Index-Futures Arbitrage in Japan

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Index-Futures Arbitrage in Japan

Y. Peter ChungInterim Dean

A. Gary Anderson Graduate School of ManagementUniversity of California

Riverside, CA [email protected]

Jun-Koo Kang

MSU Federal Credit Union Chair in Financial Institutions & InvestmentsThe Eli Broad College of BusinessMichigan State University

East Lansing, MI [email protected]

and

S. Ghon RheeK. J. Luke Distinguished Professor of International Finance and Banking

College of Business AdministrationUniversity of Hawaii

Honolulu, HI 96822-2282

[email protected]

Abstract

We examine the impact of the unique Japanese stock market microstructure on the pricing of stock index futurescontracts. We use intraday transactions data for the Nikkei 225 Futures contracts in Osaka and the correspondingNikkei 225 Index in Tokyo. Incorporating more realistic transaction-cost estimates and various institutionalimpediments in Japan, we find that the time-varying liquidity of some component shares of the index in Tokyorepresents the most critical impediment to intraday arbitrage and often causes futures prices in Osaka to deviatesignificantly and persistently from their no-arbitrage boundary, especially for longer-lived contracts.

JEL Classification: G13, G14, G18

Key Words: Stock index futures; market microstructure; transactions data; index arbitrage; Short-Sale

Constraints

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Index-Futures Arbitrage in Japan

1. Introduction

In this paper, we examine the pricing of stock index futures and the profitability of index-futures

arbitrage in light of the unique stock market microstructure and various institutional impediments in Japan.

Because we have access to the data only for the first three-year period after the introduction of the Nikkei 225

Futures in Japan (September 1988 through September 1991), our analyses are limited to the impact of market

microstructure features prevailing then in Japan on the price discovery process of stock index futures. The

available historical data include the intraday transactions prices of the Nikkei 225 Futures contracts traded on the

Osaka Securities Exchange (OSE) and minute-by-minute quotes of the Nikkei 225 Index on the Tokyo Stock

Exchange (TSE).

Market microstructure in Japan is significantly different from that in the United States, where other

global contracts are traded. There is growing evidence in the literature for the U.S. and other global markets that

market microstructure significantly affects securities pricing.1 There are numerous real-world impediments to

arbitrage trading in Japan: high transaction costs, cash margin requirements in the futures market, no responsible

market maker and relatively long execution lags in the stock market, occasional non-trading of index component

stocks, and difficulties in borrowing stocks for short sales, in addition to other traditional institutional

impediments. The tests in this study attempt to closely approximate conditions in the Japanese stock and futures

markets. We first incorporate an accurate estimate of transaction costs associated with index arbitrage in Japan.

We then investigate the ex ante profitability of trading on apparent ex post mispricing in the context of

difficulties involved in index arbitrage in Japan. The purpose of this paper is, therefore, to understand the

Japanese market microstructure, and demonstrate its impact on index futures pricing and intraday index arbitrage

opportunities at the initial stage of developing the equity index futures market in Japan.

We find that the time-varying liquidity of some component shares of the index in Tokyo and subsequent

disintegration of the stock and futures markets represent the most critical impediment to intraday arbitrage and

often cause futures prices in Osaka to deviate significantly and persistently from their no-arbitrage boundary,

especially for longer-lived contracts. This finding is in sharp contrast to earlier studies for the U.S. markets. For

1 Recent papers on the impact of market microstructure on securities pricing include Amihud and Mendelson (1987), Amihud,Mendelson, Murgia (1990), Fishman and Longstaff (1992), Grossman and Miller (1988), Grunbichler, Longstaff, and Schwartz (1994),Hamao and Hasbrouck (1995), Lehmann and Modest (1994), Madhavan (1992), and Stoll and Whaley (1990).

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example, Chung (1991), MacKinlay and Ramaswamy (1988), Neal (1990), and Stoll and Whaley (1986), among

others, report that the execution lag in arbitrage trades, the transaction costs involved, the up-tick rule for short

sales of stocks, and other trading mechanisms are the major impediments to index arbitrage in the U.S. market.

When arbitrageurs find that it is difficult or even impossible to purchase or borrow some component

shares of the index, arbitrage pressure breaks down in the absence of close substitutes. Consequently, the two

markets are less integrated, and the index futures prices can at times deviate significantly from the no-arbitrage

boundary, and the deviations can persist. We provide evidence that the stock market turnover/liquidity and

associated staleness of the index have significant impacts on the estimated boundary violations by Nikkei 225

Futures prices. We demonstrate that, if the time-varying liquidity of Nikkei 225 stocks is ignored, spurious

conclusions about the market efficiency and the relation between the futures and cash markets can be obtained

and arbitrage opportunities in Japan can be falsely identified. Thus, our results complement the importance

attached to market microstructure in the literature.

In Section 2, we describe the Nikkei 225 Index of the TSE and the corresponding Nikkei 225 Futures

contracts traded on the OSE. We also discuss the transaction cost structure in Japan. In Section 3, we discuss the

data. In Section 4, we document the extent to which the NSA futures are mispriced. In Section 5, we discuss the

various aspects of the Japanese market microstructure and tests whether they can explain the occasional surges in

the estimated mispricing of the Nikkei 225 futures documented in Section 4. Finally, we summarize and

conclude the paper in Section 5.

2. Institutional Background

2.1. Nikkei 225 Index and Nikkei 225 Futures Contracts

The Nikkei 225 Index is the most widely quoted barometer of the Japanese stock market, and is the basis

of the most popular futures contracts in Japan in terms of daily average volume and open interest. Many

Japanese index funds track the Nikkei 225 Index, just as the Standard and Poors (S&P) 500 is heavily used by

the U.S. index funds. The Nikkei 225 Index is a price-weighted index of 225 stocks listed in the First Section of

the TSE.2

Futures contracts written on the Nikkei 225 Index have been also traded abroad on Singapore Exchange

2 Refer to Bacha and Fremault-Vila (1994) for further institutional details of the Nikkei 225 Index and its futures contractsduring the study period which is similar to ours.

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(SGX, formerly Singapore International Monetary Exchange (SIMEX)) since September 3, 1986. After the

introduction of new Nikkei 225 Futures contracts in Japan on September 3, 1988, however, the offshore trading

of Nikkei 225 Futures contracts on the SGX became much less active. In contrast, the trading volume in Osaka

picked up sharply and soon passed the volume on the SGX. In 1991, the most recent sample year in our study,

the daily average trading value in Singapore was a relatively modest amount of 37 billion or 1.7% of that in

Osaka (2,182 billion). The Chicago Mercantile Exchange has also traded the Nikkei 225 Futures contracts since

September 25, 1990, but their daily average trading volume is 850 contracts in 1991 or less than 1% of that in

Osaka (87,980 contracts).

