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Inferring Fed Rate-Hike Odds from Fed Funds Futures

Article Quant Q&A · Author: i_love_rain
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Summary

The document shows an attempt to reproduce a Federal Reserve rate-hike probability displayed by a futures-market calculator. It uses two monthly fed funds futures prices to infer the implied average rates for the current and following months, then solves for the rate expected during the remaining days of the later month. The resulting implied rate is compared with the assumed target-rate increment to estimate the probability of a hike.

The calculation yields a probability below the calculator’s displayed figure, and the post asks what has been missed. It offers no answer or validation, so the arithmetic should be treated as an unresolved example rather than a reliable recipe. Such estimates depend on contract settlement conventions, day weighting, the effective funds rate’s relationship to the target range, and the precise policy-rate change assumed. The document identifies the ingredients of the calculation but does not explain the discrepancy or establish which probability is correct.

Key ideas

  • Monthly fed funds futures prices can be used to infer market-implied average rates.
  • The example weights rates by the number of days before and after a policy decision.
  • The author’s calculation does not match the probability shown by the cited market tool.
  • The post leaves the discrepancy unresolved and does not validate its probability estimate.

Tags

FuturesFixed incomeUS marketsStatistics
Full text
# CME Rate Hike Probability Calculation


# CME Rate Hike Probability Calculation












First thing first, CME has a tool to calculate fed rate hike probability from here.

As of 11/20/2017, their probability distribution was like this:

I have checked a couple Q&A sections on this site and I think I understand their logic, for example this one. I also read CME's documentation. But still i was not able to back out the probability of 91.5% for a December 2017 rate hike using their fed fund future prices. I got a probability of 85.6905%. $$r1 = 100 - 98.8432 = 1.1562$$ $$r2 = 100-98.7125 = 1.2875$$ $$1.2875 = (1.1562*12 + r*19)/31$$ which implies $r = 1.370426$, and:

$$P(\text{hike}) = (1.370426 - 1.1562)/0.25=0.856905$$

What did I missed?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.