Index arbitrage in the Japanese stock market

Swinnerton, Eugene A

INTRODUCTION

The purpose of this research is to gain insights on the extent intraday stock index arbitrage activity in the Japanese financial markets, and in particular, to assess the ability of futures mispricings, lagged futures price changes and lagged cash index value changes to predict intraday stock price changes in the Nikkei 225 Stock Index. Results will be examined and contrasted with parallel studies on U.S. index futures and cash prices.

Index arbitrage entails massive intraday transactions involving stock indexes and their corresponding futures. Short term supply and/or demand imbalances in the traded equities comprising the indexes may result thus impacting the intraday price changes of the underlying stocks. Regarding the Japanese financial markets, prior to 1989, there was virtually no index arbitrage futures trading involving the Tokyo Exchange. However, such arbitrage activity increased significantly in 1990 and 1991.(1) Understanding the behavior and intraday price effects of futures and cash index trading in different world markets is of great significance to brokerage houses, investors, portfolio managers, regulators, legislators and the major global stock and futures exchanges.

The relevant literature is discussed in Section 2. Section 3 covers the research and the data base used in the study while the results are analyzed in Section 4. Section 5 reports the principal conclusions.

RELATED LITERATURE

Studies describing the theoretical pricing of stock index futures and the relevant trading boundaries of index arbitrage in-clude works by Cornell and French (1983a, 1983b), Figlewski (1984a, 1984b), Modest and Sundaresan (1983) and Stoll and Whaley (1987). Cumulatively, their research suggests that the theoretical prices of stock index futures should reflect interest earned and dividends foregone. Early empirical research to determine any predictive information in the intraday relationship between stock index futures and the underlying index includes studies by Kawaller, P. Koch and T. Koch (1987), Finnerty and Park (1987), Herbst, McCormack, and West (1987), Stoll and Whaley (1983a), Laatsch ad Schwarz (1988) and Swinnerton, Curcio and Bennett (1988). The above authors, using diverse empirical research designs, found that lagged futures returns are strong leading indicators of the subsequent intraday price movements in their underlying indexes. Stoll and Whaley (1988a, 1988b) explain that index futures perform a price discovery role, while Swinnerton, Curcio and Bennett (1988) found futures mispricings (the trigger points of stock index arbitrage program trading), to be modest predictors of intraday stock price changes. Overpriced futures were found to be somewhat stronger predictors of intraday pricing relationship between futures and their underlying indexes has been conducted on U.S. stock and futures data. It is believed that a more complete understanding of the effects of index arbitrage on intraday stock price changes could be obtained by ex amining the Japanese markets, in particular because of their major status (Lake (1990) and because of different and changing institutional restrictions, offer substantial research opportunities. Brenner, Subrahmanyam and Uno (1989a, 1989b and 1990) empirically examined closing prices on the Japanese futures and stock markets and found evidence of arbitrageable mispricings of the stock index futures contracts. These results, however, provide little insight on intraday arbitrage activity and effects. Other research on the Japanese futures and stock markets include Kunimura (1990) who compared performance between the Nikkei 225 stocks and non-Nikkei (highly volatile) stocks, Bailey (1989) who discussed some historical and institutional details of the Nikkei 225 and OSF 50 futures markets and conducted correlation tests for price changes and futures volume, and Lake (1990) who traced the evolution of stock index futures trading in Japan. Additionally, Amihud and Mendelson (1991) examined the effects of the trading mechanism and the time at which transactions take place on the behavior of stock returns in the Japanese markets.

RESEARCH

To discern the effects of index arbitrage on the intraday price-changes in the Japanese financial markets, we will use the following ordinary least squares regression model formulated in Swinnerton, Curcio and Bennett (1988):

(Equation 1 omitted)

S sub t sub j = the cash price of the index at the j sup th minute on day t,

S sub t sub j+n = the cash price of the index at the (j +n) sup th minute on day t, with n denoting the intraday forecast period,

S sub t sub j-5 = the cash price of the index at the (j -5) sup th minute on day t,

(character omitted) sub t sub j,T = the theoretical futures price at the j sup th minute on day t for a stock index which will have cash settlement at T,

F sub t sub j,T = the actual futures price at the j sup th minute on day t for a stock index which will have cash settlement at T,

F sub t sub j-5,T = the actual futures price at the (j-5) sup th minute on day t for a stock index which will cash settlement at T.

beta sub 1 , beta sub 2 and beta sub 3 represent the regression coefficients of the corresponding independent variable: futures mispricing, lagged stock index cash price change and lagged actual futures price change, alpha and epsilon denote the intercept and random disturbance coefficients respectively.

