The ex ante profitability of index arbitrage in the new Finnish markets

Stand. J. Mgmr, Vol. 9, Suppl., pp. S117-S127,1993 Printed in Great Britain

09X-55221/93 $6.00 + 0.00 0 1993 Pergamon Press Ltd

THE EXANTE PROFITABILITY OF INDEX ARBITRAGE IN THE NEW FINNISH MARKETS

VESA PUTTONEN

Helsinki School of Economics and Business Administration

Abstract - This paper examines the efficiency of the relatively new Finnish futures market. Firstly, the relevant aspects of prior studies are incorporated into the futures pricing model. Large and persistent violations of the arbitrage conditions are reported in the empirical tests. The results from 62.x ante tests suggest that restrictions on trading, particularly related to selling stocks, are an important factor affecting the arbitrage process in the Finnish markets.

Key words: Finance, index futures, arbitrage.

INTRODUCTION

Recent empirical evidence from the Finnish markets suggests that arbitrage relations do not necessarily hold between the index and derivative instruments such as options and futures. For instance, Puttonen and Mart&amen ( 199 1) examined the Finnish stock index futures pricing for the period from May 1988 to December 1990. The futures contract traded at a substantial discount especially in the autumn. Furthermore, the violations of the arbitrage conditions increased rather than decreased with time. The reported arbitrage opportunities appear too large to be accounted for solely by tangible transaction costs. Systematic market inefficiencies cause an excess risk for hedgers who must close their positions before contract expiration. Thus, violations from basic arbitrage conditions reduce the usefulness of the new contracts as hedges against systematic risk within the stock market.

Until very recently, the tests of stock index futures market efficiency have been carried out on an expost basis. It has been assumed that an arbitrageur can establish the arbitrage position at the prices observed when the strategy is initially identified as profitable. In recent studies on the U.S. markets, ex ante tests have also been carried out (Klemkosky and Lee, 1991; Chung, 1991). The present study contributes to the existing literature on two levels. First, the ex ante profitability of index arbitrage is examined in the relatively new Finnish futures markets. The results are set into perspective by incorporating the relevant aspects of prior studies into the arbitrage model. In the ex ante tests an execution delay of one and two days is allowed in both the futures and cash markets. Secondly, attention is paid to the statistical significance of ex ante arbitrage violations. Both parametric and nonparametric tests are employed for this purpose.

The rest of this paper is organized as follows. The basic principles of stock index futures pricing are outlined in the presence of transaction costs and delayed execution in Section 2. prior empirical evidence is briefly discussed in Section 2.1. The data set and the relevant transaction costs in the Finnish markets are described in Section 3. The empirical results are presented in Section 4. The summary and conclusions are presented in the final section.

s117

S118 V. PU’ITONEN

2. THEORETICAL FRAMEWORK

The model connecting the price of a futures contract to the price of the underlying asset was first published by Cornell and French (1983):

F f,T = 6 - Q.d+365, (1)

where F1,T = the price of the futures contract at date I with maturity T; s, = the spot index value at current date t;

D~.T = the present value of known dividends paid between t and T; z = time to maturity in days, i.e. (r-r); and r = one plus the risk-free rate of interest over a given period.

As far as the interest rate effect exceeds the dividend yield effect, the fair price of a futures contract exceeds the index value, i.e. the basis is positive. In this case the futures contract is said to sell at a premium relative to the spot index. Conversely, if the interest rate effect is less than the dividend yield effect, the futures trades at a discount.

When transaction costs are incorporated into the basic pricing model, the arbitrage is profitable if the present value of the total cash flow at the expiration exceeds the total initial costs. If the futures contract is overpriced relative to its theoretical value F1,T”, an arbitrageur should short the futures contract with a transaction cost of TC,, where K,, is the transaction cost for a short position in the futures contract. Simultaneously, he should buy a basket of stocks with the transaction cost of TC,,, where Z’C,, is the transaction cost for the long position in a stock index. If the futures contract sells at t discount, an arbitrageur can form a profitable hedge by buying the futures, selling short the index and then borrowing the money needed. He then incurs the transaction costs Z’C,, and TC,,. The non-arbitrage pricing band for the futures contract becomes

Ftp - TG, - TG, < F,,T < Fr,p + Tc,, + TGs (2)

where the right-hand side inequality sets the short hedge boundary price and the left-hand side inequality sets the long hedge boundary price.

