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Influence of the Nikkei put warrant market in North America on the Japanese stock market, 1989-1993 Yuen, Ringo C.K. 1993

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INFLUENCE OF TilE NIKKEI PUT WARRANT MARKET IN NORTH AMERICAON TilE JAPANESE STOCK MARKET, 1989-1993byRINGO C.K. YUENB.Comm., The University of British Columbia, 1992A THESIS SUBMIrthD IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCE (BUSINESS ADMINISTRATION)inTHE FACULTY OF GRADUATE STUDIESTHE FACULTY OF COMMERCE AND BUSINESS ADMINISTRATIONWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIADecember 1993© Ringo C.K. Yuen, 1993in presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)______________________Department of FACUL14 OF COMHERCE sNt 8VSusIES AbI111Nl$Ts7IoThe University of British ColumbiaVancouver, CanadaDate bECEF4RER 12,1993DE-6 (2/88)ABSTRACTThis paper studies the influence on the Japanese stock (cash and futures) markets of theNikkei put warrants which were traded in Toronto and New York from February 1989 to April1993. Implied changes in the Japanese prices based on the previous days’ North Americanwarrant prices are compared to the actual price changes. Special attention is placed on theperiod from January 1990 to August 1992 when the Japanese stock market had a major decline.IITABLE OF CONTENTSAbstractTable of Contents illList of Tables ivList of Figures vI Introduction 1II Data 3ifi Methodology 8IV Empirical Tests and ResultsOvernight Variations in the Spot Nikkei Stock Average 16Overnight Variations in the Japanese NSA Futures 21Daily Variations in both the Spot NSA and the Japanese NSA Futures 26Tests using the Open-to-Close Price Movements of the Warrants 29Relationship between the Trading Volume of the Nikkei Put Warrants 30and the Absolute Changes in the Spot NSA and the NSA FuturesComparison of the Overnight and Daily Variations in both 32the Spot NSA and the Japanese NSA FuturesV Conclusion 35References 38Appendix Diagnostic Tests 40Tables 45mLIST OF TABLESTABLE I Nildcei Put Warrants traded on the Toronto Stock Exchange 45between 1989 and 1993 & Nilckei Put Warrants traded on theAmerican Stock Exchange between 1990 and 1993TABLE II Estimation of Overnight Variations in the Spot NSA using the 46Movements of the Nikkei Put WarrantsTABLE ifi Estimation of Overnight Variations in the Japanese NSA Futures 47using the Movements of the Nikkei Put WarrantsTABLE IV Estimation of Daily Variations in the Spot NSA using the 48Movements of the Nikkei Put WarrantsTABLE V Estimation of Daily Variations in the Japanese NSA Futures 49using the Movements of the Nikkei Put WarrantsTABLE VI Regression Tests using the Open-to-Close Price Movements of 50the Warrants (Fixed Exchange Rate Warrant -DXA)TABLE VII Regression Tests using the Open-to-Close Price Movements of 51the Warrants (Floating Exchange Rate Warrant - NKP.WT)TABLE Vifi The Correlation between the Trading Volume of the Nikkei Put 52Warrants and the Absolute Value of Changes in the Spot NSAand in the Japanese NSA FuturesTABLE IX The Correlation between the Changes in the Spot NSA and in 53the Japanese NSA Futures at the Opening and Closing of theJapanese MarketTABLE A-I Summary of the Diagnostic Tests (for Close-to-Close Price 54Movements of the Warrants)TABLE A-II Summary of the Diagnostic Tests (for Open-to-Close Price 55Movements of the Warrants)ivLIST OF HGURESFIGURE 1 The Daily Opening Nikkei Stock Average from February 17, 1989 4to April 23, 1993FIGURE 2 Trading Hours and Days for the Stock Exchanges in Japan, 7the U.S., and CanadaFIGURE 3 The Actual & Cumulative Numbers of DXA Prices at different 14levels of the Opening NSAFIGURE 4 The Correlation between the Overnight Variations in the Spot NSA 18and the Implied NSA Returns for the DXA Nikkei Put WarrantFIGURE 5 The Correlation between the Overnight Variations in the NSA 24Futures and the Implied NSA Returns for the DXA Nikkei Put WarrantFIGURE A-i Autocorrelation Function of Residuals (Regression of Overnight Spot 43NSA Returns on Open-to-Close Warrant Returns for DXA)FIGURE A-2 Normal Probability Plot of Residuals (Regression of Overnight Spot 43NSA Returns on Open-to-Close DXA Warrant Returns for DXA)FIGURE A-3 Time-Series Plot of Residuals (Regression of Overnight Spot NSA 44Returns on Open-to-Close DXA Warrant Returns for DXA)vI INTRODUCTIONIn this study, we consider the relationship between the prices of the Nikkei put warrants tradedin North America and the prices of the Japanese spot/cash and futures stock market. We areinterested in (1) the extent to which the price movements of the Nikkei put warrants in theprevious day influence the opening and closing prices of the Japanese stock market, (2) whetherthere is any difference between its influence on the Japanese spot/cash market and the Japanesefutures market, and (3) the extent of the difference on the influence given that such differenceexists. To supplement the price movements of the Nikkei put warrants, we also investigatewhether the trading volumes of the Nikkei put warrants have any impact on the opening andclosing prices in both the Japanese spot/cash and futures markets.There is no overlap in trading time between the North American stock markets and theJapanese stock markets. In the past, investors and traders in these two markets relied on theprevious day’s movements of the U.S. stock market to estimate the current performance of theJapanese stock market so as to hedge, or speculate their Japanese investment. The introductionof Nikkei put warrants traded on the American and Toronto Stock Exchanges provided investorsand traders an additional tool to hedge or speculate their Japanese investment. Since the payoffsof the Nikkei put warrants are direct related to the Nikkei Stock Average (225 stocks), themovements of the warrants can be potentially used to predict the near term performance of theJapanese stock market. Information about the movements of the warrants is released prior tothe opening of the Japanese stock market. Such information should be fully incorporated intothe opening price of the Japanese stock market if the markets are efficient.1Earlier research has examined the correlation of index prices between the U.S. and theJapanese stock markets. In particular, Becker, Finnerty, and Gupta (1990) report that the U.S.index returns in the previous day explain about 17% of the overnight variations in the Japaneseindex. Using the autoregressive conditionally heteroscedastic (ARCH) models, Hamao, Masulis,and Ng (1990) fmd price spillovers from the U.S. stock market to the Japanese stock market andalso fmd high correlations between the lagged U.S. index returns and the current Japanese indexreturns. Becker, Finnerty, and Tucker (1992) further investigate the intraday interdependencybetween the U.S. and the Japanese stock markets and find that the correlations between thelagged U.S. index returns and the Japanese index returns are significant but limited to the firsthour of trading in Japan. They also suggest that such significant correlations are attributable tothe so-called stale or sticky opening index price. Dravid, Richardson, and Craig (1993) reportin their recent research that the Nikkei put warrants and futures traded in the U.S. provideimportant information about the overnight variations in the Japanese index. Using the officialand delayed opening index price, they confirm that overnight information is rationallyincorporated into prices across international fmancial markets.We choose the official opening and closing prices of the Nikkei Stock Average (225stocks) and the NSA futures traded on the Osaka Securities Exchange to represent the prices ofthe Japanese spot/cash and futures markets. The data enables us not only to fmd out the extentof influence from the North American markets onto the Japanese market, but also to investigatewhether the opening price of the Nikkei Stock Average is stale.11 When a stock in the Nikkei Stock Average (225 stocks) is not traded at the open of theJapanese market, its previous day’s closing price is substituted to calculate the opening NikkeiStock Average. This is so-called the stale price effect.2Section II of this paper describes the data. Methodology used is discussed in section ifiin which different measures of the movements of the Japanese stock market and the Nilckei putwarrants are defined. The empirical tests and results are explained in section lv. We also linkthe results together to provide a better understanding of how the opening and closing prices ofthe Japanese stock market react to the movements in the prices of the warrants. Conclusionsare discussed in section V.II DATAWe examine the influence on the Japanese stock market by the movements of the U.S. andCanadian Nikkei put warrants. The data covers a four year period (U.S./Canadian data fromFebruary 17, 1989 to April 22, 1993; Japanese data from February 18, 1989 to April 23, 1993).This period is the time when the Nikkei put warrants were first and last traded. To representthe influence on the Japanese stock market, two sets of information are obtained. They are theNilckei Stock Average (225 stocks), abbreviated as NSA, and the NSA futures traded in Osaka.The NSA is an arithmetic price average computed by adding the prices of 225 stocks traded inthe first section of the Tokyo Stock Exchange and dividing by a divisor that is changed fromtime to time to adjust for stock splits, rights issues, etc.2 Daily official opening and closingprice data for the spot NSA are obtained from N.E.E.D.S. and Nihon Keizai Shimbun. The2 A complete list of the 225 stocks as of July 23, 1993 as well as the changes in thecomponent stocks between June, 1989 and April, 1993 is available from the author.3daily opening NSA for the study period is plotted in Figure 1.4540 -a)La)> 35300)10T i meFigure 1The Daily Opening Nikkei Stock Average from February 17, 1989 to April 23, 1993Furthermore, the Japanese NSA futures, abbreviated as NSA futures, were introducedby the Osaka Securities Exchange on September 3, 1988 and the underlying asset is the NSA.Brenner, Subrahmanyam, and Uno (1989) report that information affecting the spot market isspeedily incorporated into the futures price. So, the NSA futures might react faster than the spotNSA to information contained in the price movements of the Nikkei put warrants. Dailyopening and closing price data for the nearest maturity NSA futures contracts for the study4period are obtained from N.E.E.D.S. and Nihon Keizai Shimbun.There were twelve Nikkei put warrants, abbreviated as warrant, traded in New York andToronto during our study period (six in each country). Daily closing price and trading volumedata are obtained from the American Stock Exchange Daily Stock Price Record for the U.S.warrants and from the Western Database for the Canadian warrants.3 The warrant issued bythe BT Bank of Canada in February, 1989 was the first Japan-related put warrant traded on theToronto Stock Exchange. Approximately a year later, Goldman Sachs, on behalf of theKingdom of Denmark, issued the