Arbitrage costs and nonlinear adjustment in the G7 stock markets

Abstract

This paper aims to study stock price adjustments toward fundamentals due to the existence of arbitrage costs defined as the sum of transaction costs and a risky arbitrage premium associated with the uncertainty characterizing the fundamentals. Accordingly, it is shown that a two-regime STECM (Smooth Transition Error Correction Model) is appropriate to reproduce the dynamics of stock price deviations from fundamentals in the G7 countries during the period 1969-2005. This model takes into account the interdependences or contagion effects between stock markets. Deviations appear to follow a quasi random walk in the central regime when prices are near fundamentals (i.e. when arbitrage costs are greater than expected arbitrage profits, the mean reversion mechanism is inactive), while they approach a white noise in the outer regimes (i.e. when arbitrage costs are lower than expected arbitrage profits, the mean reversion is active). Interestingly, as expected when arbitrage costs are heterogeneous, the estimated STECM shows that stock price adjustments are smooth and that the convergence speed depends on the size of the deviation. Finally, using two appropriate indicators proposed by Peel and Taylor (2000), both the magnitudes of under-and overvaluation of stock price and the adjustment speed are calculated per date in the G7 countries. These indicators show that the dynamics of stock price adjustment are strongly dependent on both the date and the country under consideration.

Equity prices and fundamentals: a DDM–APT mixed approach

“…In Figure 3, we showed that the fundamental values represent trends and a substantial part of equity price fluctuations. Moreover, the magnitude of fluctuations in it p and * t i f are generally quite comparable, and this contrasts with the results in the literature obtained with stock price indices, where the fundamental values are very smooth compared to prices (Manzan, 2003;Boswijk et al, 2007;Jawadi and Prat, 2012).…”

“…3 These studies show that deviations between stock price indices and fundamentals are often large and durable, both under the rational expectation hypothesis (REH) and using the Gordon-Shapiro formula with simplifying hypotheses representing the discount rate and the expected dividend growth rate (Shiller, 1981;Campbell and Shiller, 2001;Allen and Yang, 2001;Manzan, 2003;Boswijk et al, 2007). These deviations are explained in different ways: e.g., as irrational fads (Shiller, 1981;Summer, 1986), overconfidence (Daniel et al, 1998), behavioral heterogeneity ( Barberis and Thaler, 2003;Manzan, 2003;Boswijk et al, 2007), information asymmetry and mimetic behavior (Poterba and Summers, 1988;Fama and French, 1988;Cecchetti et al, 1990; Barberis et al, 1998;Jawadi, 2006), as well as arbitrage costs including transaction costs and a premium that reflects the uncertainty characterizing the appraisal of fundamental value (Jawadi and Prat, 2012). Furthermore, acording to these related contributions, the adjustment process of stock price indices toward fundamentals is often found to be asymmetrical and nonlinear.…”

“…30 The fundamental value of a given equity is supposed common knowledge for stockholders, although each of them has their own appreciation of uncertainty about this value. 31 See Jawadi and Prat (2012)…”

“…36 Such a sophisticated process, according to which the strength of the mean-reversion depends on the importance of the deviation, could capture variability in the percentage of investors for whom arbitrage costs are greater or lower than their expected arbitrage profit. This could offer an interesting field of research, consisting of replacing the linear EMC by an STECM (Smooth Transition Error Correction Model), as for example Jawadi and Prat (2012) did for the G7 stock market indices. However, with our individual equities linked to common factors, the STECMs should be estimated simultaneously as a system for the 27 equities (i.e.…”

Measuring the speed of convergence of stock prices: A nonparametric and nonlinear approach

“…Nonlinear models have been popularly employed for financial data, because the risks associated with contrarian trading/arbitrage coupled with the transaction costs naturally suggests nonlinear structures, reflecting the fact that arbitrages occur only when deviations are large enough. 8 See among others, Boswijk et al (2007), Kim et al (2009), Chen and Kim (2011), Jawadi and Prat (2012), Kim and Kim (2015) that employ nonlinear models to analyze stock price adjustment dynamics. 9 To study the persistence properties of nonlinear stochastic models of relative stock prices, we use more general time series concepts of the convergence toward the long-run equilibrium: short-memory-inmean (SMM) and short-memory-in-distribution (SMD), which is 7 Narayan et al (2011) report fast convergence rates from a regression model with exogenous covariates, which might help increase efficiency of their estimations.…”