Monday, 30 January 2012

Be Careful with Correlations

Hello one and all,

A friend of mine brought to my attention a blog post from Mike Webb (also a friend), arguing that there was a crisis in confidence in the UK Government. The blog post is a good attempt at rigour, but I'm afraid Mike fell into a simple trap.

The argument is expressed in detail here but I think a not unfair summary is this:

1. Uk Government yields have been closely correlated with Yields from European nations..
2. In the months leading up to May 2010, there was a steep dropoff in that Correlation
3. The most natural explanation for that is uncertainty over the outcome of the election.

Statements 1 & 2 are both true, and statement 3 seems reasonable at first glance. So I can say that I liked the blog post. I particularly liked the effort he went to to double check his findings by comparing across multiple regions - UK compared to Germany, France, Italy etc.

Unfortunately his conclusion, that there was mounting suspicion over UK solvency has only a very superficial link to the data. His predictions entail maximally that UK Government Yields climbed in these months. Minimally, his explanation entails that UK yields behaved in a way that was at odds with a wide range of countries in those months.

With a Bloomberg machine able to run correlations he checks only the correlations between different Governments' yields. Unfortunately, he doesn't bother to show us what happened to the actual yields themselves.

Here are UK Yields in the relevant time period (click on the image to see it blown up):

From the graph, we see that over the period UK yields moved up a bit, down a bit, and actually ended the period that he is referring to (January - April 2010) at about the same level, maybe a tiny bit up.

Now here are the European Yields that he is referring to:

Yes, falling yields, implying pessimism over the economy and as yet no worries about fiscal solvency.

The absence of any rise in UK yields is at least a worry for the argument that investors were getting jittery about UK solvency, Now, one could argue, I suppose: "Well, what happens if there was some, external international event that dragged those other yields down, and would have dragged UK yields down as well, if it weren't for solvency jitters?"

Well lets look outside of Europe for a moment:

Ah yes, they all went up, slightly.

In other words, the drop off in correlation he refers to is explained only by a decline in Bond Yields in European countries. One would be very hard pressed to argue that suddenly investors got jittery over UK yields- There's no actual evidence for this in the data whatsoever.

So next time you look only at correlations, remember to actually look at the things you're correlating, before you jump to any conclusions!!!


  1. Ravin - firstly one correction: you say 'falling yields, implying pessimism over the economy and as yet no worries...'. You obviously meant 'optimism'.

    A quick reply after a long day in the office:

    Though I'd rather stay away from from the Rogoff vs. Krugman kind of dispute, I will try to contribute a couple of mildly technical points:

    - Mike - a simpler chart, i.e. spread (think IRS) between the yields makes a much stronger case for you ( It is far from making a super-compelling one, since the convergence of UK/German bonds can be attributed partially to a safety flight (also from the EZ). Finally I guess one can wonder whether, with the recent poor macro data, this will be the case for a long time.

    The bloomberg tool you used by default runs the correlation over 120 days, based on market close prices (in this case generic 10yr yields). Here is a chart with different correlation windows - it's a mess:

    - So now back to you, Ravin, you are on the spot of course - though there is another major problem with Mike's charts and the correlation use. The main problem is that we ought to be looking at the series of returns, not prices. This can be confusing if we're already looking at yields, but we all know that this is a de-facto 'inverted' price of the bond. It has nothing to do with intra-day rate of return. The explanation here is we ought to be using time series analysis to see a relationship. Put simply, the yield of the bond today is not independent of that yield yesterday. We could argue whether when we look at rates of return there may be some time-series component there too (investor sentiment, CTAs - more widely 'momentum'), but it would make a lot more sense to see the correlation here. So here it is, redone ( Looking at this, the answer bond traders give you Mike (70%) seems to make a tad more sense.

    Finally, to explain the seeming lead of the correlation - it is not, like you suggested, that the uncertainty is the greatest at that point. I guess the uncertainty is the greatest wherever the yield's ceiling is. Here it is largely that the market finished the major pricing-in at that point, and then bonds started trading more in tandem again (hence then the spike back up), adjusted for a level shift.


    1. Dear amrk -

      Falling bond yields are generally associated with pessimism, not optimism, over the future direction of a country's economy. When investors are worried about the state of the economy, they 'fly' away from the risks of equity and into the (relative) 'safety' of bonds. The increased demand for bonds means their price goes up. As you very correctly point out price and yield are simply inverse versions of each other - so when one goes up, the other goes down.

    2. PIIGS being a good example of that I'm guessing?

      You have a point of course. The downgrade of the US led to lower yields on US debt. Downgrade of France barely moved their yields. But this is hardly a rule – would you argue a negative growth surprise in Spain will lead to a narrowing in the government bonds' spreads? I don't think so.

      There are different mechanisms at play here – sure, debt being a more senior obligation than equity for a company is one thing. For countries the problem is trickier, as you can't directly 'own' equity in a country, so debt is not 'senior' to anything specific – though it's generally considered a safe haven and people will hold it as the closest substitute to cash. But how close a substitute to cash? While I would be reasonably happy to hold £1 cash as £1 of NPV UK debt, if a negative growth surprise comes, I'd bid lower as it becomes more likely (although still far in the tail) that the UK can eventually default on some of its obligations. For the UK the safe-haven effect may currently still outweigh the probability of default, but this can change. In the end, why isn't the Greek debt rallying? I mean, one thing they have for sure is pessimism about their economy.