An Empirical Study on the Pricing of the Kuala Lumpur Stock Exchange Composite Index Futures

Transcription

1 Asia Pacific Management Review (2004) 9(6), An Empirical Study on the Pricing of the Kuala Lumpur Stock Exchange Composite Index Futures Hsinan Hsu * and Yee Kum Chau ** Abstract Numerous studies have been carried out on the pricing of stock index futures based on the cost of carry model. However, the findings are controversial. In this paper, the pricing of the KLSE CI futures is examined under both the cost of carry model and the imperfect market model developed by Hsu and Wang [15]. The period under study is from January 2, 1996 to March 31, The overall results reveal that price expectation plays a significant role in pricing of the KLSE CI futures. In respect of the pricing of the KLSE CI futures, the cost of carry model has the lowest predictive power comparing to the imperfect market models discussed in this study. Keywords: Pricing of stock index futures; Cost of carry model; Imperfect market model; Model predictive power; KLSE CI. 1. Introduction Numerous studies on various aspects of stock index futures had been conducted in the past. However, the main concern for academic researchers as well as traders of the stock index futures is the pricing of stock index futures since it directly affects the profitability of investment strategies. In this aspect, the cost of carry model is undoubtedly the most widely used model for pricing the stock index futures. However, if this model has been very accurate in determining the stock index futures prices in the actual market, then it will not deserve such excessive studies. Findings on the pricing of stock index futures have shown that the actual stock index futures prices deviate from the theoretical prices calculated from the cost of carry model. Those empirical results showing that the actual stock * Corresponding author. Department of Finance, Southern Taiwan University of Technology, Yung-Kang City, Tainan 710, Taiwan, R.O.C. Tel: , hsinan@mail.stut. edu.tw ** Department of Business Administration, National Cheng Kung University, Tainan, Taiwan R.O.C. Tel: , ykchau9@pchome.com.tw The authors would like to thank the two anonymous referees for their valuable comments and suggestions. However, any error is, of course, ours. 1025

2 Hsinan Hsu et al. index futures prices were on average lower than that predicted using the cost of carry model include studies done by Cornell and French [6,7], Modest and Sundaresan [21], Figlewski [11], and Eytan and Harpaz [10]. Whereas Bhatt and Cakici [1] found that the opposite is true, that is, the actual stock index futures are indeed priced at a small premium relative to its theoretical value. Many have explained that this price deviation was in fact resulting from the imperfect capital market. The cost of carry model was basically developed under the assumption of perfect capital markets with no transaction cost and we know that this is a very unrealistic assumption in the real world, in which traders are facing with substantial amount of transaction costs, restrictions on short selling and usage of proceeds from short selling, unequal borrowing and lending rates and other regulations. What are the true reasons causing the deviations of actual stock index futures prices from the theoretical prices derived from the cost of carry model? Are they due mainly to the unrealistic perfect market assumptions? Or the cost of carry model itself is misspecified if used in imperfect markets? Many other studies have tried to explore more on this pricing issue. However, up to today, these queries remained unanswered. Thus, it is of grave doubt that this cost of carry model developed under the perfect market assumptions can equally be applied to the real world. Many scholars then carried out different studies to find out model for the imperfect markets. Among those, some have tried to relax some of the perfect market assumptions and incorporated market imperfections into the cost of carry model (e.g., Cornell & French [6,7], Modest & Sundaresan [21] and Klemkosky and Lee [17]), while some incorporated other important factors into the model (e.g., Hemler & Longstaff [14]). A recent imperfect model developed by Hsu and Wang [15] 1 incorporates price expectation and risk aversion factors into their model. This model argued that the hedged portfolio is not risk-free given that the actual market is not perfect. Hence, the expected return of such a hedged portfolio is not the risk-free rate but a higher rate to compensate the additional risk of holding the portfolio. This model is very similar to the cost of carry model in mathematical form, yet it has proved to be more predictive for both TAIFEX futures and SIMEX MSCI futures markets. 1 This model will be referred as the imperfect market model in the rest of this study. 1026