The quantity [F sub t sub j,T – F sub t sub j,T ] is the difference between the actual and theoretical price of the futures contract, where the theoretical stock index futures price, F sub t sub j,T is computed as:

(Equation omitted)

and where D sub 1 and t sub 1 are the amount and the timing of the dividends paid for each security, i, in the index, 1 = 1, 2, ….m, during the futures life, and R represents the market rate of interest while e denotes continuous compounding over T-t or T-t sub i .

Except for considerations unique to the individual institutional investor: taxes, transaction costs and perceived dividend uncertainty: price deviations, [F sub t sub j,T – F sub t sub j,T ] having values either > 0 or

Based on previous results, beta sub 1 is expected to be positive and significant in a one-tailed t test. beta sub 2 is also expected to be positive and significant based on Stoll and Whaley (1988). Additionally, and based on rigorous academic research, beta sub 3 is expected to be positive and significant.(2) A five minute lag for the lagged stock index and futures price change variable is deemed appropriate based on the Kawaller, Koch and Koch (1987) Stoll and Whaley (1988a) and Swinnerton, Curcio and Bennett (1988).(3)

DATA

Tick-by-tick data on the prices of the Nikkei 225 stock index futures traded on the Osaka Securities Exchange, F sub t sub j,T and minute by minute data on the securities comprising the Nikkei 225 Stock Index traded on the Tokyo Stock Exchange, S sub t sub j , for each trading day (including holidays) in the period January, 1990 through December, 1990 were used in the analysis. However, because of extensive trading gaps that occurred in the September and December contracts, only the March and June contracts were finally used in the analysis. There was a further elimination of three trading days, February 22, February 27 and April 5, due to excessive trading gaps. The resultant final sample included 42 trading days from each of the March and June contracts.

Trading in the Nikkei Stock Index on the Tokyo Exchange is conducted in distinct morning (9:00 a.m. to 11:00 a.m.) and afternoon (1:00 p.m. to 3:00 p.m.) sessions separated by a two hour break. The Nikkei Stock Index futures traded on the Osaka Securities Exchange have the same opening times for the morning and afternoon sessions as the Tokyo Stock Exchange, but close 15 minutes later in each session than the Tokyo Exchange. Thus, the results were analyzed separately for the morning sessions, the afternoon sessions and combined full day session.

The index was available once per minute while the futures were actual tick by tick transactions for all trades during each trading day. For each minute, the index price observed was matched with the closest futures price during the minute as the coincident futures quote. The analysis was restricted to the trading hours of the Tokyo Stock ExExchange. Thus, we had 121 matched observations on (F sub t sub j,T S sub t sub j ) for each of the morning and afternoon sessions or 242 matched observations for each trading day. The intraday forecast period, n, used in denoting the observation S sub t sub j+n was varied as follows: n = 5, 10, …,30 minutes. Because of the five minute lag required for the lagged independent variables and the maximum forecast period of 30 minutes in the dependent variable, 35 minutes of observations for each of the morning and afternoon trading sessions were excluded from the tests. This leaves 86 observations for each of the morning and afternoon trading sessions and thus 172 observations per day. On such days the number of observations was somewhat less than 86 for the morning sessions while such delayed openings rarely occurred in the afternoon trading sessions. To measure

(Equation omitted)

we used daily quotes on the 30 day Gensaki rate adjusted for time to expiration, (T-t), as a proxy for e sup R(T-t) . To compute:

(Equation omitted)

the cash dividend for the index, we used actual dividends, D sub i , paid to holders of record on day, t sub i , for each security,

i, in the daily quotes on the 30 day Gensaki rates adjusted for time to expiration, (T-t sub i ), as a proxy for e sup R(T-t sub i ). All data, the Nikkei Stock Index prices, the Nikkei Index Futures prices, the dividend values and the daily Gensaki rates were provided by Nihon Shimbun Inc.

