturally smooth in the latter half, particularly when compared to the Treasury Bill series. Thus the hypothesis if neutral transmission of policy rates to market rates is rejected from 1996 onwards. I would suggest that something was going on with LIBOR since at least that date!

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Comment RSSGraham wrote: Just a quick note. The purpose of this article is … [More]

Menswear wrote: Good job man [More]

Graham wrote: I forgot to point out that Generalized Error Distr… [More]

Graham wrote: The GARCH solver is using the Generalized Error Di… [More]

Soham Das wrote: However, the innovations show definite evidence fo… [More]

reg cleaning wrote: I really enjoyed your article and found it to be v… [More]

Soham Das wrote: What I am considering is, if we have a hypothetica… [More]

Graham wrote: Hi Soham, You can, in fact, predict the volati… [More]

Soham Das wrote: Hi Dr.Giller, Will it be plausible to ask, if the… [More]

Graham wrote: We're performing a linear regression of the portfo… [More]