first U.S. warrant and listed it on the American StockExchange. A detail list of the twelve warrants together with their main features is in Table I.The payoff to the warrant holders shown in Table I can be classified into floatingexchange rate payoff and fixed exchange rate payoff. For the former one, the payoff iscalculated either by converting the difference between the strike price and the closing NSA atthe exchange rate prevailing at the time of exercise or by taking the difference between the strikeprice and the dollar-equivalent closing NSA, which is converted at the prevailing exchange rate.On the other hand, the fixed exchange rate payoff is determined by converting the differencebetween the strike price and the closing NSA at a fixed conversion rate or exchange rate.Among the twelve warrants considered, eight are under the fixed exchange rate payoff categoryand four are under the floating exchange rate payoff category.Daily opening price data for the warrants is not available at the time of this study.5Payoff Category U.S. Warrant Canadian WarrantFixed Exchange Rate DXA, SXA, SXO, NKP.WT.B,EXW, PXB NKP.WT.C, TFC.WT.NFloating Exchange Rate BTB NKP.WT, NKP.WT.A,SEK.WT* : These three warrants are not included in our study.Not all twelve warrants were traded until their expiration dates. In particular, threeCanadian warrants, NKP.WT.B, SEK.WT and TFC.WT.N, were only traded for a very shortperiod of time (ranging from 9 to 21 months). Besides, these Canadian warrants were not tradedcontinuously4and this can present some difficulties in analyzing the influence on the Japanesestock market when any two consecutive trading days of these warrants were too far apart. Inorder to alleviate this problem, these three warrants are not included in our study.The payoff on three of the warrants we studied is subject to the exchange rate prevailingat the time of exercise. Therefore, daily exchange rate data for both Yen to US$ and Yen toC$ in Tokyo and New York markets are also obtained from N.E.E.D.S. and Citibase.Moreover, daily exchange rate data also serves another function in our study and it is used toconvert all US$ or C$ denominated values of the warrants into Yen so that analysis can beperformed in a common currency.4NKP.WT.B was continuously traded for about 7 months, SEK.WT for only 6 months, andTFC.WT.N for about 10 months.6American Stock ExchangeToronto Stock Exchange(Day t in the U.S. & Canada)4Osaka Securities Exchange Osaka Securities ExchangeTokyo Stock Exchange Tokyo Stock Exchange(Day t in Japan) (Day t+1 in Japan)4 . 4I I I I I I I I I I I I IEST 7pm lam 9:30am 4pm 7pm lamFigure 2Trading flours and Days for the Stock Exchanges in Japan, the U.S., and CanadaFrom Figure 2, it is obvious that there is no time interval in which all four exchangesare opening at the same time. In particular, there are three hours between the closing of theAmerican and Toronto Stock Exchanges and the opening of the Osaka and Tokyo StockExchanges. On the other hand, there are eight and a half hours between the closing of theexchanges in Japan and the opening of the exchanges in North America. Although there is nooverlapping period, a technical problem in studying the influence on the Japanese stock marketcaused by the movements of the warrants still exists and it is due to the non-synchronousholidays. To deal with the problem, observations on the movements of the Japanese stockmarket are deleted when either the U.S. or Canadian stock market is closed. Similarly, whenthe Japanese market is closed, the movements of the warrants in both the U.S. and Canadianmarkets are also deleted.7ifi METHODOLOGYTo address the issue whether the Japanese stock market was influenced by the North AmericanNikkei put warrant markets, the daily close-to-open and close-to-close returns for the spot NSAare computed. These two returns might enable us to fmd out the extent of the influence of thewarrants on the opening and closing prices of the Japanese stock market. The Japanese stockmarket is not opened concurrently with the North American stock markets. Information releasedprior to the opening of the Japanese stock market might be incorporated into the opening NSA.For instance, if the information is firm-specific, the opening stock price of that specific firmmight incorporate such information. If the information is industry-specific, the opening pricesof the major stocks in that specific industry might incorporate such information. So, a positiveinformation released prior to the opening of the Japanese stock market might result in a positiveclose-to-open return for the spot NSA.Stoll and Whaley (1990) report that all 500 stocks for the S&P 500 index are not tradeduntil five to seven minutes after the official opening of the market. Since individual stocks inthe index may not begin trading at the opening, the previous day’s closing prices of the stocksare substituted to calculate the opening index. To minimize the effect of such stale prices in theJapanese stock market, Hamao, Masulis, and Ng (1990) suggest replacing the official NSAopening price by the price quoted 15 minutes after the opening of the market. However, thisapproach implicitly assumes that most stocks for the NSA respond to the pre-trading informationwithin the first 15 minutes of trading and no new information is released during that timeinterval. In addition, Chung, Kang, and Rhee (1992) find that the volatility at the opening of8the Japanese stock market is significantly higher than any other trading hours. Thus, it isreasonable to believe that new information which might affect the component stocks for the NSAis released during the first few minutes of trading. Brenner, Subrahmanyam, and Uno (1989)report that new information affecting the Japanese spot market is speedily incorporated into theJapanese futures price. So, information released prior to the opening of the Japanese stockmarket might incorporate into the opening price of the NSA futures faster than into the openingprice of the spot NSA. In other words, the information released before the opening of theJapanese stock market might highly correlate with the close-to-open return for the NSA futures.If information released prior to trading is fully incorporated into the opening prices ofthe spot NSA and the NSA futures, their closing prices will only be affected by informationreleased during the Japanese trading hours. Even when the opening prices of the spot NSA andthe NSA futures do not incorporate all pre-trading information, the close-to-close returns forboth the spot NSA and the NSA futures and the information released prior to the opening of theJapanese stock market might not have a strong relationship.Even though there is a three hour difference between the closing of the North Americanstock markets and the opening of the Japanese stock market, investors can make use ofinformation released prior to the opening of the Japanese market (specifically, prior to threehours before the opening of the Japanese market) to trade the Japan-related securities on theNorth American markets. In particular, they can trade the warrants on the American andToronto Stock Exchanges so as to hedge or speculate the future stock prices in the Japanesemarket. Hence, the movements of the warrants might represent the information released prior9to the opening of the Japanese stock market and the daily close-to-close return for the warrantsis computed to measure such movements.The warrant can be viewed as a long term American put option. In a standard putoption, its value increases as the spot price of the underlying asset decreases. Since the warrantsand the NSA are not traded concurrently, a positive change in the price of the warrants mightimply that the pre-trading information is negative and the NSA is going to fall. Alternatively,a negative change in the price of the warrants might imply a rise in the NSA. In other words,the daily close-to-close return for the warrants might negatively correlate with the daily close-to-open and close-to-close returns for both the spot NSA and the NSA futures.However, the use of close-to-close return for the warrants might have a problem becausesuch warrant return overlaps the close-to-open and close-to-close returns for both the spot NSAand the NSA futures. To alleviate the problem, an implied opening price of the warrants canbe computed by substituting the latest closing NSA into the payoff formulae. This approachassumes that the warrants are deep in-the-money and the time premium is approximately equalto zero. For example, suppose the closing price of the spot NSA on day t is 29,320.00, thenthe implied opening price of the DXA on day t is computed as follows:0.20 x (37,516.77- Closing NSA1)Implied DXA Opening Price1 = US$145.325= US$11.281This approach might provide a good estimate of the opening warrant price when the warrants10are deep in-the-money. As the warrants go deep in-the-money, the time premium will approachzero and the intrinsic value based on the closing NSA will become a good approximation of theopening warrant price. So, the open-to-close return for the warrants is computed based on theimplied opening warrant price. Similar to previous argument, the daily open-to-close return forthe warrants might inversely correlate with the daily close-to-open and close-to-close returns forboth the spot NSA and the NSA futures.According to Clyman (1992) and Shaw, Thorp, and Ziemba (1993), an implied NSA canbe derived from the closing price of the warrants using the payoff formulae by assuming thatthe warrants are deep in-the-money and the time premium is approximately equal to zero. Forinstance, suppose the closing price of the DXA Nikkei put warrant on day t is $11, then theimplied closing price of the spot NSA on day t+1 is computed as follows:0.20 x (37,516.77- Implied NSAt+1)DXA Price1 = US$145.325Implied NSA = 37,516.77- 11 x 145.325 ÷ 0.20 = 29,523.90This ‘payoff’ approach might provide a good estimate of the closing price of the spot NSA onlywhen the warrants are deep in-the-money, due to the fact that the price of a warrant is the sumof its intrinsic value and time premium. As the warrants go deep in-the-money, the timepremium will approach zero and the price of the warrants will become a good approximation ofthe intrinsic value. Although the implied NSA may not be a good predictor for either theopening or the closing price of the NSA when the warrants are not deep in-the-money, changesin the implied NSA might reflect the market expectation of the changes in the NSA. In11particular, a positive change in the implied NSA might suggest a positive change in both the spotNSA and the NSA futures. Since information about changes in the implied NSA is releasedbefore the opening of the Japanese stock market, the close-to-close return for the implied NSAmight positively correlate with the close-to-open and close-to-close returns for both the spot NSAand the NSA futures.Unlike the standard put option, the actual intrinsic value of the warrants is impossible todetermine because the current value of the NSA is unobservable when