Separate regressions were run for each of: (1) 10 distinct mispricing ranges (each range was .4% of the theo-retical Nikkei index futures price in size and these .4% ranges extended incrementally from -2.0% to +2.0% of the given theoretical Nikkei index futures price), (2) the 6 distinct forecast periods (5, 10,….., 30 minutes), (3) the 42 distinct paired trading days based on time to contract expiration and (4) the distinct morning (A.M.) and afternoon (P.M.) trading sessions. Hence the possible no. of regressions is the product of the no. of sub-elements in each of these distinct categories. The total possible regressions for the overall sample is 5040. However, sufficient observations existed, for this sample, to run only 1476 regressions. It is recognized that besides the independent variables specified in equation (1) intraday index stock price changes may occur as a result of the random arrival of new information which may be positive or negative with respect to expectations of return on the index. Hence, we acknowledge that some of the significant beta’s to be observed may be due to the random arrival of new information and not necessarily to the independent explanatory variables specified in equation (1). Further, in the absence of contrary evidence, we assume that the probability of the arrival of either positive or negative information are equal at .5. Hence to determine the net effect on intraday index stock price changes of the independent explanatory variables in equation (1), the ratio of positive to negative beta’s is computed for each explanatory variable for any subsequently defined subsample. A ratio of positive to negative significant beta’s which approximates the value of 1.0 would be interpreted as neutral and would be due to the random arrival of new information and not to the individual explanatory variable. On the other hand, if a specific explanatory variable had a ratio of positive to negative significant beta’s which substantially exceeded 1.0, this condition would imply that the significant relationship observed between the intraday stock index price changes and the particular explanatory variable was in the direction expected. The degree to which a specific explanatory variable’s ratio of positive to negative significant beta’s exceeds 1.0 is interpreted as a measure of that variable’s relative power to Predict intraday stock index price changes. A ratio of 30 would be interpreted as substantially more predictive than a ratio of 1.5. When this approach was used on analysis of the effects of futures mispricings, lagged futures returns and lagged cash index returns on intraday stock index price changes in the U.S. financial markets, it produced results highly consistent with other methodologies which examined only one explanatory variable at a time.

Analysis of Results

Of the predictor variables tested, the positive mispricings variable, while only weakly predictive, was, in general, the strongest overall predictor of intraday stock price changes. The negative mispricings variable, while substantially less predictive than the positive mispricings factor, was the second most predic-tive of the tested variables. One exception was at the 5 minute lead time interval for the afternoon trading session results. (See FIGURE 1.) (Figure 1 omitted) However, it should be noted that (1) the predictive ability of the negative mispricings (p.m. results) deteriorates rapidly after the 5 minute lead time interval, becoming substan-tially less predictive than the positive mispricings for all intervals in the 10 to 30 minute lead time period and (2) the relatively small number of significant regressions observed for the negative mispricings at the 5 minute lead time interval increases the possibility of the observed results being somewhat of an aberration. (Refer to FIGURE 1 and TABLE 1.) (Table 1 omitted)

A comparison of the morning and afternoon session results indicates a substantially greater predictive ability of both the positive and negative mispricing variables for the afternoon sessions relative to the morning sessions. This would suggest that both long and short index arbitrage activity is substantially greater in the afternoon than in the morning session.

A comparison was made of the full day results on the predic-tive ability of the futures mispricings for the Japanese markets (FIGURE 1, Panel A,B and C and TABLE 1) with U.S. results (FIGURE 1, Panel D) as reported in Swinnerton Curcio and Bennett (1988) and Curcio, Swinnerton and Bennett (1990). We found the observed pattern of having the positive mispricings more predictive than the negative mispricings of intraday stock price changes in the Japanese markets to be consistent with that noted in the U.S. markets. Regarding the U.S. results, Swinnerton, Curcio and Bennett attributed the weaker predictive ability of the negative mispricings to the uptick restriction on short sales of common stock. This uptick restriction is an impediment to achieving simultaneity in effecting arbitrage sell programs. Institutional traders wishing to initiate an undervaluation arbitrage, but without an adequate amount of the appropriate stocks in their inventories, would have to short sell the stock and hence might be hampered by the uptick rule. In the Japanese markets, short selling restrictions (other than an uptick rule which does not exist in Japan), as well as an apparent aversion of Japanese brokers towards the handling of short sales may explain the relatively weaker predictive ability of negative versus positive mispricings. Further, it was discovered that the frequency and degree of mispricing is significantly lower for the underpriced versus the overpriced futures. This implies that, in Japan, the opportunities are fewer and the returns smaller for short versus long index arbitrage.

The lagged futures price change factor was found to be the third most predictive, of the four (if we count the positive and negative mispricings separately) predictor variables, in forecasting intraday stock price changes in the Japanese market. (Refer to FIGURE 1 and TABLE 1) This is especially evident in the afternoon session where the ratios of positive to negative significant beta’s for the lagged futures price change variable only slightly exceeds 1.0 in the 5 to 20 min. forecast periods. (Refer to FIGURE 1, Panel B and TABLE 1). This observation is in sharp contrast to the findings in Swinnerton, Curcio and Bennett (1988) and Curcio, Swinnerton and Bennett (1990) regarding the U.S. financial markets where the lagged futures returns are, typically, significantly more predictive and the strongest of the four predictors (See FIGURE, Panel D). It is also in conflict with the results obtained in Kawaller, Koch and Koch (1987), Finnerty and Park (1987), Herbst, McCormack and West (1987), Stoll and Whaley (1988a), Laatsch and Schwarz (1988) and Amihud and Mendelson (1989) Stoll and Whaley (1988a, 1988b) attribute this predictive phenomenon of lagged futures returns in the U.S. markets to the hypothesis that investor opinions are registered more quickly in the futures markets than in the stock market because it takes time to trade the many individual stocks that comprise the index.