As for the source of the Nikkei 225 Futures trading volume, about 50 to 60 percent of trading volume is

from domestic brokers, about 6 to 7 percent from foreign brokers, and about 30 percent from institutional

investors such as banks, investment trusts, business corporations, and insurance companies during the 3-year

study period. Less than 1 percent of trading volume comes from individual investors. Japanese and foreign

brokerage houses use the Nikkei 225 Futures contracts for their trading strategies; i.e., index arbitrage, portfolio

insurance, or horizontal spreading.

2.2. Transaction Cost Structure for Index Arbitrage in Japan

The actual yen value of the portfolio of 225 stocks, holding one share in each stock, is the index

multiplied by the index divisor, which is around 10 during our sample period. The value of one Nikkei 225

Futures contract is 100 times the total value of this stock portfolio, as the size of the futures contract is 1,000

times the Nikkei 225 Index. For a practical portfolio of 1,000 shares in each stock, the value of the futures

contract would be only about one-tenth of the portfolio's value. For arbitrage, an investor buying a round lot of

each of the Nikkei 225 Index component stocks would therefore have to purchase about 10 Nikkei 225 Futures

contracts on average. In this paper, our transaction-cost estimates use this scenario as a benchmark.

There are seven components of transaction costs involved in the Nikkei 225 Index arbitrage in Japan.

They include: (1) round-trip stock brokerage commissions to buy and sell the stocks on the TSE; (2) securities

transfer tax paid when stocks are sold; (3) two market-impact costs on the TSE 3; (4) one futures brokerage

commission to open a position on the OSE; (5) one market-impact cost on the OSE; (6) cost of "borrowing"

3 An implicit assumption here is that the bid-ask spread remains constant. Bae, Chan, and Cheung (1998) report that the useof bid and ask prices (rather than transaction prices) improves the analysis of mispricing based on arbitrage between Hang Seng Indexfutures and options.

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stocks for short arbitrage4; and (7) interest lost on cash margin deposits for the futures position on the OSE.

Appendix A presents the details of the transaction costs for two different types of arbitrage traders (brokers vs

institutional investors) and two different types of arbitrage trades (short vs long arbitrage).5

To get the total transaction costs as a percentage of the underlying index value, we add the three unusual

items (2, 6, and 7) to the other four traditional items. For a typical long arbitrage, it would be realistic to

estimate the total transaction costs to be 0.841% (0.781% after April 1, 1989) for brokers and 2.956% (2.706%

after April 1, 1989) for institutional investors, plus interest lost on cash margin deposits. Transaction costs are

0.1% higher for a typical short arbitrage.6

3. Data

Stock index futures can be priced by a simple arbitrage argument. If the dividends paid by the

underlying stocks and interest rates are non-stochastic, markets are perfect, and there are no taxes, the pricing

equation is:

F(t,T) = S(t)er(T-t) - D(t,T), (1)

where F(t,T) equals the futures price at time t for a contract that matures at time T; S(t) equals the spot index

value at time t; D(t,T) equals the time T value of dividends paid on the component stocks between t and T; and

r(T-t) equals the risk-free interest rate spanning the period from t to T.7

Actual Nikkei 225 Futures transaction prices on the OSE are obtained from data tapes provided by the

Daiwa Institute of Research, Ltd. These transactions data record futures prices at which trades occurred to the

nearest minute. The spot Nikkei 225 Index quotes announced at one-minute intervals by the TSE are obtained

4 Short arbitrage means that the trader short sells component stocks of the index and buys futures contracts, while longarbitrage means the opposite.

5 For the estimation of transaction costs in recent periods, refer to Frino and West (2002).

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Our estimates of transaction costs for brokers are slightly lower, while estimates for institutional investors are substantiallyhigher, than those (1.03% and 2.59%) for the SGX Nikkei 225 Futures-based arbitrage estimated by Brenner, Subrahmanyam, and Uno(1989). For the U.S. markets, Neal (1990) estimates that transaction costs were about 0.31% for the actual S&P 500-based indexarbitrages in 1989 while Stoll and Whaley (1986) report that the costs were considerably higher (0.5% to 0.75%) in earlier years. Arecent study by Fung, Mok, and Lam (2000) reports that 0.055% for the U.S. S&P 500 Futures market and 0.125% for the Hang SengFutures market in Hong Kong without presenting detailed cost breakdwon. These estimations include only commission and market-impact costs.

7 As reported in Bailey (1989), volatility of Japanese interest rates is so low that there would be no significant differencebetween the cost-of-carry forward price such as equation (1) and the continuous-time futures price. Also, the dividend yield of theNSA is not smooth as the continuous-time model requires, but is rather lumpy due to the clustering of dividend payment dates by theunderlying 225 companies in March and September.

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from the same tapes.8 Since there is no Gensaki rate for a maturity that exactly matches the maturity of the

futures contract each trading day, one-, two-, and three-month Gensaki rates are obtained from the Pacific-Basin

Capital Market (PACAP) Databases and interpolated to compute the risk-free interest rates: The Gensaki (repo)

rates are commonly used in Japan during the study period as Treasury-bill rates are in the United States.

The individual stock dividend data (actual amounts and ex-dividend dates) are obtained also from the

PACAP Databases.9 The actual dividends subsequently realized over the life of the contract are used as a proxy

for the expected dividend to be paid on the Nikkei 225 Index. The deferred value of dividends, D(t,T) in

equation (1), is computed using the Gensaki rates. This is an approximation that may not equal the market's

anticipation of future dividends. Discrepancies caused by this approximation of dividends are likely to be small,

as dividends are fairly predictable and stable in Japan.

4. Ex Post Mispricings of Nikkei 225 Futures

4.1. Frequency and Persistence of Ex Post Violations of No-Arbitrage Boundaries by Nikkei 225 FuturesPrices

To investigate first the extent to which Nikkei 225 Futures are mispriced, the theoretical futures price is

computed using equation (1) and is compared to the actual market price on a trade-by-trade basis within a day.

For the ex post test, the hypothesis is:

xp= | F*(t,T) - S(t)er(T-t) + D(t,T) | - b(t) 0, (2)

where F*(t,T) is the actual futures price and b(t) is the present value of the sum of transaction costs for arbitrage.

Let F*(t,T) - S(t)er(T-t) + D(t,T) equal v. A simple trading strategy that would profit from a mispriced futures

contract that does not satisfy equation (2) consists of selling an Nikkei 225 Futures contract, buying the

underlying Nikkei 225 Index component stocks, and holding this position until T if v is positive and v - b(t) is

positive. If v is negative and |v| - b(t) is positive, then the strategy would be to sell short the underlying index

stocks and buy the futures contract. In either case, the net profit from the arbitrage would be a positive xp,

because the futures price would converge to the spot index value at T.10

8 The time stamp in the tapes represents the transaction time, not the reporting time.

9 We extract also from the Database the daily trading volume and the outstanding number of shares for each of the Nikkei 225Index component stocks. These data are used to measure the Nikkei 225 Index spot market liquidity and turnover, which are discussedin Section 5.

