Correcting the Merton and Henriksson timing model

Abstract

This article provides evidence of a common bias found in traditional timing models, which is related with a negative correlation between timing and stock-picking abilities resulting in spurious coefficients. We consider as a possible cause for this bias the failure to include in the timing models the cost of the option implied in timing activities, and on this basis we opt for a corrected version of the Merton and Henriksson's model (1981). As far as we know, this correction has not previously been applied. Our results confirm both the existence of this bias and the correction of the problem when the cost of the option is included in timing models.

Acknowledgements

The authors would like to express their thanks to Ibercaja and to the University of Zaragoza for the Project 268-96, and to the Government of Aragon for the funding received as a Public and Official Research Group. In addition, they would like to thank the Spanish Ministry of Science (MEC) for the Project SEJ 2006–04208 grants with European co-financing of FEDER funds (European Commission, Brussels). The authors would like to thank Dr. Gonzalo Rubio for his helpful comments in a Work Seminar held in Zaragoza (May 2007), which has undoubtedly improved the article. Finally, the authors would like to thank Dr. Cheng-Few Lee for his helpful comments in a Work Seminar held in Zaragoza (October 2008).

Notes

¹ According to the Black–Scholes formula, the option value and following Merton's (1981) assumptions: S = 1, X = R_f , and e^{− rT}  = 1/R_F , it is straightforward to show that . From our data, we use the volatility implied in the at-the-money Spanish options on the Spanish equity market as σ, set T = 12 for a year, and obtain V = 0.07.

² For V = 0.07 (see footnote 1), and for a timing coefficient 0.048 from the single-factor Merton and Henriksson regression, the added value from timing skills is 0.0034 (=0.07 × 0.048). Of course, this value is at best an approximation, depending on the Black–Scholes conditions.