Pricing of Interest Rate Risk in Fed Funds Futures Contracts

Do current fed funds futures prices signal a belief by market participants that the Fed may begin raising interest rates early next year? My latest research paper suggests not.

The expectations hypothesis of the term structure of interest rates posits that an investor could expect to receive the same return from buying a 6-month T-bill as from rolling over two 3-month T-bills. Although this is an appealing hypothesis, it has been consistently rejected by empirical researchers, including Campbell and Shiller (1991), Evans and Lewis (1994), Bekaert, Hodrick and Marshall (1997), and Cochrane and Piazzesi (2005) among many others. What that literature has shown is that when the 6-month yield is higher than the 3-month, on average you’d do better with it than with rolling over the 3-months. Typically the term structure slopes up, and typically you earn a higher return from longer term securities.

In a new paper coauthored with Hitotsubashi University Professor Tatsuyoshi Okimoto, we show that arbitrage should force the predictable excess returns on bonds of longer maturities to show up as predictable gains from taking the long position in fed funds futures contracts. The average upward slope to the term structure of interest rates should imply an average upward slope to the interest rates associated with fed funds contracts of increasing maturity. One might then want to adjust these futures rates to obtain an unbiased market expectation, as suggested in a recent paper by Piazzesi and Swanson.

Professor Okimoto and I also investigate the potential predictability of holding gains from long positions in fed funds futures contracts. We find mixed evidence for predictability for the most near-term contracts, but persuasive indications of predictability for contracts beyond 4 months. One of the interesting features we document is that this predictability over the 1991-2006 period appears to be mostly due to a few particular episodes characterized by a weak economy and unusually volatile interest rates. We model returns as shifting in and out of this predictable regime, with our assessment of how likely it is that one could earn an expected profit from taking the long position on a 6-month contract indicated in the graph below. These episodes of predictable gains are characterized by weak employment growth and unusual volatility of interest rates.

Probability that 1-month holding yields from 6-month fed funds futures contracts can be successfully predicted the month before, with NBER recession dates indicated as shaded regions. Adapted from Hamilton and Okimoto (2009).

What’s that imply for where things stand at the moment? The monthly fed funds rate averaged between 15 and 22 basis points throughout the first half of this year. The solid line in the figure below plots the interest rates associated with fed funds futures contracts of different maturities as of June 30. These rose steadily to a value of 35 basis points for the December contract. Some analysts had attributed that modest slope to a belief by traders that there was some possibility that the Fed could increase its target before the end of the year, despite statements from Fed officials that seemed to suggest such a change was unlikely.

The graph also provides predictions of what these rates on fed funds futures contracts for that date should have been under two alternative scenarios. The first (shown as a turquoise dashed line) postulates that buyers of these contracts expected the fed funds rate to remain flat through the end of the year at 18 basis points (the realized average over the first half of the year), but that the contracts at that date incorporated the same pricing of interest rate risk as they did on average over the period 1991-2006. Under this scenario, the fed funds futures prices would have shown an even steeper slope than they did at that time.

Predicted interest rates on fed funds futures contracts as of June 30, 2009 under alternative scenarios, in basis points. Average: implied fed funds futures rate if market expects fed funds rate to remain at 18 basis points through the end of 2009 but futures contracts embody historical average risk premia. Regime 1: market expects fed funds rate to remain at 18 basis points through the end of 2009 but futures contracts embody risk premia appropriate if June 2009 is known to have been governed by regime 1. Actual: actual fed funds futures rates on June 30, 2009. Adapted from Hamilton and Okimoto (2009).

Conditions in 2009 are clearly outside of the range included in our sample, both in the severity of the economic downturn and in the fact that the fed funds rate had effectively bumped against the zero lower bound, which is why we did not attempt to use the most recent data in our estimation. However, we thought it was interesting to take a look at what the model would imply if we assumed that we’re currently in the weak-economy, high-uncertainty regime, again under the assumption that market participants believe there is going to be no change in the fed funds rate before the end of the year. Under that scenario (the red dotted line above), we could have seen an interest rate as high as 80 basis points for the December contract and still interpret it as consistent with a belief by market participants that the Fed is not going to change its target.

The conclusion we draw from this exercise is that the modest upward slope of the futures curve in the summer of 2009 could easily be accounted for by risk premia in these contracts, and need not be interpreted as a belief by market participants that an increase in the target fed funds rate before the end of 2009 is particularly likely.

Pricing of interest rate risk in fed funds futures contracts

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