ETF基金套利机会定价
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摘要
交易所交易基金ETFs(Exchange-Traded Funds),又称交易型开放式指数基金,在本质上是一种特殊的开放式指数基金。作为开放式基金的创新,ETF具有指数投资、费用低廉和税收优惠等优势。ETFs具有独特的一二级市场交易机制,ETFs可以在一级市场申购赎回,投资者只能用与目标指数对应的一篮子股票申购或者赎回ETFs,而不像现有开放式基金必须以现金申购赎回。ETF也可以在二级市场挂牌买卖,投资者可以像单个股票和封闭式基金那样在证券交易所直接买卖ETF份额,交易非常便利。
根据有效市场理论和无套利定价原理,ETF二级市场价格(MV)必须等于基金净值(IOPV)。然而由于跟踪能力、管理费用、供求因素以及市场惯性与信息传播速率差异引起基金价格与ETF价格反应速度原因,两者之间存在差异,因而存在套利机会。从国内外文献研究来看,国内外学者主要侧重于讨论指数型基金净值对其目标指数的跟踪误差以及ETF的套利机制,但关于ETF的套利机会的产生原因的综述以及套利机会价值的研究则很少。
本文选择华夏上证50ETF作为研究对象,研究上证50ETF二级市场价格和其基金净值之间价差的高频数据。对这些高频数据进行统计描述,并运用修正的B-S期权定价模型对ETF产生的套利机会进行定价。实证结果表明在样本期(2010年2月4日到2010年2月23日)内,根据修正的B-S模型算出按100万份交易额正向套利每份期权价值为0.00002元,即在1年时间内利用ETF套利机会大约可以赚到的收益为20元。看涨期权价值大于0,说明由于ETF跟踪误差和申购赎回时现金替代等因素存在,ETF二级市场价格与基金净值IOPV之间出现背离造成的套利机会仍然存在。在一系列假设前提下,这个套利机会是有价值的,如果正确利用这个套利机会,投资者可以获利。但另一方面,计算出来的看涨期权价值很小,也符合预期和市场的现状,因为目前套利空间已经大幅缩小,即从2010年2月份数据的分钟数据以及平均价差波动来看,目前以上证50ETF进行价差套利大幅盈利概率较小。
Exchange-traded fund (ETFs), also knowns as exchange-traded index funds, is in essence a special kind of open index fund. It's an innovative product of the open-end fund. And ETF has the exponential fitting, trade facilitation and low-cost advantages. ETF can be traded in the listing market, and investors can directly buy or sell ETF shares on the stock exchange as the indivial stock or closed-end funds, which is very convenient. The purchase and redemption of ETFs have its own characteristics, that is, investors can only use the baskets of stocks, corresponding to ETFs'targetting index, to purchase or redeem shares of ETFs, which is different from the open-end funds, purchased or redeemed by cash.
According to the efficient market theory and the no-arbitrage pricing theory, the secondary market value of ETF must equal to the fund's net value (IOPV). However, because of the tracking ability, management cost, supply and demand factors, and market inertia and information dissemination rate, there are differences between MV and IOPV, causing arbitrage opportunities. In the review of literatures, scholars focused primarily on the tracking error of ETF to its target index and ETF's arbitrage mechanism. However, there are only few researches about the reasons why there are ETF's arbitrage opportunities rising and the value of these opportunities.
This paper chooses China Shanghai 50ETF as the target to have a deep research on the high-frequency data of the spread between ETF's MV and IOPV. By statistics describing these high-frequency spreads, I use the B-S option pricing model to price the ETF's arbitrage opportunities arising from the spread. During the sample period, from Feb 4,2010 to Feb 23,2010, the empirical results show that the amount value of positive arbitrage opportunity is RMB 0.00002 for one share at a trade which has totally 100 million shares, or the total amount value for one arbitrage trading is RMB 20. The Call option value of the positive arbitrage opportunity is greater than 0, indicating the arbitrage opportunity exists because of the tracking error or the cash alternative in the purchase and redemption.
In a series of assumptions, ETF's arbitrage opportunities resulted from the spread between MV and IOPV is valuable. And if the investors can correctly take advantage of the arbitrage opportunities, they can profit. However, on the other hand, the calculated value of call options from the adjusted B-S option pricing mode is very small, which is also in line with the expectations and the market situation, because the current arbitrage space of China Shanghai 50ETF has been significantly reduced. There is very small probability that investors can profit from taking advantage of the ETF's arbitrage opportunites from the sample period.
根据有效市场理论和无套利定价原理,ETF二级市场价格(MV)必须等于基金净值(IOPV)。然而由于跟踪能力、管理费用、供求因素以及市场惯性与信息传播速率差异引起基金价格与ETF价格反应速度原因,两者之间存在差异,因而存在套利机会。从国内外文献研究来看,国内外学者主要侧重于讨论指数型基金净值对其目标指数的跟踪误差以及ETF的套利机制,但关于ETF的套利机会的产生原因的综述以及套利机会价值的研究则很少。
本文选择华夏上证50ETF作为研究对象,研究上证50ETF二级市场价格和其基金净值之间价差的高频数据。对这些高频数据进行统计描述,并运用修正的B-S期权定价模型对ETF产生的套利机会进行定价。实证结果表明在样本期(2010年2月4日到2010年2月23日)内,根据修正的B-S模型算出按100万份交易额正向套利每份期权价值为0.00002元,即在1年时间内利用ETF套利机会大约可以赚到的收益为20元。看涨期权价值大于0,说明由于ETF跟踪误差和申购赎回时现金替代等因素存在,ETF二级市场价格与基金净值IOPV之间出现背离造成的套利机会仍然存在。在一系列假设前提下,这个套利机会是有价值的,如果正确利用这个套利机会,投资者可以获利。但另一方面,计算出来的看涨期权价值很小,也符合预期和市场的现状,因为目前套利空间已经大幅缩小,即从2010年2月份数据的分钟数据以及平均价差波动来看,目前以上证50ETF进行价差套利大幅盈利概率较小。
Exchange-traded fund (ETFs), also knowns as exchange-traded index funds, is in essence a special kind of open index fund. It's an innovative product of the open-end fund. And ETF has the exponential fitting, trade facilitation and low-cost advantages. ETF can be traded in the listing market, and investors can directly buy or sell ETF shares on the stock exchange as the indivial stock or closed-end funds, which is very convenient. The purchase and redemption of ETFs have its own characteristics, that is, investors can only use the baskets of stocks, corresponding to ETFs'targetting index, to purchase or redeem shares of ETFs, which is different from the open-end funds, purchased or redeemed by cash.