the warrants are tradingin the North American stock markets. So, there are possibilities that the warrants can be tradedeither at a premium or at a discount relative to the latest closing NSA. If the warrants aretraded at a premium, the NSA is expected to fall. Conversely, if the warrants are traded at adiscount, the NSA is expected to rise. Similar to the payoff approach, the daily premium ordiscount of the warrants can be computed by taking the difference between the market price ofthe warrants and the price obtained by substituting the latest closing price of the NSA into thepayoff formulae. This approach also assumes that the warrants are deep in-the-money and thetime premium is approximately equal to zero. For example, consider the DXA Nikkei putwarrant again. Suppose the market closing price of the DXA on day t is $11 and the closingprice of the spot NSA on day t is 29,320.00, then the premium of the DXA on day t iscomputed as follows:5Discount is represented by a negative premium.120.20 x Max[37,516.77- Close NSA1, 0]Premium1=Pt- US$145.325= 11 - 0.20 x (37,516.77- 29,320.00) ÷ 145.325=- US$ 0.28 (Discount)Similar to the payoff approach for calculating the implied NSA, this approach might provide agood estimate of the premium or discount only when the warrants are deep in-the-money. Infact, when the warrants are not deep in-the-money, the premium computed under this approachincludes the time premium. However, changes in the premium or discount might correspondto the market expectation of the changes in the NSA. Specifically, when changes in thepremium or discount are positive (i.e. an increase in premium or a decrease in discount), theNSA is expected to fall. On the other hand, when changes in the premium or discount isnegative (i.e. a decrease in premium or an increase in discount), the NSA is expected to rise.Hence, a positive change in the premium or discount might inversely correlate with the close-to-open and close-to-close returns for both the spot NSA and the NSA futures.The approaches described above for calculating the implied NSA and warrant premiumrely heavily on two assumptions: the warrants are deep in-the-money and the time premium isapproximately equal to zero. In fact, the warrants we studied were deep in-the-money in mostof the time. For instance, consider the DXA Nikkei put warrant. It has a strike price of37,516.77. Suppose DXA is considered to be deep in-the-money when the NSA is below 30,000at the time of trading, then 84% of the DXA quotes are deep in-the-money. The distributionsof the actual and cumulative numbers of the DXA quotes are shown graphically in Figure 3.13In addition, the average time premium for the DXA is about -0.10, which is very close to zero.Cumulative No of DXA Closing prices0 100 200 300 400 500 600 700 800 900I I I I I I I14000s 1500015000 s cc 16000_______16000s 17000__ __________17000 s ,l..,.c 18000_10000 6 < 1900019000s < 2000020000 ).< 2100021000e 2200022000 e N,-s23000LflIUUUUflFUUUUUWUUI 23000 •s 24000iiuuuwuInn 24000 s NLc 2500025000 5 2600026000 •s Nl, c 270007000 s c 2800028000 s < 2900029000 s < 30000300006 ).c 3100031000 s ..c 3200032000 s < 3300033000 < 340004000 s 4. < 3500035000 s 4. < 3600036000 s < 3700037000s X< 300000 50 100 150Actual No of DXA Closing PricesNo of DXA prices when opening NSA is within the labeled range—.,L._Cumulative no of OXA prices when openTng NSA is less than the labeled NSANote: the etrike price of DXA Is 37..516.77Figure 3The Actual & Cumulative Numbers of DXA Prices at different levels of the Opening NSASeveral authors have reported different models to price the warrants (for instance, Chen,Sears, and Shahrokhi (1992) and Dravid, Richardson, and Sun (1993)). However, a model-based approach is not chosen in this study to compute the implied NSA and the premium ordiscount of the warrants, because a model-based approach requires a correct pricing model andan accurate estimate of the model parameters (i.e. interest rate, dividend yield, exchange rateand volatility of the NSA).14Becker, Finnerty, and Gupta (1990) report that correlations between the returns for thespot NSA and S&P 500 in a common currency are slightly lower than in their local currencies.To test whether the same result occurs in the warrants, the daily common currency returns forthe warrants, yen-equivalent premium and the changes in the yen-equivalent premium are alsocomputed. Then, all empirical tests are performed in both local and common currencies. If thesame result happens in the warrants, the tests using the local currency returns will have at leastthe same or better outcomes than the tests using the common currency returns.Karpoff (1987) finds that both return and absolute return for the U.S. indices arepositively correlated with trading volume. Bailey (1989) also reports that absolute return for theJapanese indices and trading volume of the respective futures contracts are correlated.Specifically, he finds positive correlations between the absolute close-to-close return for theOsaka Stock 50 Index and the trading volume of the Osaka Stock 50 futures and also betweenthe absolute close-to-close return for the spot NSA and the trading volume of the NSA futurestraded on the Singapore International Monetary Exchange. Although Bailey (1989) and otherauthors only show a positive correlation between the absolute index return and the futurestrading volume, the same relationship might also hold between the absolute spot NSA and NSAfutures returns and the trading volume of the warrants because the warrants’ payoffs are subjectto the closing NSA at the time of exercise. Hence, the daily absolute close-to-open and close-toclose returns for both the spot NSA and the NSA futures are computed. The total daily tradingvolume of the warrants as well as the dollar-equivalent and yen-equivalent trading volumes arealso calculated. So, a large trading volume of the warrants on day t might result in a largeabsolute changes in the spot NSA and the NSA futures on day t+1. In other words, the total15trading volume of the warrants might positively correlate with both the absolute close-to-openand close-to-close returns for the spot NSA and the NSA futures.IV EMPIRICAL TESTS AND RESULTSOvernight Variations in the Spot Nikkei Stock AverageTo investigate the extent of the overnight variations in the spot NSA that can be explained bythe movements of the warrants in the previous day, we regress the close-to-open returns for thespot NSA on (1) the close-to-close returns for each warrant in both local and commoncurrencies, (2) the close-to-close returns for the implied NSA derived from the price of eachwarrant, and (3) the changes in the premium and yen-equivalent premium of each warrant. Thegeneral form of regression is as follows:=+ ÷a2IMPr + pj(C + Ewhere 50 is the close-to-open return for the spot NSA from day t-1 to day t, P is the close-to-close return for the warrant from day t-1 to day t, IMP is the close-to-close return for theimplied NSA from day i-i to day t, and PM is the change in the premium of the warrant fromday t-1 to day t. If the movements of the warrants explain the overnight variations in the spotNSA, the values of the coefficients a1 and a3 are expected to be negative whereas a2 is expectedto be positive.16Table II reports the results of the regressions of the overnight variations in the spot NSAon the three different measures of the movements of the warrants.6 Similar to Becker, Finnerty,and Gupta (1990) and Hamao, Masulis, and Ng (1990), the overnight variations in the spot NSAand the movements of the warrants are found to be significantly correlated. In particular, thereis a correlation of -0.405 between the overnight changes in the spot NSA and the changes in theprice of the fixed exchange rate warrants. The same correlation for the floating exchange ratewarrants is slightly lower and it is -0.358. In other words, the fixed and floating rate warrantreturns can explain 16.4% and 12.8% of the overnight variations in the spot NSA respectively.These correlations are significant at the 1% level and are consistent with the theory that theopening price of the spot NSA is expected to fall when there is an increase in the price of thewarrants in the previous day or vice versa. Moreover, it is reasonable to have a lowercorrelation for the floating rate warrants because the price of the floating rate warrants containsan additional factor: exchange rate.The changes in the implied NSA and in the price of the warrants might have the sameexplanatory power on the overnight variations in the spot NSA since the implied NSA which iscalculated using the payoff approach is simply a linear transformation of the warrant’s price.So, the correlations between the overnight changes in the spot NSA and the changes in theimplied NSA might be as same as the correlations with the changes in the price of the warrants.However, the results in Table II show that the changes in the implied NSA for the fixed6 This paper only reports the results of two warrants (fixed exchange rate warrant- DXAand floating exchange rate warrant - NKP.WT) and the results for the remaining warrants areavailable from the author.17exchange rate warrants explain 2 1.0% of the overnight variations in the spot NSA, which is4.6% more relative to the use of the changes in the price of the warrants. Dravid, Richardson,and Craig (1993) also report that when the fixed exchange rate warrants are deep in-the-money,the implied NSA returns which are calculated using the model-based approach outperform thewarrant returns in explaining the overnight variations in the spot NSA by about 4.6%. Figure4 shows the correlation between the overnight variations in the spot NSA and the implied NSAreturns for the DXA Nikkei put warrant graphically.0a)- 0.05-I-J09-C’)04-,a)C) -0.054-,0:1)U,0C)—o.