How is this probability (45%) of Fed raising rates 3 times in 2017 calculated from Fed Funds market?

The probability of the Fed raising rates 3 times in 2017 is above 45%.

What data and formula is used to calculate this probability?

This Financial Times article is published on 17Dec2016.

She portended that three rate rises were in the pipeline for next year, more than had been expected.

Second, the market actually believed her. The sharp rise in bond yields that has followed, with the US 10-year Treasury now yielding more than 2.6 per cent for the first time in more than two years, shows this.

So does the fed funds futures market, where investors place bets on the future path of rates. On election eve, this market put the chance of three rate rises next year at less than 5 per cent. By Wednesday, before Ms Yellen spoke, this had risen to about 30. Now it stands just above 45 per cent.

• This seems to be related: quant.stackexchange.com/questions/18890/…
– AK88
Commented Dec 18, 2016 at 11:06
• It is related but not the same. This question involves 3 rate hikes. The calculation will be different. Commented Dec 18, 2016 at 11:08
• This doesn't answer your question but things like nadex.com/markets/events/contract-specifications let you bet directly on single Fed Fund increases.
– user59
Commented Dec 19, 2016 at 19:42

Using the following data from 12/18/16: Jan 2017 Fed funds futures =9936, Jan 2018 Fed Funds futures =9877 implies that 99.36-98.77 = 59bp of hikes are built in for 2017. IF you assume the only two possibilities are 2 hikes or 3 hikes (meaning, 50bp or 75bp of hikes, assuming each hike would be 25bp), then by simple linear interpolation the probability of 3 hikes must be (59-50)/(75-50)= 36%

The above is a commonly used method when there are only two realistic possibilities, so the only data you need is the correct fed funds futures contract. If there are more possibilities, you need to utilize the options market in order to obtain more information. For example, if the Fed hikes 3 times the Fed fund futures will be at about 98.61. We look at the options market:

Jan 2018 98.6875 put option = 0.095, Jan 2018 98.625 put option = 0.0775, Therefore Jan 2018 98.6875-98.625 put spread = 0.0175, but the max payoff of this put spread is 0.0625

so the implied probability of the put spread being in the money (ie futures<98.625) is 175/625 = 28%, a slightly different answer. This is equivalent to the probability of at least 3 hikes.

For some reason I'm not getting 45%, but the market may have moved, or the option prices i am using may be stale. Anyway i hope this illustrates the methods typically used.

• I got the same result with the probability argument but it was not very clear to me how you came up with (59-50)/(75-50)= 36%.
– SRKX
Commented Dec 22, 2016 at 1:40
• @SRKX I believe he's using the formula similar to the voted answer quant.stackexchange.com/questions/18890/…
– Sky
Commented Dec 22, 2016 at 2:50
• @Sky yeah it seems it needs to be explicit in the answer then...
– SRKX
Commented Dec 22, 2016 at 5:50
• @dm63 Thank you! Very nice answer! Do you think the contracts one year a way are liquid enough to warrant a comment like "the market prices in 3 hikes"? I mean, of course we have the data so we might as well look at it but the significance could be low. Any comments on that would be very welcome! Commented Jun 23, 2017 at 9:41

It is not taken from options. The numbers are taken from the Fed Watch tool provided by the CME, who list the Fed Funds Futures. There entire methodology is available here - which details several examples.

If you "chain" successive months you will get the same answer. You can see this by selecting Dec 2018 with the tool and seeing the probability is currently 25.7% (it has fallen in recent days).