3 Asia Pacific Management Review (2004) 9(6), In this paper, both the cost of carry model and the imperfect market model will be used to examine the stock index futures price of the Malaysian futures market so as to understand whether this developing futures market is functioning as well as those developed futures markets. Furthermore, the accurate pricing of the FKLI is very important for the Malaysian equities investors in conducting arbitrage and hedge. 2 In this aspect, this futures contract is referring as Kuala Lumpur Stock Exchange Composite Index Futures Contract (FKLI). 3 It is traded on the Malaysia Derivatives Exchange (MDEX) since December 15, The underlying stock index is Kuala Lumpur Stock Exchange Composite Index (KLSE CI). 4 Specifically, the purposes of this study are: (1) To test the adequacy of the cost of carry model in KLSE CI futures market. (2) To compare the performance of the cost of carry model and the imperfect market model in explaining the actual KLSE CI futures prices. (3) To examine the impacts of stock market volatility and other important factors including instantaneous growth rate, time to maturity and risk free interest rate on logarithm of futures/spot price ratio. The remainder of this study is organized as follows. In the next section, the related literature will be reviewed. In section 3, the methodology and the data involved in this study will be discussed and its empirical results will be summarized in section 4. Finally in the last section, conclusions from this study will be drawn. 2. Literature Review 2.1 The Stock Index Futures Pricing Model in a Perfect Market The cost of carry model for stock index futures is developed by Cornell and French [6] under the assumptions of perfect capital markets (i.e., no taxes, no transaction costs and no restrictions on short selling, and perfect divisibility of assets), constant risk-free rate, and constant and continuous dividend yield, then the futures price for the stock index can be expressed 2 Sophisticated investors will calculate the hedge ratio of the FKLI. Thus, an appropriate pricing model of the FKLI is necessary for the Malaysian investors. 3 FKLI contracts are traded electronically through KATS (an automatic trading system). This is also to ensure timely and secure access by all market participants located throughout the country. 4 The KLSE CI was first introduced by the KLSE in Today, it has established itself as the benchmark for the Malaysian equities market. The KLSE CI, a market-weighted index, is made up of 100 component stocks listed on the Main Board of the KLSE. 1027

4 Hsinan Hsu et al. by: F where ( r d )( T t ) ( S t ) = S t e, (1) S t is stock index price at time t, r is risk-free interest rate, d is dividend yield, and T t is time to maturity. If both sides of equation (1) are unequal, then arbitrage opportunities arise and will drive the futures prices back to the equilibrium price. In real markets, we often observed that actual futures prices are different from theoretical futures prices. Not even that, we did find that the actual futures prices are in fact lower than the spot prices in many cases. This could not be true given that our risk-free rates are always greater than our dividend yields. By applying equation (1), the futures prices must then greater than the spot prices. But, why did these phenomena occur in the real markets for both developed futures markets like USA and developing markets such as Malaysia and Taiwan? Many studies have been carried out to find an answer for this financial puzzle. A number of possible explanations have been proposed and basically, they can be grouped into two broad categories as follows. (1) Market Equilibrium The arbitrage argument clearly depends upon a theoretical world of perfect markets. However, in the real markets, four main market imperfections listed below operate to complicate and disturb the relationship between futures and spot prices. (a) Transaction costs: There are direct and indirect transaction costs associated with trading of stocks and futures. These include brokerage commissions, clearing fees, stamp duty, capital gains taxes, and market impact costs. Many researchers believed that the existence of transaction costs is the main reason causing the deviation from futures theoretical prices. For instance, after taking taxes into the model, Klemkosky and Lee [17] found that the frequency of mispricing reduced dramatically. They also found that member traders who have the lowest transaction costs have more opportunities to engage in profitable index arbitrage than institutional investors. Whereas, Cornell and French [6] found that the actual stock index futures prices were on average lower than that predicted from the cost of carry 1028