Generally, an implementable trading rule generating profits should be specified to demon- strate market inefficiency. Galai (1983) argues that many of the tests of option market efficiency do not specify a trading strategy which a trader could have duplicated. To set up a trading strategy after observing signals, the arbitrageur must frequently place simultaneous orders in at least two different markets. A price change in any of these markets can eliminate the arbitrage opportunity. Thus, ex ante tests should be carried out when testing market efficiency.

To understand the idea behind the ex ante tests in the futures markets, let us observe the fol- lowing example. The traditional tests assume that, upon observing a violation at time t, the arbitrageur can establish an arbitrage position at the prices prevailing when the hedge is initially identified as profitable. Suppose that the futures contract trades under its theoretical value implied by the cost-of-carry model, i.e. F,,T < (S, - D,,,)r 7B65. The arbitrageur can guarantee a profit by buying the futures contract, selling the index and then lending (buying bills) F,,yd365 + D,,. The position will be held until the expiration T. Then, the stocks are purchased back and the loan will have grown to F,,T + D,,f12”65. The cash flows are presented in Table 1.

The underlying assumption of the strategy is that it produces the positive amount of S, - (Fl,y-Ta65 + DtT) now and the cash flow of zero at the expiration in any circumstances. Normally, however, the’investors are not able to trade at the prices observed at the time of violation (0. Therefore, the violation will be a signal and the investor enters the market at t + 1 by construct-

Table 1. The cash flow characteristics of an ex post long hedge

Strategy Cash flow at t Cash flow at expiration T

Buy the futures contract - S* - FLT

Short the FOX index + S, - S* - D,,Ta

Lend - (F,,P” + 43 F,.T + 4.P”

Total S, - (F,,ffi5 + 4.r) 0

S* = index value at expiration; F,,, = price of the futures contract at date t with maturity T, S, = spot index value on the current date t; D,,T = present value of known dividends paid between t and T; T = time to maturity in days, i.e. (T- t); r = one plus the risk-free rate of interest over a given period.

ing a portfolio of a long position in the futures and a short position in the index and treasure bills. Since there is no guarantee that the prices used in the strategy are equal to the prices which led to the signal [i.e. F,,T < (S, - D,,&ti65], there is no guarantee for non-negative returns. The arbitrage becomes even more unpredictable when all the relevant transaction costs are included.

2.1. Prior empirical evidence Early studies in this area have generally suggested that futures contracts have traded at a dis-

count relative to their theoretical price (Figlewski, 1984; Cornell and French, 1983, on the U.S. markets; Bailey 1989; Brenner et al. 1989, on the Japanese markets; Yadav and Pope 1990 on the U.K. markets; Rindell 1989; Bane and Westman, 1992, on the Swedish markets). Recently, Bhatt and Cakici (1990), Chung (1991) and Klemkosky and Lee (1991) have found the mispricing of S&P 500 contract to be generally small but positive. Brenner et al. (1990) have also reported that arbitrage opportunities in Japan have declined substantially as the markets have matured and the rules on arbitrage trading have been eased by reducing the securities transfer tax and relaxing the short selling constraints on arbitrage activity. Similar results were reported by Yadav and Pope (1990), who examined the UK FTSE-100 stock index futures pricing before and after the Big Bang in 1987.

