Yield Curve Trading - 1

Some Basics First

I am sure you have all heard of the yield curve and maybe even tried using it in your investing journey. It is hard to avoid mentioning it these days as there is an increasingly sharp focus on the inversion of specific segments of the US yield curve, like the 2-10s curve below.

In reality, the yield curve is a derivative of the bond market’s near-term maturity/duration preference expressed across various market participants. What do I mean by that? Naturally, the anticipation of Fed-steered monetary policy will anchor and determine where shorter-dated maturities can trade according to market expectations. Similarly, longer-dated maturities are taking not only monetary policy paths but also inflation and risk-premia into consideration. Many are using the term premia as an intellectual tool to analyse the richness of certain points across the curve. You can study more here. I personally think that’s all over-thinking as nobody in the market that I have ever come across has or is pricing term premia.

Basics of Arbitrage & Carry

As a non-arbitrage proposition, it has to hold that any maturity bond has to give you the same ex-ante total return expectation for, say, a one-year holding period.

An example:

A 1-year bond yielding 5% and a 2-year bond yielding 4% should give you the same holding-period return. That’s where forward rates come into play that is derived by computing what current spot rates over varying maturities are yielding. In our example, to calculate the 1-year rate in 1 year’s time, you can (rule of approximation) take the 2-year bond yielding 4% (2 x 4) and subtract the 1-year bond yield (1 x 5), which should give you 3%. The accurate mathematical equation would be like this:

(1.04)^2 / (1.05)^1 -1 = 3.01%

All that means is that the 1-year rate in 1 year’s time would have to be 3.01% for you to have exactly the same annual return of 5% over the holding period of a year.

How? The 1-year bond return is known at 5%, and the 2-year bond carries a yield of 4% and gains 1% in capital gains as rates rally from 4% to 3%. The 2-year bond becomes a 1-year bond in a year’s time.

The reality, of course, is that the spot curve rarely converges to the forward curve. Forwards, however, can give you a good insight into expectations and what the carry of a position is. Very simplistically, a bond carry is comprised of obviously the coupon or yield and the roll-down yield as well the expected conversion to its forward rates. If your forward rate, like in the above’s example of the 2-year bond, is lower than your bond yield, you are running a negative carry position, purely as the bond would need to fall to the required forward rate, crystallising capital gains for you have a same horizon return as the one year bond.

A similar analysis can be done on yield curves as a whole, where the current spot curve converges to the forward curve. Generally, yield curve flattening trades are carrying highly negatively. Without going into much detail in this post (I will cover this in another post), yield curve trades are duration neutral, i.e. for a 2-10s flattener, you will have to sell quite a bit more 2-year bonds than 10-year bonds. In bond futures, the ratio will be roughly 3 to 1. This also implied a certain amount of leverage when trading curves.

Generally, the real money community (pension funds, large institutional asset managers, etc.) are structurally in flatteners, using their short-end exposures in government bonds as funding to buy corporates, emerging markets etc. It is practically impossible for them to be in steepeners, given the large cash and leverage requirements to heavily overweight the front end.

Further Reading

If you want to dig a bit deeper into the topic, I would suggest downloading the file I have set up for sharing here. This is part 1 of Antti Ilmanen's phenomenal work. He is basically the god of yield curves with a career spanning multiple decades from Salomon Brothers to Brevan Howard and now AQR. He is a lovely guy too. I will upload the rest of his work in due course, although I think you will also be able to find it on the web somewhere.

Music

Easy listening. I came across this slightly trippy yet very upbeat track while trying to find new tunes. Hope you enjoy it as much as I did!

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Paper Alfa

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