fed funds futures (kuttner krueger)

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  • THE Fpo Fuxns FurunpsRanr AS A PnEnrcroR oFFEosRAr RgsERVE Porrcv

    JOEL T. KRUEGERKENNETH N. KUTTNER

    INTRODUCTION

    Monetary policy's effects on the economy are pervasive, and the Federalfunds rate plays a central role in the Federal Reserve's implementation ofits policy. Changes in the Federal funds rate rapidly affect other moneymarket interest rates, and changing expectations of future policy can sig-nificantly influence stock and bond prices. As demonstrated by Bernankeand Blinder (1992), changes in the Federal funds rate also have signifi-cant effects on real economic activity. I It is not surprising, therefore, thatthe Fed funds futures market has received increasing attention as a gaugeof expected Federal Reserve policy actions.2'

    How well does the Fed funds futures market anticipate changes inthe Federal funds rate? This article addresses that question by evaluatingthe futures market's one- and two-month-ahead forecasts of the fundsrate. Specifically, it assesses the efficiency of the Fed funds futures marketby testing the market's forecasts for the properties implied by rational

    lThe Federal funds rate is also an ingredient in more sophisticated measures of monetarypolicyasdescribcd in Bernanke and Mihov (1995) and Strongin (1995). Those measures also incorporate thevolume of nonborrowed and total reserves.2See, for example, McGee (1995).The authors thank Charlie Evans, David Marshall, Jim Moser, and two anonymous referees for theircomments and suggestions. The opinions expressed here are the authors'own, and they do not reflectthe official positions of PPM America or the Federal Reserve System. Address correspondence to:Kenneth Kuttner,6l9 Uris Hall, Columbia University, NewYork, NY 10027.

    Joel T. Krueger is a Co-Director of Fixed lncome Quantitatiue Research at PPMAmerica.

    Kenneth N. I{uttner is a Visiting Assistant Professor at Columbia Business School.

    The Journal of Futures Markets, Vol. 16, No. 8, 865-879 (1996)O 1996 by John Wiley & Sons, lnc. ccc 027 0 -7 31 4/96/08086s- 1 5

  • 866 Krueger and Kuttner

    expectations. Over the 1989-1994 period, the futures-based forecastsgenerally satisfy this criterion: incorporating additional data available toinvestors when the contracts are priced yields only marginal improve-ments over the futures-only forecasts. Of the indicators considered, onlythe change in the inflation rate and the spread between three-monthcommercial paper and the Fed funds rates are statistically significant inwithin-sample tests of rationality at the 0.05 level. These indicators donot tangibly improve out-of-sample forecasts, however.

    THE FED FUNDS FUTURES MARKET

    Fed funds futures contracts are designed to hedge against (or speculateon) changes in the overnight effective Fed funds rate, which is the interestrate prevailing in the interbank market for overnight reserves. The Chi-cago Board of Trade (CBT) offers contracts on the Fed funds rate at avariety of maturities.3 The most popular of these are the one- and two-month contracts, and the "spot month" contract based on the remainderof the current month's rate.4 They are marked to market on each tradingday, and final cash settlement occurs on the first business day followingthe last day of the contract month.5

    The settlement price for the contract is based on the relevant month'saverage effective overnight Fed funds rate as reported by the Federal Re-serve Bank of New York. The average includes weekends and holidays,whose rates are carried over from the rate prevailing on the most recentbusiness day.6 The pre-tax profits for an investor long in Fed funds con-tracts purchased on date r for delivery in month s, rd, is proportional tothe difference between the futures rate,/f , and the average of the month'sFed funds rate, rt,

    - fsJt

    3The CBT nou,rcfers to Fed funds lutures as Thirty-Day Interest Rate futures.aThe price of the spot month contract is a rveightcd average of the prer.ious overnight Fed fundsrates for the month and thc tcrm rate for the remainder ol the month. For example, the Januarysettlement price applied to a futures contract purchased on January 1 I rvould be I 0/3 I X thc averageovernight Fed funds rate for previous l0 days + 2ll3l x the term Fed funds rate fbr the 21 daysremaining in the contract month.5For all but the spot month contract, the CBT limits pricc fluctuations to 150 basis points daily. Thelimit is expandcd to 225 basis points rvhen the limit is reached on three consecutive trading days.Further details on the market's operation can be found in "Thirty-Day Interest Ratc Futures forShort-Term Interest Ratc N{anagcment," Kuprianov (1993), and Carlson, Nlclntire, and Thomson(ree5).64. uniform 30-day month is used in calculating the tick size.