-iFigure 4The Correlation between the Overnight Variations in the Spot NSA and the Implied NSAReturns for the DXA Nikkei Put WarrantOn the other hand, the implied NSA returns for the floating exchange rate warrants onlyexplain 10.5% of the overnight variations in the spot NSA, which is 2.3% less than the use ofthe warrant returns. This difference might be again due to the floating exchange rate.According to the payoff approach, the implied NSA for the floating rate warrants is computed—4 — —z —i 0 2 2 4 5Thousr,dt h.The Cloee—to—Operi Pettjrrie 1or the Spot NSA18based on not only the closing price of the warrants but also the exchange rate prevailing at theclosing of the American Stock Exchange. Since an additional exchange rate factor is requiredin the payoffapproach when calculating the implied NSA returns for the floating rate warrants,it is obvious that the correlation between the implied NSA returns for the floating rate warrantsand the overnight variations in the spot NSA is much lower.The changes in the premium of the warrants, as predicted by theory, have a significantnegative correlation with the overnight variations in the spot NSA. In particular, the correlationsbetween the changes in the premium of the warrants and the overnight changes in the spot NSAare -0.361 for the fixed exchange rate warrants and -0.253 for the floating exchange ratewarrants. The changes in the premium of the fixed and floating rate warrants alone explain13.0% and 6.4% of the overnight variations in the spot NSA respectively. Although thesecorrelations are lower than the correlations between the overnight NSA returns and either thewarrant returns or the implied NSA returns, they are significant at the 1 % level. Hence, whenthere is a positive change in the premium of the warrants in the previous day (i.e. either anincrease in premium or a decrease in discount), the opening price of the spot NSA is expectedto fall or vice versa. In addition, an additional exchange rate is required in the payoffapproachwhen calculating the premium of the floating rate warrants, Hence, it is reasonable to have alower correlation between the changes in the warrant’s premium and the overnight variations inthe spot NSA.Table II also reports the results of regressions of the overnight variations in the spot NSAon two measures together. Specifically, we regress the overnight NSA returns on (1) both the19warrant returns and the changes in the premium of the warrants and (2) both the implied NSAreturns and the changes in the premium of the warrants. Since neither the warrant returns northe implied NSA returns are highly correlated with the changes in the premium of the warrants,7the two-factor models might explain the variations in the spot NSA better than the one-factormodels. In fact, results in Table II confirm that the two-factor models outperform the one-factormodels by about 3% for the fixed rate warrants and about 1.5% for the floating rate warrants.All coefficients of the two-factor models are also significant at the 1 % level except the constantterms significant at the 5% level. In other words, the warrant returns together with the changesin the premium of the warrants explain 20.1% and 14.4% of the overnight NSA returns for thefixed and floating rate warrants respectively.The results improve to 23.4% and 11.9% for the fixed and floating rate warrants whenthe changes in the premium are added to the regressions of the overnight NSA returns on theimplied NSA returns. Furthermore, the coefficients of the warrant returns and the implied NSAreturns in the two-factor models do not differ significantly from the same coefficients in the one-factor models. However, the coefficients of the changes in the premium of the warrants in thetwo-factor models, though significant, drop as much as a half of the same coefficients in the one-factor models. Hence, the warrant returns and the implied NSA returns appear to capture mostof the pre-trading information which might affect the Japanese stock market, whereas thechanges in the premium of the warrants seem to play a supporting role in explaining thethe DXA, the correlation between the warrant returns and the changes in the warrantpremium is 0.455 and the correlation between the implied NSA returns and the changes in thewarrant premium is -0.463 (both correlations are significant at the 1% level). The similarcorrelations for the NKP are 0.355 and -0.415 respectively.20overnight changes in the spot NSA.To investigate whether the exchange rate can affect the results, regressions are alsocalculated on a common currency basis.8 Similar to Becker, Finnerty, and Gupta (1990), allcorrelations between the overnight variations in the spot NSA and the three different yen-equivalent measures of the movements of the warrants are about the same (i.e. at most ±0.006)as the correlations calculated on the local currency basis. Even for the floating exchange ratewarrants, the common currency models only outperform the local currency models by roughly0.4% in explaining the overnight NSA returns. Thus, it is reasonable to believe that theregressions of the overnight variations in the spot NSA on the movements of the warrants whichare measured in their local currencies are sufficient.Overnight VariaUons in the Japanese NSA FuturesSince the movements of the warrants only explain at most 23.4% of the overnight variations inthe spot NSA and it is reported that the futures price responds to new information faster thanthe spot price, it is interesting to find the extent of the overnight variations in the Japanese NSAfutures that can be explained by the movements of the warrants in the previous day. Inparticular, we regress the close-to-open returns for the NSA futures traded on the OsakaSecurities Exchange on (1) the close-to-close returns for each warrant in both local and common8 Since the regression results calculated on the common currency basis are very similar tothe results based on the local currency, we only include the local currency results. The commoncurrency results for the warrants are available from the author.21currencies, (2) the close-to-close returns for the implied NSA derived from the price of eachwarrant, and (3) the changes in the premium and yen-equivalent premium of each warrant. Thegeneral form of regression is as follows:FCO=y0+y1Pr+y?MPr+y3M-”+cwhere F° is the close-to-open return for the NSA future from day t-1 to day t, P is the close-to-close return for the warrant from day t-1 to day t, IMP is the close-to-close return for theimplied NSA from day t-1 to day t, and PM is the change in the premium of the warrant fromday t-1 to day t. If the movements of the warrants explain the overnight variations in the NSAfutures, the values of the coefficients y and ‘y are expected to be negative whereas 72 isexpected to be positive.Table ifi reports the results of the regressions of the overnight variations in the NSAfutures on the three different measures of the movements of the warrants. Similar to the resultsfor the spot NSA, the overnight variations in the NSA futures and the movements of thewarrants are also found to be significantly correlated. In particular, the correlations betweenthe overnight changes in the NSA futures and the changes in the warrant’s price are -0.574 forthe fixed exchange rate warrants and -0.507 for the floating exchange rate warrants. In otherwords, the fixed and floating rate warrant returns explain 33.0% and 25.7% of the overnightvariations in the NSA futures respectively. These correlations again are significant at the 1 %level and are consistent with the theory that the opening price of the NSA futures is expectedto fall when there is an increase in the price of the warrants in the previous day or vice versa.22Moreover, it is reasonable to have a lower correlation for the floating rate warrants because theprice of the floating rate warrants contains an additional factor: exchange rate.Furthermore, the correlation between the overnight variations in the NSA futures and thechanges in the implied NSA for the fixed exchange rate warrants is 0.600 (the correlation isshown graphically in Figure 5). It means that the implied NSA returns for the fixed ratewarrants explain 36.0% of the overnight movements in the NSA futures, which is 3.0% morerelative to the use of the warrant returns. Since the 3.0% improvement in explaining theovernight variations in the NSA futures is about the same as the improvement when the impliedNSA returns are calculated using the model-based approach, this result suggests that the impliedNSA returns which are calculated using the payoff approach might be acceptable. Unlike theresults for the spot NSA, the implied NSA returns for the floating exchange rate warrantsexplain 29.4% of the overnight variations in the NSA futures, which is 3.7% more relative tothe use of the warrant returns. Even though the exchange rate is involved in thepayoffapproachwhen calculating the implied NSA returns for the floating rate warrants, this additional factorappears to improve the explanatory power of the implied NSA returns on the overnightvariations in the NSA futures.Similar to the results for the spot NSA, the changes in the premium of the warrants alsohave a significant negative correlation with the overnight variations in the NSA futures. Inparticular, the correlations between the changes in the premium of the warrants and theovernight changes in the NSA futures are -0.445 for the fixed exchange rate warrants and -0.391for the floating exchange rate warrants. Hence, the changes in the premium of the fixed and230.10a)- 0.05L.0cnt0.1-3a.)(00C.) -o.o(00C.)—0. ‘1C) -0.IFIgure 5The Correlation between the Overnight Variations in the NSA Futures and the ImpliedNSA Returns for the DXA Nilckei Put Warrantfloating rate warrants alone explain 19.8% and 15.3% of the overnight NSA futures returnsrespectively. Although these correlations are lower than the correlations between the overnightvariations in the NSA futures and either the warrant returns or the implied NSA returns, theyare significant at the 1 % level. Thus, when there is a positive change in the premium of thewarrants in the previous day (i.e. either an increase in premium or a decrease in discount), theopening price of the NSA futures is expected to fall or vice versa. Furthermore, exchange rateis involved when calculating the premium of the floating rate warrants. It is reasonable to havea lower correlation between the changes in the warrant’s premium and the overnight changes inthe NSA futures.The results of regressions of the overnight variations in the NSA futures on two measuresThe CIoee-to—oper, Returrie -for the NSA Futuree0 • 0524together are also shown in Table IV. The two-factor models outperform the one-factor modelsby about 3.5% for both the fixed and floating rate warrants. In other words, the warrant returnstogether with the changes in the premium of the warrants explain 36.8% and 30.3% of theovernight variations in the NSA futures for the fixed and floating rate warrants respectively.The results improve to 39.0% and 32.0% for the fixed and floating rate warrants when thechanges in the premium are added to the regressions of the overnight NSA futures returns onthe changes in the implied NSA. All coefficients of the two-factor models are also significantat the 1 % level. Furthermore, the coefficients of the warrant returns and the implied NSAreturns in the two-factor models do not differ significantly from the same coefficients in the one-factor models. However, the coefficients of the changes in the premium of the warrants in thetwo-factor models drop as much as 55% of the same coefficients in the one-factor models.Hence, the warrant returns and the implied NSA returns appear to capture most of the pretrading information which might affect the Japanese stock market, whereas the changes in thepremium of the warrants seem to play a very minor role in explaining the overnight changes inthe NSA futures.In addition, similar regressions are also calculated on a common currency basis toinvestigate whether the exchange rate can affect the results. All correlations between theovernight variations in the NSA futures and the three different yen-equivalent measures of themovements of the warrants are roughly the same (i.e. at most ±0.004) as the correlationscalculated on the local currency basis. Even