What factors increase the risk of incurring high market impact costs?

Abstract

This article applies quantile regression to assess the factors that influence the risk of incurring high trading costs. Using data on the equity trades of the world's second largest pension fund in the first quarter of 2002, we show that trade timing, momentum, volatility and the type of broker intermediation are the major determinants of the risk of incurring high trading costs. Such risk is increased substantially by either high or low momentum and by strong volatility. Moreover, agency trades are substantially more risky in terms of trading costs than similar principal trades. Finally, we show that the quantile regression model succeeds well in forecasting future trading costs.

Acknowledgements

The authors are grateful to an anonymous referee, the participants of the research seminars at De Nederlandsche Bank and University of Twente, as well as the participants of the 2006 Dauphine workshop in Paris and the 2006 ESEM in Vienna. The usual disclaimer applies.

Notes

² This is the total invested capital in July 2007.

³ For a detailed exposition of the trading process at ABP, we refer to Bikker et al. (2007)

⁴ The dataset was created on the basis of the post-trade analysis provided by ABP, in combination with additional data from Factset and Reuters. The information on the characteristics of the exchanges under-involved were obtained from the World Federation of Exchanges and the exchanges themselves.

⁵ As a robustness check, we have also calculated confidence bounds for the quantile regression estimates using Chernozhukov (2005)'s extremal quantile regression approach (for which we used the R code available from the author's web site). The resulting confidence bounds were very close to the current ones. Therefore, we do not depict them in Figs 1–4.

⁶ We notice that interaction terms such as the product of relative trade size and volatility are not included in the regression model as their impact on market impact costs is not significant.

⁷ We note that the pension fund itself decides whether it wants to trade on an agency/single or principal basis. Clearly, the pension fund's choice for either an agency/single or principal trade may be affected by the expected market impact costs of the trade, which, in turn, is one of the determinants of the initial choice for a specific trade type. This may cause a selectivity or selection bias, see Heckman (1976, 1979). For a detailed survey of the selectivity bias literature, we refer to Vella (1998). When the selection effect is ignored, the resulting estimators may be inconsistent. To assess the possible selectivity effects regarding the choice of trade type, we conducted a similar analysis as Madhavan and Cheng (1997). Using a two-stage estimation procedure, we estimated a probit model to explain the choice for an agency/single or principal trade and a regression model with a correction factor for selectivity effects depending on the probit-specification. We did not establish significant evidence for a selection bias.

⁸ This test is implemented in the Quantreg package in R.

⁹ The (technical) results of the Khmaladze (1981) test are available from the authors upon request.

¹⁰ In the year 2002, January was bearish and February was quite flat. However, the out-of-sample month of March was bullish.

¹¹ Clearly I depends on τ ₀ , but we omit any subscripts for simplicity of notation.

¹² Alternatively, we could compare the quantile regression model to the heteroskedastic regression model. However, at some points this model produces negative values of the conditional SD. This is not a surprise, since the model does not restrict the conditional SD to positive values. Instead, it is more practical to work with a different specification for the conditional variance, for instance exp(Xγ)′ or (Xγ)². However, our investigations show that such a specification performs very similarly to the homoskedastic regression model. Therefore, we apply the simplest specification, which is the latter model.

¹³ The empirical distribution is based on the (in-sample) observed model residuals and assigns equal probability mass to each observed value.

¹⁴ We notice that it would be clearly wrong to approximate the quantile regression model by dividing the dependent variable into sub-sets according to its unconditional distribution and by subsequently applying ordinary least squares to these sub-sets. The example of Hallock et al., (2004) demonstrates that such truncation of the dependent variable can lead to erroneous conclusions, due to the selection bias of Heckman (1979).