"Something Disquieting Is Afoot" For U.S. Bond Markets

Submitted by Salil Mehta via Statistical Ideas blog,

We replicate a previous chart showing extreme daily moves in the U.S. stock market.  This time though, we focus on U.S. bonds and show that something disquieting is afoot.  As we approach this month's well anticipated Federal Open Market Committee meeting, market participants are interested in knowing what acceleration there might be going into year end, in extreme bond volatility.


We see some kinship with the stock market chart linked above.  Namely that during the global financial crisis, there was a dramatic uptick in market gyrations (both up and down).  At a high-level, this is where the commonalities disappear.  The two charts are otherwise probabilistically different (>90% significance on a few nonparametric model fits) than one another.  By way of reference, seeing greater than a 0.5% daily move in the bond markets (in either direction, and as proxied by the Vanguard total bond market index), or seeing greater than a 2.0% daily move in the stock market accounts for ~8% of all trading days (over 9 years or more than 2200 trading days) in each of their respective markets.  Or roughly a 4%-5% tail risk - since for stocks and surprisingly not for bonds there is actually a slight wider tail on the losing end of the distribution versus the gaining end.  Notice in the chart above, a more balanced split between years where there are more extreme down-days versus years where there are more extreme up-days?

Now we show the extreme moves for both assets, jointly, in the chart below.  Grey for stocks, and pink for bonds.  One can appreciate that in a respectable recent bulk of the 9-year history, 2010 on through 2014, the probability relationship (between extreme risk for bonds and for stocks) entirely dissolves!

We essentially have some false starts, where there is a risk surge in one asset class but not the other (e.g., 2013).  But we know that when a catastrophe in the markets occur, as we saw on Black Monday, we only need one asset class in distress (not multiple).  And when things move fast, it could be difficult to stay ahead of the loss measures.  Bonds too, which at that time moved only a fraction in magnitude relative to equities are hardly a diverse shelter from the storm.  Note that there were no extreme moves in bonds overall during all of July and August 2015, and only 2 extreme moves in all of 2012 (both to the downside) despite the major Greece debt downgrades inspiring global markets' havoc!

But now as we end 2015 we still notice that things are different.  Both stocks and bonds have seen a pick-up in their frequency of extremely volatile days (in both directions).  There is no certainty that things are not destabilizing in both markets, jointly.  Advanced algorithms can detect a probabilistic cluster that includes the rise in risk during 2007 as a similar year (along with a couple other years).  And we know what happened in the year following 2007.

Clearly this pattern of looking at higher risk in both major asset classes (bonds and stocks), leading to momentum in at least one asset class, isn't a sure thing.  Nothing is, but there is a high probability relationship that tilts the odds in favor of soon having a bout of extreme risk (correlation of 0.5).  The analogy is as if you notice an ember smoldering in a combustible forest you might be only somewhat cautious, perhaps even rationalizing it away.  But if you then notice a second ember smoking up...