for the floating exchange rate warrants, thecommon currency models only outperform the local currency models by roughly 0.5% inexplaining the overnight NSA futures returns. Thus, it is reasonable to believe that the25regressions of the overnight variations in the NSA futures on the movements of the warrantswhich are measured in their local currencies are sufficient.Daily Vadations in both the Spot NSA and the Japanese NSA FuturesSince the payoff of the warrants are based on the closing NSA at the time of exercise, it isinteresting to further investigate whether the movements of the warrants in the previous day canexplain the extent of the daily variations in both the spot NSA and the Japanese NSA futures,we regress the close-to--close returns for each of the spot NSA and the NSA futures on (1) theclose—to-close returns for each warrant in both local and common currencies, (2) the close-to-close returns for the implied NSA derived from the price of each warrant, and (3) the changesin the premium and yen-equivalent premium of each warrant. The general forms of regressionsare as follows:SC = po+pip:+pzIMp:c÷pspMc+e= + + AJMP7 + pcc +where S is the close-to-close return for the spot NSA from day t-1 to day t, F is the close-to-close return for the NSA futures from day t-1 to day t, P is the close-to-close return for thewarrant from day t-1 to day t, IMP is the close-to-close return for the implied NSA from dayt-1 to day t, and PM is the change in the premium of the warrant from day t-1 to day t. Ifthe movements of the warrants explain the daily variations in the spot NSA and the NSA futures,the values of the coefficients I3, fl, X1 and X3 are expected to be negative whereas 2 and X2 are26expected to be positive.Table IV reports the results of the regressions of the daily variations in the spot NSA onthe three different measures of the movements of the warrants and the similar regression resultsfor the NSA futures are shown in Table VI. The daily variations in both the spot NSA and theNSA futures are also found to have significant correlations with the movements of the warrants.In particular, the correlation between the changes in the price of the warrants and the dailychanges in either the spot NSA or the NSA futures is about -0.345. In other words, the warrantreturns explain about 12% of the daily variations in the spot NSA and in the NSA futures.These correlations are significant at the 1 % level and again are consistent with the theory thatthe closing prices of the spot NSA and the NSA futures are expected to fall when there is anincrease in the price of the warrants in the previous day or vice versa. Moreover, it isinteresting to note that there is no significant difference between the fixed and floating ratewarrants in explaining the daily variations in both the spot NSA and the NSA futures.In addition, the correlations between the changes in the implied NSA and the dailyvariations in both the spot NSA and the NSA futures are about 0.352. It means that the impliedNSA returns explain roughly 12% of the daily variations in the spot NSA and the NSA futures,which is about the same relative to the use of the warrant returns. Besides, the changes in thepremium of the warrants are also found to have significant negative correlations with the dailyvariations in both the spot NSA and the NSA futures. In particular, the correlation between thechanges in the premium of the warrants and the daily changes in the spot NSA is about -0.329and the correlation between the changes in the premium and the daily changes in the NSA27futures is about -0.282. In other words, the changes in the premium of the warrants aloneexplain 11 % and 8% of the daily variations in the spot NSA and the NSA futures respectively.Since the correlations are significant at the 1 % level, the closing prices of the spot NSA and theNSA futures are expected to fall when there is a positive change in the premium of the warrantsin the previous day (i.e. either an increase in premium or a decrease in discount) or vice versa.The results in Tables IV and V also confirm that the two-factor models outperform theone-factor models by about 3.7% for the daily variations in the spot NSA and about 2.0% forthe daily variations in the NSA futures. All coefficients of the two-factor models are alsosignificant at the 1 % level except the constant terms. In other words, the warrant returnstogether with the changes in the premium of the warrants explain roughly 16% of the dailyvariations in the spot NSA and the implied NSA returns explain about 14% of the dailyvariations in the NSA futures when the changes in the premium are added to the regressions.Furthermore, the coefficients of the warrant returns and the implied NSA returns in the two-factor models do not differ significantly from the same coefficients in the one-factor models.However, the coefficients of the changes in the premium of the warrants in the two-factormodels drop as much as a half of the same coefficients in the one-factor models. Hence, thewarrant returns and the implied NSA returns appear to capture most of the pre-tradinginformation which might affect the Japanese stock market, whereas the changes in the premiumof the warrants seem to play a very minor role in explaining the daily changes in both the spotNSA and the NSA futures. Moreover, regressions are also calculated on a common currencybasis and the results are very much the same as on the local currency basis. Thus, it isreasonable to believe that the regressions of the daily variations in the spot NSA or the NSA28futures on the movements of the warrants which are measured in their local currencies aresufficient.Tests using the Open-to-Close Price Movements of the WarrantsThe objective of this section is to investigate whether the open-to-close price movements of thewarrants can be used to explain more about the overnight and daily variations in the spot NSAand the NSA futures. Specifically, we substitute the open-to-close price movements of thewarrants for the close-to-close price movements in all regression tests described above. Theresults are reported in Table VI and Table VII for the fixed and floating exchange rate warrantsrespectively.Similar to results using the close-to-close price movements of the warrants, the open-to-close price movements of the warrants are also found to be significantly correlated with theovernight variations in the spot NSA. In particular, the average correlation between theovernight variations in the spot NSA and the open-to-close warrant returns is about -0.411. Thesame correlation for the open-to-close implied NSA returns is roughly 0.452. In other words,the open-to-close returns for the warrants and the implied NSA explain about 16.7% and 20.4%of the overnight variations in the spot NSA respectively.The overnight variations in the NSA futures and the open-to-close price movements ofthe warrants are also found to be significantly correlated. The average correlation between theovernight variations in the NSA futures and the open-to-close returns for the warrants is -0.54029and the same correlation for the open-to-close implied NSA returns is about 0.560. The resultssuggest that the open-to-close returns for the warrants and the implied NSA explain about 29.0%and 31.3% of the overnight variations in the NSA futures respectively.In fact, the regression results using the open-to-close price movements of the warrantsare about the same as the results using the close-to-close price movements of the warrants. Inother words, the open-to-close price movements of the warrants might not explain more aboutthe overnight and daily variations in the spot NSA and the NSA futures. Even though the close-to-close price movements of the warrants overlap with both the overnight and daily variationsin the spot NSA and the NSA futures, the regression results using the close-to-close warrantprice movements are quite satisfactory.Relationship between the Tmding Volume of the Nikkei Put Warrants and the AbsoluteChanges in the Spot NSA and the NSA FuturesTo investigate whether the trading volume of the warrants in the previous day has any influenceon the absolute changes in the spot NSA and the Japanese NSA futures, we calculate thecorrelations between the trading volume of the warrants (in unit-volume, dollar-equivalentvolume and yen-equivalent volume) in the previous day and various measures of the movementsof the Japanese stock market: (1) the close-to-open absolute returns for the spot NSA and theNSA futures, (2) the close-to-close absolute returns for the spot NSA and the NSA futures, and(3) the absolute ratios of the NSA futures price over the spot NSA at open and close.30Table Vifi reports the correlations between the sum of the trading volume of all warrantsand the various measures of the movements of the Japanese market. In contrast to Bailey(1989), the trading volume of the warrants is found to have a significant and negative correlationwith the absolute overnight variations in the spot NSA. In other words, when the warrants areheavily traded in the previous day, the absolute overnight changes in the spot NSA are expectedto be small. On the other hand, the correlation between the trading volume of the warrants andthe absolute overnight returns for the NSA futures is found to be significant positive. Since thecorrelation is significant at the 1% level, it is consistent with the theory that when the warrantsare heavily traded in the previous day, the absolute overnight changes in the NSA futures areexpected to be large. The correlation is more significant and higher when the trading volumeof the warrants is measured in terms of dollar- or yen-equivalent volume than in terms of unitvolume.Moreover, the correlation between the trading volume and the absolute daily returns forthe spot NSA is significant and positive. Therefore, when the warrants are heavily traded in theprevious day, large absolute daily changes in the spot NSA are expected. In other words, thetrading volume information of the warrants in the previous day might not have a major influenceon the opening price of the spot NSA; however, it might have a significant impact on the closingprice of the spot NSA. Furthermore, the correlation between the trading volume and theabsolute daily returns for the NSA futures is also significant and positive, but is less than thecorrelation between the trading volume and the overnight returns for the NSA futures. So, whenthe warrants are heavily traded in the previous day, the absolute overnight changes in the NSAfutures are expected to be larger than their absolute daily changes. Hence, the correlation31suggests that the trading volume information of the warrants in the previous day might bespeedily incorporated into the opening price of the NSA futures and such information might havea smaller impact on the closing price of the NSA futures.Comparison of the Overnight and Daily Variations in both the Spot NSA and the JapaneseNSA FuturesThe results in Tables II to V show the extent of the overnight and daily variations in both thespot NSA and the Japanese