September 1, 2003 Federal Reserve Bank of Cleveland An Option for Anticipating Fed Action by John B. Carlson, William R. Melick, and Erkin Y. Sahinoz Options on CBOT fed funds futures are The implied rates derived from fed funds quite possibly the best means available futures prices have produced accurate Options contracts on federal funds to express market opinions about what predictions of the actual funds rate over futures, a new financial instrument the Fed might or might not do at the horizons of a few months. upcoming meetings. introduced earlier this year, can be One limitation of using futures as a pre- analyzed to gauge public expectations —Chicago Board of Trade dictor, however, is that the implied futures M onetary policy meetings attract considerable media attention, especially rates reveal little or nothing about the dis- tribution of beliefs. For example, suppose of future Fed actions. The real bonus is that they can detect differences of opinion when markets see more than when the economic outlook is highly the implied future rate is 121/2 basis points two possible outcomes for an FOMC uncertain, as it has been in recent below the current fed funds rate. Does this meeting as well as the likelihood asso- months. The Federal Open Market Com- suggest even odds of a 25 basis point cut? ciated with each. mittee (FOMC)—the Fed’s main mone- Or is it possible that a few market partici- tary policymaking arm—meets every six pants expect a 50 basis point cut while the weeks or so to choose a target for the majority expect no change? Predictors Thus, a buyer (or seller) can “lock in” federal funds rate for the following that do account for such variance in a certain interest rate on a borrowed intermeeting period. The fed funds rate beliefs can be obtained, in principle, from (or loaned) amount—specified to be is the interest rate paid on overnight another financial instrument known as an $5 million for each contract. In practice loans made largely between banks. It is option. Options on fed funds futures are the loan is not extended; rather, the commonly viewed as an anchor for all very new—in March, the Chicago Board difference between the market rate and interest rates, especially at shorter matu- of Trade (CBOT) began to offer them due the settlement rate is settled in cash. rities. Immediately after a meeting, the partly to an increase in the volume of FOMC releases a statement explaining trading in the futures contract. Fed funds futures have a number of its decision. The statement language is characteristics that distinguish them analyzed carefully by market analysts This Economic Commentary describes from other futures. These characteristics for any clue about actions the FOMC the new option and develops the intu- reflect unique institutional details of the might take in the future. ition behind the notion that information underlying market. For example, unlike on the distribution of opinion may be interest rates on car loans or mortgages, Just prior to an FOMC meeting, the derived from options prices. Estimates of the fed funds rate is on average aligned financial press is rife with speculation the probabilities of alternative July out- with the target federal funds rate, which about the likelihood of possible Fed comes are reported for the day before is chosen as a deliberative act of policy- actions. For example, one might read an and the day after the May and June makers. The fed funds market provides a account that purports “even odds” of a FOMC meetings. The estimates are con- convenient outlet in which banks can rate cut of 1/4 percentage point or 25 basis sistent with opinion as revealed in the buy or sell reserves to offset both the points—the smallest increment the financial press. The reader not familiar anticipated and unanticipated impact of FOMC typically employs. Odds assess- with or in need of review of the termi- payments on their reserve positions. ments are sometimes based on an inter- nology associated with options or The ultimate supplier of reserves is the pretation of fed funds futures prices from futures is referred to the sidebar on the Federal Reserve, which provides them contracts around the meeting month. next page. either through open market operations— Because such futures effectively entitle ■ Fed Funds Futures performed by the Domestic Trading holders to borrow at some future date at a Fed funds futures are interest rate futures Desk at the New York Fed—or lending specified rate, their prices reflect an opin- contracts that are based on the monthly at the discount window. ion about anticipated policy actions. Unanticipated actions and surprises in the average fed funds rate for each month Open market operations are guided by policy statement, in turn, induce immedi- traded. In simple terms, one can think of the objective of supplying the amount of ate changes in fed funds futures prices. the contract as specifying a predeter- reserves necessary to achieve a target for mined average rate for a given month. the federal funds rate. Although the fed ISSN 0428-1276 Reports in the financial press, however, Options, Futures, and Futures Options suggested that market expectations were not limited to only two possible policy Options are financial claims that take one of two basic forms: outcomes. The New York Times business section, for example, reported on May 9 • A call option is a claim that gives its owner the right to purchase some asset for a specified price—known as an exercise or strike price—on or before a that some investment banks were specified expiration date. expecting a rate cut of 50 basis points. Thus, it is more reasonable to assume When an option contract allows for exercise any time on or before the expi- that in May market participants were ration date, it is called an American option. Options that allow for exercise expecting at least three possible out- only at maturity are known as European options. If the market price of the comes for the June meeting. In this case, asset is above the strike price, the call option is said to be “in the money.” one needs information from at least two With an American option, the owner can immediately “call away” the asset independent sources. The newly traded and earn a profit equal to the difference between the market price and the options on fed funds futures provide a strike price. With a European option, the owner would have to wait