Fed Funds Rate Predictions

FAQs

What is the Chicago Board of Trade?
The Chicago Board of Trade is an organization for people who want to buy and sell certain types of contracts to each other. This kind of organization is called an exchange. Only members are allowed to do business there, but members can be brokers and so buy and sell for others who are not members. The types of contracts bought and sold at the CBOT are futures and options (see below), which are popular because they help individuals and businesses manage financial risks. The terms of the contracts are set by the CBOT, but the members negotiate their prices. Note that in 2007, the CBOT merged with the Chicago Mercantile Exchange (CME) to form the CME Group. CME Group now operates CBOT along with three other exchanges—CME, NYMEX, and COMEX.

For an overview of the CBOT, read the profile page on the CME Group web site.
What is a futures contract?
A futures contract is an agreement, traded on a futures exchange, to deliver a commodity or financial instrument for an agreed upon price – the futures price – at a standardized future date.
What is a 30-day fed funds futures contract?
A fed funds futures contract is an interest rate futures; i.e. a futures contract whose value is based on a fixed-income security or interest rate. The underlying interest rate for the fed funds futures contract is the average daily effective federal funds rate for the delivery month. The final settlement price for a contract is 100 minus this average rate.

Unlike some other futures, a fed funds futures contract does not involve the actual delivery of the commodity or asset underlying the futures. Instead, fed funds futures are cash settled. In cases where the purchaser of a futures contract does not sell it at a later date, the net cash settlement between the buyer and seller from the point of purchase to expiration is the difference between the final settlement price and the price the futures contract was purchased for.
How can fed funds futures be used to gauge expectations of the federal funds rate?
This is best illustrated by example. On October 31, 2005, the fed funds futures contract with a February 2006 delivery date of had a settlement price of 95.55. Abstracting from transaction costs, a purchaser of this futures contract at this price would profit if and only if 100 minus February’s average effective fed funds ended up above 95.55. This would happen if February’s average effective fed funds ended up below 4.45%. Similarly, someone selling this futures contract at a price of 95.55 would profit if the average February effective fed funds ended up above 4.45%.

Assuming risk neutrality, market expectations of the February 2006 fed funds rate should have been about 4.45% on average on October 31, 2005. If they were much higher, for example, market participants would have been willing to sell this contract at slightly below the prevailing price of 95.55 and expected to make a profit, thereby driving the futures price below what it was observed to have been.

Changes in the fed funds target rate on nonscheduled meetings have been rare since 1994 and there were no scheduled FOMC meetings in February 2006. So it is not unreasonable to assume that market participants expected the target rate chosen at the January 2006 meeting to carry over through all of February. Since the effective fed funds rate is generally close to the target on average – in February 2006 the average effective rate was 4.491% compared to a target of 4.50% – market expectations of the average effective rate in February should have been close to the expected target rate chosen at the January meeting. Assuming risk neutrality, on October 31, 2005 the expected value of the target rate chosen at the January FOMC meeting should have been approximately 4.45%.
What is a fed funds futures rate?
For a given fed funds futures contract, the fed funds futures rate is 100 minus the current price of the contract. At final settlement, the fed funds futures rate is the monthly average effective fed funds rate in the delivery month. The fed funds futures rate is often used as a gauge of the expected value of this monthly average.
What is an option?
An option is a financial claim that gives its owner the right, but not the obligation, to perform a specified transaction during a specified period of time. Two of the most common types of options are call options and put options. A call option is a claim that gives its holder the right to buy some asset for a specified price, called the strike or exercise price, during a specified period of time. A put option gives its owner the right to sell some asset for a specified price during a specified period of time.
What is an option on a federal funds futures contract?
An option on a futures contract is an option where the underlying asset is a futures contract. Both put and call options can be traded on fed funds futures contracts. An option on a fed funds futures contract can be exercised any time at or before its specified expiration date. Options with this feature are known as American options. Options that can only be exercised at expiration are called European options. For simplification, the options are treated as if they were European when estimating implied probabilities. This simplification should have little material impact on the results.