10 The "buy and hold to maturity" strategy is only one possible strategy and may not be optimal for arbitrageurs. See Brennanand Schwartz (1990) for details.

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In Panel A of Table 1, we report the frequency and average size of ex post violations of futures price

boundaries for the most heavily traded, nearest maturity Nikkei 225 Futures contracts. It appears that mispricings

are very frequent for brokers, who pay relatively lower transaction costs, with a few large surges to about 40 to

58 percent (March 1989, June 1990, and March 1991 contracts), though about 26 percent on average. In contrast,

ex post mispricing and subsequent index arbitrage opportunities are rare for institutional investors, whose

transaction costs are much higher. Among twelve contract maturities examined, a significant percentage of

mispricings (2.4%) occurs only for the June 1990 contracts.11

It is noteworthy that mispricings, though frequent, are in most cases small: The average size of

mispricings is 119.8 index points during our sample period, which represents the first three years of Nikkei 225

Futures contract trading on the OSE. It is about 0.41% deviation from the no-arbitrage cost-of-carry price with

transaction costs considered.12

[INSERT TABLE 1]

To examine the persistence of mispricings, we also compute the average number of subsequent violations

that follow each observed ex post violation. Persistent violations, especially if present on an intraday basis, can

be evidence of underestimated transaction costs, impediment to arbitrage, or noise. We find that mispricings are

clustered and persistent.13 The persistence has not significantly changed over the sample years. It implies that

the serious clustering or persistence of ex post violations was not due to pure "noise". Also, as suggested earlier,

it does not appear to be due to underestimated transaction costs either.

4.2. Relation between Mispricings and the Longevity of Nikkei 225 Futures Contracts

Mispricings documented in Table 1 can be due to hidden costs or impediments associated with arbitrage.

Arbitrageurs may face some costs that are not easily quantifiable, and presumably those costs are positively

related to the longevity of futures contracts, as discussed in MacKinlay and Ramaswamy (1988).

To investigate whether there exists an observable systematic relation between mispricings and the days to

11 Institutional trades account for about 30% of Nikkei 225 Futures trading volume. Our results, therefore, suggest that most ofthe institutional trades are non-arbitrage related (e.g., hedging).

12 As for the U.S. contracts, MacKinlay and Ramaswamy (1988) report an average deviation of 0.32% for the S&P 500contracts during the first four years of trading (1982-86), whereas Chung (1991) reports an average deviation of 0.17% for the MajorMarket Index (MMI) contracts during the first two years of trading (1984-86).

13 Detailed results are not reported to save space but can be obtained from the authors upon request. MacKinlay andRamaswamy (1988) report a similar persistence in the ex post mispricings for the S&P 500 contracts even when reasonable estimates oftransaction costs are incorporated.

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maturity of Nikkei 225 Futures contracts, we stratify the observed ex post mispricings by days to maturity of

futures contracts. Results indicate that the size and frequency of mispricings monotonically increase with longer-

lived contracts.14 For example, the average size of mispricings for days to maturity of 1-19 days is 29.2 index

points (or 0.11% from the no-arbitrage boundary with transaction costs), whereas it is 212.6 index points (or

0.72%) for the "80 days or longer" group. Further, more than 85% (181,749 out of 212,684) of all the

mispricings during our sample period occur for contracts that have at least 40 days prior to expiration.

Figure 1 depicts the time-series behavior of the daily average size of ex post mispricings for our sample

of 751 trading days. It shows that there are occasional but big surges in the estimated mispricings. Interestingly,

those days with large mispricings closely match the earlier trading days of the new contracts.

5. Explanations for Occasionally Large and Clustered Mispricings of Nikkei 225 Futures

Why are the estimated mispricings clustered and persistent with a few big surges, especially for longer-

lived contracts, even after the Nikkei 225 Futures market went through its infant stage? In this section, we

attempt to provide some answers for this question. In doing so, we discuss the Japanese stock market

microstructure in Tokyo and its potential impacts on index arbitrage. Our primary goal is to test whether it can

explain the puzzling big surges in estimated mispricing of the Nikkei 225 Futures contracts in Osaka.

5.1. Execution Lag: Ex Ante Tests

Ex post tests in the previous section assume instantaneous execution of stock-futures arbitrage trades, and

they may overstate the profits of index arbitrage, because traders are not guaranteed execution of their orders at

the observed prices. Ex ante tests allowing a reasonable execution lag should be used instead. Accordingly, our

hypothesis is now different:15

xa = F*(t+,T) - S(t+)er(T-t) + D(t,T) - b(t+) 0 if v is positive, or

= -[F*(t+,T) - S(t+)er(T-t) + D(t,T)] - b(t+) 0 if v is negative (3)

where F*(t+,T) is the first actual futures price following an execution lag after t, S(t +) represents the ex ante

index value at t+ following an execution lag, b(t+) is the time t+ present value of the sum of transaction costs

incurred in the arbitrage, and xa is, therefore, the ex ante arbitrage profit at t+, triggered by a mispricing signal

14 Detailed results are not reported but can be obtained from the authors.

15 For an earlier study that explains the reasons why ex ante tests are important and why they are what should be used formarket efficiency studies, see Dann, Mayers, and Raab (1977).

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(a positive xp) at t. It is assumed that traders can use 100 percent of short-sale proceeds and can borrow stocks

for short sale. Also, traders are assumed to be able to borrow or lend money at the riskless Gensaki rate.

The TSE, where the component shares of the index are traded, is a purely order-driven, computerized

auction market without any responsible market-maker or "specialist". Instead, "Saitori" members maintain a

central order book for each of their "franchise" stocks allocated by the exchange, and they match orders in

accordance with price priority and time preference. (See Lehmann and Modest (1994) for more details.) Thus,

there is no guarantee that orders will be executed in a reasonably short period of time, which means more risk for

arbitrageurs. Third, one important requirement for index arbitrage is quick execution of stock baskets. In the

New York Stock Exchange (NYSE), a 200-stock basket takes less than five minutes to execute through "Super-

Dot". This capability does not yet exist on the TSE.16

Five minutes is a conservative estimate by Japanese practitioners of the minimum time lag between the

observance of mispricing signals and the execution of orders simultaneously in the stock and the futures markets.

Since speedy execution capabilities do not yet exist on the TSE, even the five-minute lag may overestimate the

speed of execution on the TSE. Our ex ante tests are repeated for a range of alternative execution lags.

In Panel B of Table 1, we summarize ex ante violations by Nikkei 225 Futures prices, assuming that

traders can execute their orders at the first available futures and spot index prices at least five, ten, or fifteen

minutes after they observe ex post mispricings. Some notable points emerge. First, the numbers of executable

trades are significantly (6 to 14%) less than comparable frequencies of ex post violations in the same table,

obviously because some trades cannot be executed within the same day the violations occur, due to the execution

lag. Thus, ex post tests in the previous section significantly overestimate the frequency of intraday arbitrage

opportunities.