Yadav and Pope (1990) were among the first who carried out ex ante tests when examining the efficiency of futures markets. They assumed, however, that a trade is executed only if the mispricing has not moved within the transaction cost bound in the intervening period. This overlooks the possibility that this may be difficult and that there is no guarantee of receiving only non-negative returns. Recently, Klemkosky and Lee (1991) examined ex ante profitability of S&P 500 futures markets by forming the long or short arbitrage hedge after the hedge initially signalled an expost arbitrage profit. To test the null hypothesis, that arbitrage profits are zero, the excess rate of such a hedge was regressed on the excess rate of market return. The idea was that if the arbitrage portfolio is hedged against general market movements, the slope coefficient of the regres- sion line, which represents the sensitivity of hedge returns to market returns, should not be significantly different from zero. The statistically significant vertical intercept has been interpreted as a signal of significant arbitrage profits leading to rejection of the null hypothesis. The results of standard OLS regressions must, however, be interpreted with caution when analysing the statistical significance of arbitrage profits.*

*The controversial finding that arbitrage profits and excess returns from long hedges are higher for institutional investors than for member fvms may result from the methodology used. The methodology neglected the observations when no arbitrage profits are present. Only mispriced observations were included.

s120 V. PUTTONEN

More recently, Chung (1991) investigated the profitability of index arbitrage for the CBOT Major Market Index contracts by conducting ex ante tests with minute-by-minute data. The results suggest that previous studies significantly overestimate the size and frequency of profitable arbitrage. Interestingly, the size of arbitrage profits from executable short sales was much smaller and more volatile than that from long arbitrage. In fact, the average size of arbitrage profits from short hedges was significantly negative for every lag (20 s - 5 min) assumed. It thus becomes interesting to study the ex ante profitability of short arbitrage hedges in the Finnish markets, where a substantial part of the violations has occurred at the lower arbitrage limit.

3. THEDATA

3.1. FOX index and-future series

FOX is a market value weighted index of 25 major stocks quoted on the Helsinki Stock Exchange (HeSE). The base figure of the FOX index was at 500.00 on 7 March 1988. One index point equals 100 Finnish marks. FOX index futures expire six times a year in February, April, June, August, October and December. Since the expiration period of each futures contract is four months, there is always a supply of instruments with a remaining time to expiration of at least two months. The settlement of the contract is in cash. Daily closing prices at 15.30 are used in this study. The main data set is based on the nearby contract, because it has been more liquid than the next nearest futures contract.

The stock series selected to form the FOX index is the top 25 shares on the HeSE in terms of median daily trading during the previous half of the calendar year. The composition of the index is revised semi-annually. A new structure comes into force at the beginning of February and August (Hemesniemi, 1991). The index is updated as a stock transaction occurs. This may naturally result in a stale index because of discontinuous trading with stocks (Cohen et al., 1986). The effect of this should, however, be minimal as the index consists of only 25 stocks. If infrequent trading causes problems, it is expected to be most apparent in autumn 1990. Figure 1 shows the monthly average percentage of observations when no trading occurs in the index stocks. *

The most illiquid month was February 1990, when more than 35% of the stocks were not traded. This is due to the bank employees union striking at that time. In the 198Os, less than 5% of the index stocks were on the average not traded on a daily basis. During the 199Os, the trading frequency became lessened, approximately 5-15% of the index stocks (14 stocks of total 25) were not traded every day.

3.2. Interest rates and dividends Daily quotations of the Helibor rate (Helsinki Interbank Offered Rate) are used to measure the

risk-free interest rate. Since there is no interest rate for the maturity which matches exactly the futures contracts for each trading day, we use the rate which is closest corresponding to the maturity. Although this approach is not theoretically correct, the errors induced by this approximation are assumed to be minimal.

The fair futures price is obtained by subtracting the present value of future dividends from

*The percentage is calculated by dividing the number of observations when no trades occur by the total number of monthly observations (25 X number of trading days) and multiplying by 100.

EXAhTE PROPTL4RtLITY OF INDEX ARBITRAGE s121

40

35

30

25

% 20

15

10

5

0

J/89FM AM JJ AS ON DJ/90F MA MJ JA SO ND

Month Fig. 1. Monthly average percentage of observations when no trading occurs in the index stocks. The FOX index consists

of the 25 most liquid stocks traded on the Helsinki Stock Exchange.

the current index value and considering the carrying costs. For this purpose, dividends and ex- dividend dates were collected from the annual reports of the firms having stock series included in the FOX basket.

