# 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.

## 1 Answer

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.

• Thanks for your detailed computation. However I am not sure how you can infer the probability from this average rate $r$. E.g. if $r>37.5$, you would have a probability $>1$. Probably you are assuming that the probability for a rate decrease is $0$, and that the rate will increase if only by $0.25$. Please elaborate on all your assumptions in the answer. – emcor Dec 13 '15 at 22:57
• Answer updated. From Fed funds futures, you can only compute probabilities of two outcomes. It's a common assumption that the hike size is 25bp (the Fed has rarely deviated from this since 1994). – Helin Dec 13 '15 at 23:00
• If the interest is paid at the end of December, please include time value in your calculation to be exact. Please explain the appropriate discount rate. – emcor Dec 14 '15 at 11:19
• No discounting is involved in this exercise. The current futures settlement price is, by definition, the arithmetic average of the daily fed funds effective rate (as expected by the market). – Helin Dec 14 '15 at 12:41
• @user25064 Thanks. WIRP is definitely a great tool. CME themselves provides a tool for this as well (cmegroup.com/trading/interest-rates/countdown-to-fomc.html), although I don't remember if I do it in the same way as them. – Helin Dec 14 '15 at 18:26