Estimating a Fed Rate-Hike Probability from Fed Funds Futures
Summary
The note shows how to infer a market-implied probability of a Federal Reserve rate hike from a monthly fed funds futures settlement. Because the contract settles against the average effective federal funds rate across the month, its price reflects both the days before a possible policy change and the days after it. The example separates those periods, solves for the implied rate in the latter part of the month, then treats that rate as a probability-weighted average of a hike and no change.
The calculation produces an estimated 79% chance of a 25-basis-point hike in the stated December 2015 example. It is an approximation: it equates the target and effective rates, uses the midpoint of the target range, and assumes only two outcomes. The implied probability therefore depends on those assumptions and on the contract’s averaging convention; it is not a direct observation of traders’ individual beliefs.
Key ideas
- Monthly fed funds futures reflect the average effective rate over the contract month.
- A policy change partway through the month affects only the days after that change.
- The settlement can be converted into an implied average rate for the remaining days.
- A two-outcome model translates that implied rate into a hike probability.
- The estimate depends on simplifying assumptions about rates and possible policy outcomes.
Tags
Full text
# Dec 16: FED rate hike?
# Dec 16: FED rate hike?
Various news articles state that next Wednesday a rate hike by the FED was expected.
Yet when I look at fed-rate futures, nobody seems to expect that: http://www.cmegroup.com/trading/interest-rates/stir/30-day-federal-fund.html
Can someone with industry insight elaborate on what traders expect?
Verbal answers on what is currently expected regarding the FED's rate hike are also accepted.
## Answer by Helin (score 12, accepted)
https://quant.stackexchange.com/a/22311
Fed funds futures settle into the average daily Fed Funds effective rates over the month. The December 2015 futures contract therefore covers the current Fed funds target rate (0-25bp) for 16 days, and then the new rate range (expected to be 25-50bp) for 15 days.
To compute the exact probability of a rate hike involves some assumptions. For simplicity, let's ignore the difference between Fed funds target rate and Fed funds effective rate. Further, let's use the mid-point of the Fed funds target range as the target rate. For the first 16 days of December then, we are talking about an average realized rate of 12.5 bp (mid point between 0 and 25 bp). As of last Friday, Dec FF contract settled at 99.78, implying a rate of 22bp. To get to this settlement price, the target "rate" for the final 15 days must satisfy $$ 22 = \frac{12.5 \times 16 + r \times 15}{31}.$$ This suggests $r = 32.133333333 \text{ bp}$.
Now the only thing left is to compute the probability of a hike. Let $p$ be the probability of a 25 bp hike (from 12.5 to 37.5), and $1-p$ be the probability of being on hold (staying at 12.5). Then we have $$ 37.5 p + 12.5\times (1 - p) = 32.1333. $$ This implies that the market is pricing in a $(32.13 - 12.5)/25 = 79\%$ probability of a rate hike in December.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.