Second, there are substantial differences between the size of the ex post mispricing and the realized profit

on the resulting ex ante trade, especially for the more recent contracts (September 1990, December 1990, March

1991, and September 1991 contracts) with the exception of the June 1991 contracts. For example, the most

recent September 1991 contracts violate the ex post no-arbitrage boundary 26,024 times, with an average

mispricing of 23.6 index points. The corresponding ex ante arbitrage profits are on average 3.3 index points with

16 The TSE's CORES (Computer-assisted Order Routing and Execution System), implemented on January 23, 1982, isanalogous to the NYSE's DOT (Designated Order Turnaround) system, but is much slower. On March 18, 1991, the TSE put FORES(Floor Order Routing and Execution System) into operation for 150 of the most active stocks.

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a five minute lag, -7.8 index points with a ten minute lag, and -12.1 index points with a fifteen minute lag. This

implies that the Nikkei 225 Futures contract prices in Osaka have recently tended to respond to ex post

mispricings quickly enough to eliminate profit opportunities---again, with the exception of a few contract

maturities.

Nevertheless, our major question still remains unanswered. Ex ante tests, although they substantially

improve the picture of the Nikkei 225 Futures market efficiency, cannot solve the puzzling surges in estimated ex

post mispricings.

5.2. Difficulties in Short Sales of Index Stocks

Even though short sales (Kara-Uri) are permitted and there is no uptick rule in the TSE, short sales are

very difficult in practice, making short arbitrage more costly. 17 Share lending (Kashi-Kabu) is a huge business in

Japan.18 Big Japanese institutions, such as life insurance companies and trust banks, earn a fee of up to 1-1.5

percent, though 0.1% on the average, of the market value of the shares they lend to brokers. Furthermore, the

lender institution often demands back the shares it had already lent, so that brokers are forced to buy shares in the

market prematurely in order to cover their short positions.

To investigate whether difficulties related to short sale of stocks can be responsible for occasional big

surges in mispricing of futures contracts, we examine the average size and the frequency of observed ex post

mispricings, and the resulting ex ante arbitrage profits, separately for long and short arbitrages. We merely

mention the results in passing, as they are not strikingly different. First, the mean and the standard deviation of

ex ante profits from executable short arbitrages are about the same as those from comparable long arbitrages.

Furthermore, only 3.4 percent of all ex post violations (7,271 out of 212,684) are signals for short arbitrage for

brokers. In brief, difficulties in short sales of stocks do not seem to be a major reason for our puzzle.19,20

17 The up-tick rule was introduced as of March 15, 2002.

18 See The Economist, 18th April 1992, pages 82-85.

19 The shares lent from Japanese institutions are often called back at the end of the fiscal year for reporting purposes. The endof the fiscal year for Japanese corporations is typically March. One can, therefore, suspect that this may explain the occasional, yetsomewhat cyclical, ex post violations in Figure 1. Mispricings are, in fact, most frequent and the largest on average in the months ofMarch (58.7% and 186.6 index points) during our sample period. However, this seemingly seasonal effect is not consistent with thepredominantly overpriced futures in March nor can it explain the surges in other months (e.g., September (36.2% and 80.2 indexpoints)).

20 In contrast, Fung and Draper (1999) report that changes in short sale regulations affect mispricing of Hang Seng IndexFutures contracts.

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5.3. Nikkei 225 Index Component Stocks Spot Market Turnover/Liquidity in Tokyo

So far, it appears that the Nikkei 225 Futures prices on the OSE do not experience a rather smooth

learning curve. We, therefore, propose and test one explanation for this puzzle.

The Japanese stock market is in many respects much less liquid than its U.S. counterpart. Buying (short

selling) the Nikkei 225 Index component stocks, for example, means bidding for (borrowing) closely held shares,

a nearly impossible task at times. Furthermore, liquidity of some Nikkei 225 Index component shares varies

greatly over time. During our sample period of 751 trading days, 48 (15) Nikkei 225 Index component stocks

experienced at least one (four) zero-turnover trading day while 102 trading days experience zero-turnover for at

least one component share. Appendix B lists the forty-eight stocks that experience at least one zero-turnover day

along with their industry classifications.

For the U.S. market, Harris (1989a) documents the impact of the liquidity of index stocks on the basis

(i.e., the difference between the underlying index value and the futures price) for a ten-day period surrounding the

October 1987 stock market crash. One can argue that the time-varying liquidity of index stocks can be a

significant factor for the pricing of index futures even in the U.S. market. To address this issue, we examine the

Wall Street Journal, S&P Stock Guide, S&P 500 Information Bulletin, and Report of the Presidential Task Force

on Market Mechanisms (1988), for October 1987, the most likely month with liquidity problems. We also poll a

few exchange specialists. It appears that none of the S&P 500 stocks experienced non-trading on any trading day

in October 1987. Of course, for some stocks, trading was thin, opening was delayed due to order imbalances,

trading was at times suspended, and it may have taken unusually long before traders could buy or sell some of the

S&P 500 stocks, but it was not impossible. Thus, the magnitude of the time-varying liquidity problem in the

U.S. stock market, even during an exceptional period, is quite different from that in the Japanese market, where

the nonsynchronous trading problem is greatest due to (unpredictable) non-trading, not thin trading, of index

component stocks.

In order to provide distribution-free results on the relationship between the turnover/liquidity of

component shares of the Nikkei 225 Index and mispricings of the Nikkei 225 Futures, we report in Table 2

estimates of Spearman's rank correlation coefficients. Four alternative measures of the stock market

turnover/liquidity are used. The first one (TONUMBER) is the daily number of shares traded for all Nikkei 225

Index component stocks. The second one (TOPERCENT) is TONUMBER divided by the total number of daily

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outstanding shares for all 225 stocks. The third one (NZEROTO) represents the daily number of NSA stocks

whose turnover is zero. The last one (NLOWTO) represents the daily number of NSA stocks whose turnover is

lower than its own time-series average for the sample period.

[INSERT TABLE 2]

Results suggest that the Nikkei 225 Index spot market turnover/liquidity is significantly related to

boundary violations by Nikkei 225 Futures prices. There are significant negative correlations between the

measures of stock market turnover (TONUMBER or TOPERCENT) and the daily average size (VIOSIZE) and

the daily frequency (VIOFREQ) of boundary violations. The correlation is significantly positive when

NZEROTO or NLOWTO is used instead as a measure of spot market turnover/liquidity. This is an interesting

finding in the following sense: When one component share of the index is not traded at all on the TSE, the

arbitrage link between the stock and the futures markets does not exist and subsequent mispricings occur and

persist because traders cannot execute their arbitrage trade orders in the stock market. 21 This problem becomes

more serious as the number of non-traded (or thinly-traded) shares increases, as evidenced in Table 2. Still, the

TSE reports an index value that is seriously stale. Thus, frequent and clustered mispricings of the Nikkei 225

Futures in Osaka can be partially, but by no means wholly, blamed on the poor turnover/liquidity of some

component shares in Tokyo and the subsequent staleness of the reported index, not necessarily on market

inefficiency.22

Therefore, the estimated ex ante violations, perhaps including the large ones shown in Table 1,

may not necessarily represent "real" arbitrage opportunities.