NSA futures that can be explained by the movements of thewarrants. It is obvious that the movements of the warrants in the previous day explain theovernight variations in both the spot NSA and the NSA futures better than their daily variations.For instance, the implied NSA returns for the fixed exchange rate warrants explain 21% and36% of the overnight variations in the spot NSA and the NSA futures respectively; however,they only explain about 11% of the daily variations in the spot NSA and the NSA futures. Itmight be due to the fact that the warrants are traded prior to the opening of the Japanese stockmarket and thus any information which is contained in the price movements of the warrantsmight be incorporated into the opening prices of the spot NSA and the NSA futures. Moreover,new information which affects the Japanese stock market might be released during the Japanesetrading hours, and therefore the closing prices of both the spot NSA and the NSA futures mightcorrelate less with the movements of the warrants. Hence, it is reasonable to believe that themovements of the warrants in the North American markets in the previous day might have asignificant and substantial influence on the opening prices of the Japanese stock market, butmight only have a relative minor influence on the closing prices.32In addition, the movements of the warrants explain the overnight variations in the NSAfutures more than the overnight variations in the spot NSA. For example, the implied NSAreturns for the fixed exchange rate warrants explain 36% of the overnight variations in the NSAfutures, but explain only 21% of the overnight variations in the spot NSA. The difference iseven larger for the floating exchange rate warrants (i.e. the implied NSA returns explain 29%of the overnight variations in the NSA futures and only 10% of the overnight variations in thespot NSA). The results are consistent with the fmding reported by Brenner, Subrahmanyam,and Uno (1989) that information affecting the spot market is speedily incorporated into thefutures price. Therefore, the pre-trading information, which is contained in the price movementsof the warrants and might influence the spot NSA, seems to be speedily incorporated into theopening price of the NSA futures. So, the movements of the warrants explain the overnightvariations in the NSA futures better than the overnight variations in the spot NSA.On the other hand, the movements of the warrants explain about the same daily variationsin both the spot NSA and the NSA futures. For instance, the implied NSA returns for the fixedexchange rate warrants explain about 11% of the daily variations in both the spot NSA and theNSA futures. For the floating exchange rate warrants, the implied NSA returns explain about13% of the daily variations in the spot NSA and the NSA futures. The results suggest that (1)the pre-trading information which is contained in the price movements of the warrants mightreflect more on the opening price of the NSA futures than on the opening price of the spot NSA;(2) the closing prices of both the spot NSA and the NSA futures appear to incorporate the samepre-trading information and new information released during the Japanese trading hours; (3)during the Japanese trading hours, the spot NSA seems to incorporate the pre-trading33information which has not yet reflected on its opening price; and (4) the NSA futures openingprice might incorporate most of the pre-trading information and during the Japanese tradinghours, the NSA futures appear to adjust mostly to the newly released information.At the first glance, the results are consistent with the theory that the official opening priceof the spot NSA is stale. Since individual stocks for the NSA may not begin trading at theopening of the Japanese stock market, the previous day’s closing prices of the stocks aresubstituted to calculate the spot NSA. Thus, the overnight variations in the spot NSA is lesscorrelated with the movements of the warrants. However, the results in Table VIII raise anotherconcern about the stale opening price of the spot NSA. In particular, the trading volume of thewarrants has about the same correlation with the absolute overnight changes in the NSA futuresand with the absolute daily changes in the spot NSA. On the other hand, the trading volume isnegatively correlated with the absolute overnight changes in the spot NSA and is less positivelycorrelated with the absolute daily changes in the NSA futures. Thus, the results suggest that theNSA futures might rapidly incorporate trading volume information of the warrants into itsopening price, whereas the spot NSA might not incorporate such information into its openingprice. Instead, during the Japanese trading hours, the spot NSA appear to be led by theovernight changes in the NSA futures to adjust its price accordingly.To support the above findings, we also calculate the correlations between the overnightand daily changes in the spot NSA and in the NSA futures. The results in Table IX show thatthe daily changes in the spot NSA and the NSA futures are significantly correlated; however,the correlation between their overnight changes, though significant, is relatively small. In34particular, the correlation between the daily changes in the spot NSA and the NSA futures is0.857 but the correlation between their overnight changes is only 0.452. Thus, the resultssuggest that the overnight changes in the spot NSA and the NSA futures might not be the same,whereas at the end of the Japanese trading day, the changes in the spot NSA from the previousday’s closing price might be very close to the same changes in the NSA futures. Moreover, itis interesting to note that the correlation between the overnight and daily changes in the NSAfutures is 0.660 and the same correlation for the spot NSA is only 0.347. Also, there is acorrelation of 0.5 18 between the daily changes in the spot NSA and the overnight changes in theNSA futures. Since the correlations are significant at the 1% level, the results suggest that thechanges in the NSA futures might mostly be taken place at the opening of the market, whereasthe changes in the spot NSA might mainly be taken place during the trading hours. In otherwords, the changes in the spot NSA might be led by the changes in the NSA futures, and hencethe Japanese spot/cash market might be led by the Japanese futures market. Since themovements of the warrants explain a significant portion of overnight variations in the NSAfutures, it is reasonable to believe that the Nikkei put warrants traded in North America mighthave a significant influence on the Japanese stock market.V CONCLUSIONThis paper reports the correlation of the Nikkei put warrants traded in the North America on theJapanese stock market from 1989 to 1993. In particular, we examine the relationship betweenthe movements of the warrants and the overnight and daily variations in the spot NSA and the35Japanese NSA futures. The implied NSA returns derived from the price of the warrants aresatisfactory in explaining the overnight and daily variations. Specifically, the implied NSAreturns explain as much as 40% of the overnight variations in both the spot NSA and the NSAfutures; however, only a small percentage of the daily variations in the spot NSA and the NSAfutures is explained by the implied NSA returns. This finding is consistent with the theory thatthe information contained in the price movements of the warrants is released prior to the openingof the Japanese stock market and is rapidly incorporated into the opening prices of the spot NSAand the NSA futures.Moreover, we fmd that the implied NSA returns explain the overnight variations in theNSA futures much better than the overnight variations in the spot NSA. On the other hand,about the same daily variations in both the spot NSA and the NSA futures is explained by theimplied NSA returns. So, the results suggest that the movements of the warrants might havemore influence on the NSA futures opening price than on the spot NSA opening price but havethe same and smaller influence on the closing prices of both the spot NSA and the NSA futures.Furthermore, we also examine the relationship between the trading volume of thewarrants and changes in the spot NSA and the NSA futures. The results show that tradingvolume of the warrants has strong ties with (1) the absolute overnight returns in the NSAfutures, (2) the absolute daily returns in the spot NSA, and (3) the absolute daily returns in theNSA futures. On the other hand, the results indicate that there exists a negative relationshipbetween the trading volume and the absolute overnight returns in the spot NSA.36The above fmdings suggest that the opening price of the spot NSA might be stale.However, when we examine the correlations between the overnight and daily returns for boththe spot NSA and the NSA futures, we find that the daily returns for the spot NSA and the NSAfutures are highly correlated, whereas their overnight returns are less correlated. Besides, thedaily returns for the spot NSA are more correlated with the overnight returns for the NSAfutures than with the daily returns for the spot NSA. Also, the overnight and daily returns forthe NSA futures are very correlated. It is reasonable to believe that the movements of theNikkei put warrants traded in the North American markets might have a significant influenceon the opening price of the Japanese NSA futures, whereas the spot NSA might observe theopening price of the NSA futures and adjust its price accordingly during the trading hours.37REFERENCESBailey, W. 1989. “The Market for Japanese Stock Index Futures: Some PreliminaryEvidence.” Journal of Futures Markets 9.4: 283-295.Becker, K.G., J.E. Finnerty, and M. Gupta. 1990. “The Intertemporal Relation Between theU.S. and Japanese Stock Markets.” Journal ofFinance 45.4: 1297-1306.Becker, K.G., J.E. Finnerty, and A. L. Tucker. 1992. “The Intraday InterdependenceStructure Between U.S. and Japanese Equity Markets.” Journal ofFinancial Research15.1: 27-37.Brenner, M., M.G. Subrahmanyam, and J. Uno. 1989. “Stock Index Futures Arbitrage in theJapanese Markets.” Japan and the World Economy (June): 303-330.Brenner, M., M.G. Subrahmanyam, and J. Uno. 1990. “Arbitrage Opportunities in theJapanese Stock and Futures Markets.” Financial Analysts Journal 46.2: 14-24.Brock, W.A. and A.W. Kleidon. 1992. “Periodic Market Closure and Trading Volume. AModel of Intraday Bids and Asks.” Journal ofEconomic Dynamics and Control 16: 451-489.Chen, K.C., R.S. Sears, and M. Shahrokhi. 1992. “Pricing Nilckei Put Warrants: SomeEmpirical Evidence.” Journal of Financial Research 15.3: 231-251.Chung, Y.P., J.K. Kang, and S.G. Rhee. 1992. “An Intraday Transactions Data Test of NilckeiStock Average Index Futures Price Behavior and Index Arbitrage Profitability.” WorkingPaper. University of California, Riverside.Clyman, D.R. 1992. “Arbitrage and Fixed Exchange Rate Nikkei Put Warrants.” WorkingPaper. Harvard Business School.Dravid, A., M. Richardson, and A. Craig. 