The dividend stream on well-diversified indices can well be expected to be continuous through the year in the U.S. markets. This is not the case in Finland. Finnish companies generally pay dividends once a year, usually in March or April. Generally, no dividends are expected during the rest of the year. This may have been a factor contributing to uncertainty in index futures pricing during the spring in Finland. This theory has been supported by the U.S. data of Bhatt and Cakici (1990), who reported the dividend yield to be positively related to futures mis-pricing.

Table 2 shows the effect of the future dividend stream on the theoretical fair value of the near-

Table 2. The effect of dividends on the fair value of futures contracts

Contract Index points Percentage

Mean Max. Mean Max.

Jun. 1988 Aug. 1988 Oct. 1988 Dec. 1988 Feb. 1989 Apr. 1989 Jun. 1989 Aug. 1989 Oct. 1989 Dec. 1989 Feb. 1990 Apr. 1990 Jun. 1990 Aug. 1990 Oct. 1990 Dec. 1990

1.24 2.58 - -

0.22 -

0.47 -

- - - - - - - -

- 12.78 1.99 - -

- 1.14 0.21

- 1.97 0.30

- - - -

- 0.43

14.21 1.65 -

- - 0.04 0.09 1.74 2.66 0.20 0.36

0.18 9.16 0.92 - - - - - - - - - - -

The effect is calculated as the present value of dividends to be paid on the index stocks before the expiration of the futures contract. The percentage effect is calculated as a percentage of the index value.

s122 V. PUTTONEN

by futures contract. The resulting effect is presented in both index points and as a percentage of the FOX index. As the effect of dividends fluctuates between zero for many contracts and 14.21 index points for the April 1990 contract, we can see that neglecting the dividends or assuming a constant dividend yield would greatly distort the futures pricing. This is particularly true for the contracts which mature in April.

3.3. Transaction costs in the Finnish markets The costs of opening and closing an arbitrage position in the Finnish stock index markets

involve commissions in the market place (HeSE and FOM), stamp duties* and market impacts in both the stock and futures markets. If the position is held until the expiration, no market impact costs are incurred, because the stocks and futures can be sold or purchased at the market-close prices. However, there are commissions to be paid upon liquidating the position. In addition, a stamp duty has to be paid on the profit received from the futures contract position.

Certain costs are incurred when trading in the Finnish markets that need to be considered. The costs vary according to which category the dealer belongs. Traders on the FOM can be divided into three categories: market makers, brokers and final cust0mers.t The explicit transaction costs for an arbitrageur acting as a market maker in the futures market consist of the fixed commissions of the options exchange and a stamp duty. The commissions consist of a clearing fee when opening the position and a closing fee when reversing it. The final customer also has to pay a brokerage fee of about 60 marks. If an arbitrageur acts as a broker on the HeSE, the only direct cost incurred in the stock market is the stamp duty. The explicit transaction costs in the Finnish markets are presented in Puttonen (1992).

Implicit costs are more difficult to calculate. Implicit costs are usually estimated by the bid-ask spread, the difference between the highest quote to buy and the lowest offer to sell. Financial assets are generally bought at the ask price and sold at the bid price. As is noted by Phillips and Smith (1980), the estimation of the appropriate magnitude of this cost is no simple matter and is not easily resolved. In practice, trades occur also inside the spread, not only at the bid or ask. The actual bid-ask spread for futures contracts was used in this study. Puttonen (1992) reported that the bid-ask spreads in the FOX futures market have increased with time in spite of the decreased commissions of the FOM. This was explained by the heavy fall in market volumes. The bid-ask spreads in the Finnish market were clearly greater compared with the spreads reported by Yadav and Pope (1990) for the U.K. futures market.

The bid and ask quotes of the stock market were not available for this study. Keim (1989) has provided statistics for bid-ask spreads for NYSE, AMEX and OTC NMC stocks on the U.S. markets. The median spread for the four largest deciles of the OTC NMC stocks was under 1%. Yadav and Pope (1990) examined the stocks included in the FTSE-100 index quoted on the International Stock Exchange in London. They reported an average spread of about 1%. Trading on the Helsinki Stock Exchange can be said to be less frequent than its U.S. and U.K. counter- parts. On the other hand, the FOX index consists of the 25 most liquid stocks. Therefore, an estimate of a 2% bid-ask spread (i.e. + 1% market impact) is used.