5.4. Spot Market Turnover/Liquidity and Autocorrelation of Price Changes of the Nikkei 225 Index and theNikkei 225 Futures

The reported index quote, such as the one we use, is not a perfect measure of the true value of the cash

index because the component shares of a stock index are not traded continuously. This means that the reported

21 One can argue that substitutes may be found for the non-traded index component stocks in quasi-arbitrage. We poll Japanesebrokers in order to elicit the practitioners' point of view on this issue. The general consensus is that close substitutes are hard to find

because those non-traded index stocks are most likely closely-held shares whose idiosyncratic risks and liquidity are quite differentfrom those of potential substitutes (e.g., frequently traded stocks with similar betas). See Harris (1989b) for a method of identifyingpotential substitutes for the S&P 500 stocks.

22 Index futures trading in Japan has been controversial, and there has always been tension between the regulators and activearbitrageurs. The Japanese Ministry of Finance and the TSE have, at least implicitly, subscribed to the view that index arbitrage causesexcess volatility in the stock market. Accordingly, the regulations on the Nikkei 225 Futures trading have changed several times duringour sample period. See Miller (1993) and Futures, June 1992, pages 48-50 for details. We investigate whether those changes inregulations, often in the direction of increasing impediments, are also responsible for those occasional surges in estimated mispricingsof Nikkei 225 Futures. We look very hard for such evidence by stratifying our sample on the basis of different regulation regimes. Wemerely mention the results here in passing, as they are not very striking. In particular, we find no evidence that increased (cash andtotal) margin requirements or tighter price limits on the OSE can explain this phenomenon.

12


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index can lag behind the true value of the index. To investigate the degree to which the reported Nikkei 225

Index represents the stale cash value of the index, we first calculate the serial correlations of price-change series

during the entire sample period. If we find that futures price changes are not serially correlated but the index

changes are, then this can be evidence of the nonsynchronous trading problem and subsequent stale index

quotation.23

Panel A of Table 3 indicates that the futures price series for 5-minute intervals display some evidence of

statistically significant serial correlation up to the third lag. However, the futures price series for 15-minute

intervals display little evidence of significant serial correlation beyond the first lag: The first-order

autocorrelation (on the average, 0.052) is statistically significant but economically trivial, given the large sample

size.24 In contrast, the reported Nikkei 225 Index is significantly autocorrelated, though diminishing as we

lengthen the interval. The third and higher lags do not display any significant autocorrelation when the 15-

minute-interval data are used. However, the first-order autocorrelation (on the average, 0.244) of the index price

series is statistically and economically significant even with the 15-minute-interval data. Given the significant

autocorrelation for our minute-by-minute spot index data, our empirical results should be interpreted accordingly.

[INSERT TABLE 3]

We then investigate whether there exists a significant relation between the non-trading problem of the

index stocks and the staleness of the spot index quotes. In Panel B of Table 3, we compare the autocorrelations

of index and futures prices between days when all Nikkei 225 Index component stocks are traded (649 days) and

days when at least one stock is not traded at all (102 days). Results indicate that the index quote change series is

about two to three times more serially correlated during those 102 days than it is during the comparable 649 days,

whereas the futures price change series does not show any significant difference between the two groups.

Clearly, nonsynchronous trading of component stocks causes the index quote to be more autocorrelated, a

phenomenon discussed in detail in Harris (1989a). Also, the size and frequency of ex post violations are larger

on average when at least one stock is not traded at all, especially for longer-lived contracts that have at least 40

23 For the effects of infrequent trading of component stocks on autocorrelation in the U.S. index, see Harris (1989a), MacKinlayand Ramaswamy (1988), and Miller, Muthuswamy, and Whaley (1994).

24 We believe that observed positive autocorrelations are partially attributed to price limits imposed on the Nikkei 225Futures trading. Refer to Berkman and Steenbeek (1998) and Martens and Steenbeek (2001).

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days prior to expiration.25

We have similar inferences from results in Panel C of Table 3. We first stratify trading days into deciles

according to their daily average size of ex post violations. We then calculate the autocorrelations of price-

change series for the top 10% (76 days) of the sample days, and compare them with the autocorrelations for the

342 days for which no violation occurs. The spot index price-change series is again about two to three times

more autocorrelated for those 76 days than it is for the 342 no-violation days. Further, those 76 days represent

days for which most (96.8%) of the actual futures prices deviate a lot (268.3 index points) from the no-arbitrage

boundary and persist throughout the day. In fact, 75 out of those 76 days experience mispricings only for longer-

lived contracts.26 Note that autocorrelations of the futures price-change series show some difference between the

two groups, though the difference is much less pronounced than that for autocorrelations of the spot index price-

change series. In sum, we reaffirm that the estimated ex ante violations, especially the large ones shown in Table

1, do not necessarily represent real arbitrage profits.

6. Summary and Conclusions

The purpose of this paper is to understand the unique Japanese market microstructure and demonstrate its

impact on pricing index futures during the initial three years after the launching of the Nikkei 225 Futures in

Osaka. We examine the minute-by-minute Nikkei 225 Index quotes of the TSE and the corresponding index

futures transactions data of the OSE.

We first find that the Nikkei 225 Futures contract prices on the OSE have tended to deviate frequently,

on average 0.41%, from theoretical no-arbitrage prices with transaction costs. Also, observed ex post mispricings

are clustered and persistent. Finally, the size and the frequency of ex post mispricings increase with longer-lived

contracts. These findings are broadly similar to what has been observed by other authors in studies of the U.S.

markets.

25 Differences in size and frequency are not very big. Recall, however, that the size and frequency of ex post violations arepositively related to the number of non-traded component shares of the index. One may also suspect that it is more likely that thintrading in all or some stocks in general may be the cause of higher positive serial correlations of the index. This point of view isaddressed by stratifying the 751 sample trading days into deciles, based on the trading depth variables in Table 2 (TONUMBER,TOPERCENT, and NLOWTO). We do not, however, find any significant differences in serial correlations of the index among days ofvarious trading depth. Thus, non-trading of one or more stocks on a given day is a much more serious constraint to arbitrageurs thanthin-trading of all or some stocks.