5 Asia Pacific Management Review (2004) 9(6), model. They believed that this is caused by the different tax treatments applied to stocks and futures transactions. Gains and losses from stock and futures instruments are treated differently in tax regime. In futures market, any unrealized gains or losses are to be recognized as actual gains or losses at end of the tax year. On the other hand, any unrealized gains or losses of a stock remain unrealized at end of the tax year. Hence, a stock portfolio offers the investor a timing option. An investor can deduct losses at short-term capital gains tax rates if the value of the portfolio declines; if it goes up, the investor may extend his holding period to take advantage of lower long-term capital gains tax rates. 5 Thus, this tax-timing option could give extra value to the stocks relative to the futures. Modest and Sundaresan [21] showed that when transaction costs are recognized, the futures prices can fluctuate within a bounded interval without giving rise to any arbitrage profits. Both upper and lower bounds of the interval should incorporate all transaction costs involved. However, due to the nature of quasi-arbitrage, 6 one will expect the future prices to fluctuate within the no-arbitrage bounds of those traders having the lowest transaction costs. (b) Restrictions on short selling: There are restrictions on short selling and even if short selling is allowed, full use of the proceeds is not permitted too. Then, it will not be feasible to invest the full amount in the money market and hence restrict the operation of the reverse cash-and-carry arbitrage. 7 In some cases, for instance, traders are allowed to sell short a stock only on an uptick. Thus, when the actual futures prices fell below the lower bound of the no-arbitrage bounds, a reverse cash-and-carry arbitrage is not feasible to drive the prices back to the no-arbitrage bounds. (c) Unequal borrowing and lending rates: In actual market, traders face higher borrowing rates than lending rates. Klemkosky and Lee [17] also believe that differential borrowing and lending rates in real world will widen the boundaries of the deterministic futures prices. They have incorporated this consideration together with other imperfections such as transaction costs, dividend uncertainty and taxes to examine the arbitrage opportunities of the 5 After the Tax Reform Act of 1986 (USA), 40% of the gains or losses from futures are to be treated as short-term gains or losses while 60% are treated as long-term gains or losses. However, both rates are set equal since then. 6 Arbitrage opportunities are only possible for those facing lower transaction costs and these arbitrage activities will then drive the prices back to equilibrium. 7 This involves buying futures and selling short the equivalent of stock index. The position is then held until the futures expire, at which time the stocks are repurchased. 1029

6 Hsinan Hsu et al. S&P 500 index futures. They found that the frequency of mispricing has decreased notably using their model. (D) Stock price movements and tracking risk: The underlying instrument of stock index futures is stock index which is made up of a basket of stocks. In conducting arbitrage, buying or selling futures contract is easy, however, buying or selling stock index is not as easy. To buy or sell the whole basket of stocks will delay the execution of orders for some stocks that may end up with buying or selling at a price different from what is intended. Moreover, generating a stock portfolio that exactly matches the relevant stock index is costly. Therefore in practice, traders and especially arbitrageurs usually construct a representative basket of stocks that closely track the activity of the stock index in order to execute a near arbitrage transaction. However, this creates tracking errors between the portfolio on hand and the stock index, creating imperfect arbitrage. Other market imperfections that may also cause price deviation include uncertainties about payment and timing of dividends, payments of dividends are not continuous, stocks and futures contracts may not divisible into any amount, asymmetric information among investors and interest rate may not be constant during the contract life. In combination, all these arguments give a set of persuasive reasons why there should be downward pressure on the futures price relative to the theoretical prices. Nevertheless, it seems unlikely that they are sufficient to explain the full amount of the futures discounts encountered in the market. (2) Market Disequilibrium It is noted that the mispricing issue is more serious in a less-established futures market especially at its beginning trading stage. Figlewski [11] regards this disequilibrium situation as a transitory phenomenon caused by unfamiliarity with the new markets and institutional inertia in developing systems to take advantage of the arbitrage opportunities. According to Figlewski [11], such futures discounts should diminish finally as large investors begin to integrate stock index futures into their overall equity investment programs. In his study on both stock index futures contracts on NYSE Index and S&P 500 index, he found that the futures discounts were smaller in the second half of the sample period than in the first, implying that actual futures prices did not deviate as far from their theoretical levels in the later period as they did at the beginning. 1030

7 Asia Pacific Management Review (2004) 9(6), The Cost of Carry Model in an Imperfect Market Since many researchers believe that the price deviation was a result of the unrealistic perfect market assumptions under the cost of carry model, some of them have actually relaxed some of the perfect market assumptions in their studies to test for the adequacy of their modified model in real world situation. Cornell and French [6] extended the traditional cost of carry model by introducing seasonal dividends, stochastic interest rates, a simple tax structure and tax timing option. 8 However, the actual stock index futures prices are still generally lower than that predicted from this extended model. Modest and Sundaresan [21] not only showed that the futures price can fluctuate within a bounded interval with the existence of transaction costs, they also recognized that restriction on the use of short selling proceeds will result in futures deviation from theoretical prices. In their studies, they examined the actual futures prices of S&P 500 futures contract with their theoretical prices under the assumptions that investors have 0%, 50% and 100% use of the proceeds respectively from short selling. The results show that when investors have zero use of proceeds, actual futures prices lie within the theoretical bounds implying no arbitrage opportunities. When investors have 50% use of proceeds, except for few occasional occurrences, there are no arbitrage opportunities. While when full use of proceeds is available to investors, actual prices violate the theoretical bounds. This is very clear that restriction on use of short selling proceeds itself may not be able to explain futures discount fully. Klemkosky and Lee [17] incorporated transaction costs, taxes, differential borrowing and lending rates, seasonal dividend payouts, marking-tomarket effect into the traditional model to examine if any arbitrage opportunities exist for S&P 500 futures. The study reveals that the S&P 500 futures contract is more often overpriced than underpriced during the test period. However, the frequency of mispricing decreases dramatically when taxes are considered and as the futures contract approaches maturity. It also reveals that member traders have more opportunity to engage in profitable index arbitrage than institutional investors. Although that study suggests that all 8 When the tax-timing option consideration is included in the extended model, they found that the predicted prices are lower. They also found that the relative value of the timing option increases with maturity. However, in their later studies, they found that this tax-timing option does not significantly affect the futures prices. 1031