1993. “Explaining Overnight Variation in JapaneseStock Returns: The Information Content of Derivative Securities.” Working Paper.Wharton School of the University of Pennsylvania.Dravid, A., M. Richardson, and T.S. Sun. 1993. “Pricing Foreign Index Contingent Claims:An Application to Nikkei Index Warrants.” forthcoming in Journal ofDerivatives.Hamao, Y., R.W. Masulis, and V. Ng. 1990. “Correlations in Price Changes and VolatilityAcross International Stock Markets.” Review of Financial Studies 3.2: 281-307.Hamao, Y. 1991. “Japanese Financial Markets: An Overview.” in W. Ziemba, W. Bailey,and Y. Hamao, eds., Japanese Financial Market Research: 3-21.38Karpoff, J.M. 1987. “The Relation between Price Changes and Trading Volume: A Survey.”Journal ofFinancial and Quantitative Analysis 22: 109-123.Karolyi, G.A. 1993. “Stock Market Volatility Around Expiration Days in Japan.” WorkingPaper. Ohio State University.Merton, M.H. 1.992. “The Economics and Politics of Index Arbitrage in the U.S. and Japan.”Address presented at the 4th Annual Pacific-Basin Capital Markets Research Conference(July), Hong Kong.Shaw, J., E.O. Thorp, and W.T. Ziemba. 1993. “Convergence to Efficiency of the Nikkei PutWarrant Market of 1989-1990.” Working Paper. University of British Columbia.Stoll, H.R. and R.E. Whaley. 1990. “Stock Market Returns and Volatility.” Review ofFinancial Studies 3: 37-71.Tufano, P. 1992. “Goldman, Sachs & Co. Nikkei Put Warrants - 1989.” Harvard BusinessSchool Case: N9-292-113 (Rev. 1/16/93).Ziemba, W.T., W. Bailey, and Y. Hamao, eds. 1991. Japanese Financial Market Research.The Netherlands: Elsevier Science.Ziemba, W.T. and S.L. Schwartz. 1992. Invest Japan: The Structure, Performance andOpportunities of the Stock and Bond Markets. Chicago: Probus.39APPENIMXDiagnostic Test&Several diagnostic tests are performed to ensure that the results obtained from the linearregression models in this study are conclusive. The tests include checking whether the followingassumptions of a linear regression model are satisfied:1. The residuals should be approximately independent of one another - no autocorrelation.2. The residuals should be normally distributed - normality.3. The residuals should have approximately the same variance - homoscedasticity.Moreover, the day of the week and January effects are also tested to ensure that the regressionmodels in this study are not misspecifled. Results of the diagnostic tests are summarized inTable A-I for regressions on the close-to-close price movements of the warrants and Table A-ilfor regressions on the open-to-close price movements of the warrants.9The first assumption means that there should be independence between successiveresiduals. To test the presence of autocorrelation in the regression models, the correspondinglagged observations are included into the original regression models and the Durbin-Watsonstatistics are calculated. As seen from the Table A-I and Table A-il, most of the observed dvalues are significant at the 5% level and are about 2 which is above the upper critical value ofthe Durbin-Watson statistic given the sample size. However, the coefficients of the laggedOnly the test results for DXA are reported in this paper.40observations in several models are significant. It raises some concern about the autocorrelationeffect in the models. To investigate whether the effect is significant, the autocorrelationfunctions of the residuals are produced and one of the plots is shown in Figure A-i. Based onthe resulting plots, no clear pattern of residuals over time is found. Using the Bartlett’sformula,1° the theoretical autocorrelations of each lag are computed and tested with theestimated autocorrelation coefficients shown in the autocorrelation function plots. Only the firstlag is found to be marginally significant in several models. Therefore, it is reasonable to believethat autocorrelation of the first lag might exist in some models but its effect is minimal. Sincethe objective of this paper is to investigate whether the movements of the Nikkei put warrantscontain any information that can influence the Japanese stock market, the regression models inthis paper do not include the lagged variables.To test the second assumption, the normal scores of residuals are computed and thenormal probability plots are produced. One of the normal probability plots is shown in FigureA-2. Based on the resulting plots, the residuals are found to be significantly correlated withtheir normal scores. Hence, we can conclude that the residuals are normally distributed.To determine whether the homoscedasticity is maintained in the regression models, thetime-series plots of residuals are produced and one of the plots is shown in Figure A-3. Theresulting plots show that homoscedasticity is maintained in most of the regression models exceptthat a slightly less homoscedasticity is found in models for overnight variations in the spot NSA.10 Compute Var(rk) (i + 2 t2) ÷ n, where rk: estimated autocorrelation of lag k;i: 1 to k-i; n: number of observations.41Since the heteroscedasticity is marginal and is only found in this specific group of models, theregression models in this paper are not adjusted for the heteroscedasticity.Furthermore, dummy variables for the days of the week and January are also includedinto the original regression models. If the original regression models were misspecifled and thedays of the week and/or January did influence the dependent variables, the coefficients of therespective dummy variables would be significant. However, the results show that all coefficientsof the dummy variables for the days of the week and January are small and insignificant (exceptWednesday and January which have some marginal influence in some models). To maintain theconsistency among models, the regression models in this paper do not include these twovariables.42Au-tocorre I at Ton—1 -0.5 0 0.5Figure A-i : Autocorrelation Function of Residuals(Regression of Overnight Spot NSA Returns on Open-to-Close Warrant Returns for DXA)L00—3 —2Figure A-2 : Normal Probabifity Plot of Residuals(Regression of Overnight Spot NSA Returns on Open-to-Close Warrant Returns for DXA)-0. oo,iea-0. 011288—0.018844 I—0.017275-0.109298—0.010713—0.033278 •-0.067626 —-0.05075 ——0.023736 I—0.039005 •—0.000902—0. 011587—0.089544 —— 0.0911210.0157950.05504— 0.05338I 0.0321630.094739• 0.052544— 0.0900390. 0142010.00325I 0.03748— 0.0622150.014330.021397— 0.0976260.002179— 0.0783590.019981432Ia—1—2—3-4- xxxx:-;;;x>x- xI I I—1 0 1 2 3Standard T zed Rca T due I43I! n 0• a IE I IStandardizedResidualIIUP304P3U.—1 3 (pTABLEINildcei PutWarrantstradedontheTorontoStockExchangebetween1989and1993SymbolIssuerExpiryPayoffof OneWarrantPeriodofTradingNKP.WTBTBankofCanada92/02/17C$0.1168xMax(32,174.00-NSA,0)÷Ex(T/C$)89/02/17-92/02/10NKP.WT.ABTBankofCanada92/06/15C$0.1031xMax(270.54-NSA+Ex(T/C$),0)89/06/14-92/06/12SeriesIINKP.WT.BBTBankofCanada93/03/16C$2.50+7.25%xMax(37,460.32-NSA,0)÷37,460.3290/03/20-91/12/19SeriesifiNKP.WT.CBTBankofCanada93/04/10C$2.50÷7.25%xMax(29,843.34-NSA,0)÷29,843.3490/04/10-93/03/29SeriesIVSEK.WTABSvenskExportkredit92/11/16C$0.1168xMax(35,963.74-NSA,0)+Ex(T/C$)90/02/22-90/11/22SeriesIITFC.’WT.NTrilonFinancial Corp93/02/22C$2.75÷7.00%xMax(37,460.32-NSA,0)÷37,460.3290/02/22-91/07/09Nikkei PutWarrantstradedontheAmericanStockExchangebetween1990and1993SymbolIssuerj__ExpiryPayoffofOneWarrantPeriodofTradingBTBBankersTrustCorp93/01/16US$0.50xMax(37,206.42-NSA,0)+Ex(Z/US$)90/02/01-93/01/11DXAKingdomofDenmark93/01/03US$0.20xMax(37,516.77-NSA,0)÷145.32590/01/15-92/12/31EXWASEksportfinans93/04/22US$0.20xMax(29,424.58-NSA,0)÷158.84090/04/27-93/04/22PXBPaineWebberOpInc93/04/08US$0.20xMax(29,249.06-NSA,0)+159.80090/04/18-93/04/08SXASalomonInc93/01/19US$0.20xMax(36,821.14-NSA,0)+145.52090/01/18-93/01/19SXOSalomonInc93/02/16US$0.20xMax(37,471.99-NSA,0)÷144.55090/02/16-93/02/16NSA:TheclosingNikkeiStockAverageatthetimeof exerciseSources:TorontoStockExchangeReviewandStandard&Poor’sStockReportsASEEx:ExchangerateatthetimeofexerciseTABLE IIEstimation of Overnight Variations in the Spot NSAusing the Movements of the Nikkei Put WarrantsThis table reports the regressions of the close-to-open returns for the spot NSA (50) on theclose-to-close returns for the fixed and floating exchange rate warrants (P), the close-to-closereturns for the implied NSA derived from the price of the warrants (IMP) and the changes inthe premium of the warrants (PM). The regressions investigate the relation between theovernight changes in the spot NSA and the three different measures of the movements of thewarrants. Returns are calculated as loge price relatives. t-values are shown in parentheses andF-values are shown in square brackets. The general form of regression is as follows:Warrant Constant a0 P° a1 IMPC. a2 PMC.c a3 Adj R2 CorrelationFixed Rate 0.000141 -0.017574 16.4% -0.405DXA (2.42) * (-11.76) # [138.39] #0.000140 0.040047 21.0% 0.458(2.46)* (13.69)# [187.52]#0.000089 -0.001184 13.0% -0.361(1.50) (-10.28) # [105.70] #0.000124 -0.013088 -0.000715 20.1%(2.17) * (-7.88) # (-5.69) #0.000127 0.032359 -0.000590 23.4%(2.26) * (9.80) # (-4.75) #Floating Rate 0.000489 -0.014255 12.8% -0.358NKP.WT (5.94) # (-10.04) # [100.78] #0.000490 0.055294 10.5% 0.324(5.88) # (8.98) # [80.70] #0.000449 -0.001869 6.4% -0.253(5.27)# (-6.87)# [47.17]#0.000477 -0.012174 -0.001012 14.4%(5.84) # (-8.00) # (-3.59) #0.000477 0.044923 -0.000983 11.9%(5.76)# (6.54)# (-3.31)#*: Significant at a 5% level#: SignifIcant ata 1% level46TABLE ifiEstimation of Overnight Variations in the Japanese NSA Futuresusing the Movements of the Nikkei Put WarrantsThis table reports the regressions of the close-to-open returns for the Japanese NSA futures (F°)on the close-to-close returns for the fixed and floating exchange rate warrants (P), the close-to-close returns for the implied NSA derived from the price of the warrants (IMP) and thechanges in the premium of the warrants (PM). The regressions investigate the relationbetween the overnight changes in the Japanese NSA futures and the three different measures ofthe movements of the warrants. Returns are calculated as log, price relatives. t-values areshown in parentheses and F-values are shown in square brackets. The general form ofregression is as follows:= +PCC÷2IM CC+PIPICC+Warrant Constant P°’ ‘y1 IMP°72 PM”y3 Adj R2 CorrelationFixed Rate 0.000741 -0.139386 33.0% -0.574DXA (2.54) # (-18.66) # [348.23] #0.000705 0.292870 36.0% 0.600(2.47)* (19.91)# [396.45]#0.000341 -0.008151 19.8% -0.445(1.07) (-13.19) # [173.91] #0.000644 -0.113861 -0.004066 36.8%(2.27) * (-13.81) # (-6.52) #0.000625 0.245380 -0.003642 39.0%(2.24) * (14.89) # (-5.89) #Floating Rate 0.000682 -0.071230 25.7% -0.507NKP.WT (2.55) # (-15.43) # [237.961 #0.000711 0.326010 29.4% 0.542(2.73) # (16.92) # [286.43] #0.000477 -0.010168 15.3% -0.391(1.67) (-11.15)# [124.25]#0.000609 -0.058839 -0.006024 30.3%(2.35) * (-12.16) # (-6.73) #0.000648 0.276220 -0.004719 32.0%(2.53) # (12.99) # (-5.13) #*: Significant at a 5% level#: Sigrnficantata 1% level47TABLE 1YEstimation of Daily Variations in the Spot NSAusing the Movements of the Nikkei Put WarrantsThis table reports the regressions of the