26 A tracking portfolio containing a smaller basket of liquid Nikkei 225 Index stocks must allow for a greater margin oftracking errors and more costly portfolio adjustments prior to expiration of longer-lived contracts. Consequently, larger deviations maybe required to induce arbitrageurs to take a position in longer-term contracts. This can be an important reason for larger estimatedmispricings of longer-lived contracts, as some component stocks of the Nikkei 225 Index are occasionally not traded. At the sametime, however, tracking is imperfect and index arbitrage is not risk-free.

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One question that remains unanswered is why there were occasional but big surges in estimated ex ante

arbitrage profits as well as ex post mispricings even after the Japanese index futures market went through its

infant stage. We find that the question cannot be satisfactorily answered by those conventional market

microstructure factors such as delays in execution, underestimated transaction costs, or difficulties in short sales

of index stocks. We, therefore, propose and test one potential explanation for this puzzle: the time-varying

liquidity of some Nikkei 225 Index component shares on the TSE, especially for those closely-held shares.

We provide evidence that the puzzling surges in the estimated mispricings of the Nikkei 225 Futures in

Osaka can be partially, but by no means entirely, blamed on the poor turnover/liquidity of some component

shares in Tokyo and the subsequent staleness of the reported index. Accordingly, the estimated ex ante

violations, especially the large ones observed occasionally for long-lived contracts, do not necessarily represent

real arbitrage profits. If the time-varying liquidity and occasional non-trading of component stocks of the Nikkei

225 Index are ignored, spurious conclusions about market efficiency and the relation between the futures and

cash markets can be obtained and arbitrage opportunities in Japan can be falsely identified.

Nevertheless, one should be cautious in interpreting our results. Trading restrictions and execution risks

in the Japanese stock and index futures markets may be more severe than what we can quantify in this paper.

Future researchers, with the use of intraday transactions data for 225 component stocks, would also find it useful

to address further issues of thinly-traded Nikkei 225 Index component stocks, such as (1) can a smaller basket of

liquid stocks do a good job of tracking the index? (2) can arbitrage profits be identified using a liquid subgroup

of stocks? and (3) what would the arbitrage opportunities look like in Japan if the effect of the non- (or thin-)

trading problem is eliminated using the method discussed in Harris (1989)?

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Acknowledgements

We are grateful for the comments and suggestions received on earlier drafts from Obiyathulla Bacha,

Warren Bailey, Kalok Chan, Mark Grinblatt, Herb Johnson, Andrew Lo, Craig MacKinlay, David Mayers,

Merton Miller, Myron Slovin, Richard Smith, Patrick Traichal, Anne F. Vila, and the participants in finance

seminars at Arizona State, Boston University, City University of Hong Kong, Hitotsubashi, Korea Securities

Research Institute, and Rhode Island. Special thanks are due to the Daiwa Institute of Research, Ltd., especially

Toru Fukuda, for supplying the data, and Minoru Nakamura, Hisao Tanaka, and Takao Tsutsumi of the Osaka

Securities Exchange and Benjamin Foo, Susie Liau, and Dennis Seet of the Singapore Exchange (formerly the

Singapore International Monetary Exchange) for answering many questions.

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Appendix A: Estimation of Transaction Costs for Typical Index Arbitrage in Japan

These estimates are in terms of percentages of the underlying index value, and for our sample period ofSeptember 9, 1988 to September 12, 1991. Some of the costs were changed afterward. Long arbitrage meansthat the trader buys component stocks of the index and sells futures contracts while short arbitrage means theopposite.___________________________________________________________________________________________

Institutional Investors Brokers------------------------------------------------------------------------------------------------------------------------------------------------(1) Stock Brokerage Commissions (Round-Trip) 1.700% 0.010%(2) Security Transfer Tax 0.550%/0.300% 0.180%/0.120%(3) Market-Impact (Two for Stocks) 0.600% 0.600%(4) Futures Brokerage Commissions (One-Way) 0.056% 0.001%(5) Market-impact (One for Futures) 0.050% 0.050%(6) Cost of Borrowing Stocks for Short Sales 0.100% 0.100%(7) Futures Margin in Cash (% of Contract Value) 3%/5%/7%/8% 0%/0%/2%/5%------------------------------------------------------------------------------------------------------------------------------------------------Total Long Arbitrage 2.956%/ 2.706% + IM 0.841%/ 0.781% + IM

Short Arbitrage 3.056%/ 2.806% + IM 0.941%/ 0.881% + IM___________________________________________________________________________________________

a. Brokers pay only the round-trip usage fees (0.0048% to the TSE and 0.0041% to Saitori members).b. The tax law changed on April 1, 1989.c. There are two stock market-impact costs instead of one, as in the U.S. stock market, and they represent the effective bid-ask

spreads for a given transaction size. Since the market-on-close or market-on-open order is not guaranteed an execution in theabsence of a responsible market maker, it is realistic to assume that sizable transactions cannot be undertaken in the stockmarket without changing the previous market price when arbitrageurs wind up their spot position. Note that there are no costsin closing stock positions on the NYSE on expiration days of futures since a market-on-close order eliminates the marketimpact cost.

d. Brokers pay a usage fee for opening the position through the final settlement of contracts.e. In the U.S., brokers can lend stocks in street name, but in Japan institutions normally charge a fee of 0.1% of the value of

shares lent for "lending" the stocks. Note that this estimate is very conservative, though somewhat typical, and mayunderestimate the true costs associated with borrowing stocks for short sale since those institutions occasionally demand up to1-1.5%.

f. It is mostly one tick.g. This is a unique feature of Nikkei 225 Futures contracts in Osaka. Margin cannot be withdrawn until the position is closed,

and a fixed percentage of the contract value should be put up in non-interest-bearing cash, forcing a positive net investmentfor index "arbitrage". Numbers indicate the percentage of the contract value that must be put in cash on or after880903/900824/910103/910627; IM = interest lost on cash margin. This is different from the other global contracts, wherethe initial margin can be put up in interest-bearing securities and the variation margin can be withdrawn depending on thedirection of the market in relation to the position of the trader.