8 Hsinan Hsu et al. these elements especially taxes, transaction costs and timing option do affect the futures prices, but it cannot fully explain the futures discount occurred in the real world. 2.3 The Stock Index Futures Pricing Model in an Imperfect Market We have seen that neither the cost of carry model nor the extended cost of carry model can fully explain the futures discount in the real world. Does this imply that there are other important factors being left out from the model, or there should be other models that can better explain the actual stock index futures prices? According to Hemler & Longstaff [14], the cost of carry model assumes that the stock market is exogenous and thus could fail to capture the dynamic interactions between spot and futures markets. 9 They also believe that futures and forward prices need not be equal if interest rates are stochastic. 10 Moreover, there are many empirical evidences showing systematic pricing deviations from the cost of carry model. Thus, they believe that there should be other better models to explain the real world situation. In connection to this, they developed a general equilibrium model of stock index futures prices with stochastic interest rates and market volatility. 11 In their studies on NYSE stock index futures prices for the period of , they found that both the risk free interest rate and market volatility have significant explanatory power on the logarithm of the futures/spot price ratio. These results are consistent with their equilibrium model. In a study on stock index option, Figlewski [12] examined the impact of market imperfections and found that the standard arbitrage was exposed to large risk and transaction costs in the actual market. Thus, he concluded that there is wide room for price expectation and risk aversion to play a very important role in the determination of the option prices in real option markets. In the same vein, Hsu and Wang [15] came up with a stock index futures pricing model for the imperfect market. The underlying idea is that both the price expectation and risk aversion factors are important in determining stock index futures prices in the real world. These ideas are very much un- 9 In fact, many have found that spot and futures markets are interdependent. 10 Traditional cost of carry model assumes that interest rates are constant, i.e., non-stochastic, implying that futures and forward prices are equal. 11 This model is built upon the framework developed by Cox, Ingersoll, and Ross [8] on their general equilibrium model of discount bond futures prices in an economy with stochastic interest rates. 1032

9 Asia Pacific Management Review (2004) 9(6), derstandable since we are well taught by the idea that futures have a price discovery function. If futures have a price discovery function, we will expect to see that market observers being able to form estimates of what the price of the stock index will be at a certain time by using the information contained in futures prices today. On the other hand, if one could easily predict the futures prices using the cost of carry model calculated from known stock index prices, dividend yields, interest rates and time to maturity, so where does this price discovery function come about? Thus, expectations play a very important role in establishing futures prices. In this aspect, if traders are risk-averse, 12 then the futures prices can differ from the expected spot price in future. In Hsu and Wang s [15] study, they found that the S&P 500 index futures indeed have price discovery function, especially during bull-market and during the later part of their test period. In Hsu and Wang s [15] model, a hedged portfolio, P, consisting of stock index and stock index futures is formed. Since actual markets are not perfect, arbitrage mechanism cannot be carried out freely as it should and hence, index arbitrage is no longer risk free and thus should be compensated at a higher return (or growth rate). The underlying assumptions of this model are as follows: (1) The underlying stock index pays a continuous constant dividend yield, d, during the life of the stock index futures contract. (2) The degree of market imperfections remains constant throughout the life of the stock index futures contract. (3) The underlying stock index price, S, follows a geometric Wiener process. A Wiener process for stock prices is assumed, and a hedged portfolio is formed. Then, using the same argument as the Black and Scholes [2] option pricing model, they showed that the stock index futures price 13 in an imperfect market is: F ( u p d )( T t ), = S e (2) ( S t) t where S t is stock index price at time t, u p is instantaneous growth rate 12 If speculators assess that the expected profit (difference between futures price and expected spot price in future) is too small to cover their risk exposure, they will not pursue the arbitrage and hence no market forces to drive the futures price into exact equality with the expected spot price in future. 13 For details on the working to the equation, please refer to Hsu and Wang [15]. 1033

