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行政院國家科學委員會補助專題研究計畫成果報告
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※ 台灣股票市場價格密集性之研究 ※
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計畫類別：■個別型計畫 □整合型計畫
計畫編號：NSC 90－2416－H－011－002－
執行期間： 90 年 8 月 1 日至 91 年 7 月 31 日
計畫主持人：黃彥聖 台灣科技大學企業管理系 共同主持人：傅澤偉 國防管理學院
計畫參與人員：
本成果報告包括以下應繳交之附件：
□赴國外出差或研習心得報告一份
□赴大陸地區出差或研習心得報告一份
□出席國際學術會議心得報告及發表之論文各一份
□國際合作研究計畫國外研究報告書一份
執行單位：國立台灣科技大學企業管理系
中 華 民 國 91 年 8 月 28 日
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一、 中文摘要
本計畫探討台灣證券交易所上市公司股票價格之密集性，亦即，股票之價 格是否集中於特定之數字，以利於交易之進行。樣本期間自 1993-99。針對開盤 價與收盤價加以研究，結果發現顯著之價格密集性。其中，開盤價之價格密集 性，較收盤價之價格密集性為顯著。
由於證券市場於開盤時之資訊不對稱程度，較收盤時之資訊不對稱為嚴 重，本計畫之發現，支持價格解析假說(price resolution hypothesis)，亦即不具內 部資訊之交易者，較傾向於以特定整數之價格交易，以使交易易於成交，其中，
在開盤時更是如此，因此造成了開盤時之價格密集性較著著。
關鍵字: 價格密集性 Abstract
This paper examines the price clustering effect for stocks listed on the Taiwan Stock Exchange over 1993-99. Since uninformed traders do not possess perfect information about the true value of the security, these traders may prefer a price increment larger than the tick size to reduce negotiation costs. Thus, the price resolution hypothesis asserts that price clustering leads to a smaller negotiation cost for uninformed traders.
Moreover, the price resolution hypothesis would predict a higher degree of price clustering for opening prices than for closing prices. The result of more significant clustering for the opening prices than for the closing prices would support the price resolution hypothesis in that uninformed traders utilize large price increments to resolve the issue of information asymmetry.
The result indicates significant price clustering for both closing prices and opening prices. Moreover, the degree of price clustering is higher for opening prices than for closing prices. These results are consistent with the explanation of the price resolution hypothesis.
Keywords: price clustering
二、 緣由與目的
Price clustering refers to the tendency of security prices to lie on certain natural multiples of tick size. Price clustering has been found to exist in several security markets. Ball, Torus, and Tschoegl (1985) report price clustering in the London gold market. Harris (1991) documents that stock prices lie more frequently on even-eighths than on odd-eighths for the US equity market. Bessembinder (1994)
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notes spread clustering in the US$/DM quotes. Gwilym, Clare, and Stephen (1998) find that around 98% of quoted and traded prices for LIFFE stock index derivatives occur at even ticks. Hameed and Terry find price clustering for stocks listed on the Stock Exchange of Singapore. Booth et al (2000) report prevalent price clustering in the Finnish stock exchange. Hasbrouck (1999a, b) analyze the impact of tick size and price clustering and proposes simple strategies for modeling price discreteness and clustering.
This project examines the price clustering effect using daily data from the Taiwan Stock Exchange. The unique nature of the order-driven call market method in the Taiwan Stock Exchange provides a natural experiment to test the relevant hypotheses. The results indicate significant price clustering in both the opening and the closing prices. Moreover, the degree of price clustering is significantly higher in the opening prices than in the closing prices. These results are consistent with the explanation of the price resolution hypothesis.
三、 內容
The sample contains all stocks listed on the Taiwan Stock Exchange for the period from 1993 to 1999. Stock prices in the NT$15-150 range are collected for both the opening and the closing prices. As shown in Table 1, the price range of NT$15-50, with a tick size of NT$0.1, represents 64.4% of all observations. In contrast, the closing prices in the NT$50-150 range, with a tick size of NT$0.5, accounts for 24.0% of all observations. Data in the ranges of NT$15-50 and NT$50-150 allow an examination of the impact of tick size on price clustering.
Consistent with the prediction of the price resolution hypothesis, the result indicates significant price clustering. Within the price range of NT$15-50, the most commonly observed closing prices are those ending in the whole dollar (13.43%), followed by the half dollar (11.68%). These two prices reflect a price increment of NT$0.5, which is much larger than the minimum tick size of NT$0.1. The next commonly observed digits are NT$0.2 (10.24%) and NT$0.8 (10.23%). Again, the price increment of NT$0.2 is twice as large as the minimum tick size. However, the degree of price clustering on the other two even-digits of NT$0.4 and NT$0.6 is lower, probably due to their proximity to the half dollar.
The above results are comparable with the price clustering result reported by Hameed and Terry (1998, p.855) for stocks listed on the Stock Exchange of Singapore. They note that the tick size for stocks in the range of $1.01-$3.00 is $0.01.
In their Table 3, they report most commonly observed closing prices ending in $0.00 (16.68%), followed by the $0.05 (11.98%). Their next commonly observed digits are
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$0.02 (9.91%) and $0.08 (10.45%).
四、 參考文獻
Ball, C.A., Torus, W.A., Tschoegl, A.E., 1985. The degree of price resolution: the case of the gold market. Journal of Futures Markets 5, 29-43.
Bessembinder, H., 1997. The degree of Price resolution and equity trading cost.
Journal of Financial Economics 45, 9-34.
Booth, G., Kallunki, J., Lin, J., Martikainen, T., 2000. Internationalization and stock price clustering: Finnish evidence. Journal of International Money and Finance 19(5), 737-751.
Brown, S., Laux, P., Schachter, B., 1991. On the existenc e of an optimal tick size. Review of Futures Markets 10, 50-72.
Chang, R., Hsu, S.T., Huang, N.K., Rhee, S.G., 1999. The effects of trading methods on volatility and liquidity: Evidence from the Taiwan Stock Exchange. Journal of Business Finance & Accounti ng 26(1)&(2), 137-170.
Christie, W.G., Schultz, P. H., 1994a. Why do Nasdaq market makers avoid odd-eighth quotes? Journal of Finance 49, 1813-1840.
Christie, W.G., Harris, L., Schultz, P. H., 1994b. Why did Nasdaq market makers stop avoiding odd-eighth quotes? Journal of Finance 49, 1841-1860.
Goldstein, M.A., Kavajecz, K.A., 2000. Eighths, sixteenths, and market depth: Changes in tick size and liquidity provision on the NYSE, Journal of Financial Economics 56, 125-149.
Gwilym, O., Clare, A., Stephen, T, 1998. Extreme price clustering in the London equity index futures and options markets, Journal of Banking and Finance 22, 1193-1206.
Hameed, A., Terry, E., 1998. The effect of tick size on price clustering and trading volume. Journal of Business Finance & A ccounting 25(7)&(8), 849-867.
Harris, L.E., 1991. Stock price clustering and discreteness. Review of Financial Studies 4, 389-415.
Harris, L., 1994. Minimum price variations, discrete bid-ask spreads, and quotation sizes. Review of Financial Studies 7, 149-178.
Hasbrouck, J., 1999a. Security bid/ask dynamics with discreteness and clustering: Simple strategies for modeling and estimation. Journal of Financial Markets 2, 1-28.