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Appendix B: Summary of NSA Index Stocks That Experience At Least One Non-TradingDay during the Period of September 9, 1988 to September 12, 1991 (751 Trading days)

__________________________________________________________________________________________Firm Name Industry Number of Nontrading days

------------------------------------------------------------------------------------------------------------------------------------------------

1 SUMITOMO COAL MINING Mining 12 NISSHIN FLOUR MILLING Foods 1

3 TAITO Foods 114 TAKARA SHUZO Foods 15 GODO SHUSEI Foods 76 HONEN CORPORATION Foods 47 KIKKOMAN CORP. Foods 38 KATAKURA INDUSTRIES Textiles 189 NISSHINBO INDUSTRIES Textiles 1

10 JAPAN WOOL TEXTILE Textiles 211 DAITO WOOLEN Textiles 1212 TEIKOKU SEN-I Textiles 2013 TOHO RAYON Textiles 414 MITSUBISHI PAPER MILLS Pulp & paper 115 HOKUETSU PAPER MILLS Pulp & paper 116 RASA INDUSTRIES Chemical 417 NIPPON CARBIDE Chemical 2

18 ASAHI DENKA KOGYO K.K. Chemical 219 NOF CORP. Chemical 120 DAINIPPON PHARM. Chemical 121 NIPPON OIL Petroleum 122 SHOWA SHELL SEKIYU K.K. Petroleum 123 MITSUBISHI OIL Petroleum 124 NIPPON CARBON Glass & ceramics 125 NORITAKE Glass & ceramics 126 SHINAGAWA REFRACTORIES Glass & ceramics 227 NIPPON STAINLESS STEEL Iron & steel 428 NIPPON METAL INDUSTRY Iron & steel 129 TOHO ZINC Nonferrous metal 330 SHIMURA KAKO Nonferrous metal 331 TOKYO ROPE MFG. Metal Product 132 OKUMA CORPORATION Machinery 1

33 NIPPON PISTON RING Transportation equipment 534 YUASA CORP. Electric machinery 335 HINO MOTORS Electric machinery 136 SUZUKI MOTOR Electric machinery 137 TAKASHIMAYA Retail 138 MATSUZAKAYA Retail 2339 SAKURA BANK Bank 140 JAPAN SECS FINANCE Securities 141 NAVIX LINE LTD Shipping 642 JAPAN AIRLINES CO. LTD. Air Transportation 543 MITSUBISHI WAREHOUSE Warehousing & Wharfing 144 MITSUI-SOKO CO. LTD. Warehousing & Wharfing 245 SHOCHIKU Services 546 TOHO Services 1147 TOEI CO. LTD. Services 2

48 TOKYO DOME CORPORATION Services 1____________________________________________________________________________

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Table 1Frequency and Size of Ex Post and Ex Ante Violations of Futures Price Boundaries of

Nikkei 225 Futures Contractsa

Hypothesis for ex post violations: xp = |F*(t,T) - S(t)er(T-t) + D(t,T)| - b(t) 0 where F*(t,T) is the actual futures price at time t for a

contract that matures at time T; S(t) is the ex post index value at t; b(t) is the present value of the sum of transaction costs at t; D(t,T) isthe time T value of dividends paid on component stocks between t and T; and r(T-t) is the risk-free interest rate spanning the period fromt to T. Ex post violations mean that traders can make positive profits assuming that they can execute orders at the observed index quote

and futures price, both adjusted for bid-ask spreads. Hypothesis for ex ante violations: xa = F*(t+,T) - S(t+)er(T-t) + D(t,T) - b(t+) 0 if

futures contracts are overpriced at t, or -[F*(t+,T) - S(t+)er(T-t) + D(t,T)] -b(t+) 0 otherwise, where F*(t+,T) is the actual futures price at

time t+ for a contract that matures at time T; S(t+) is the ex ante index value at t+; and b(t+) is the time t+ present value of the sum of

transaction costs. Ex ante violations represent the ex ante arbitrage profits at t+ (xa) triggered by mispricing signals (xp) assuming

that traders can execute their orders at the next index quote and the next available futures price following an execution lag after theyobserve mispricing signals. Sample period is September 9, 1988 to September 12, 1991.______________________________________________________________________________________________________________

Panel A: Ex Post Violations | Panel B: Ex Ante Violations

_________________________________________________|____________________________________________________________

| 5-min execution lag 10-min execution lag 15-min execution

| ------------------- -------------------- -----------------

Num. Frequencyb Sizec | Number Size of Number Size of Number Size of

of Trader of Ex Post of Ex Post | of Arbitrage of Arbitrage of Arbitrage

Contract Obs. Typea Violations Violations | Tradesd Profits Trades Profits Trades Profits

---------------- --------------------------------|-----------------------------------------------------------

Mar 89 26143 Broker 13900(53.2%) 87.0(0.3%)| 12982 84.8( 0.3%) 12354 83.3( 0.3%) 11666 83.8( 0.

|

Jun 89 31669 Broker 7686(24.3%) 358.1(1.1%)| 7292 356.4( 1.1%) 6913 356.7( 1.1%) 6580 356.1( 1.

|

Sep 89 40270 Broker 801( 2.0%) 19.6(0.1%)| 718 -12.5(-0.0%) 660 -30.9(-0.1%) 592 -35.3(-0.

|

Dec 89 38391 Broker 6320(16.5%) 248.4(0.7%)| 5907 245.0( 0.7%) 5623 245.9( 0.7%) 5312 245.8( 0.

|

Mar 90 64737 Broker 10226(15.8%) 66.2(0.2%)| 9597 49.3( 0.1%) 9187 43.4( 0.1%) 8736 42.8( 0.

|

Jun 90 87771 Broker 50601(57.7%) 194.0(0.6%)| 48193 187.6( 0.6%) 46224 184.1( 0.6%) 44030 181.1( 0.

I. Inv. 2118( 2.4%) 76.1(0.2%)| 1994 62.9( 0.2%) 1902 51.6( 0.2%) 1776 44.1( 0.

|

Sep 90 92779 Broker 18210(19.6%) 34.2(0.1%)| 17014 12.9( 0.0%) 16042 -0.8( 0.0%) 14977 -6.0(-0.

|

Dec 90 51338 Broker 9320(18.2%) 96.3(0.4%)| 8404 71.3( 0.3%) 7875 60.0( 0.3%) 7633 55.8( 0.

I. Inv. 39( 0.1%) 62.7(0.3%)| 23 90.0( 0.4%) 21 -0.3(-0.0%) 21 -31.1(-0.|

Mar 91 81401 Broker 32494(39.9%) 36.9(0.2%)| 30806 24.0( 0.1%) 29389 18.0( 0.1%) 28174 17.6( 0.

|

Jun 91 26071 Broker 33724(26.8%) 175.0(0.6%)| 32042 167.4( 0.6%) 30441 165.7( 0.6%) 28646 165.7( 0.

I. Inv. 8( 0.0%) 5.1(0.0%)| 8 -101.0(-0.4%) 8 -128.2(-0.5%) 8 -95.0(-0.

|

Sep 91 39233 Broker 26024(18.7%) 23.6(0.1%)| 24814 3.3( 0.0%) 2373 -7.8(-0.0%) 22924 -12.1(-0.

|

Overall 811991 Broker 212684(26.2%) 119.8(0.4%)|200801 108.1( 0.4%) 19134 103.4( 0.3%) 182005 101.2( 0.3

I. Inv. 2165( 0.3%) 75.6(0.2%)| 2025 62.5( 0.2%) 1931 50.3( 0.2%) 1805 42.6( 0.

_________________________________________________|____________________________________________________________

a For our estimates of transaction costs, see Appendix A. We report results for institutional investors (I. Inv.) onlyfor contracts for which ex post mispricings are observed.

b The percentage out of total number of observations is reported in parentheses.

c In terms of index points: a full index point is equivalent to 1,000 per contract. The percentage deviation from the no-arbcost-of-carry price (with transaction costs considered) is reported in parentheses.

d The number of executable trades are significantly less than comparable frequencies of ex post violations because sometrades cannot be executed within the same day the violations occur, due to the execution lag.

