Explaining Constant Maturity Volatility
and the theory of relativity
A reader,
(thank you!) commented from Focus in the Midst of Noise:A quick explainer or a post on interpolating "constant maturity" vols would be very helpful. Also is this information tradable? I mean, as we are interpolating, there is no real 7day straddle out there for us to trade on.
As a note for both me and readers, I really appreciate the comments because it helps me to determine what is interesting and also gives me a topic to write about 😊.
A little bit of history about “constant maturity” assets. This is, as far as I know, about fixed income instruments. You may ask “what is the yield on 10-year US Treasuries?” You may want to know what the yield is on current 10s (the most recently issued and most liquid). It is issued quarterly and may be 2 months old and there may be other US Treasuries in that area (prior bonds issued originally as 20-year or 30-year securities and have aged into the 10-year region). It may even more than 2 months since the current 10s were issued because if rates have not changed much, then the Treasury department may just do a “re-opening” which is what issuing more of an existing note is called (this is for any maturity). If your goal is to buy US Treasuries of 10-year maturity, then any of them will be functional for you. If your goal is to create analytics or simply choose an area of the yield curve to invest in, then having a target that is comparable over time is quite useful. Or, it is likely a very good choice for basing the price of other (derivative) securities. For instance, someone’s mortgage may be based on a 1-year Constant Maturity Treasury (CMT).
Why is this needed?
Let’s say you want to look at the 2s-10s yield curve for economic analysis. This is around 50bps right now and you want to build a regression. If you used the current 10yr rather than the CMT, you would run into problems because the current 10yr might be significantly shorter than 10yrs. If the curve is 50bps from CMT 2s to CMT 10s, then there is 6.25bps of steepness each year (on average). 10s are auctioned quarterly and there may be a reopening. So it is not unusual for the current 10yr to be 9.5 years instead of 10. Going with the current 10 might give a 2s-10s measure of 46.9 bps (50 - 6.25 bps/yr * 0.5 yrs). That may not seem like much, but it will definitely ruin a model. This gets even more impactful for more sophisticated spreads, like a 2s-5s-10s butterfly1.
For short dated Treasuries, particular dates or coupons2, will trade rich or cheap depending corporate and investor demand. An example would be a bill that expires just before taxes are due. That Tbill would be in high demand as treasurers of corporations know in advance that they will be needing higher amounts of USD to pay their taxes at that time. Having an investment that matures just after tax day does not help. So that date may trade 5bps rich to where a model might otherwise expect. I was never a market maker in Tbills, so I don’t know all the ins and outs, but I traded on the money market desk, so I know enough to know that things get very specific especially as maturity approaches (say inside 1 month).
Sometimes certain Treasuries are used as hedges against other things, such as swaps or futures. One such note would be the “cheapest to deliver” for the various futures contracts. This can distort the pricing of a particular note as all of a sudden the nature of that particular security deviates from being part of a yield curve and, instead, is an ingredient into a financial engineering recipe.
Like everything else, the tools that you are using depend on your purpose. Are you trying to get a general sense of interest rates or implied volatility? Or are you making a market? Are you a top down portfolio manager or are you trying to construct a trade around a particular event coming up in the next 3 days? Heck, is implied volatility even the right metric for analyzing 7-day options? Maybe I should be doing the price value of the straddle itself? And, if so, in absolute dollars or in percent of spot?
Going back to the original post which was going into further detail on my daily sheet, my purpose is to both get myself into the mindset for the day (like warming up before a game) and also to get a general sense of what is going on. Having the checklist does not, in itself, deliver the goods. It is meant to be the starting point of getting to what is important on that day. I might be looking at the 7-day CMV but I’m also looking at the calendar to see what may be happening over the next 7 days. Put a pin in that for a moment.
Funny enough, last week’s post “The Average is not the Distribution” discusses the idea of having assumptions baked into your tools. That, in itself, is not a problem. The problem is not being aware of it or simply having it being the “air of your environment”3 so that you don’t even realize it is an assumption. Constant maturity vols (or interest rates) have the same sort of embedded assumption. In this case the assumption is that all days are created equal. Or, maybe better, the assumption is that calendar time = business time4. That is not always the case.
