Fed Odds: Math

Credit Monday Morning Macro

FFQ9: “no cut” = 97.86871 & “25bp cut tmrw” = 98.05419, we can work out what mkt px 97.885 implies. That is: 97.885 = 98.05419 * X + 97.86871 * (1 – X), where X = prob% of a cut tmrw. Apply a little grade-school math: X = 8.78%.


At its most extreme this morning, I’d estimate the mkt was pricing in almost 10% probability of a 25bp cut by the Fed tomorrow. How do I figure? It’s based on FFQ9 (August Fed Funds futures).

WARNING: This will involve some basic math.

FFQ9 is the 30-day August Federal Funds futures contract. It’s priced as a simple average of Daily Effective Federal Funds Rate (hereafter “EFFR”) for each day of the month. That rate is published in arrears (i.e. what’s published today is yesterday’s rate) on a daily basis at 9:00am EST by the New York Fed. It’s currently 2.13% (3bps over IOER).

IMPORTANT NOTE: There’s an extremely large number of realistic possible outcomes, including those where IOER continues to drift lower. There are reasons relating to the plumbing of the money markets that make this unlikely, but it’s a possibility. I’m only addressing the one which is most pressing: the market-implied probability of an emergency Fed ease. 

Here’s a table showing how this daily calculation works with 3 different scenarios which I’ll discuss in more detail below. 

No color = days we already know, Orange = future days (we don’t know today’s rate yet), Red = assumes the Fed cuts

EFFR has been trading anywhere from flat vs IOER to 5bps over for the better part of the last 6 months. When the Fed cut rates on July 31, EFFR went down by 26bps – from 2.40% to 2.14%. It stayed at 2.14% for the first two business days of the month, then went to 2.13%.

Because EFFR stayed at 2.14% on Friday August 2nd, that means according to the calculation methodology that the first 4 days of the month (i.e. the non-business days of Sat & Sun) also get counted as 2.14%. Therefore, assuming the Fed doesn’t do anything the rest of the month, the fair value of FFQ9 would be calculated as the simple average of 4 days at 2.14% and 27 days at 2.13%. Therefore price = 100 – rate = 97.86871.

But FFQ9 traded at 97.885 this morning! So what gives?

Clearly the mkt is pricing in some probability of EFFR being much lower that 2.13% at some point this month. But when? Emergency eases are just that: “emergencies”. They’re not telegraphed ahead of time or scheduled. So, we can only calculate probabilities by making an assumption about the day of the cut. 

Let’s take an example. Say the Fed cuts by 25bps on the last Thursday of the month (8/29), for whatever reason. EFFR only falls on the day AFTER a Fed cut (it wouldn’t take effect the same day), so we’d have two days of 2.13% – 25bps = 1.88% (8/30 & 8/31). Under that scenario FFQ9 = 97.88484. Close to current market pricing. But that’s assuming a 100% probability of a cut on 8/29. Markets don’t work in 0% or 100% probabilities. It’s frequently something in between. So then, what’s the probability of the Fed cutting 25bps TOMORROW?

If the Fed cut 25bps tomorrow, that would mean we’d have 4 days of 2.14%, 4 days of 2.13% (both today – which we don’t know yet – and tmrw would be 2.13% along with Monday & Tuesday’s rates), and 23 days of 1.88%. That price works out to 98.05419. Given that, we can work out what the probability assigned to this outcome should be.

If “no cut” = 97.86871 and “25bp cut tmrw” = 98.05419, we can work out what a market price of 97.885 implies. That is:

97.885 = 98.05419 * X + 97.86871 * (1 – X), where X = probability of a cut tmrw.

By applying a little elementary algebra, X = 8.78% or ~9%. 

Now, clearly, there’s a lot at work here. The market has to price in all possible paths of cuts which could theoretically take place on any day (including a weekend, in theory, which would cause EFFR to take effect at the lower rate on the following Monday). As I’m writing this, FFQ9 has ticked back lower, suggesting that the market is assigning less probability to a forthcoming emergency ease. But it’s clearly a fluid situation. SPX another -5% might alter the entire calculus.

Also, EFFR could drift lower relative to IOER. I would emphasize “could”. We “could” also drift higher. The odds of those events are roughly offsetting, to be conservative. We spent the last month trading closer to 5bps over IOER (which, if applied to the scenario for the rest of this month, would imply an even higher mkt-implied probability for emergency Fed action). 


Brian Twomey

FED Rates: Odss Priced

Credit to Monday Morning Macro

For those looking for a more detailed way of thinking about “odds”, a brief practitioners’ guide below. 

First, the September “odds”. The simplistic way to think about the pricing of odds for Fed cuts at upcoming meetings is to look at how many basis points lower that rate is versus the current spot rate. Right now, here’s what those rates look like vs the 1-month “spot” rate.

What’s currently priced into each of the mtgs this year.

In other words, the September FOMC is pricing in a total of 34.5bps, the October meeting is pricing in just over 2 “cuts” between now & then, and the December meeting is priced for just under 3 “cuts”.

What’s crucially important is this: just because the September FOMC has 34.5bps priced in, that doesn’t mean that there’s a 62% chance of a 25bps cut & a 38% chance of a 50bps cut.

If that were true, then that would mean you’d need to think there was 0% chance of the Fed staying on hold (it’s low, to be sure, but nothing’s 0% until it’s realized) *and* more importantly 0% chance of the Fed cutting by any more than 50bps. Clearly, that can’t be the case either. The Fed has routinely cut by more than 50bps in a crisis (the GFC, for example) and they will again. There’s a better way of doing this, and it involves using the options market.

Using current Fed Funds curves & fwd FRA/OIS, we can fit all possible Fed “paths” between now & the end of this year to current mkt pricing of the Eurodollar & OTC swaption mkt. The resulting probability distribution returns a shape of the fwd OIS curve for each meeting.


Brian Twomey


Fed Rates, CME Tool, Term Premium

Credit to Monday Morning Macro

One brief note on methodology: the CME “FedTool” has a similar probability tree but it calculates the odds using binary Markov chains. In a nutshell, this means that they only allow for 1 of 2 outcomes to be altered at a given meeting. If you think the Fed could either stay on hold, cut by 25, cut by 50, or more (which the options market is telling us is a possibility – why else would somebody be wanting to pay anything at all for something like the EDU9 98.50 calls?), then a binary chained decision tree isn’t correct. Look closely at the CME tool, they show zero probability for an “on hold” result. Even in this cynical world of second guessing policymakers, we should know that can’t be correct with more than a month still to go…


3. Funding

One of the aspects of the financial crisis that was so devastating to the credit market was the fact that funding spreads experienced a seizure unlike anything they’d seen previously. Steps were taken in the aftermath to buttress the industry against this happening again, but we still see periodic flare-ups in funding markets that often precede meaningful volatility in other asset classes. The most popular measure of this to follow is the spread between bank borrowing rates (representing unsecured credit) & the overnight Fed rate (representing secured credit): LIBOR vs OIS, also referred to as FRA/OIS (FRA = forward rate agreement). When this spread widens, it indicates funding stress is present. The Dec 19 future associated with this spread is now at its widest levels since early February 2018.


The Federal Reserve tracks what’s called “Term Premium”. The best way to understand this is as a measure of what compensation you’re receiving (once you strip out all the effects of inflation & some other econometric factors) for owning Treasuries. This seems like a sensible measure to watch: if you’re getting 1.625% in interest for 10-year bonds, but the inflation rate is the same – then it’s not really all that much compensation you’re earning in the end.

Currently, we’re at -1.21%. That’s easily the lowest since the Fed started tracking this in 1960.


Brian Twomey