Intra-Day Tests of the Efficiency of the Treasury Bill Futures Market

Abstract

In this paper we use intra-day prices to examine the efficiency of the Treasury bill futures market. The use of intra-day data allows us to carefully match in time trades in the futures and cash markets. By matching trades and allowing delays between observing apparent inefficiencies and the trade, we are examining realistic trading strategies. We find profitable arbitrage, swaps and a preferred strategy for initial purchase. These profits do not depend on an assumption of an equilibrium model. Hence these tests are direct tests of efficiency rather than a joint test of efficiency and equilibrium. T HIS paper examines the efficiency of the Treasury bill futures market. This subject has been examined before by Capozza and Cornell (1979), Cornell (1981), Lang and Rasche (1978), Rendleman and Carabini (1979), Vignola and Dale (1979), Poole (1978), and Puglisi (1978). There are a number of reasons why this paper makes an important contribution to the literature. The first reason is that by using trade by trade futures prices we can make more realistic assumptions about the pnces at which trades could have taken place. This paper uses intra-day prices to examine efficiency. Prior studies at best used closing prices to examine apparent inefficiencies and assumed that transactions took place at these closing prices. There are two problems with this procedure. First, simultaneous transactions cannot actually occur at closing prices. There is almost an hour difference between the closing of the Chicago futures and New York spot markets. Thus when the closing spot market price is observed the futures market has been closed for about an hour. Closing prices could be used to judge apparent discrepancies. However, it would be necessary to execute trades at the open. Making decisions based on closing prices and then assuming trades can take place at these prices is an approximation which could significantly affect results. In addition, using only closing prices ignores any intra-day trades which could lead to profits. In this study we match in time intra-day prices in the spot and futures market. These matched prices are used to identify apparently profitable trading rules. We then assume trades take place at prices which are observed later in the day. This is a test of a trading rule which an investor could actually follow. As we discuss later in the paper, our results differ from prior studies. These differences are primarily due to using intra-day prices and carefully matching times so that information used to initiate trades would actually be available to the investor at the time of the trade. The second reason is that we examine more complex trading strategies than those which have been employed in other studies. The random walk literature provides a useful analogy. The original random walk studies simply correlated past and future prices or returns. Later studies examined filter rules and other more complicated trading rules. In this study we employ alternative trading rules of increased complexity to test for the existence of trading profits. Finally, we explicitly examine the consequence of T-bills futures contracts being futures rather than forward contracts. Futures contracts, unlike forward contracts, involve flows every settlement day. The intermediate cash flows on futures contracts can affect the profitability of any strategy. The only prior study that even considered this effect is the one by Rendleman and Carabini (1979). They used the theoretical model of Cox, Ingersoll and Ross (1981) to try to estimate whether the difference between forward and futures prices was likely to be large enough to affect the payoff from alternative trading strategies. This is a useful first attempt. However, ultimately the effect of daily settlement or marking-to-the-market has to be examined directly as part of trading strategies to see if it affects the outcome of these strategies. There are other problems with prior studies. These involve gross estimates of prices and averaging data in a way that can mask inefficiencies. Since these problems are discussed in some detail in Rendleman and Carabini, there is no reason to review them further here. Probably no area in finance has received more attention than the efficiency literature. The reader may well wonder why, even given the approximaReceived for publication August 23, 1982. Revision accepted for publication May 20, 1983. * New York University, New York University, and Baruch College, respectively. The authors would like to thank the Center for the Study of Futures Markets at Columbia Business School for financial support.