close-to-close returns for the spot NSA (S) on theclose-to--close returns for the fixed and floating exchange rate warrants (P), the close-to-closereturns for the implied NSA derived from the price of the warrants (Th1P) and the changes inthe premium of the warrants (PM). The regressions investigate the relation between the dailychanges in the spot NSA and the three different measures of the movements of the warrants.Returns are calculated as loge price relatives. t-values are shown in parentheses and F-valuesare shown in square brackets. The general form of regression is as follows:SC=0÷p1P+p2’MPr+p3Mr+Warrant Constant () P IMP (2 PM Adj R2 CorrelationFixed Rate -0.000398 -0.163320 12.6% -0.355DXA (-0.63) (-10.10) # [101.91] #-0.000471 0.312290 11.4% 0.338(-0.74) (9.52) # [90.61] #-0.000891 -0.012214 12.3% -0.351(-1.41) (-9.97) # [99.44] N-0.000594 -0.111830 -0.008203 16.9%(-0.96) (-6.24)# (-6.05)#-0.000659 0.201250 -0.008516 15.9%(-1.06) (5.49)# (-6.19)#Floating Rate -0.000195 -0.088609 11.7% -0.342NXP.WT (-0.36) (-9.57) # [91.59] N-0.000155 0.412980 13.9% 0.373(-0.29) (10.55)# [111.40]#-0.000467 -0.014639 9.4% -0.307(-0.86) (-8.43) N [71.11] N-0.000313 -0.068406 -0.009822 15.3%(-0.59) (-6.97) N (-5.41) N-0.000265 0.326460 -0.008200 16.2%(-0.51) (7.52) # (-4.37) N*: Significant at a 5% levelN: Significant ata 1% level48TABLE VEstimation of Daily Variations in the Japanese NSA Futuresusing the Movements of the Nikkei Put WarrantsThis table reports the regressions of the close-to-close returns for the Japanese NSA futures (F)on the close-to-close returns for the fixed and floating exchange rate warrants (P), the close-to-close returns for the implied NSA derived from the price of the warrants (IMP) and thechanges in the premium of the warrants (PM). The regressions investigate the relationbetween the daily changes in the Japanese NSA futures and the three different measures of themovements of the warrants. Returns are calculated as loge price relatives. t-values are shownin parentheses and F-values are shown in square brackets. The general form of regression isas follows:=+ +A2IMP +A3PM’ ÷Warrant Constant ) P X1 IMP X2 PM X3 Adj R2 CorrelationFixed Rate -0.000647 -0.147770 12.0% -0.346DXA (-1.10) (-9.81) # [96.29] #-0.000708 0.287680 11.2% 0.335(-1.20) (9.45) # [89.21] #-0.001078 -0.009431 8.6% -0.293(-1.80) (-8.13)# [66.05]#-0.000774 -0.114310 -0.005331 14.1%(-1.33) (-6.76) # (-4.17) #-0.000828 0.216610 -0.005451 13.4%(-1.42) (6.27)# (4.21)#Floating Rate -0.000459 -0.081811 11.3% -0.336NKP.WT (-0.91) (-9.36) # [87.67] #-0.000424 0.375850 13.0% 0.361(-0.85) (10.15) # [103.04] #-0.000698 -0.012182 7.3% -0.270(-1.35) (-7.37) # [54.34] #-0.000549 -0.066367 -0.007509 13.7%(-1.10) (-7.11) # (-4.35) #-0.000505 0.3 12320 -0.006022 14.4%(-1.01) (7.56)# (-3.37)#*: Significant ata5% level#: Significant ata 1% level49TABLE VIRegression Tests using the Open-to-Close Price Movements of the Nikkei Put Warrants(Fixed Exchange Rate Warrant - DXA)This table reports the regressions of [1] the close-to-open returns for the spot NSA (Sco), [2] theclose-to-open returns for the Japanese NSA futures (Fc0), [3] the close-to-close returns for thespot NSA (S), [4] the close-to-close returns for the NSA futures (F), [5] the ratio of the NSAfutures opening price to the spot NSA opening price (F°/S°), and [6] the ratio of the NSA futuresclosing price to the spot NSA closing price (F/SC) on the open-to-close returns for the DXA -fixed exchange rate warrants (P°) and the open-to-close returns for the implied NSA derivedfrom the warrant prices (IMP°). Returns are calculated as loge price relatives. t-values areshown in parentheses and F-values are shown in square brackets.Dependent Variable Constant P° IMP° Adj R2 CorrelationS° -0.000041 -0.030368 15.0% -0.390(-0.56) (-9.66) # [93.39] #-0.000133 0.059508 19.3% 0.440(-1.82) (11.20)# [125.50]#F°° -0.000626 -0.202720 27.6% -0.526(-1.87) (-14.13) # [199.61] #-0.001120 0.361480 29.2% 0.541(-3.31) # (14.69) # [215.84] #S° -0.001948 -0.248990 10.8% -0.330(-2.67) # (-7.99) # [63.92] #-0.002597 0.456350 12.0% 0.349(-3.52)# (8.51)# [72.45]#F -0.001869 -0.221150 9.2% -0.307(-2;65) # (-7.35) # [54.00] #-0.002411 0.395530 9.8% 0.316(-3.37) # (7.60) # [57.83] #F°/S° 0.007968 -0.174830 12.4% -0.355(16.88) # (-8.66) # [75.08] #0.007586 0.299000 12.1% 0.351(15.73) # (8.53) # [72.75] #F/Sc 0.008632 0.025350 0.2% 0.063(21.94)# (1.51) [2.27]0.008757 -0.063780 0.7% -0.095(21.88) # (-2.19) * [4.81] **: Significant at a 5% level#: Significantata 1% level50TABLE VIIRegression Tests using the Open-to-Close Price Movements of the Nikkei Put Warrants(Floating Exchange Rate Warrant - NKP.WT)This table reports the regressions of [1] the close-to-open returns for the spot NSA (Sco), [2] theclose-to-open returns for the Japanese NSA futures (F°), [3] the close-to-close returns for thespot NSA (S), [4] the close-to-close returns for the NSA futures (F), [5] the ratio of the NSAfutures opening price to the spot NSA opening price (PIS°), and [6] the ratio of the NSA futuresclosing price to the spot NSA closing price (P/S on the open-to-close returns for the DXA -fixed exchange rate warrants (P°) and the open-to-close returns for the implied NSA derivedfrom the warrant prices (IMP°). Returns are calculated as loge price relatives. t-values areshown in parentheses and F-values are shown in square brackets.Dependent Variable Constant P° IMP° Adj R2 CorrelationS°° -0.000164 -0.016838 18.3% -0.431(-1.80) (-8.53) # [72.83] #-0.000217 0.058017 21.4% 0.465(-2.38) * (9.38) # [87.91] NF° -0.001193 -0.121280 30.4% -0.553(-2.52) * (-11.86) N [140.66] #-0.001512 0.406330 33.4% 0.580(-3.22)# (12.71)# [161.62]#S° -0.002989 -0.142480 13.5% -0.371(-3.23) # (-7.14) # [51.02] N-0.003385 0.481460 15.2% 0.392(-3.65)# (7.62)# [58.14]#F -0.002793 -0.134480 11.7% -0.346(-2.95) # (-6.58) N [43.33] #-0.003187 0.458700 13.3% 0.369(-3.35)# (7.09)# [50.30]#F°/S° 0.010341 -0.094700 12.5% -0.354(16.06)# (-6.82)# [46.53]#0.010040 0.327580 14.6% 0.386(15.59) N (7.48) N [55.91] NP/S° 0.011566 0.017730 0.5% 0.089(22.08)# (1.57) [2.46]0.011533 -0.043470 0.1% -0.071(21.70)# (-1.20) [1.45]*: Significant at a 5% levelN: Significant ata 1% level51TABLE VifiThe Correlation between the Trading Volume of the Nikkei Put Warrantsand the Absolute Value of Changes in the Spot NSA and in the Japanese NSA FuturesThis table reports the correlations of the trading volume of the Nikkei Put Warrants with (1) theclose-to-open absolute returns for the spot NSA (I S° I) and for the NSA futures (I F° I) (2) theclose-to-close absolute returns for the spot NSA (IS I) and for the NSA futures (I FC I) and(3) the absolute ratios of the NSA futures price over the spot NSA at open (I F/So I) and at close(I FC/SC I). The correlations show the effect of the trading volume of the Nikkei Put Warrantson the absolute changes in both the spot NSA and the Japanese NSA futures over the studyperiod (February 17, 1989 to April 23, 1993). Returns and ratios are calculated as log, pricerelatives. F-values are shown in the parentheses.TRADING VOLUME I S’° I Fl IS’ I I F0*I I I I F/SiUNiT-VOLUME -0.220 0.300 0.288 0.241 0.266 0.216(40.09) # (77.80) # (71.01) # (48.45) # (59.79) # (38.45) NDOLLAR-VOLUME -0.195 0.336 0.356 0.292 0.245 0.249(31.05) N (99.93) N (113.89) N (73.00) N (50.25) N (51.84) NYEN-VOLUME -0.200 0.328 0.350 0.288 0.251 0.252(32.79) N (94.60) N (109.47) N (70.74) N (52.63) N (53.43) NN : Significant at a 1% l.velUnit-Volume : The sum of the trading volume of all Nikkei Put WarrantsDollar-Volume: The sum of the dollar-equivalent trading volume of all warrantswhich is computed by multiplying the unit volume to the respective dollar priceYen-Volume : The sum of the yen-equivalent trading volume of all warrantswhich is computed by multiplying the unit volume to the respective yen-equivalent price52TABLE IXThe Correlation between the Changes in the Spot NSA and in the Japanese NSA Futuresat the Open and Close of the Japanese MarketThis table reports the correlations between the close-to-open and close-to-close returns for thespot NSA (S°, SC_C) and the same returns for the Japanese NSA futures (F°, F). Thecorrelations show the relationship between the changes in the spot NSA and the changes in theJapanese NSA futures at the open and close of the Japanese market over the study period(February 17, 1989 to April 23, 1993). Returns are calculated as loge price relatives. F-valuesare shown in the parentheses.SC Sce FCo Fe_CS0 1S 0.347 (141.07) # 1F° 0.452 (264.05) # 0.518 (378.84) # 1FC_C 0.293 (96.47) # 0.857 (2860.14) # 0.660 (795.58) # 1#: significant at a 1 % level53TABLEA-ISummRryof the.DiagnosticTests(for Close-to-ClosePriceMovementsof theWarrants)DependontVariableLaggedP,.1IMP,.1PM,.1D-W:dvalueTeat:1NormalityTeat:2HumoscedasticityTest3DayoftheWeekEffectTest:4JanuaryEffectSiN1.94*NonnalSlightlyNon-constantInsignificantInsignificantN1.92•NormalSlightlyNon-constantInsignificantInsignificantNNN2.06*NormalSlightlyNon-constantInsignificantInsignificantiNN2.02•NormalSlightlyNon-constantInsignificantInsignificantS°NN2.04*NormalConstantInsignificantInsignificantNN2.12*NormalConstantInsignificantInsignificantiNN2.09*NormalConstantInsignificantInsignificantNi2.12*NormalConstantInsignificantInsignificantP,IN2.06NormalCoInsignificantInsignificant•N2.13*NormalCorntanlInsignificantInsignificant‘NN2.16NormalCotInsignificantInsignificantiNN2.18NormalCocalantInsignificantInsigniflcm1NN2.00aNormalConstantMarginal SignificantonInsigniflcWednesdayNN2.08*NormalConstantMarginalSignificantonInsignificantWednesdayNN2.04*NormalConstantMarginal SignificantonInsignificantWednesdayINi2.08*NormalConstantMarginalSignificantonInsignificantWednesday*:Sig..if5aiga5%ielN:Signiflcantatal%leveli:Insigniflcant1:Resultsarebasedonthe nonnalprobabilityplotofresidualsvecaustheirnormalscores2:Resultsarebasedonthetilno-seneeplotofresiduals3:Resultsarebasedonthesignificanceofthecoefficiontsofthedummyvariablesforthedayoftheweek4:Resultsarebasedonthesignificanceofthecoefficionts ofthedummyvariablesforJanuaryTABLEA-ilSummaryoftheDiagnosticTests(for Open-to-ClosePriceMovementsoftheWarrants)•:Significantata5%levelI:Signiflcantsta1%leveli:Insignificant1:Resultsarebasedonthe normalprebibilityplotofresidualsversustheirnormalscores2:Resultsarebusedenthetirm-serics plotofresiduals3:Resultsarebusedonthesignificanceofthecoefficients ofthedummyvariablesforthedayoftheweek4:Resultsarebasedonthesignificanceofthecoefficientsof thedummyvariablesforJanuacyU’U’DependentVariableLaggedP,1MP1D-W:dvalueTest:1NonnahtyTeat3HomoscedasticityTest1flayoftheWeekEffectTest4JanuaryEffectS°11.81*NormalConstantInsignificantInsignificantiI1.80*NormalConstantInsignificantInsignificantSriN1.87wNormalConstantMarginalSignificant onWednesdayInsignificantN1.87*NormalConstantMarginalSignificant onWednesdayInsignificantF°N1.671NormalConstantInsignificantSignificant1N1.701NormalConstantInsignificantSignificantFr1N1.89*NormalConstantMarginalSignificantonWednesdayInsignificant1N1.91*NormalConstantMarginalSignificantonWednesdayInsignificant

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