Gilts, Brevixity And The U.K. Downgrade

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The recent downgrade of the UK post-Brexit has injected further anguish into the markets.

Historically, the UK has defaulted on its debt, but then issued perpetuities which have been redeemed in their entirety.

However, examining the duration and convexity of the longest maturity gilt shows that if rates rise, the gilt market will likely react in a volatile fashion.

Gilts, Brevixity and the UK downgrade

"You can't drive straight on a twisting lane" - Russian proverb

In case readers are wondering about what "Brevixity" means, it is a word I concocted, a combination of Brexit and convexity. Convexity, explored further below, is the reaction of a bond's duration to changes in interest rates. It is important, since traditionally what is calculated is the reaction of a bond's price to changes in rates. And in the wake of Brexit, it's relevant to look forward and see what might happen to the UK bond market if rates rise. The best variable to capture that is the convexity of a bond. And in the case of the gilt market, which has some of the longest maturity bonds in the world, this becomes especially relevant. But before that a little context and some history.

One of the earliest examples of sovereign default occurred in the UK.

The country which before Brexit had an AA+ rating (now AA), was one of the earliest countries in history to default on its debt. For history fanatics, the first UK default (and most probably the first ever default) occurred when Edward II defaulted to his Florentine bankers in 1340 as a result of running up ruinous debt in his wars with France. A great book that documents all of this is Reinhart and Rogoff's book. However, since then other countries have taken pride of place in the sorry history of sovereign external defaults (including of course, the usual suspects such as Russia, Argentina, Greece, etc.) It is reassuring to note that the latest known UK default occurred in 1932, when Neville Chamberlain exercised the UK's government rights to call in the 5% war loan.

It should be noted that the UK government has had a history of issuing perpetuities. These perpetuities sometimes dated back to Napoleonic times. The last remaining undated gilt was redeemed in July 2015. In fact, on that date, according to the UK debt management office, a 2½% annuity was redeemed dating back to 1853, an annuity issued in exchange for South Sea stock, irony of ironies!

Future behavior of long-dated gilts depends on volatility and convexity.

While the history lesson may be interesting, the purpose of this article is to look forward to the gilt market post-Brexit and post-downgrade. For that purpose, I will examine a classic long-dated gilt - namely the 4% Treasury gilt, with maturity January 22, 2060. As the following graph shows, the current yield curve is "humped," yet I chose the longest maturity gilts to look at the "worst case scenarios" with respect to duration.


The delightful data set provided by the UK debt management office has daily durations, going back to however long one wants to. For my purposes, I went back to 2014 to see how this bond has reacted to changes in the yield and react it did. Of course, longer maturity bonds are expected to be more volatile, but I didn't expect the following graph. Not only is the duration increasing with time, it also seems to be becoming more volatile.

Of course, to really address how this gilt (or the gilt market in general) will react to future inevitable interest rate increases as a result of the downgrade, it is appropriate to look at the convexity or approximately how the duration itself changes with interest rate changes (or technically the second derivative of the graph below the duration graph).


Generally speaking, the convexity of the price-yield graph will be positive. But not always. Due to the daily duration data, I was able to calculate how the convexity itself changes over time. What I found was tremendous variation in the convexity. So while for the whole period the average convexity was 1430, since the beginning of the year the convexity has declined to -1.8!


What does this say for future trends?

Calculating the convexity may seem a technical exercise, but it is useful to understand how quickly the gilt market reacts to changes in rates. Think of it as measuring the acceleration (or deceleration) of a car. With a positive convexity, as rates rise (or drop) prices move the opposite direction in an accelerated way. Or, if interest rates rise in the UK, we can expect prices to decline, but faster and faster. In other words, greater volatility to be expected, although the recent dramatic decline in convexity means that the market is probably more stable than one would think.

But even if the gilt market is stable, what is more troubling is the volatility in the convexity, which means one can't bank on that stability going forward. What does this mean for gilts? If rates rise, even the instability won't be stable.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.