10 Hsinan Hsu et al. of the hedged portfolio, d is dividend yield, and T t is time to maturity from time t. Note that this model is similar to the cost of carry model in mathematical form. The only difference is that rather than risk-free interest rate, r, this model suggests that the hedged portfolio earns some other rates (instantaneous growth rate) and denoted as u p. In fact, the imperfect market model is a generalization model of the cost of carry model. When u p equals to r, then the two models are identical. Using this model to explore S&P 500 and SIMEX MSCI Taiwan Stock Index futures, Hsu and Wang [15, 16] found that their model could explain the actual stock index futures prices much better than the cost of carry model during the test period. In another study, Liu [20] found a similar result on the TAIMEX Taiwan Stock Index futures market. These studies also showed that the instantaneous growth rate of the hedged portfolio is not equal to the risk-free interest rate. 3. Methodology and Data 3.1 Testing Adequacy of the Cost of Carry Model This is to examine whether the cost of carry model gives rise to significant arbitrage opportunities in the actual KLSE CI futures market. That is, to test whether the actual stock index futures prices are within the no-arbitrage bounds of the theoretical futures prices. Meanwhile, in this study, the actual KLSE CI futures price will also be tested against the spot index price since actual stock index prices in Taiwan futures market were found to be lower than its underlying spot index prices in a substantial part of times. This will not be true if the cost of carry model is correct by applying equation (1). (1) No-Arbitrage Bounds To compare the actual and theoretical futures prices, it is important to first define the no-arbitrage bounds for the theoretical futures prices. As illustrated in Section 2, due to the imperfections in the actual market, the no-arbitrage futures prices should be in a range of prices rather than a deterministic price. Following the framework proposed in Chung [5], the noarbitrage bounds of this study is designed as follows: b St < AFt F( S, t) < b St (3) where F S, t is theoretical futures AF is actual futures price at time t, ( ) t 1034

11 Asia Pacific Management Review (2004) 9(6), price at time t calculated from equation (1), S t is stock index price at time t, and b is total transaction costs incurred in the arbitrage. The above equation can be rearranged to the following manner by adding F ( S, t) and deducting S t on each term to facilitate the comparison between the actual futures prices and the spot index prices. 14 ( S, t) (1 + b) St < AFt St < F( S, t) (1 b St F ) (4) Total transaction costs involved in an index arbitrage include: (a) round-trip commissions to buy and sell stocks in the spot market (b) one-way commission to open a position in the futures market 15 (c) two-way market impact cost in the stock market 16 (d) one-way market impact cost in the futures market (e) tracking error in the stock market In this paper, it is assumed that traders can use 100% of short-sale proceeds. Although, at present Malaysia has banned short selling in the stock market, however, as the major traders in the market are those member firms and institutional investors who have substantial holdings in the stock market, these traders are not affected by the restriction on short selling as they can still implement the reverse cash-and carry strategy by selling their stocks on hand. Commissions involved are straightforward since they are set by the Exchange. In the following table, commissions involved are shown (expressed in term of percentage on stock values). However, the market impact costs and tracking error are not easy to compute and can only base on rough estimates. Many studies in USA took half of the bid-ask spread as one-way market impact costs of buying or selling a stock. For instance, Klemkosky and Lee [17] considered USD 1/16 as 14 This difference between the actual futures prices and spot index prices (AF t S t ) is referred as basis. 15 Since in the standard index arbitrage, traders are assumed to close out futures position only at expiration, thus, investors are subject to one-way commission and one-way market impact cost in the futures market. 16 As the final settlement of futures bases on the average value of KLSE CI for the last half hour of trading (excluding the highest and lowest values), traders cannot close out his (her) spot position at futures expiration with execution of market on close/open so as to avoid one-way market impact cost of stock market. 1035