An option on a fed funds futures contract is distinguished by three features; the delivery date of the underlying futures contract, whether it is a call option or put option, and the strike price. An example is the call option written on the February 2006 futures contract with a strike price of 95.75. As is show in Appendix 1 of Recovering Market Expectations of FOMC Rate Changes with Options on Federal Funds Futures, this option is equivalent to a put option on the February 2006 fed funds futures rate with a strike price of 100 – 95.75 = 4.25. When analyzing options prices, it is easier to use think in terms of this transformed option.
Why would one use options on a fed funds futures contract to estimate market expectations of alternative target rates instead of just the underlying futures contract?
This is best illustrated by example. As described in Q3, on October 31, 2005 the expected value of the target fed funds rate chosen at the January 2006 FOMC meeting should have been approximately 4.45%. This is consistent with a market perception 80% probability of the FOMC choosing a target 4.50% and a 20% probability of choosing 4.25%. However if a priori, 4.00%, 4.25%, 4.50% and 4.75% were considered plausible target rates, than both of the following scenarios are consistent with an expected target rate of 4.45% chosen at the January meeting.

Scenario 1

Target rate chosen at
January 2006
FOMC meeting

Hypothetical probability
on October 31, 2005

4.00%
0%
4.25%
20%
4.50%
80%
4.75%
0%

 

Scenario 2

Target rate chosen at
January 2006
FOMC meeting

Hypothetical probability
on October 31, 2005

4.00%
10%
4.25%
15%
4.50%
60%
4.75%
15%

 

The February 2006 futures price cannot give any insight about which of these two scenarios is a better characterization of market expectations. But the options written on the February 2006 futures contract can. One such option, taken from Q6, is the put option written on the February fed funds futures rate, with a strike price equal to 4.25. On October 31, 2005 the February futures rate was 4.45. The option was out of the money, since the holder of the option would take a loss by immediately selling the contract at a lower futures rate than the current one. However, on October 31 some market participant(s) still purchased this option. A buyer of this contract could only gain if the futures rate fell below 4.25 or, under the assumptions of Recovering Market Expectations of FOMC Rate Changes with Options on Federal Funds Futures, the FOMC set the target at its January 2006 meeting at 4.00% (or lower). This suggests market participants put some positive probability of the FOMC choosing a target rate lower than 4.25% at the January 2006 meeting. Using the outcomes in scenarios 1 and 2 and October 31 option prices, the Carlson-Craig-Melick probability estimates were:

 

Target rate chosen at
January 2006
FOMC meeting

Carlson-Craig-Melick
estimates
on October 31, 2005

4.00%
7%
4.25%
15%
4.50%
69%
4.75%
9%
Can one estimate market expectations for any scheduled FOMC meeting?
Although fed funds futures contracts can have delivery months up to 23 months in the future, trading is generally thin for futures contracts with delivery months beyond 9 months. Furthermore there are often not enough outstanding options on fed funds futures with delivery months beyond 6 months in the future to be able to estimate a reasonable number of possible target rates for FOMC meetings more than 6 months in the future. So data limitations generally limit estimation of implied probabilities of alternative fed funds target rates to no more than 3 to 4 meetings in the futures.

If the calendar month following the month of an FOMC meeting does not have a scheduled meeting, like the March 27/28, 2006 meeting, implied probabilities of alternative targets chosen at the meeting can be estimated as long as there is sufficient options data.

Implied probabilities of alternative target rates, can always be estimated for the next meeting. If the next meeting is followed by another meeting in the subsequent calendar month, than the estimates will generally be less accurate than they otherwise would be, and the accuracy of the estimates is inversely related to how late in the month the meeting is.

In other cases, implied probabilities for a meeting can sometimes be estimated with a joint estimation technique. For example, prior to the March 27/28, 2006 meeting, implied probabilities for alternative target rate paths for the March meeting and the May 10 meeting could be estimated (with less than ideal accuracy). The probabilities of alternative targets chosen at the May meeting could then be recovered from the path probabilities.
Which price quotes are used to determine the probabilities?
The options prices are settlement quotes from open outcry traded options on 30-day fed funds futures contracts. Open outcry trading ends at 3:00 EST.

In cases where the price of a futures contract is used in addition to the prices of the options written on the contract, the futures price used is also the open outcry settlement quote.