According to the efficient market theory and the no-arbitrage pricing theory, the secondary market value of ETF must equal to the fund's net value (IOPV). However, because of the tracking ability, management cost, supply and demand factors, and market inertia and information dissemination rate, there are differences between MV and IOPV, causing arbitrage opportunities. In the review of literatures, scholars focused primarily on the tracking error of ETF to its target index and ETF's arbitrage mechanism. However, there are only few researches about the reasons why there are ETF's arbitrage opportunities rising and the value of these opportunities.
This paper chooses China Shanghai 50ETF as the target to have a deep research on the high-frequency data of the spread between ETF's MV and IOPV. By statistics describing these high-frequency spreads, I use the B-S option pricing model to price the ETF's arbitrage opportunities arising from the spread. During the sample period, from Feb 4,2010 to Feb 23,2010, the empirical results show that the amount value of positive arbitrage opportunity is RMB 0.00002 for one share at a trade which has totally 100 million shares, or the total amount value for one arbitrage trading is RMB 20. The Call option value of the positive arbitrage opportunity is greater than 0, indicating the arbitrage opportunity exists because of the tracking error or the cash alternative in the purchase and redemption.
In a series of assumptions, ETF's arbitrage opportunities resulted from the spread between MV and IOPV is valuable. And if the investors can correctly take advantage of the arbitrage opportunities, they can profit. However, on the other hand, the calculated value of call options from the adjusted B-S option pricing mode is very small, which is also in line with the expectations and the market situation, because the current arbitrage space of China Shanghai 50ETF has been significantly reduced. There is very small probability that investors can profit from taking advantage of the ETF's arbitrage opportunites from the sample period.
引文
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[3]Barberis, Nicolas, Richard Thaler. A Survey of Behavioral Finance [M]. Handbook of the Economics of Finance,2003.
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[5]Campbell J Y, Kyle A. Smart money, noise trading, and stock price behavior [J]. Review of Economics Studies,1993, (60):1-34.
[6]Chu, Q.C. and W.G. Hsieh. Pricing Efficiency of the S&P 500 Index Market: Evidence from the Standard and Poor's depositary Receipts [J]. The Journal of Futures Markets,2002, (22):877-900.
[7]Chu, Q.C., W.G. Hsieh, and Y.Tse. Price Discovery on the S&P 500 Index Markets: an Analysis of Spot Index, Index Futures, and SPDR [J]. International Review of Financial Analysis,1999, (8):21-34.
[8]Daniel K, Hirshleifer D, Subramanyam A. Investor Psychology and Securitiy Market Under-and Overreactions [J]. Journal of Finance,1998, (53):1839-1885.
[9]Daniel Kahneman, Amos Tversky. Prospect Theory:an Analysis of Decision Under Risk [J]. Econometrica,1979, (47):263-291.
[10]De Long J B, Shleifer A, Summers L, etal. Noise Trader Risk in Financial Markets [J]. Journal of Political Economy,1990,98:703-738.
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[14]Fremault, A. Stock Index Futures and Index Arbitrage in a Rational Expectations Mode [J]. Journal of Business,1991, (64):523-547.
[15]Gastineau, G. L. Exchange-traded funds:An Introduction [J]. Journal of Portfolio Management,2001,(27).
[16]Gastineau, G. L. The Exchange-Trade Funds Manual [M]. New York:John Wily and Sons Press,2002:5-11.
[17]Gorton, G. and G. Pennacchi. Securitiy Baskets and Index-linked Securities [J]. Journal of Business,1993, (66):1-27.
[18]Hasbrouck, Joel. Intraday Price Formation in the Market for U.S. Equity Indexes.
[19]John C Hull. Options, Futures, and other Derivative Securities [M]. New York: Prentice-Hall,1997:228-260.
[20]Lu, Marsden. NZSE-10 Index Fund Units and the Market Efficiency of the Index Futures:Evidence from the New Zealand Market [R]. Presented for the 7th Annual Conference of APFA, Shanghai,2000.
[21]Morgan Stanley Equity Research. Exchange-Traded Funds:Global Summary, 2003.
[22]Park, T.H. and Switzer, L.N. Index Participation Units and Performance of Index Futures Markets:Evidence from the Toronto 35 Index Participation Units Market. [J]. Journal of Futures Markets,1995, (15):187-200.
[23]Richard H. Thaler. the End of Behavioral Finance [J]. Financial Analysts of Journal,1999:18-27.
[24]Richard J Curcio, Joanna M Lipka, John H Thornton Jr. Cubes and the Individual Investor [J]. Financial Service Review,2004, (13).
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