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Table 2Spot Market Turnover/Liquidity on the Tokyo Stock Exchange and

Size and Frequency of Ex Post Boundary Violations of Nikkei 225 Futures Contracts

Four measures of the spot market turnover/liquidity are used. TONUMBER is the daily number of shares traded for all 225 componentstocks of the NSA; TOPERCENT is TONUMBER divided by the total number of daily outstanding shares for the 225 stocks;NZEROTO represents the daily number of NSA stocks whose turnover is zero; and NLOWTO represents the daily number of NSAstocks whose turnover is lower than its own time series average for the sample period. VIOFREQ and VIOSIZE represent the dailyfrequency and the daily average size of boundary violations by NSA index futures prices, respectively. Sample period is fromSeptember 9, 1988 to September 12, 1991.

________________________________________________________________________________________________________

Panel A: Distributions of Daily NSA Spot Market Turnover/Liquidity and Ex Post Boundary Violations by NSA Future________________________________________________________________________________________________________

Variable Obs Mean Median Std Dev Min Max

-----------------------------------------------------------------------------------------------------------------------------------------------------------

TONUMBER 751 389940000 307970000 278720000 87433288 2051916302TOPERCENT 751 0.00242 0.001866 0.001745 0.000514 0.013328

NZEROTOa 102 1.84 1 1.79 1 8NLOWTO 751 170.06 179 37.42 28 222

VIOSIZEb 751 39.33 6.33 88.94 0 675.54

VIOFREQc 751 23.15 1.48 34.97 0 100

________________________________________________________________________________________________________

Panel B: Nonparametric Correlations between NSA Spot Market Turnover/Liquidity and Ex Post Boundary Violations

NSA Futures Pricesd

________________________________________________________________________________________________________

TONUMBER TOPERCENT NZEROTOe NLOWTO

-----------------------------------------------------------------------------------------------------------------------------------------------------------

VIOSIZE -0.167 -0.175 0.204 0.112

(0.0001) (0.0001) (0.0397) (0.0021)

VIOFREQ -0.188 -0.195 0.201 0.131(0.0001) (0.0001) (0.0424) (0.0030)

________________________________________________________________________________________________________

a Forth-eight (fifteen) stocks experience at least one (four) zero-turnover trading day.

b In terms of index points: a full index point is equivalent to 1,000 per contract.

c The percentage out of daily number of observations.

d The reported test statistic is the Spearman's rank correlation with p-values in parentheses.

e

Correlation between NZEROTO and VIOSIZE (or VIOFREQ) is calculated using only those 102 trading days forwhich at least one index component share is not traded at all.

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Table 3

Autocorrelations of Changes in the Nikkei 225 Index and Its Futures Prices and

Ex Post Boundary Violations by NSA Futures Pricesa

________________________________________________________________________________________________________

Panel A: Autocorrelation coefficients for the entire sample period (751 trading days)b

________________________________________________________________________________________________________

5-Minute Interval Data 10-Minute Interval Data 15-Minute Interval Data

-----------------------------------------------------------------------------------------------------------------------------------------------------------

Nikkei Nikkei Nikkei Nikkei Nikkei NikkeiLag Futures Obs Index Obs Futures Obs Index Obs Futures ObsIndex Obs

-----------------------------------------------------------------------------------------------------------------------------------------------------------

1 0.046* 31649 0.323* 33260 0.056* 14441 0.271* 15140 0.052* 8697 0.244* 91022 0.021* 30179 0.171* 31772 0.005 12971 0.116* 13652 0.017 7231 0.058* 76163 0.018* 28709 0.112* 30284 0.031* 11504 0.044* 12165 0.007 5768 -0.010 61304 0.002 27239 0.070* 28796 0.023 10038 0.004 10678 0.032 4319 0.017 4644________________________________________________________________________________________________________

Panel B: Comparison of 649 sample trading days for which all 225 NSA component stocks are traded and 102 sample

trading days for which at least one index component stock is not traded at allc

________________________________________________________________________________________________________

Autocorrelations of 5-minute Price Change Series Daily Average Violat

-----------------------------------------------------------------------------------------------------------------------------------------------------------

Nikkei Index Nikkei Futures All Contracts L/T Con

1st 2nd 3rd 1st 2nd 3rd Sized Freq(%)e Size Forder order order order order order

-----------------------------------------------------------------------------------------------------------------------------------------------------------

649 Days 0.273 0.126 0.075 0.049 0.025 0.019 38.7 22.8 63.6 (all stocks traded) (28904)(27614)(26324) (27903)(26620) (25337) (88.9) (34.6)

102 Days 0.529 0.355 0.262 0.035 0.003 0.013 43.2 25.5 (not all stocks traded) (4357) (4159) (3961) (3746) (3559) (3372) (89.2) (37.2) (113.5) ________________________________________________________________________________________________________

Panel C: Comparison of 342 sample trading days for which no boundary violation occurs at all and 76 sample tradingdays whose daily average sizes of violations are among top 10% of the sample days

________________________________________________________________________________________________________

Autocorrelations of 5-minute Price Change Series Daily Average Violat

-----------------------------------------------------------------------------------------------------------------------------------------------------------

NSA Index NSA Futures All Contracts L/T Contr1st 2nd 3rd 1st 2nd 3rd Size Freq(%) Size Freorder order order order order order

-----------------------------------------------------------------------------------------------------------------------------------------------------------

342 Days 0.272 0.148 0.110 0.039 0.013 0.016 0 0 0 (no violation at all) (15015)(14336)(13657) (14374)(13708)(13042)

76 Days 0.521 0.356 0.260 0.086 0.062 0.036 268.3 96.8 2(top 10% violations) (3300) (3150) (3000) (3050) (2904) (2758) (127.5) (10.6) (126.6) (4________________________________________________________________________________________________________

a Futures price change is represented by the rate of change in futures price at t from t-1 ({(F*(t,T) - F*(t-1,T)} /F*(t-,T)); index price change is measured by the rate of return for the index at t from t-1 ({S(t) - S(t-1)} / S(t-1)).

b Reported coefficients are the averages computed from 751 trading days in the sample. Coefficients with * aresignificant at 1%.

c The number of observations is in parenthesis.

d In terms of index points: a full index point is equivalent to 1,000 per contract. Standard deviation is in parenthesis.

e The percentage out of daily number of observations. Standard deviation is in parenthesis.

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f L/T contracts represents contracts that have at least 40 days prior to expiration.

Date post:	08-Apr-2018
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Index-Futures Arbitrage in Japan

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