12 Hsinan Hsu et al. Table 1 Commissions on Trading of Stocks and Futures Contracts Buy (Sell) a stock Buy (Sell) a futures contract Brokerage Commissions 0.75% % b Clearing Fees 0.04% % b Stamp Duty % a - Total % 0.075% a This is the average stamp duty computed by Tan [25] during his test period. b First, compute per-index fee (i.e., commission/rm100), then divide by average spot index of 800 during the test period from January 2, 1996 to March 31, one-way market impact cost. 17 However, in Malaysian stock market, the bid-ask spread is not uniform for all stocks with different price ranges. The minimum bid (or tick) that one can bid for stocks at different price ranges is guided by the KLSE. These ticks range from RM0.005 for stocks priced below RM1 to RM0.50 for stocks priced above RM100. To compute the market impact costs of stock market in this paper, the weighted average method used in Lin and Tzang [19] will be employed. The formula is: n i= 1 T i Pi P i Qi Pi Qi i (5) where T i is minimum bid (tick) for component stock i, P i is stock price of component stock i, and Q i is number of shares outstanding for stock i in the market. In connection to this, Tan [25] estimated this market impact costs to be % for KLSE stock market in his sample period from December 1995 to March Since the applicable minimum bid remains unchanged at present and thus the % will be used in this study as the one-way market impact costs of stock market. Meanwhile, Tan [25] also estimated the average tracking error to be 0.224% in his study. This tracking error was estimated during the said sam- 17 This being half of the bid-ask spread. In USA, this bid-ask spread of USD1/8 is applicable to all stocks even with different market prices. 1036

13 Asia Pacific Management Review (2004) 9(6), ple period by comparing the return of the stock index and some hedged funds constructed from 40~50 stocks. The same figure will be used in this study. On the other hand, market impact costs for futures market are not considered here. Transaction costs of trading futures itself is relatively much smaller than trading of stocks due to its leverage effect and since it only requires a single transaction as opposed to buying baskets of stocks. In fact, Wang et al. [27] and Smith and Whaley [22] in their studies on market impact cost of S&P 500 futures, found that the bid-ask spread is generally very small. Based on the above, the total transaction costs, b, expressed in percentage on spot index value, S t, are as in table 2 below. In this paper, three levels of total transaction costs, b, are considered, i.e., 2.0%, 2.5% and 3.0%. This is a rough estimate based on the above calculations and other costs that are not considered in this study such as opportunity cost, market impact costs of futures, execution risk, effect of position limit and marked-to-market. (2) Verifying the cost of carry model in KLSE CI futures market In this part, we will use the actual data observed in the market to get an appropriate regression equation on the stock index futures prices. Then, the coefficients of the explanatory variables will be verified against those of the cost of carry model. Table 2 Total Transaction Costs Involved in Index Arbitrage Stocks Futures Buy (%) Sell (%) Buy or Sell (%) Commissions % % 0.075% Market Impact Costs % % - Tracking Error 0.112% a 0.112% a - Sub-total % % 0.075% Grand Total 2.742% a Here, tracking error of 0.224% is divided into two merely for presentation purposes only. In fact, the full amount of the tracking error should be attributed to the buying (selling) and subsequently selling (buying) the baskets of stocks replicating the stock index. 1037

14 Hsinan Hsu et al. In an imperfect market, we base our analysis on equation (2). Taking natural logarithm at both sides of equation (2), we have: ln Ft = ln St + ( u p d)( T t) (6) For estimating purposes, the regression model can be written as: ln Ft = α 0 + α1 ln St + α 2 ( T t) + ε t (7) The cost of carry model also can be written in the similar form as: ( r d )( T t) ln Ft = ln St + (8) From the above, if the cost of carry model is adequate for KLSE CI futures market, then α 0 = 0, α 1 = 1 and α 2 = r d. When transaction cost, b, is considered, α 0 and α 1 should remain as 0 and 1 respectively, while α 2 = r d + b. In this study, the dividend yields 18, d, is estimated to be % per annum. This is computed from dividends of the year using weighted average method. In order to estimate these coefficients of the equation and to verify the values of α 0, α 1 and α 2, the following regression related problems are considered. (a) Multicollinearity If multicollinearity exists, the ordinary least squares estimators will still be BLUE, but one or more of the estimators can turn out to be individually insignificant. If this is the case, it is important to identify which explanatory variables are linearly related and isolate their influences on the explained variable. In this study, this is done via examining the Variance Inflation Factor (VIF) of each explanatory variable. 1 VIF = (9) i 2 ( 1 R ) (b) Heteroskedasticity i 18 Companies in Malaysia can have different accounting year-end and normally pay their dividends at different point in time during a year. Thus, in overall, the payment of dividends of all firms can be viewed as being carried out throughout the year and hence the concept of dividend yield is applied. 19 After perused through the dividend records of all component stocks during my test period, found that the dividend payout amounts are quite consistent during these years. Hence, the dividend yield of % calculated from a single year (2001) is a reasonable estimate for dividends of the whole test period. 1038

