# Using the Federal Funds Futures Contract Prices to Predict Fed Moves

Explanation of rate changes.

The federal funds futures market has been run by the Chicago Board of Trade since 1988 as a way for banks and other companies and firms to hedge against movements in the federal funds rate. Even individuals can use this market to make a bet on the next move if one feels others are misreading the Fed.

The CBOT trading price for federal funds futures is based on settlement at 100 minus the effective average federal funds rate (as determined and publicly reported by the Federal Reserve Bank of New York). Therefore, prices in this futures market will move inversely, but in a very predictable manner with changes in the expected federal funds rates in the settlement month. (Details about trading units, contract standards and cash settlement procedures are available at the CBOT Web site)

Assuming no market failures or significant risk aversion effects, the CBOT futures price should provide an unbiased forecast of the expected average of the federal funds rate in the contract month.

In mathematical terms: 100 - F = RF = E [R]
where F is the futures price, RF is the futures rate, and E[R] is the expected average rate.

The expected value for the average would be the sum each possible rate (Ri), times the probability of each possible rate on each day (pi,j , where j denotes the day), divided by the number of days in the month (n): E[R] = å i å j (Ri. * pi,j ) / n

Probabilities for a Fed move can be calculated by making two additional assumptions: (1) the actual rates during the contract month equals (on average) the target on each day and (2) the possible cases are limited to either no change or one initial target rate and one change (on only one day).

Using these assumptions and a few additional terms: R1 for the initial target rate, p for the probability of a move on a specific date, m for day of move in month, n for number of days in month, and dR for change in rate, you get

E[R] = R1 + p * (1-m/n) * dR

So

p = (F - R1) / ( (1-m/n) * dR)

Three examples:

 October 26, 1999 November 1999 futures contract price = 94.67 (so expected rate is 5.33%)Target rate at time 5.25% (set August 24, 1999)Assuming the only possible move is a 25 basis point increase on November 16 and this holds for the next 14 days: (5.33 - 5.25) / ((14/30) * .25) = 68.6 % January 26, 2000 April 2000 futures contract price = 94.03 (so expected rate is 5.97%)Target rate at time 5.50% (set November 16, 1999)Assuming a move on February 2 to a 5.75% target and the other possible move is on March 21 that holds for the next six weeks:(5.97 - 5.75) / ((30/30) * .25) = 88.0 % May 13, 2000 May 2000 futures contract price = 93.775 (so expected rate is 6.225%)This calculation is tougher because the choices at the May 16 FOMC meeting seemed to be either a 25 basis point hike or a 50 basis point, with next to no chance of holding at the 6% target set in March. The first step is to compute the May federal funds average with the minimum 6.25% rate after May 15   6.129% = (15/31)* 6% + (16/31) * 6.25% This average rate is then used as the base rate, yielding   (6.225 - 6.129) / (16/30) * .25) = 74.4 % as the implied probability of a 50 basis point hike (as opposed to a 25 basis point hike).

#### Related Resources

 • More Federal Reserve Analysis • FOMC Monetary Policy Release Page • CME Group FedWatch Probability Tree • Academic Research on Futures Predictive Power.