An FOMC announcement date or an employment situation report date reprent entirely different volatility prospects than a day that does not have that sort of data release. Weekends are different than weekdays. This can matter a whole lot if the FOMC meeting is 3 days from now vs a month. There a couple of things at play here. First is the relationship between calendar and business days. And second is the relationship about how much events matter for different expiries.
Let’s start with number 2. Specific events matter differently for short dated options and longer dated options. This may seem obvious, but it is worth examining for a quick moment. Longer dated options (and longer dated fixed income instruments) live in the world of the law of large numbers. In the world governed by the law of large numbers things like “mean reversion” and just generally being able to make reasonable predictions about a distribution have some meaning. In the world governed by the law of small numbers, well this is the land of GFL (good “fugazi” luck) predicting that. This is the land where the FOMC announcement lives and where crypto (ETH!) can drop 20% in a 15-minute price bar on Sunday evening (NY time). Here, 7d CMV may be a good measure to start with but may need significant additional information about data releases and positioning.
Coming back to number 1 and where we left the pin, we need to assess the relationship between calendar and business days. Here we need to think about what scheduled data may be released, who may be the President and what is their predilection for over the weekend announcements, how much leverage is in the system, and is the asset at all-time-highs? This is not limited; there are hundreds of such questions that mean different things at different times. All of this means that measuring CMV is not only incomplete, but so is looking at specific expirations. We need something that at least begins to turn calendar days into business days. Which is to say to come up with a weighting scheme of some sort. The best description of this is Kris Abdelmessih’s post on variance time. I must warn you that even that is not the endpoint. One may decide that non-farm payroll dates are worth 2 calendar days, but still in your head need to figure out that this one is more like 1.5 calendar days and another might be worth 4.
When I started writing this post, I was concerned it would be too short. And now, it seems like a lot. Let me leave you with a takeaway or 2:
There are alternatives to using synthetic constant maturity assets. One can use the raw dates that are tradable. The clear advantage is that it actually exists and is tradable. The disadvantage is frequently that unless there is continuous data, discrete dates are going to create irregularities that will cause problems for models. On the other hand, using CMV for trading inputs may cause problems for pnl’s.
In measuring volatility, it makes sense to have different perspectives. Are you trading where things are dominated by the law of large numbers? Or where “anything goes”?
Probably the best takeaway is that when something matters a lot, measure it in multiple ways. This may be measuring option implied volatility or it may be measuring an economy.
This is not easy. This is one of the areas where the professionals and the amateurs separate. There is no substitute for doing the work.
An investor might use a butterfly to allocate across the curve. Right now, 2s-5’s is 10bps, but 5s-10s is 38bps. So the butterfly is -28bps. An interpretation might be: “Hey, I can either buy a 5-yr or buy the combination of 2’s and 10’s. If I buy 2’s and 10’s then I pick up an extra 28bps into my portfolio”. Trust me when I tell you that there are all sorts of additional risk & reward parameters to incorporate into this decision, but this is a start. A post on butterflies will be forthcoming.
The coupon refers to the amount of interest paid according to the note’s schedule. For example, there may be a 2 1/4% of Nov 15, 2025 that has a coupon of 2.25% with interest paid semi-annually. This is different than the YTM (yield to maturity) which incorporates the current price and the coupon of the note to determine its yield.
Meaning that it such an assumed part of our being that it we fail to notice it. It is like how we don’t give much thought about the air or breathing.
Calendar vs. business time may not be immediately clear. Calendar time is, as is probably clear, represents the literal calendar day. Business time matters a lot. As a general rule, in trading the first 30 minutes of trading (the open) matter a lot more than 11:30a to noon. If you work at a fast food restaurant, the lunchtime rush from 11:30a to 1:30p is a lot different than from 9:30a-11:30a. That’s business time. Both are technically 2 hours (calendar time), but they mean completely different things to the people working there.
Thank you!!!
This was a nice explainer 😄