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How Higher Rates Cause Big Changes in the Bond Contract

October 17, 2023 4 comments

Two weeks ago I pointed out one of the effects of higher interest rates is that leveraged return strategies get swiftly worse as rates rise. Today, I want to talk about another result of higher interest rates which is, to me, much more fun and exciting. It involves the Treasury Bond cash-futures basis.

I know, that doesn’t sound so interesting. For many years, it hasn’t been. But lately, it has gotten really, really interesting – and institutional fixed-income investors and hedgers need to know that one of the major effects of higher interest rates is that it makes the bond contract negatively convex, not to mention that right now the bond contract also looks wildly expensive.

Some background is required. The CBOT bond futures contract (and the other bond contracts such as the Ultra, the (10y) Note, the 5y, and the 2y) calls for the physical delivery of actual Treasury securities, rather than cash settlement. Right now, thanks to ‘robust’ Treasury issuance patterns, there are an amazing 54 securities that are deliverable against the December bond futures contract. The futures contract short may deliver any of these bonds to satisfy his obligations under the contract, and may do so any time within the delivery month.

Now, if we just said the short can deliver any bond, the short would obviously choose the lowest-priced bond. The lowest-coupon bond is almost always going to be the lowest-priced; right now, the 1.125%-8/15/2040 sports a dollar price of 55.5.[1] But if we already know what bond is going to be deliverable, and it’s always the optimal bond to deliver, then the futures contract is just a forward contract on that bond, and it becomes very uninteresting (not to mention that liquidity of that one bond will determine the liquidity of the contract). So, when the contract was developed the CBOT determined that when the bond is delivered it will be priced, relative to the contract’s price, according to a conversion factor that is meant to put all of the bonds on more or less similar footing.[2] The price that the contract short gets paid when he delivers that particular bond is determined by the futures price, the factor, and the accrued interest on the delivery date…and not the price of the bond in the market.

Because the conversion factor is fixed, but the bonds all have different durations, which bond is cheapest-to-deliver (“CTD”) changes as interest rates change. When interest rates fall, short-duration bonds rise in price more slowly than long-duration bonds and so they get relatively cheaper and tend to become CTD. When interest rates rise, long-duration bonds fall in price more quickly than short-duration bonds and so tend to become CTD in that circumstance. And here’s the rub: when interest rates were well below the 6% “contract rate”, the CTD bond got locked at the shortest-duration deliverable, which also usually happened to be the shortest-maturity deliverable, because that bond got cheaper and cheaper and cheaper as the market rose and rose and rose. The consequence is that the bond contract, as mentioned earlier, eventually did become just a forward contract on the CTD (and a short-duration CTD at that), which meant that the volatility of the futures contract was lower, the implied volatility of futures options was lower, and the price of the futures contract was uninteresting to arbitrageurs because it was very obviously the forward price of the CTD. And this situation persisted for decades. The last time the bond and 10-year note yielded as much as 6% (which is where all of the excitement is maximized, since after all the conversion factor is designed to make them all more or less interchangeable at that level) was 2000. [Coincidentally or not, that was right about the time I stopped being exclusively a fixed-income relative value strategist/salesman and started trading options, and then inflation.]

So, now the long bond yields 4.96% and the deliverable bonds in the December bond contract basket have yields between 5.03% and 5.22%. This starts to get interesting. As of today, the CTD bond is the 4.75%-Feb 15, 2041. If you buy that bond and sell the contract,[3] then the worst possible case for you is that you deliver that bond into the contract and lose roughly 12/32nds after carry.

However.

Because you are short the futures contract, you can deliver whatever bond is most-advantageous to you at the time you elect to deliver. If any other bond is cheaper than the 4.75s-Feb41, then you buy that bond, sell the Feb41s, and deliver. And obviously, that’s a gain to you. And you can make that switch as often as you like, up until delivery.

Can you predict approximately when the bonds will switch? Sure, because we know the bonds’ durations we can estimate the CTD – and the value of switching – for normal yield curve shifts. While the steepening and flattening of the deliverable curve also matter, remember that anything that adds volatility to the potential switch point adds value to you, the futures short. Here is, roughly, the expected basis at delivery of that Feb41 bond.

Now isn’t this interesting? If the bond market rallies, then we know that shorter-duration bonds will become CTD, pushing the Feb 41s out. And if the bond market sells off, then we know that longer-duration bonds will replace the Feb 41s as CTD. Notice that this looks something like an options strangle? That’s because it essentially is. You own a strangle, and you’re paying 12/32nds for that strangle. (Spoiler alert: you can sell a comparable options position in the market for roughly 28/32nds, making the basis of that bond about half a point cheap, or equivalently the futures are about half a point rich.

Okay – if you’re not a fixed-income relative value strategist…and let’s face it, they’re a dying breed…then why do you care?

If you’re a plain old bond portfolio manager, you may use futures as a hedge for your position; you might use futures to get long bonds quickly without having to buy actual bonds, or because you aren’t allowed to repo your physical bonds but you can get some of the same benefits by buying the futures contract. You might buy options on futures to get convexity on your position, or to hedge the negative convexity in your mortgage portfolio.

Well guess what! None of that stuff works the same way it did 15 months ago!

Because longer-duration bonds are CTD now, the contract has more volatility. Which means the options on those futures have more implied volatility. Also, the bond contract is no longer guaranteed to be within a tick of fair value because the CTD is locked. When I worked for JP Morgan’s futures group, we thought if the futures contract got 6 ticks rich or cheap it was exciting. Well, we’re looking at a futures contract that’s a half-point mispriced![4]

Finally – as I said, the bond contract now has negative convexity, which means that when you are long the contract you will underperform in a rally and underperform in a selloff (while earning the net basis of 12 ticks, in a best case). Because when you own the bond contract you have the opposite position I’ve illustrated above: you’re short a strangle. If you’re long the contract then as the market sells off the bond contract will go down faster and faster as it tracks longer and longer duration deliverables. And if the market rallies, the contract will rise slower and slower as it tracks shorter duration deliverables. The implication is that especially because the bond contract is rich, it is great as a hedge for long cash positions at the moment, and a pretty bad hedge for short positions. And it’s great to hedge long mortgage positions, since when you sell the contract you also pick up some convexity rather than adding to your short-convexity position.

This all sounds, I’m sure, very “inside baseball.” And it is, because most of the people who used to trade this stuff and understood it are retired, have moved to corner offices, or are old inflation guys who just wonder why we don’t have a deliverable TIPS contract. But just as with my article two weeks ago, it’s something that I think it important to point out. We’re so obsessed with the ‘macro’ implications of higher rates, we stand to miss some of the really important implications on the ‘micro’ side of things!


[1] I’m using decimals to make this more accessible to non-bond folks, but we all know that this really means 55-16.

[2] The conversion factor is the answer to the question, “what would the price of this bond be if, on the first day of the delivery month, it were to yield exactly 6% to maturity”? So the aforementioned 1-1/8 of Aug-40s have a conversion factor into the December contract of 0.4938 while the 3-7/8 of Aug-40 has a conversion factor of 0.7794.

[3] I am abstracting here from the more technical nuances of how one weights a bond basis trade, again for brevity and accessibility.

[4] There’s a big caveat here in that the yield curve dynamics in my model for the shape of the deliverable bond yield curve are out-of-date, as I haven’t used this model in years…so the contract might be anywhere from 10 ticks to 20 ticks rich. But it’s rich!

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