until potential source of such information. expiration to earn a profit. ■ Fed Funds Futures Options • A put option, on the other hand, gives its holder the right to sell some asset As described more completely in the for a specified price on or before some specified date. An owner of a put sidebar at left, an option is a contract will exercise the claim only when the market price is below the exercise that allows one to buy (call) or sell (put) price. some asset at a preset price on or before some specified expiration date. The pre- It is worth noting that options are created only by an act of buying and sell- set price is known as an exercise or ing. Thus, for every owner of an option there must be a seller, called an strike price. The new option on fed option writer. The seller confers the rights of the option for a payment, the funds futures is an option to buy (in the price of the option. Thus, an owner or holder of an option has all the rights case of a call) or sell (in the case of a and the seller has all the obligations. One might think of the right to exer- put) one fed funds contract with strike cise as the product the option writer sells. price intervals of 61/4 basis points. It is an American option, meaning that it may An option on a future or a futures option is one that takes a futures contract as be exercised any time on or before its the underlying asset. A futures contract calls for delivery of an asset or some expiration date. derived cash value at a specified delivery date for an agreed-upon price—a futures price—to be paid at a specified date. Most options on futures are cash In both goods and asset markets, prices settled, meaning that the option writer must provide the cash equivalent of the may experience periods of high variabil- difference between the futures price and the strike price to the option buyer. ity and relative stability. For example, crude oil prices are enormously volatile during periods of geopolitical uncer- tainty but can also exhibit long periods funds rate may vary day to day in price is used to forecast the actual fed with little change in prices. If under- response to uncontrollable market fac- funds effective rate. Thus, the May 7 lying prices become more volatile, this tors, Desk actions are generally success- settlement price for July was factoring in increases the chance of a large payoff ful in achieving the target on average. some probability of a rate cut from the for the options owner, but it does not The monthly mean deviation from the then-current target rate of 1.25 percent. increase the chance of a large loss since target is zero over the past five years the owner can always choose not to with a standard deviation of 5 basis Now assume for the moment that in exercise the option. Hence, the option’s points. Thus, the monthly average funds May, market participants expected the price will increase with increases in the rate is effectively determined by the choice at the June 25 FOMC meeting to underlying asset’s volatility. Thus, an deliberative act of the FOMC through be limited to either no change or a cut of option’s price will be related to market its choice for the funds rate target. 25 basis points and no other change views about future volatility in the price before August. Under this assumption, of the underlying good or asset. How- Fed funds futures contracts are listed on one might draw the conclusion that the ever, even more detailed information the CBOT for the current month and for July settlement price implied that a cut can be extracted if options are being each of the 24 months that follow. The was more likely than no change since the traded at several different strike prices. futures settlement price is calculated as expected rate was below an even-odds 100 minus the monthly average of the expected rate of halfway between 1.25 Options prices typically differ across overnight fed funds rates. For example, and 1.00, that is, 1.125 percent. As long alternative strike prices, a difference that the July contract settlement price on as one assumes only two outcomes, one reflects the distribution of underlying May 7 of 98.905 implies a futures rate can calculate odds from a single futures opinion. For example, consider two call of 1.095 percent. price. Because with only two choices, options, one with a high strike price and the probability of no change must equal one with a low strike price. The option The correspondence between the rate one minus the probability of a 25 basis- with the low strike price will always be implied by the futures price and the point cut; only one piece of information at least as valuable and almost always expected fed funds target rate is straight- is necessary to pin down the odds. more valuable than the option with the forward since there is no evidence of bias high strike price because it is more when the two-months-ahead futures likely that the underlying price will FIGURE 1 IMPLIED PROBABILITIES FOR ALTERNATIVE JULY TARGET FEDERAL FUNDS RATES Panel A: May 5 and 7, 2003 Panel B: June 24 and 26, 2003 Probability Probability 0.8 1.0 0.9 0.7 May 5, 2003 June 24, 2003 May 7, 2003 0.8 June 26, 2003 0.6 0.7 0.5 0.6 0.4 0.5 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0.75 1.00 1.25 0.75 1.0 1.25 (50 bp rate cut) (25 bp rate cut) (no change) (6/24 = 50 bp cut (6/24 = 25 bp cut (6/24 = no change 6/25 = 25 bp cut) 6/26 = no change) 6/25 = 25 bp hike) SOURCE: Probabilities are calculated by the authors using prices from options on July 2003 federal funds futures that trade on the Chicago Board of Trade. exceed the lower strike price. The big- ■ Estimating the Probabilities change occurs, the market expects a ger the difference between the low and of Policy Outcomes 50 basis point cut to be more likely than high option prices, relative to the differ- Panel A of figure 1 reveals estimates of a 25 basis point cut. Given that the ence in the strike prices, the higher the the probabilities for each of these three estimates did not vary substantially probability market participants assign possible outcomes as reflected in options between the two days, the statement to the price of the underlying asset set- prices for the July fed funds futures released at the end of the May 6 FOMC tling above the low strike price but contract on May 5 and May 7, the days meeting appears to have had no measur- below the high strike price. If, on the prior