本文以日內資料研究台灣證券交易所於2005年3月1日實施股價升降單位新制後，市場交易因子與股價報酬波動率的變化；延伸討論市場參與者對新訊息之反應，進而評估實施股價升降單位新制之成效。本文首先比較四種常用來衡量報酬波動率的方法，並從中挑選出最穩健的測度方式；接著藉此分析股價日報酬波動率與市場交易因子之間的關係；最後，由於日內股價報酬波動的軌跡呈現U型曲線，為突顯波動較劇烈之時段股價報酬波動率是否亦隨股價升降單位縮小而趨緩，故著眼交易日開盤後一小時及收盤前一小時，再次檢驗上述關係。實證結果支持股價升降單位縮小使實現波動率大幅降低且交易筆數密切影響股價報酬波動率，且不論在日資料與日內資料都呈現相似結論；並發現愈接近開、收盤的時間點，股價報酬波動率降低比例亦愈大，顯示升降單位新制達成政策目的。

In this study, we address the impact of the tick size reduction on the Taiwan Stock Exchange on March 1, 2005. We propose to investigate the variations of trading activities and return volatility, discuss investors' behaviors to the new information and evaluate the tick size reduction by analyzing intraday data. First, we select the most robust volatility measure for our study from four commonly used ones. Second, we examine the relationship between daily return volatility and trading activities. Eventually, due to the commonly observed U-shaped pattern of intraday return volatility, we re-examine the intraday relation between return volatility and trading activities. Our empirical results based on the robust realized volatility confirm that both daily and intraday return volatility decline significantly after the tick size reduction, and number of trades is a prominent trading factor in explaining realized volatility. More interestingly, we observe that the percentage decrease in realized volatility is most pronounced for trading sessions near the beginning or the ending of each trading day. Overall, our empirical findings support the arguments for tick size reduction intended by policymakers.

1 Introduction 1
2 Tick Size Reduction in Taiwan 7
3 Volatility Measures 10
3.1 Four Volatility Measures 10
3.2 Comparison of Volatility Measures 14
4 Realized Volatility and Trading Activities 20
4.1 Daily Evidences 20
4.2 Intraday Evidences 26
4.3 Concluding Remarks on Volatility and Trading Relation 34
5 Conclusions 36
References 38

Admati, A. R. and P. Pfleiderer (1988). “A Theory of Intraday Patterns: Volume and Price Variability,” The Review of Financial Studies, 1, 3-40.

Ahn, H. J., C. Cao, and H. Choe (1996). “Tick Size, Spread, and Volume,” Journal of Financial Intermediation, 5, 2-22.

Andersen, T.G., T. Bollerslev, F. X. Diebold, and H. Ebens (2001). “The Distribution of Realized Stock Return Volatility,” Journal of Financial Economics, 61, 43-76.

Bacidore, J. M. (1997). “The impact of Decimalization on Market Quality: An Empirical Investigation of the Toronto Stock Exchange,” Journal of Financial Intermediation, 6, 92-120.

Bessembinder, H. (2000). “Tick Size, Spreads, and Liquidity: An Analysis of Nasdaq Securities Trading near Ten Dollars,” Journal of Financial Intermediation, 9, 213-239.

Bollerslev, T. (1986). “Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Economics, 31, 307-327.

Chan, K., Y. P. Chung, and H. Johnson (1995). “The Intraday Behavior of Bid-Ask Spreads for NYSE Stocks and CBOE Options,” Journal of Financial and Qualitative Analysis, 30, 329-346.

Chan, K. and W. M. Fong (2000). “Trade Size, Order Imbalance, and the Volatility-Volume Relation,” Journal of Financial Economics, 57, 247-273.

Chan, C. C. and W. M. Fong (2006). “Realized volatility and transactions,” Journal of Banking & Finance, 30, 2063-2085.

Clark, P. K. (1973). “A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices,” Econometrica, 41, 135-155.

