Degree of market imperfection and the pricing of stock index futures

Abstract

Capital markets are imperfect. Market imperfections differ among markets. This study uses a theoretical valuation model derived by Hsu and Wang (2004) to estimate the degrees of market imperfection for mature and immature markets, and tests the applicability of the model. Moreover, this study proposes some theoretical hypotheses and empirical tests regarding the relationship between the degree of market imperfection and futures pricing. The evidence indicates that the Hsu and Wang (2004) model appears to provide a reasonable measure of the degree of market imperfection for real capital markets. The theoretical hypotheses and empirical results indicate that larger market imperfections are relatively more mispriced based on the model of perfect-market assumption, suggesting that the impact of market imperfection on the pricing of stock index futures is enormous, and cannot be neglected. Thus, when investors more closely examine the applicability of the cost of carry model for pricing mature and immature futures markets, they should note the degree of imperfection for the markets in which they are participating.

Acknowledgements

The authors thank the Editor, Professor Mark Taylor, and Associate Editor for their extremely helpful comments and suggestions.

Notes

¹ Kollias and Metaxas (2001) indicate that in practice FX (Foreign Exchange) triangular arbitrage may not be riskless since a few seconds are not enough for the arbitrageur to lock the arbitrage profits. Butterworth and Holmes (2002) argue that execution risk and short sales restrictions impede index arbitrage in the UK.

² See, for example, Cornell and French (1983a, b), Modest and Sunderesan (1983), Peters (1985), Gould (1988), Brenner et al. (1989), Buhler and Kempf (1995), Brailsford and Cusack (1997), Huang et al. (1998), Fung and Draper (1999), and Gay and Jung (1999).

³ Since stock index futures contracts were introduced in US markets in February 1982, academic researchers and practitioners have been interested in the relationship between index futures prices and underlying index prices. In particular, researchers have studied the explanatory power of the cost of carry model and the dynamic relationship between index futures prices and spot index prices.

⁴ Writing the cost of carry model in return form, Brooks et al. (1999) demonstrate that the futures and index returns are correlated perfectly and positively contemporaneously.

⁵ In results not reported here, we repeat our tests using the exponentially weighted moving average method and find that the results are similar to those of the equally weighted moving average method.

⁶ If the underlying stock index pays irregular lumpiness of dividends, F_cost,t and AF_t can be expressed as

where D_t is the sum of the present values of all cash dividends distributed by the underlying component stocks at time t during the life of the futures contract; d_i is the cash dividend per share for stock i during the life of the futures contract; w_i is the weight of stock i in the index; t_i is the time that stock i pays the cash dividend; and p_{i , t} is the price of stock i at time t. From (13′) and (14′), we obtain

⁷ Although pinpointing the start of the Asian financial crisis is difficult, analysts often point to the 17% devaluation of the Thai baht on 2 July 1997 as the triggering event. By the second half of 1997 and during 1998, stock markets in the Asia-Pacific region displayed dramatic declines. Particularly, in the period from April to October of 1998, a crucial period during which Taiwanese corporations encountered financial difficulties owing to the Crisis, investors obviously expected that the Taiwan stock index would decline in the future. During this crucial period, the SGX-DT MSCI Taiwan stock index dropped from 374.56 on 7 April to 232.62 on 3 September, a decline of almost 142 points over just a few months, and it was not until the middle of October 1998, that the decline abated. Thus, this study defines the Asian crisis period as the period from 2 July 1997 to 15 October 1998. Additionally, owing to the listing of TAIFEX Taiwan stock index futures occurring only on 21 July 1998, the Asian crisis period is only analysed for the SGX-DT futures.

⁸ This study defines the negative basis as AF_t  < S_t . The basis is defined as the difference between the actual price of index futures and the spot index price, AF_t  − S_t .