A Warped WIRP

Bloomberg created a function that claims to give the odds of a Fed move by interpolating from the Fed funds futures and options contracts. It is widely used, but I remain a skeptic.

Bloomberg created a function that claims to give the odds of a Fed move by interpolating from the Fed funds futures and options contracts. It is widely used, but I remain a skeptic.

It uses assumptions that are not particularly transparent. These are particularly important given that unlike past cycles, the Federal Reserve has adopted a target range for Fed funds. Where Fed funds trade relative to its range key for the futures contract, but is unknown. In addition, the incorporation on options pricing, which often thinly traded with wide spreads between bids and offers, needlessly inject noise into the calculation.

Bloomberg over-engineers its analysis. It is helpful to return to basics. The Fed funds futures contracts settle at the average effective Fed funds. The December meeting concludes on December 16. The effective Fed funds rate has been averaging 14 bp.

If we assume that, the Fed funds average 14 bp through the Fed meeting (14 bp times 16 days equal 224). What should we assume for the second half of the month? One idea is that it averages the middle of the new range as it has averaged around the middle of the old range. So if Fed funds average 37 bp in the second half of December (37 bp times 15 days equal 555). We add the two sums together (224 plus 555) we get 779. We divide by 31 to get the daily average (779/31), and we get 25.1. Currently, the December contract has an implied yield of 20.5 bp.

Fair value ranges from 14 bp on the idea that it does not raise rate this year to 25.1 bp on a quarter-point hike. At 20.5 bp, the December contract implies at 58.6% chance of a hike. The difference between the current effective Fed funds rate and effective rate on a 25 bp hike is 11.1 bp and the December contract. Of that 11.1 bp, the December contract has priced in 6.5 (6.5 divided by 11.1 equals 58.6%).  Bloomberg’s WIRP calculation says there is a 36.4% chance of a 25 bp hike the target range at the December FOMC meeting. 

What if the effective Fed funds rate does not average the middle of its range?  What if the reason it has averaged the middle of its current range has to do with the zero boundary?  Unlike past tightening cycles, the Federal Reserve now pays interest on excess reserves.  It pays a rate equivalent to the upper end of the target range. 

What if, in order to provide the maximum incentive to keep the excess reserves parked at the Fed, the central bank provides sufficient liquidity to keep the effective Fed funds at the lower end of its new range?  That would be 25 bp rather than the 37 bp assumed in our earlier exercise.  Fair value of the December contract would be the 14 bp for the first 16 days and then 25 bp for the remaining 15 days divided by 31 days of the month ((14 times 16) plus (25 times 15))/31 or 19.3 bp.

With the December contract implying 20.5 bp, this would be perfectly consistent with a rate hike in December, discounted by the market.  This illustrates the importance of the assumption of where Fed funds average after the hike.  WIRP simply skirts this issue.  Reasonable people can and do differ.  It is worth knowing the assumptions behind the calculations.  Over-engineering means that even when there is no change in the pricing of the futures contract, a change in options pricing or volatility translates into a change in the WIRP probability assessment.

Rather than taking a blackbox answer, one can calculate what the market is discounting quickly and easily.  One needs to know simply the meeting schedule during the month, where Fed funds are averaging before the meeting, and an assumption about where it will average after the meeting.  The Fed funds futures contract settles at the average effective rate over the course of the month rather than at the policy rate.

Why I Don’t Use Bloomberg’s WIRP Function is republished with permission from Marc to Market