Foster, F. and S. Viswanathan (1993). “Variations in Trading Volume, Return Volatility, and Trading Costs: Evidence on Recent Price Formation Models,” Journal of Finance, 48, 187-211.
French, K. R. (1980). “Stock Returns and the Weekend Effect,” Journal of Financial Economics, 8, 55-69.

French, K. R., G. W. Schwert, and R. F. Stambaugh (1987). “Expected Stock Returns and Volatility,” Journal of Financial Economics, 19, 3-29.

Gencay, R., M. M. Dacorogna,U. A. Muller, R. B. Olsen, and O. V. Pictet (2001). An Introduction to High-Frequency Finance, San Diego: Academic Press.

Gencay, R., G. Ballocchi, M. M. Dacorogna, R. B. Olsen, and O. V. Pictet (2002). “Real-Time Trading Models and the Statistical Properties of Foreign Exchange Rates,” International Economic Review, 43, 463-492.

Glosten, L. and L. Harris (1988). “Estimating the Components of the Bid–Ask Spread,” Journal of Financial Economics, 21, 123–142.

Guillaume, D. M., O. V. Pictet, and M. M. Dacorogna (1994). “On the Intraday Performance of GARCH Processes,” Olsen & Associates, Zurich, mimeo.

Harris L.E. (1991). “Stock Price Clustering and Discreteness,” Review of Financial Studies, 4, 389-415.

Harris, L.E. (1994). “Minimum Price Variations, Discrete Bid-Ask Spreads, and Quotation Sizes,” Review of Financial Studies, 7, 149-178.

Hau, H. (2002). “The Role of Transaction Costs for Financial Volatility: Evidence from the Paris Bourse,” working paper.

Jain, P. C. and G. H. Joh (1988). “The Dependence between Hourly Prices and Trading Volume,” Journal of Financial and Quantitative Analysis, 23, 269-284.

Jones, C. M., G. Kaul, and M. L. Lipson (1994). “Transactions, Volume, and Volatility,” Review of Financial Studies, 7, 631-651.

Ke, M. C., C. H. Jiang, and Y. S. Huang (2004). “The Impact of Tick Size on Intraday Stock Price Behavior: Evidence from the Taiwan Stock Exchange,” Pacific-Basin Finance Journal, 12, 19-39.

Keim, D. B. and R. F. Stambaugh (1984). “A Further Investigation of the Weekend Effect in Stock Returns,” Journal of Finance, 39, 819-835.

Lau, S. T. and T. H. Mcinish (1995). “Reducing Tick Size on the Stock Exchange of Singapore,” Pacific-Basin Finance Journal, 3, 485-496.

O'Hara, M. (1995). Market Microstructure Theory, UK: Blackwell.

Porter, D. C. and D. G. Weaver (1997). “Tick Size and Market Quality,” Financial Management, 26, 5-26.

Ronen, T. and D. G.Weaver (2001). “'Teenies' Anyone?” Journal of Financial Markets, 4, 231-260.

Schwert, G. W. (1989a). “Business Cycles, Financial Crises and Stock Volatility,” Carnegie-Rochester Conference Series on Public Policy, 31, 83-125.

Schwen, G. W. (1989b). “Why Does Stock Market Volatility Change Over Time?” Journal of Finance, 44, 1115-1153.

Schwert, G. W. (1990). “Stock Volatility and the Crash of '87,” The Review of Financial Studies, 3, 77-102.

Van Ness, R., B. Van Ness, and S. Pruitt (2000). “The Impact of the Reduction in Tick Increments in Major U.S. Markets on Spreads, Depth, and Volatility,” Review of Quantitative Finance and Accounting, 15, 153-167.

Van Ness, R. and K. H. Chung (2001). “Order Handling Rules, Tick Size, and the Intraday Pattern of Bid-ask Spreads for Nasdaq Stocks,” Journal of Financial Markets, 4, 143-161.