Inferring a Rate-Hike Probability from Short-Term Rates

Summary

The document shows how to infer a market-implied probability of a 25-basis-point rate hike from one- and two-month rates, assuming only two possible outcomes: no change or a hike. It compounds the current rate under the unchanged scenario, then compares that value with the result of applying the higher rate for the later month. The observed two-month rate is placed between these scenario values to estimate the probability assigned to the hike.

For the stated example, this interpolation yields an 80% implied probability. The estimate depends on the two-outcome assumption and on treating the quoted rates as comparable annualized rates for the relevant periods. It is an inference from market pricing, not a direct measure of the actual chance of a policy change; additional possible outcomes, conventions, or pricing effects could change the interpretation.

Key ideas

• Compare compounded values under the unchanged-rate and hike scenarios to interpret the longer-term rate.
• The implied probability comes from locating the observed rate between the two scenario values.
• The example assumes only two outcomes: no rate change or a 25-basis-point increase.
• An inferred market probability depends on the scenario assumptions and rate conventions.

Tags

# Probability of interest rate hike using 30 and 60 day rates


# Probability of interest rate hike using 30 and 60 day rates












How can I calculate the probability of a rate hike of 25 bps if 30 day rate is 3% and 60 day rate is 3.1%? I thought I need the implied federal funds rate but it is not given.

## Answer by demully (score 1)

https://quant.stackexchange.com/a/50874

Market participants usually look at the Eurodollar, Euribor, Short Sterling strips etc. These are discrete forecasts of a rate at a discrete point in time. So if Mar is 3.0% and Jun is 3.1%, then there is a 40% chance of a 25bp hike priced in Q2 etc.

For your example, it's 80%. There are two scenarios = unchanged, or a hike. If unchanged, then I compound two months of current 3.0% annual rates. 1 becomes 1.00494. If the hike, then compound one month at 3.0% and one at 3.25%. 1 becomes 1.00514. Compound two months at the 3.1% 60 day rate, 1 becomes 1.00510. This is at the 80% percentile of the range between the two scenarios.

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.