15 Asia Pacific Management Review (2004) 9(6), One of the assumptions of the classical regression model is that the disturbance terms (μ i ) have equal variance, i.e., Var(μ i ) = σ 2. The consequence of the disturbance variances to be different from observation to observation (i.e. heteroskedasticity) is that the OLS estimators are no longer having minimum variance (efficient) although they are still linear and unbiased. Hence, the resulted hypothesis testing and confidence intervals are no longer reliable. (c) Autocorrelation To detect the autocorrelation of regression equation, the Durbin-Watson d statistic test (D-W test) is used. If presence of autocorrelation is found, then Cochrane-Orcutt procedures will be used for estimation. (d) GARCH model The classical regression model assumes that there is no autocorrelation between the disturbance terms and the disturbance terms have equal variance (i.e., homoskedasticity). However, studies have pointed out that in many cases, these assumptions are violated in the areas dealing with financial assets returns. Bollerslev, Chou and Kroner [4] show that the GARCH(1,1) model is adequate and sufficient to capture and deal with these violations. In this paper the Lagrangian Multiplier Test (LM test 20 ) will be used to determine the existence of GARCH effect in the regression model. If yes, GARCH model will be used in estimating the regression model. Otherwise, the normal procedures will be used. 3.2 Comparing the Predictive Powers of the Two Models There are lots of controversies about the usefulness of the cost of carry model in the imperfect world. Thus, the predictive power of both the cost of carry and the imperfect market model will be examined in this study in the context of KLSE CI futures market. However, the theoretical futures prices must first be computed before comparison to the actual prices can be made. (1) Theoretical futures prices under the cost of carry model From equation (1), the explanatory variables include S t, r, d, and T t. Data on S t and T t can easily be observed in the market. As the markets 20 The LM statistic is asymptotically distributed as a χ 2 (q) under normal conditions and is computed as the number of observations times the R 2 from the test regression. The null hypothesis in this test regression is no serial correlation up to lag order q. If the computed n R 2 is greater than the critical values of χ 2 (q), then reject the null hypothesis. The equation should be re-specified since the residuals are serially correlated and vice versa. 1039

16 Hsinan Hsu et al. for the local government bonds are inactive and lack of liquidity, the average one-month fixed deposit interest rate of all commercial banks will be used as a surrogate to the risk-free interest rate, r. Whereas the dividend yields of % will be used as explained in section 3.1(2) of this study. (2) Theoretical futures prices under imperfect market model The explanatory variables are basically the same as per (1), except that the instantaneous growth rate, u p, will be estimated in the following manners: (a) Implied Method The instantaneous growth rate, u p, can be implied from equation (2) with input from actual futures and spot index prices, dividend yields and time to maturity, i.e., 1 Ft u p, t = ln + d (10) T t St In this paper, the instantaneous growth rate, u p,t-1 is used as an estimate for instantaneous growth rate, u p,t at time t. 21 (b) Adaptive Expectations Method In the current context, this model in its simplest form can be expressed as: ) ) ) u p, t = ut 1 + λ ( ut 1 ut 1 ) (11) ) where u p, t is expected growth rate of stock index futures at time t, u t 1 is actual growth rate of stock index futures at time t-1, and λ is adaptive expectation coefficient where 0< λ <1. This means that the expected growth rate for current period t equals to the expected growth rate for previous period adjusted for prediction error. In this case, if λ=1, the expected growth rate for t will equal to the actual growth rate of t-1. This is similar to that generated from implied method in part (a). The above equation can be generalized to the following form: ) u λu λ 2 ( λ) u + λ(1 λ) u... p, t = t t 2 t 3 + (12) 21 At time T, the time to maturity (T-t) will equal to zero and the implied growth rate at time T will not be able to calculate and use to estimate the implied growth rate at T+1. Hence, the implied growth rate at T+1 will be deleted from the study. 1040

