Option replication and the performance of a market timer

The Treynor and Mazuy framework is a widely used return-based model of market timing. However, existing corrections to the regression intercept can be manipulated through derivatives trading. Because they are conceptually flawed, these corrections produce biased performance measures. This paper aims to get back to Henriksson and Merton’s initial idea of option replication to overcome this issue and adapt the market timing model to various kinds of trading strategies and return-generating processes.

This paper proposes a theoretical adjustment based on Merton’s option replication approach adapted to the Treynor and Mazuy specification. The linear and quadratic coefficients of the regression are exploited to assess the cost of the replicating option that yields similar convexity for a passive portfolio. A similar reasoning applies for various timing patterns and in multi-factor models.

The proposed framework induces a potential rebalancing risk and involves the delicate issue of choosing the cheapest option. This paper shows that these issues can be overcome for reasonable tolerance levels. The option replication approach is a workable approach for practical applications.

The adaptation of Merton’s reasoning to the Treynor and Mazuy model has surprisingly never been proposed so far. This paper has the potential to correct for a pervasive bias in the estimation of the performance of a market timer in the context of this very popular quadratic regression setup. Because of the power of the option replication approach, the reasoning is shown to be applicable to multi-factor models, negative timing and market neutral strategies. This paper could fuel empirical studies that would shed new light on the genuine market timing skills of active portfolio managers.