In the case of index arbitrage, there is a choice also between trading all the stocks in the index basket and using only some of the major stocks that closely match the index. In this study, we ignore the effect of the tracking error for the sake of simplicity. Furthermore, the difference between borrowing and lending rates is ignored here by arguing that it is negligible for big

*The stamp duty was removed at the beginning of May 1992. tFor a detailed description of the market organization see Eklund et al. (1990).

EXANTE PROFITABILITY OF INDEX ARBITRAGE S123

Table 3. Level of futures mispricing in the near contract: summary statistics excluding transaction costs

Period Mean (%) S.D. (%) Min. (%) Max. (%) pl P2 P3

5/88-l 2/90 -1.30 1.89 -9.60 2.22 0.91 0.84 0.81

S.D. = standard deviation; Min = largest negative; Max. = largest positive; pl, p2 and p3 are autocorrelation coefficients of lags 1,2 and 3 days, respectively. Deviations from the theoretical “fair” futures price are measured as

F--F,, erT = x 100,

F !ix‘x

where F_ = actual market price and Fulmr = theoretical fair price of a futures contract.

investors. Also, the margin requirements are ignored since they can be posted in the form of stocks or bonds on which the investor continues to earn dividends and interest.

4. THE COST-OF-CARRY MISPBICING SERIES

Evidence on the mispricing of FOX futures in the absence of transaction costs is presented in Table 3. The percentage of mispricing of the near contract is calculated. A week prior to the expiration of the near contract the analysis is shifted to the next contract. The futures contract has on the average traded at a discount. In addition to the size and the sign of mispricing, it is of particular interest to examine the tendency of mispricing to persist or reverse itself. For the U.K. markets, Yadav and Pope reported first-order coefficients of 0.88 before and 0.66 after the Big Bang. Compared with the coefficients reported by Yadav and Pope, the mispricing in the Finnish markets seems to be more path dependent. Interestingly, the autocorrelation coefftcients in the Finnish markets are almost the same as those reported in the first few years of the Japanese market (Brenner et al., 1989).

4.1. The ex post and ex ante resfs of market eficiency A general approach to the context of arbitrage relationships is to define efficiency in terms of

a trader with the lowest transaction costs. The reasoning is as follows: all investors must satisfy their own marginal conditions for price equilibrium to occur. Naturally, the lowest-cost trader can continue trading on smallest price errors. The hedge will be formed instantaneously as the market prices imply an arbitrage opportunity. If the prices do not violate the arbitrage bounds, the excess return for a hedge is zero. In the ex ante tests, the hedge will be formed one day after the hedge initially signals an arbitrage profit. Note that the ex ante hedge may result in a negative value as well as in a positive value.

Table 4 presents the profitability of ex post and ex ante trading rules. The profits are calculated on a per hedge basis and the market impact in the stock market is assumed to be 1% of the underlying index value. The results show that the use of ex anre rule does not reduce the arbitrage profits significantly. This is in accordance with the previous finding that n&pricing in the Finnish markets is path dependent. Since there were only four deviations from the upper cost-of-carry limit during the entire sample period, no reliable conclusions can be made about the difference between the profitability of short and long hedges. It seems, however, that there have existed persistent arbitrage opportunities particularly for owners of large stock portfolios who could have

s124 V. PUTTONEN

Table 4. The profitability of expose and ex ante strategies (in Finnish marks) for 732 observations from 2 May 1988 to 21 December 1990

Ex post

Strategy

Short hedge by market maker Long hedge by market maker Short hedge by final customer Long hedge by final customer

# (%)

228 (31.1) 4 (0.5)

