The Importance of Liquidity in Index Futures Pricing: Modelling and Empirical Evidence

Several empirical studies report that asset liquidity has a significant impact on asset prices. For example, Amihud and Mendelson (1986), Silber (1991), Kadlec and McConnell (1994), and Brennan and Subrahmanyam (1996) report that stock prices are c.p. the lower, the lower stock liquidity is. For bond markets similar evidence is reported by Sarig and Warga (1989), Amihud and Mendelson (1991), Boudoukh and Whitelaw (1991), Warga (1992), Kamara (1994), and Kempf and Uhrig-Homburg (2000). In this paper, the impact of liquidity on index futures prices is studied theoretically and empirically. I derive a theoretical two-factor pricing model where the index futures price depends on the index level and the illiquidity of the future. The two factors are the index level and the costs of illiquidity proxied by the bid-ask spread in the empirical study. The model provides an analytical solution for imperfectly liquid index futures. The fair price of an imperfectly liquid future is determined by the cost-of-carry price and a discount function due to illiquidity. The price discount depends on the maturity of the contract and its bid-ask spread. The model is tested in the sample and out of the sample using data on the German futures market. I show that the model explains futures prices significantly better than the cost-of-carry model and the two-factor model of Ramaswamy and Sundaresan (1985) do. The superiority of the liquidity model increases with the maturity of the contract. All models explain the prices of short contracts pretty well, but only the liquidity model provides a good explanation for the prices of index futures with long time to maturity. The pricing error of the liquidity model is much smaller than the error of both benchmark models. My main conclusion of the empirical study is that only index risk matters for short contracts, whereas index and liquidity risks matter for long contracts. Address Prof. Dr. Alexander Kempf University of Cologne Department of Finance 50932 Cologne, Germany Phone: (+49)-221-470-2714 Fax: (+49)-221-470-3992 E-mail: [email protected]