How to calculate fed funds rate probabilities from futures prices
Quick answer
To calculate Fed Funds rate probabilities, use the formula: Post-meeting rate = (ZQ implied rate × days in month - pre-meeting days × current EFFR) / post-meeting days. Then P(25bp cut) = (current EFFR - post-meeting rate) / 0.25. For example, if EFFR is 5.33% and the implied post-meeting rate is 5.12%, the probability of a 25bp cut is (5.33 - 5.12) / 0.25 = 84%.
The formula
The implied probability of a Federal Reserve rate change can be extracted from Fed Funds futures (ZQ contracts). This is the foundation of every 'rate probability' tool in finance, including CME's FedWatch.
The core formula relies on a simple observation: ZQ futures settle at the average effective federal funds rate (EFFR) for the delivery month. Since FOMC meetings happen on specific dates within the month, the pre-meeting and post-meeting rates are day-weighted.
The day-weighted calculation
For a meeting on day D of a month with N total days:
ZQ implied rate = (D × pre-meeting rate + (N - D) × post-meeting rate) / N
Rearranging for the post-meeting rate:
Post-meeting rate = (ZQ rate × N - D × pre-meeting rate) / (N - D)
This gives you the market-implied rate after the FOMC decision. The probability of a 25bp cut is then:
P(cut) = (current rate - post-meeting rate) / 0.25
Worked example with current data
Let's work through a concrete example. Suppose:
• Current EFFR: 5.33% (midpoint of 5.25-5.50% target range)
• Current-month ZQ: 94.79 (implied average EFFR of 5.21%)
• FOMC meeting: day 13 of a 30-day month
Step 1 — post-meeting rate:
Post-meeting rate = (5.21 × 30 - 13 × 5.33) / 17 = (156.30 - 69.29) / 17 = 5.118%
Step 2 — probability of a 25bp cut to 5.00-5.25% (midpoint 5.08%):
P(25bp cut) = (5.33 - 5.118) / (5.33 - 5.08) = 0.212 / 0.25 = 84.8%
P(no change) = 1 - 84.8% = 15.2%
In Excel
The Excel formula for the post-meeting rate is:
=(B2*C2 - D2*E2) / (C2 - D2)
Where B2 = ZQ implied rate, C2 = days in month, D2 = meeting day, E2 = current EFFR.
For the probability:
=(E2 - F2) / 0.25
Where F2 = post-meeting implied rate.
For future meetings
Meetings beyond the current month require the conditional probability tree approach. Each meeting's probability depends on what happened at the previous meeting. The math gets more complex but follows the same day-weighted logic applied recursively.
See our full FedWatch methodology article for the complete multi-meeting calculation.
Or skip the calculation entirely
Quadesto implements the full FedWatch probability calculation automatically. Connect your ZQ futures data source (or use our live feed) and see the probabilities for all upcoming FOMC meetings instantly. Every number is auditable — click any probability to see the underlying calculation.