84 (11.5) 0

Mean

+701.6 +277.1 f726.6

Min. Max. Sum*

+2.1 +3329.9 157.0 +159.9 +362.3 1.1

+23.2 +2642.8 62.0

Ex ante

Strategy

One-day execution lag Short hedge by MM

Long hedge by MM Short hedge by FC Long hedge by FC

Two-day execution lag Short hedge by MM Long hedge by MM Short hedge by FC Long hedge by FC

No. Mean Min. Max. Sum* #pas (%) beg

228 +605.2 -820.7 +3329.9 136.0 189 (25.8) 39

4 +177.0 -240.7 +362.3 0.7 3 (0.4) 84 +562.8 -1090.3 +2642.8 47.0 63 (8.6) 2: 0

228 +533.9 -1230.8 +3329.9 119.0 175 (23.9) 53 4 +88.2 -240.7 +362.3 0.3 2 (0.3) 2

84 +453.8 -1997.1 +2642.8 38.0 60 (8.2) 24 0

# = times the strategy is triggered; Mean = mean profit from the strategies (in Finnish marks); Min. and Max. = mm- imum profit (maximum loss) and maximum profit from the strategy; sum = sum of all the arbitrage profits; #pas and #hteg = number of profitable and unprofitable hedges; % in parentheses = the percentage of all the observations (732). *Thousands of Finnish marks.

implemented a so-called quasi-short arbitrage strategy; by selling the index stocks and buying the futures contracts, the institutions and managers & stock index funds and pension funds should have enforced the lower bound of the cost-of-carry model. It is quite surprising that this has not happened even after allowing an execution delay of two days.

The statistical significance of the ex unte arbitrage profits is presented in Table 5. First, the standard t-test is employed in order to test whether the arbitrage profits are statistically different from zero. To allow for further conclusions about the distributional properties of arbitrage profits the Shapir-Wilk W-test statistics, skewness and kurtosis, and quartiles of violations are reported. Since the profits do not follow the normal distribution in every case the non-parametric Sign Test is also employed. The Sign Test shows that the arbitrage strategies are more often profitable than unprofitable.

The corresponding figures are presented in Table 6 in percentage form. The results do not significantly differ from those reported in Finnish marks. Note that the mean profits for the final customer from the short hedge is greater than the profits for the market maker. The total profit for the market maker is, however, much greater than those for the final customer, which can be seen from Table 4.

Before judging the Finnish stock index futures market as inefficient some further discussion is needed. Firstly, the futures market may be informationally more efficient than the underlying stock market in predicting the future movements of stock prices. After comparing the difference in predictability of positive and negative cash in&x returns, Puttonen (1993) suggests that the impossibility of short selling of stocks is an important factor increasing the price discovery of

EX Ah’TE PROFITABILITY OF INDEX ARBITRAGE s125

Table 5. The statistical significance of ex nnre violations from the cost-of-carry model in the FOX markets for 732 observations from 2 May 1988 to 21 December 1990

Strategy

Quartiles of violations

t s-w Skew KUlt Ql Med. 42 Sign

One-day execution lag Short hedge by MM Long hedge by MM Short hedge by FC

12.57*** 0.943*** 0.909 1.187 122.4 449.2 1077.4 10.00*** 1.25 0.758* -1.878 3.580 11.5 293.1 342.4 1.50 7.23*** 0.976 0.439 0.644 -4.1 570.5 984.5 4.69***

Two-day execution lag Short hedge by MM Long hedge by MM Short hedge by FC

10.25*** 0.961*** 0.721 0.836 29.6 391.0 1052.3 8.15*** 0.59 0.865 -0.195 A.722 -‘166.0 115.7 342.4 0.50 5.14*** 0.985 4.008 1.020 -110.3 424.1 944.8 4.04***

Ql and Q2 = lower and upper quartiles of percentage spreads; Med. = median. t = The t-statistics under the null hypothesis that arbitrage profits are zero on average; S-W = the Shapiro-Wilk W-

test statistics under the null hypothesis that arbitrage profits are normally distributed; Sign = the nonparametric Sign Test statistics under the null hypothesis that the number of profitable positions is equal to the number of unprofitable positions; Hl: number of positive violations > number of negative violations; ***, **, * = the null hypothesis is rejected at the 0.001, 0.01 and 0.05 levels of significance.

