Nonlinear adjustment of investors’ holding periods for common stocks in the presence of unobserved transactions costs: evidence from the UK equity market

Abstract

We estimate a model of holding period adjustment for four stock indices in the UK over the period 1980 to 2004. We postulate zone-symmetric investor preferences that result in an estimable ESTAR (Exponential Smooth Transition Autoregressive) model of the holding period for common stocks as a function of stock price volatility, market value and the bid-ask spread. These models suggest that there exists a nontrading zone due to the presence of transactions costs over and above the usual bid-ask spread. Normally such costs are not directly observed thus we need to deduce their influence by observing investors’ responses to asset price shocks that necessitate trading. We show that the speed of adjustment increases as a function of deviations from the optimum. We present strong evidence of nonlinearities in the adjustment process that can be modelled by the proposed ESTAR model. We find that for heavily traded firms, such as those included in the FTSE 100, even small misalignments of the holding period from its ‘optimal’ value, trigger trading. However, transactions costs (other than the bid-ask spread) prevent such rapid adjustment in the other indices.

Notes

¹ See among others Stoll (1978), Hamilton (1976), Marsh and Rock (1986) and Atkins and Dyl (1990).

² Note that all the variables apart from the dummies in Equation 10 are estimated in logs, due to the excess skewness and kurtosis of the data.

³ For more details see Terasvirta (1994, pp. 211–2).

⁴ Phillips–Peron unit root tests were also applied to e_t . The results (not reported) indicate that e_t is clearly stationary at all significance levels.

⁵ The nonlinearity present in the FTSE All Share index suggests that aggregation does not affect the nonlinear dynamics of the disaggregated data.

⁶ Notice that the scaling of (e_{t − d}  − c) in the transition function makes it possible to judge the size of α (Granger and Terasvirta, 1993, pp. 123, 153).

⁷ Notes: The ESTAR results are based on optimal holding period estimates where the variance of monthly returns represent the volatility. For robustness, we also compute the volatility of returns with the use of an Autoregressive Conditional Heteroscedasticity model (ARCH) with one lag structure. The results are identical and are therefore not reported.