The rate of change in financial markets has accelerated in recent years, with an unprecedented proliferation of new markets and instruments. This dissertation focuses on several important issues in market microstructure, including tick size, arbitrage efficiency and market liquidity.
The first essay in this dissertation investigates the impact of decimalization (penny pricing) on the arbitrage relationship between index exchange-traded funds (ETFs) and E-mini index futures. Our empirical results reveal that subsequent to penny pricing, there is a significant fall in the mean ex-ante arbitrage profit, especially in the cases with higher transaction costs. Using the method of ordinary least squares (OLS) and quantile regressions to control for the influences of changes in other market characteristics, we find that the overall pricing efficiency has deteriorated in the post-decimalization period. From the quantile regression analyses, it is found that the pricing efficiency is improved only when an extremely large mispricing signal is observed, implying that due to increased execution risk after decimalization, arbitragers will only execute trades when the expected profit is large enough.
These results are consistent with the hypothesis that, due to the lowered market depth and increased execution risks, the introduction of decimalization has in general resulted in weakening the ability and willingness of arbitrageurs to initiate arbitrage trades, which subsequently leads to a reduction in the general efficiency of the cash/futures pricing system.
The second essay examines the effects of the internal and external corporate governance mechanisms, on equity liquidity, arguing that those companies adopting poor disclosure practices and weak shareholder rights will experience serious information asymmetry. Since poor corporate governance leads to greater information asymmetry, liquidity providers will incur relatively higher adverse information risks and will therefore offer higher information asymmetry components in their effective bid-ask spreads. The Transparency and Disclosure
(T&D) rankings, the governance index (GI) and the entrenchment index (EI) of the individual stocks on the S&P 500 index are employed to examine whether firms with greater T&D ranking and lower score in these two index have lower information asymmetry components and lower stock spreads. Our results reveal that the economic costs of equity liquidity, i.e., the effective spread and the asymmetric information cost, are greater for those companies with poor corporate governance.
In summary, the essays of this dissertation provide some insights into the issues of market microstructure, emphasize on the importance of tick size and corporate governance on financial markets. The research results would furnish us with the empirical evidences to explain the occasion of some distinctive phenomena in financial markets. The results, therefore, should be treated circumspectly.
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A PPENDIX: Q UANTILE R EGRESSION
Quantile regression, developed by Koenker and Bassett (1978), is an extension of the classical least squares estimation of the conditional mean to a collection of models for different conditional quantile functions. In this appendix, the lecture notes of Kuan (2004) and the book of Koenker (2005) are quoted to interpret the computation and inference of the quantile regression estimator.
A1. The Method of Quantile Regression
This section is extracted from the lecture notes of Kuan (2004). Given the data
(
y x′ for t, t)
'This specification can approximate a particular conditional quantile of yt provided that β is estimated properly.
The θth quantile regression estimator of β can be obtained by minimizing its sample counterpart, i.e., the average of asymmetrically weighted absolute errors with weight θ on positive errors and weight
(
θ −1)
on negative errors:Hence, a regression estimated via the method of LAD is in effect a special case of conditional quantile regression and is usually referred to as a “median regression”.
Let ρθ denote the so-called “check” function such that ρθ
( )
a =θa if a≥0 andwhere 1A is the indicator function of the event A . The first order condition of minimizing (A2) is
A2. Computation of the Estimator
This section is also extracted from the lecture notes of Kuan (2004). The quantile regression estimator βˆθ is not easy to compute because it does not have a closed form. It can also be seen that the objective function (A2) is not differentiable everywhere so that standard numerical optimization method is not readily applicable.
In practice, the quantile regression estimates are usually computed by solving a linear programming problem. To see this, write the linear specification as
( ) ( )
We can then write the linear specification as where 0 is the k-dimensional vector of zeros and 1 denotes the T -dimensional vector of ones, it follows that the objective function (A2) is c′z T. Minimizing (A2) is thus equivalent to minimizing c′z with respect to z, subject to the constraint that y= Az and that
zcontains only non-negative elements.
To solve the linear programming problem, Barrodale and Roberts (1974) designed a simplex-based algorithm for LAD estimation, which was subsequently extended by Koenker and d’Orey (1987) to quantile regression estimation. Koenker and Park (1996) also extend the interior method of Karmarkar (1984) to quantile regression.
A3. Inference for Quantile Regression: The Bootstrap
There is quite an extensive literature on the use of the bootstrap and related resampling schemes for quantile regression. Efron (1982) suggested the residual bootstrap for a nonlinear median regression problem, and this form of the bootstrap has been considered by De Angelis et al. (1993) and several others.
This section is mainly to refer to chapter 3 in the book of Koenker (2005). In the linear quantile regression setting, let
( )
⎥and let FˆT denote the empirical distribution of the residuals, eˆt = yt −x′tβˆθ, with respect to
De Angelis et al. (1993) show that under iid error conditions the distribution of the bootstrapped βθ*s,
βθ , there are several options that have been considered for constructing tests and confidence intervals. Most straightforwardly, one can compute the empirical covariance matrix of the realizations and construct tests and confidence intervals directly from it. Alternatively, one can form percentile intervals as discussed, for example, by Efron and Tibshirani (1993). Many important practical aspects of the implementation of the bootstrap, including the crucial question of how to choose the number of replications, N , are treated by Andrews and Buchinsky (2000, 2001).