Market timing ability and mutual funds: a heterogeneous agent approach

Abstract

This paper proposes a novel approach to determine whether mutual funds time the market. The proposed approach builds on a heterogeneous agent model, where investors switch between cash and stocks depending on a certain switching rule. This approach is more flexible, intuitive, and parsimonious than the traditional convexity approach. Applying this model to a sample of 400 US equity mutual funds, we find that 41.5% of the funds in our sample have negative market timing skills and only 3.25% positive skills. Twenty percent of funds apply a forward-looking approach in deciding on market timing, and 13.75% a backward-looking approach. We find that growth funds tend to be more backward-looking and income funds tend to be more forward-looking.

Keywords:

• Mutual funds
• Market timing
• Agent based models
• Heterogeneous agent model

JEL Classification:

• G11
• G23

Acknowledgement

Part of this paper was written while Zwinkels was visiting Auckland University of Technology, whose hospitality he gratefully acknowledges.

Notes

¹An alternate approach to the return-based measure has been employed by Jiang et al. (2007). This study employs portfolio fund holding information to calculate a fund beta based on the weighted average of the betas of the individual stocks held. The timing measure is then calculated as the covariance between the fund beta and the return on the market. Jiang et al. (2007) show that this measure results in a reduction in funds with negative timing ability with most funds showing insignificant but positive timing ability.

²As a consequence, equation (1) cannot be estimated by ordinary least squares (OLS), but needs to be estimated by constrained maximum likelihood estimation (MLE), where these restrictions can be imposed. Alternatively, one could resort to constrained OLS estimation, also known as the Kuhn–Tucker Estimator (see, e.g. Gourieroux et al. (1982)). However, as our full model needs to be estimated by MLE, we also resort to this model for our benchmark.

³We use the exponent in the denominator to ensure that we cannot divide by zero.

⁴Returns of the fund obviously cause assets under management directly, but also indirectly by attracting capital inflows (Sirri and Tufano 1998).

⁵We cannot conduct a simple t-test on this coefficient, as (1) we obtain the parameter from a constrained MLE, and (2) the standard t-test often turns out to be insignificant in these models as the switching parameter γ enters the model nonlinearly. We therefore perform a Likelihood Ratio (LR) test with two degrees of freedom that compares the performance of equation (2) (the model with timing) with the performance of equation (1) (the model without timing). A significant increase in model fit suggests significant evidence of market timing.

⁶We also look at the significance of switching implied by the traditional model and our approach. Again, the correlation between these two is very strong at a value of 0.75.

⁷The concave relationship, especially visible in the lower left quadrant, is explained by the nonlinear functional form of the switching function (4); the marginal effect of a change in γ decreases as γ becomes larger (in absolute sense).