Meeting-implied probability from a fed funds futures price
Source:R/converters.R
q_from_ffutures.RdConverts the price of the 30-day fed funds futures contract for a
meeting month into the probability of a rate move of size step,
using the standard month-average extraction: the contract settles on
the monthly average effective rate, the pre-meeting rate applies
through the decision day, so
$$r_{post} = \frac{M\,\bar r - d\, r_{pre}}{M - d}, \qquad
q = \frac{r_{post} - r_{pre}}{step},$$
with \(\bar r = 100 - \mathrm{price}\), M calendar days in the
month, and d the day of the month of the decision.
Arguments
- price
Futures price(s), e.g.
95.21.- pre_rate
Effective rate prevailing before the meeting (percent, e.g.
5.33).- meeting_date
Decision date(s) (
Date); see fomc_meetings.- step
Assumed move size in percentage points (default
0.25).
Value
A tibble with columns meeting_date, implied_avg,
implied_post, delta_rate, and q (probability of one step
move; sign of delta_rate gives the direction).
Details
q is the probability of a single move of step under a two-point
assumption (no change vs. one move). Values outside \([0,1]\)
indicate that more than one step (or a move of the opposite sign) is
priced: q = 1.6 means 25bp fully priced plus a 60% chance of a
second step; negative values indicate a priced move of the opposite
sign. Flag, don't drop. For a decision on the last day(s) of the
month the denominator degenerates — use the next-month contract.
Intermeeting moves and months with two meetings violate the two-point
assumption; flag such periods separately.
Examples
# decision on the 15th of a 30-day month, pre-meeting rate 5.33%,
# futures at 94.79 -> a 25bp cut is priced with ~96% probability
q_from_ffutures(94.79, pre_rate = 5.33,
meeting_date = as.Date("2024-09-15"), step = -0.25)
#> # A tibble: 1 × 5
#> meeting_date implied_avg implied_post delta_rate q
#> <date> <dbl> <dbl> <dbl> <dbl>
#> 1 2024-09-15 5.21 5.09 -0.240 0.960