to and after the FOMC meeting. able effect on the distribution of opinion other hand, the difference between the Given the rarity of intermeeting policy about July. low and high options prices is not sig- actions, it is reasonable to assume no nificantly different from the difference As the June FOMC meeting approached, further action will be taken between the in the strike prices, then market partici- however, the odds shifted in favor of a June 25 and the August 12 meetings. pants see only a small chance of the rate cut. Panel B of figure 1 shows that Hence, the three outcomes would corre- underlying asset price settling between our estimates based on options prices the spond to average fed funds yields for the two strike prices. Thus, in principle, day before the meeting place the highest July of 0.75 percent, 1 percent, and options written on several strike prices odds on a 50 basis point cut, with very 1.25 percent. Our example, therefore, reveal a greater amount of information small probability of no change. After the embodies an assessment in early May about market opinion than the single 25 basis point cut was announced, mar- of the probabilities for each of the con- underlying futures price. ket participants saw little chance of an sidered outcomes for the forthcoming intermeeting move that would further June meeting. Because their underlying prices are change the target rate in July. The odds based on a deliberative choice, fed Interestingly, the implications of our of remaining at a target of 1.0 percent funds futures prices will reflect opinion results contrast with the opinion one were greater than 9 out of 10. on probabilities of a limited set of out- might draw from a simple assessment comes, whereas changes in competitive The calculations behind figure 1 are based on just the fed funds futures price. market prices typically arise from a dis- subject to some limitations. First, the For example, because the fed funds tribution resembling a bell curve. For probabilities shown are recovered under futures price on that day was more than example, in early May, market analysts the assumption that market participants halfway between no change and a 25 might have conceivably expected three are risk neutral or indifferent to risk. basis point cut, one might interpret the outcomes for the meeting in late June: That is, the calculations assume that odds of a cut being greater than 50/50. no change, a 25 basis point cut, or a market participants would be indifferent 50 basis point cut. For each possible Our estimates of the probabilities of a between receiving $1 in the future and a outcome there is, in principle, a corre- change by July are less than 50/50 in the 50/50 chance of receiving $0 or $2 in sponding probability. days around the May meeting. They the future. This may not be problematic suggest that the probability of no change if large institutions that are relatively in the target rate is about 0.6. The proba- indifferent to risk dominate trading in bility of a change is thus 0.4, but if a this market. Second, to simplify the calculations, we assumed that the options are European when they are upcoming meetings. We offer one such actually American. This assumption will estimate. Though very preliminary, our John B. Carlson is an economic advisor at have no material impact on the recov- results suggest that the new option The Federal Reserve Bank of Cleveland. ered probabilities because, according to shows promise in revealing a deeper William R. Melick is an associate professor of options pricing theory, the options used assessment of market opinion. economics at Kenyon College and a research in the calculations were not likely to be associate at the Federal Reserve Bank of exercised early. Finally, and most impor- ■ Recommended Reading Cleveland, and Erkin Sahinoz is an economic tantly, the trading volumes for these new Kenneth Kuttner, 2001, “Monetary Pol- research analyst at the Bank. The authors option contracts are still relatively small. icy Surprises and Interest Rates: Evi- thank Ben Craig for helpful discussions. Trading may not be sufficiently deep to dence from the Fed Funds Futures Mar- The views expressed here are those of the reflect broad market opinion. If the mar- ket.” Journal of Monetary Economics, authors and not necessarily those of the Fed- ket for these options develops, we could vol. 47, no. 3, pp. 523–44. eral Reserve Bank of Cleveland, the Board of have much more confidence in the prob- Governors of the Federal Reserve System, or Ed Nosal, 2001, “How Well Does the abilities that are recovered. its staff. Federal Funds Futures Rate Predict the ■ A Promising New Predictor? Future Federal Funds Rate?” Federal Economic Commentary is published by the The CBOT’s new option on fed funds Reserve Bank of Cleveland, Economic Research Department of the Federal Reserve futures has been advertised as quite Commentary, October 1. Bank of Cleveland. To receive copies or to be possibly the best means available to placed on the mailing list, e-mail your request Ben Craig, 2002, “Options and the to email@example.com or fax it to express market opinions about what the Future: What Do Markets Think?” 216-579-3050. Economic Commentary is also Fed might or might not do at the Federal Reserve Bank of Cleveland, available at the Cleveland Fed’s site on the upcoming meetings. Whether the new Economic Commentary, October 1. World Wide Web: www.clev.frb.org/research, instrument lives up to such a billing remains to be seen. Nevertheless, where glossaries of terms are provided. Daniel Altman, 2003, “Fed Is Starting options do contain potential informa- to Fret over Falling Prices.” New York We invite comments, questions, and sugges- tion not revealed in futures prices alone. Times, Business Section (Section C), tions. E-mail us at firstname.lastname@example.org. Indeed, under some reasonable assump- May 9. tions, one may estimate the distribution of opinion on expected policy actions at Chicago Board of Trade, <http://www.cbot.com/>. PRSRT STD Federal Reserve Bank of Cleveland U.S. Postage Paid Research Department Cleveland, OH P.O. Box 6387 Permit No. 385 Cleveland, OH 44101 Return Service Requested: Please send corrected mailing label to the above address. Material may be reprinted if the source is credited. Please send copies of reprinted material to the editor.
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