The evidence obtained in this research would tend to suggest that index futures perform little, if any, price discovery role in the Japanese financial markets. A price discovery function for index futures in Japan may be impeded by the country’s regulatory structure which limits index futures price moves and, in general, governs index futures trading. Japanese stack index futures markets are regulated by the countries’ Securities and Exchange Laws with general oversight provided by the Ministry of Finance. Additionally, a specially designated group of stock exchange members, referred to as Saitori on the Tokyo exchange and Nakadachi on the Osaka exchange, is empowered to set and expand futures price change limits, adjust margin requirements and regulate the total volume of trading. On any given day, if trading conditions warrant it, and with the goal of maintaining orderly, sound markets, the Saitori or the Nakadachi may make discretionary changes in these trading rules. By contrast in the U.S., index futures markets rules governing such items as price change limits and margin requirements are generally fixed. Modifications of such rules may be effected by U.S. regulators, but usually only after extensive deliberations and with significant advance notice. Hence, in Japan, the potential for spontaneous changes in futures trading rules, based on the discretionary decisions of a small group of specially empowered exchange members, may create greater uncertainty for traders in the Japanese index futures markets than would be encountered in corresponding U.S. markets. Such may alter futures trading behavior in Japan from what might typically be expected based on the U.S. experience. Also, the disproportionately greater frequency and degree of overvalued versus undervalued index futures, which extends throughout the sample period, suggests the existence of a significant positive bias (inefficiency) in the pricing of index futures in the Japanese markets. Such a bias could deter investors from registering their opinions more rapidly in the index futures than in the underlying stocks. However, whatever the cases, the evidence suggests that the price discovery role of index futures may indeed be country specific.

The lagged cash index return variable was the least predictive of the four test variables in the Japanese financial markets. This variable was only slightly predictive at the 5 minute lead time period and nonpredictive at subsequent lead times. These results are similar to those found for U.S. financial markets in Swinnerton, Curcio and Bennett (1988) and Curcio, Swinnerton and Bennett (1990). The result is also consistent with intraday serial correlation results for cash index returns obtained by Stoll and Whaley (1988) using U.S. data.

Summary and Conclusions

Direct empirical tests were conducted to determine the effects of index arbitrage on intraday stock price changes in the Japanese stock markets. The object relationship was determined by empirically assessing, through a regression format, the predictive ability of futures mispricings, lagged cash index price changes and lagged futures price changes thought to impact intraday stock price moves. The following conclusions were obtained:

Index arbitrage activity has a modest impact on intraday stock price changes in the Japanese financial markets. The effects are substantially more pronounced for long as opposed to short arbitrage. This difference appears to be due to institutional impediments and other barriers to short selling of the stock index, a typically essential step in effecting the undervaluation arbitrage. Also, there are substantially fewer opportunities and lower potential returns available for undervaluation versus overvaluation arbitrage. Additionally, the effects of all index arbitrage activity appears to be substantially greater for the afternoon versus the morning sessions.

The lagged futures price change variable is only slightly predictive of intraday stock price changes, and substantially less predictive than either of the mispricing variables. This finding is in sharp contrast with the results of comparable studies on U.S futures and cash index markets in which the lagged futures value change variable has been typically determined to be the strongest predictor of intraday stock price moves. The most significant of these results is that they tend to suggest that stock index futures perform little, if any, price discovery role in the Japanese financial markets. A price discovery function for index futures in Japan may be impeded by the country’s regulatory structure which limits index futures price moves and governs overall trading in index futures. Also, the existence of a significant and persistent overvaluation bias in the pricing of index futures in the Japanese markets may deter investors from registering their opinions more rapidly in the index futures than in the underlying stocks. Whatever the cause, the evidence suggests that the price discovery function of stock index futures may indeed be country specific.

The lagged cash index price change variable was the least predictive of the factors tested for predicting intraday stock price changes in Japan. This variable was only slightly predictive at the 5 minute lead time interval and non-predictive for subsequent lead times. Such results are not dissimilar to findings in compar able studies on U.S. data.

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