Feasibility of riskless hedged portfolios in imperfect markets

Abstract

The Black–Scholes model (1973) is developed under the concept of the riskless hedged portfolio by hedging the call option against the underlying stock. If the riskless hedged portfolio is feasible, investors’ preference is independent of option pricing and the implied growth rate of stock price will be the riskless interest rate. Noticeably, the feasibility of this concept is based on the perfect market assumptions and no riskless arbitrage opportunity. However, none of the conditions of perfect capital markets is true in real capital markets. Therefore, whether the growth rate of the hedged portfolio is the riskless interest rate is an interesting and challenging topic. The purpose of this article is to provide a theoretical relationship between the return of the hedged portfolio and risk in imperfect markets. This theoretical foundation can be viewed as a supplementary work to Hsu and Wang (2004) and Wang and Hsu (2006).

Acknowledgements

The authors would like to thank the Editor Professor Mark Taylor and Associate Editor for their extremely helpful comments. The first author would like to thank the National Science Council Taiwan for financial support. (NSC 91-2416-H-006-040).

Notes

¹ For example, Boness (1964) and Sprenkle (1964) models.

² See Black and Scholes (1973), p. 640.