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									                                                                                                                                          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 4d.subscriptions@clev.frb.org 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 editor@clev.frb.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/>.

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