futures and options markets. Secondly, an investor with bullish expectations is able to buy either stocks or futures. But if he wants to hold a stock portfolio that differs from the index portfolio he may prefer the actual shares instead of futures contracts. This has also been suggested by

Figlewski (1984) and Bane and Westman (1992). Generally, the stocks in the portfolio are selected so that they are expected to outperform the market. For these investors the futures contract may not be a good substitute for the current position. As brokers and institutional investors claim,

the illiquidity of the market, voting power connected with the stocks, and fiscal reasons proba- bly prevent arbitrage activity and partly explain the existence of a discount in the stock index futures.

We also have to acknowledge the fact that a straightforward assumption of an equal execution

Table 6. The profitability and statistical significance of the ex ante strategy (in percentages) from 2 May 1988 to 21 December 1990

Strategy Mean Min.

Quartiles of violations

Max. t s-w Skew Kurt Ql Med. Q2

One-day execution lag Short hedge by MM Long hedge by MM Short hedge by FC

1.34 -1.48 7.26 12.31*** 0.907*** 1.150 1.296 0.24 0.94 2.14 0.28 -0.38 0.58 0.754* 1.26 -1.885 3.602 0.00 0.47 0.55 1.36 -2.09 5.81 7.55*** 0.969 0.504 0.117 -0.01 1.23 2.30

Two-day execution lag Short hedge by MM Long hedge by MM Short hedge by FC

1.19 -2.23 7.26 10.24*** 0.930*** 0.976 0.980 0.07 0.82 2.11 0.14 -0.38 0.58 0.59 0.864 -0.196 4.730 -0.26 0.18 0.55 1.15 -3.48 5.81 5.79*** 0.981 0.250 0.248 -0.19 0.90 2.28

Mean = mean percentage profit from the strategies; Min. and Max. = minimum profit (maximum loss) and maximum profit from the strategy; Ql and 42 lower and upper quartiles of percentages spreads; Med. = median.

t = The r-statistics under the null hypothesis that arbitrage profits are zero on average; S-W = The Shapiro-Wilk W- test statistics under the null hypothesis that arbitrage profits are normally distributed; ***, **, * = the null hypothesis is rejected at the 0.001, 0.01 and 0.05 levels of significance.

S126 V. PUTTONEN

delay in both the stock and futures markets may not be justified. Furthermore, the execution delay depends on the market’s activity at particular points in time. Intra-day price and volume data would be needed for further research on the length of the execution delay.

5. SUMMARY AND CONCLUSIONS

Daily closing values of the FOX index and the nearest maturity futures contracts were used to examine the profitability of index arbitrage in the Finnish markets. Both exposte and ex ante tests were carried out. Frequent and statistically significant violations of the cost-of-carry lower boundary were reported. Particularly, investors long in the index stocks have been able to exploit the arbitrage opportunities since arbitrage opportunities have existed even after allowing an execution delay of two days. The empirical findings are thus inconsistent with the cost- of-carry theory and support the claim that the Finnish stock index futures market is ineffi-

cient.

Even though the empirical findings are inconsistent with the cost-of-carry theory and indicate inefficiency in the Finnish stock index futures market we must be careful when making far-reach- ing conclusions. In addition to the tangible transaction costs considered in this study, there are also intangible transaction costs particularly when trading in the stock market. The results suggest that caution is warranted when applying models based on the absence of arbitrage. Since violations were reported with respect to the simplest cost-of-carry arbitrage condition, the factors

preventing effective arbitrage will also affect the results of more advanced testing procedures.

Acknowledgemenrs - I am grateful for the comments and suggestions of Tom Berglund, Antti Kanto, Ragnar Lindgren and Teppo Martikainen, and participants at the Nordic Research Symposium on Contingent Claims Analysis in Finance and at the Finnish Options Market (FOM). I wish to thank the FOM for providing the data.

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The ex ante profitability of index arbitrage in the new Finnish markets