Research Background and Objectives

When markets are perfect and there are no transaction costs in arbitrage, the prices of a derivative and its underlying stock are perfectly related according to the law of one price.

However, actual market prices commonly deviate from this no-arbitrage condition because of market imperfections such as transaction costs and price uncertainty due to noise trader risk.

Since arbitrage activities occur only when the price difference between a derivative asset and its underlying asset price is large enough to cover transaction costs, a mean-reversion dynamic behavior of the price difference between them can be more significantly observed.

Hence, the threshold vector error correction model (VECM) could potentially be more meaningful in characterizing their price dynamics.

The relationship between nonlinear error correction models and cointegration has attracted considerable attention in recent years. Applications of the threshold cointegration, introduced by Balke and Fomby (1997), are especially popular, evidenced by the many references reviewed in Hansen and Seo (2002) on the multivariate threshold VECM. More recently, Peel and Taylor (2002) used a univariate threshold autoregressive model and multivariate threshold VECM to investigate the covered interest rate arbitrage in the interwar period and found strong support for the Keynes-Einzig conjecture. Enders and Chumrusphonlert (2004) applied a threshold cointegration methodology to explore the properties of long-run purchasing power parity in the Pacific nations and found that asymmetric adjustments of nominal exchange rates play an important role in eliminating deviations from long-run purchasing power parity.

Most studies on price transmission using threshold models tend to use either one threshold to separate the adjustment process into two regimes (Balke and Fomby, 1997;

Enders and Granger, 1998; Abdulai, 2002; Deidda and Fattouh, 2002; Escribano and Mira, 2002; Hansen and Seo, 2002; Cook, 2003; Cook and Manning, 2003; Sephton, 2003; Oscar, Carmen, and Vicente, 2004; Arestis, Cipollini, and Fattouh, 2004; Bajo-Rubio, Díaz-Roldán, and Esteve, 2004) or two thresholds to separate the adjustment process into three regimes (Obstfeld and Taylor, 1997; Goodwin and Piggott, 2001; Serra and Goodwin, 2002; Seo, 2003).

This dissertation uses the absolute value of the error correction term as a threshold variable. In addition to the merit of parsimony in the modeling of threshold effect, this assumption is reasonable since transaction costs tend to be symmetric for the long and short positions in the arbitrage. This dissertation employs the threshold VECM to investigate two areas: (1) the dynamic relationship between the prices of American Depository Receipts (ADRs) and their underlying stocks and (2) the effect of transaction cost reductions and the lead-lag relationship between the Taiwan Futures Exchange (TAIFEX) electronic index and futures.

Given increasing global competition, many companies have chosen to raise capital in the U.S. by issuing ADRs in order to diversify their capital market risk, while also reducing the overall cost of capital and promoting the firm’s reputation in the global market. Through the purchase of ADRs, investors can also indirectly invest in foreign securities as a means of circumventing foreign exchange barriers and various investment regulations. Thus, for both

foreign investors and issuing companies alike, ADRs have become one of the most popular financial instruments currently in use.

Therefore, this study explores both the existence of various arbitrage regimes and causal linkages between the prices of ADRs and their underlying stocks. This study begins by identifying the location of possible thresholds and then exploring the relationship leading to the determination of the error correction term in a two-regime strategy. Secondly, this study estimates a threshold cointegration framework in both the short-run and the long-run and finds that a significant threshold effect exists in the error correction term of the prices of ADRs and their underlying stocks. The first part of this dissertation begins research on the dynamic relationship between the prices of ADRs and their underlying stocks.

On July 21, 1998, Taiwan introduced its own index futures contract to be traded on TAIFEX, which was called TAIFEX futures. One year later, in order to meet a strong market demand, TAIFEX began operating two stock indexes: the Electronic Sector Index Futures (TEF) and the Finance Sector Index Futures (TEI).

The futures market and the spot market naturally share trading information with each other. When information is traded smoothly, the futures and spot markets should have the same price reaction and price change simultaneously, according to Fama’s (1965) concept of market efficiency. However, Abhyankar (1995) has pointed out a difference in market mechanics. Futures markets reflect information more rapidly than spot markets, as the futures market has price discovery and information transmission. Based on the time lag between the futures and spot markets, which creates a return lead-lag relationship, there is an inconsistency between the two. This inconsistency not only provides arbitrage opportunities,

but also transmits the information from the futures market to the spot market by the arbitrageurs.

Therefore, this study explores both pre- and post-tax reduction adjustment and the causal relationship between prices of the TEF and the TEI through linear and nonlinear models and changes in the threshold value. Moreover, it estimates the tax reduction after linear and nonlinear models and examines their in-sample properties. An out-of-sample comparison is also conducted to determine the forecasting performance of the linear and threshold VECM.

Obviously, transaction costs prevent arbitrageurs from realizing many valuable opportunities, as the mean-reversion will occur only when the deviation is large.

This study investigates the lead-lag relationship between prices of the TEF and the TEI in both pre- and post-tax reduction periods. Because of a tax reduction, the transaction costs become lower for investors who are using arbitrage. Therefore, when invertors exploit arbitrage opportunities, the lower spread cost between prices of the TEF and the TEI and the threshold value will bring a change. Arbitrage is not available when spread cost phenomena exist in an environment with transaction costs. It is only when spreads are larger than transaction costs that arbitrage opportunities exist. This study investigates the effects of linear and threshold VECM on the accuracy of forecasting arbitrage opportunities. The second part of this dissertation begins research on the effect of transaction cost reductions and the lead-lag relationship between the TAIFEX electronic index and futures.