The information content of interest rate futures and time-varying risk premia

Abstract

The objective of the present study is to examine the price discovery hypothesis in the short sterling futures market. The analytical framework employed, to examine the interaction between spot and futures rates, is based on a VAR cointegration model. The current research takes into account the necessary conditions, when testing the unbiasedness of the futures market, as well as the issues of risk neutrality and the rational use of all available and relevant information. The paper finds that the price discovery hypothesis holds for up to seven weeks prior to maturity of the futures contract. Furthermore, an examination of the sample period over which efficiency does not hold, provides evidence for the presence of time-varying risk premia. The findings also suggest that the premium and the expected spot change volatility are statistically significant, with the former being slightly lower than the latter.

Acknowledgements

The author is grateful to George Alexandrov, Amir Alizadeh, Paul Dawson, Gerry Dickinson, Elena Kalotychou, Ian Marsh and Gulnur Muratoglu for many stimulating discussions and helpful comments. The usual disclaimer applies.

Notes

thinsp;In pure arbitrage situations a cash position is financed with borrowed funds, while quasi-arbitrage transactions incorporate securities actually owned.

thinsp;The estimates, although consistent, are not efficient and unbiased and the test procedure does not have a well-defined limiting distribution. For more discussion see Johnston (1972) pp. 304–6, Stock (1987), Elam and Dixon (1988), Shen and Wang (1990).

thinsp;For an excellent and thorough discussion on cointegration analysis see Harris (1995). The technical issues discussed in this paper are mainly a brief summary of what Harris (1995) analyses in various chapters.

thinsp;The maximum likelihood framework has the additional virtues of facilitating inferences concerning the structure and relative importance of the cointagrating vectors, as well as providing relatively powerful tests when the model is correctly specified.

thinsp;This type of VAR model has been advocated most notably by Sims (1980) as a way to estimate dynamic relationships among jointly endogenous variables without imposing strong a priori restrictions such as particular structural relationships and/or the exogeneity of some of the variables. As its name implies, this consists in regressing each current variable in the model on all the variables in the model lagged a certain number of times.

thinsp;As discussed in the data, the paper employs 12 different cointegration regressions representing the 12 different weeks prior to maturity for each futures contract.

thinsp;An I(d) variable indicates that it needs to be differenced d times in order to achieve stationarity. All individual variables included in Z _t need not be I(1) as is often incorrectly assumed. To find cointegration among nonstationary variables, only two of the variables have to be I(1).

thinsp;r columns of β form r linearly independent combinations of the variables in Z _t each of which is stationary and p − r columns of β form I(1) common trends.

thinsp;Care should be taken when collecting the data since these contracts used to expire on the second Wednesday of the delivery month until September 1985 inclusive.

 Futures rates upon expiration could be used, based on the fact that even if a nonzero basis is observed arbitrage movements would force rates convergence.

 Dickey and Fuller (1979) propose the DF test, testing the null that a series contains a unit root, and the ADF test in case the errors are autocorrelated. Sargan and Bhargava (1983) propose the CRDW test based on the usual Durbin–Watson statistic. Phillips and Perron (1988) developed a nonparametric test based on the Phillips (1987) Z-test, which involves transforming the test statistic to eliminate any autocorrelation in the model. There are also procedures testing the null that a series is stationary, see Khan and Ogaki (1992).

 For more detailed information on these technical aspects see Harris (1995).

 The rank of a matrix is equal to the number of its characteristic roots that differ from zero. Note that once the rank of Π (r linearly independent columns) is known, then it is known that the last (p − r) columns of α are zero and thus that the last (p − r) columns of β are nonstationary and do not enter Equation 2. Thus, it is in this sense that the dimensions of α and β can be reduced to (p × r).

 See, for example, Velu et al. (1986).

 Q = restricted maximised likelihood/unrestricted maximized likelihood. A selection of the asymptotic tables for making inference when the dimension of the system is less than five is given in Johansen and Juselius (1990). Osterwald-Lenum (1992) has extended the dimension of the tables up to 11 and included the case of a trend in the cointegration space. For a mathematical derivation of the asymptotic distributions, see Johansen (1988, 1991).

 This explains why the eigenvectors corresponding to the largest r eigenvalues are chosen to be the cointegrating vectors.