    I

    7ti #u'

  • Fed Funds Fate 867

    (l)?I3

    where M is the number of calendar days in the month. Arbitrage by risk-neutral investors implies no predictable profit opportunities, or Er(z{) :0, which in turn implies that the futures rate is equal to the average ofexpected future realized rates on Fed funds,

    fi_ E;(#:,,) :o

    where E, represents the mathematical expectation conditional on infor-mation available to investors at time t.7

    A number of previous studies have analyzed the T-bill futures mar-ket, including: Rendleman (1979);Hedge and McDonald (1986); Pateland Zeckhauser (1990); Cole, Impson, and Reichenstein (1991); andHafer, Hein, and MacDonald (1992). These studies found that futuresrates generally f.ield accurate predictions of future spot T-bill rates atmost horizons, and rarely fail to satisfi' properties of rational forecasts.The only prominent exception to this pattern is Howard (1982), whofound that simple time-series models dominate futures-based forecastsat short horizons.

    Two features distinguishing the Fed funds futures market from theLIBOR, T-bill, and Eurodollar markets are its short history and its rela-tively small size. T-bill futures have been traded since 1976, while theFed funds futures market has edsted only since October, 1988. The vol-ume of Fed funds contracts traded in 1992 was only one-fourth that ofT-bill futures, and one-third that of LIBOR contracrs.8 In light of themarket's relatively short track record, the efficiency of the Fed funds mar-ket is an open question.

    ARE FED FUNDS FUTURES FORECASTSRAIIONAL?

    This section examines forecasts of the Fed funds rate based on the one-and two-month-ahead Fed funds futures contracts. Specifically, it reportstests of the unbiasedness and rationality properties implied by eq. (l).The forecasts are unbiased if the futures rate is, on average, equal to theTBecause the futures price anticipates thc realized Fed funds rate instead of the Fed's target rate,technical factors affccting the Opcn N'larket Desk's ability to hit the target rate may, in principle,alfect the futures rate. In practice, the discrepancy between the target and the realized rates largelydisappears in monthly averages, however. Carlson, Nlclntire, and Thomson (1995) found that themean absolute deviation bets,een the eflcctive and target rates is no more than slv basis points.sThe Fed funds futures market has grorvn rapidly since 1994. By the third quarter of 1995, thevolume of contracts traded and open interest have both reached levels comparable to those of the T-bill futures markct.

  • 868 Krueger and Kuttner

    realized spot rate. The rationality property says that the Fed funds futuresrate should incorporate all available information useful for predicting thefunds rate. This implies that no variable available in month t should beable to predict the futures market's errorin forecasting the month t * Ifunds rate. The out-of-sample forecasting performance of the futures-based forecasts is also examined, and compared to the performance ofalternative forecasts.

    Figure I plots the data used in the analysis: the monthly average ofthe effective overnight Fed funds rate and the corresponding Fed fundsfutures rate for the period from May 17, 1989, through December 7,1994. ln general, the implied funds rate is very close to the spot rate,especially close to the settlement date. The one-month-ahead contract,as expected) seems to track the actual rate very closely, while the forecasterror associated with the two-month-ahead contract appears somewhatlarger. Overall, little bias is apparent in either of the two futures rates.Only from 1990 to mid-1992, when Federal Reserve policy led to a sharpdecline in the Fed funds rate, is there a persistent discrepancy. Duringthis period, the futures rate consistently overforecast the spot rate, sug-gesting that the decline in the funds rate was to some extent unantici-pated by market participants.

    Evidence from Monthly Data

    Using data at a monthly frequency, the unbiasedness and rationalityprop-erties are easily tested by regressing the spread between the futures rateand the realized spot rate on a constant and a variety of economic indi-cators investors might plausibly have used to predict the Fed funds rate.For the k-month-ahead futures rate, the regressions are of the form:

    j'r-o - lt+r, : a + 0(L)xr-t * ut+k (2)

    where F1*pis the average funds rate prevailing in month t + k, ^r'djt*kis the average futures rate for the month t + k contract, priced in montht.e The forecast error is ur*7r. Candidate indicators, xr, are included in theregression by way of the lag pollmomial, 0(L).ln cases where the t-datedindicator is not known at time t, , is set to one to introduce an additionallag; in other cases, I is zero.lo Unbiasedness implies a : O, and rationalitythat 0(L) : g.

    eRegressions of this form impose a unit coefficient orji*1. Tests not reported in the article confirmthat the restriction is easily satisfied, paralleling Patel and Zeckhauser's (1990) findings for T-billfutures rates.