17 Asia Pacific Management Review (2004) 9(6), where λ+λ(1-λ)+λ(1-λ) 2 + +λ(1-λ) k =1. Thus, not only the actual growth rate of the previous period relates to the expected growth rate of current period, those of earlier periods do have impact on formulation of current period expected growth rate. However, since 0< λ <1, the more distant the actual growth rate related to, the less impact it ) will impose on u p, t. When express in regression form, it will be: u p, t = wo + w1u t 1 + w2ut wnut n + ε t (13) The problem associated with this model is that it does not tell where to stop. That is, to include how many periods in the model. Either inclusion of irrelevant variables or omitting relevant variables in the model will expose to specification error which causes OLS estimators no longer be BLUE. In this study, u p,t is first regressed with u t-1, then u t-2, u t-3 will be added into the model one by one until the adjusted R 2 stops increases. To estimate this regression equation, similar procedures as mentioned in section 3.1(2)(a)~(d) will be applied, except that Durbin h test 22 instead of Durbin-Watson d test will be used in detecting autocorrelation. (3) Predictive power of both models After theoretical futures prices are estimated from both the cost of carry and the imperfect market models, their predictive powers can be measured by the percentage of estimation error as shown below: Z where t AFt F( S, t) = (14) F ( S, t) Z t is percentage of estimation error at time t, S t AF t is actual futures price at time t, and ( ) F, is theoretical futures price at time t. For all set of data, Z t values are computed for both models. Let the means of Z t values under the cost of carry model and the imperfect market model are λ 1 and λ 2 respectively. Then, test these estimation errors individually, that is, whether λ 1 and λ 2 are significantly different from zero. If the model is very accurate, it should have minimum estimation error. Accordingly, Z t values will not significantly different from zero and H 0 will not be rejected. In this case, the magnitude of the t-statistic can also serve as a guide to differentiate how significantly the mean of Z t values is differed from zero. 22 Durbin h test is applicable to autoregressive model while Durbin-Watson d test is not. 1041

18 Hsinan Hsu et al. 3.3 Testing the Impacts of Stock Market Volatility and Other Important Factors on Logarithm of Futures/Spot Price Ratio As mentioned in Section 2, Hemler & Longstaff [14] in a study on NYSE index futures market found that both risk free interest rate and market volatility have significant explanatory power on the logarithm of the futures/spot price ratio. These results are consistent with their equilibrium model, but not with the cost of carry model. The traditional cost of carry model does not consider the impact of market volatility on stock index futures pricing, however, their equilibrium model has shown that market volatility is also important in stock index futures pricing besides interest rate, spot index price, time to maturity and dividend yields. Thus, in this paper, the impact of market volatility on KLSE CI futures market is also examined on the logarithm of the futures/spot price ratio together with other factors as illustrated below: Ft 2 ln = α + α u p t + α σ t + α ( T t) + α rt + ε t S 0 1, (15) t where σ 2 = market volatility (stock index). All other variables except market volatility had been explained earlier. Market volatility here is measured by the variance of daily return of the spot index. The steps are as follows: (1) Compute daily market return: Stk R tk = ln St, k 1 (16) where R tk is stock return for the kth day in month t, and S tk is stock price for the kth day in month t. (2) Compute variances of the daily return as 23 : N ( R R ) σ t = 1 tk t (17) N k= 1 where R tk is return of k th trading day in month t, R t is average return in 23 The trading days of KLSE CI futures in the test period are between 231 to 236 days. 1042

19 Asia Pacific Management Review (2004) 9(6), month t, and N is the number of trading days in month t. (3) The regression analysis of equation (15) will follow those that described in section 3.1(2) (a)~(d). 3.4 The Data The period covered under this study is from January 2, 1996 to March 31, Perused through the trade volume of the futures contracts over the years, noted that the near month volume is substantially higher than contracts of other months. Hence, only the near month contract is considered in this study. As mentioned earlier, markets for the local government bonds are inactive and lack of liquidity, hence the average one-month fixed deposit interest rate of all commercial banks are used as a surrogate to the risk-free interest rate, r. Both the closing stock index and futures prices employed in this study are used. The sources of data employed in this study are summarized in Table 3. Table 3 Sources of Data Symbol Variables Source Period Form S t KLSE Composite Index (KLSE CI) January 2, 1996 to March 31, 2002 Daily (Closing) F t FKLI Prices (KLSE CI futures) January 2, 1996 to March 31, 2002 Daily (Closing) r Average of 1-month fixed deposit rates offered by all commercial banks January 1996 to March 2002 Monthly (End of month) d Dividend yields calculated from 2001 dividend records of all component stocks Investors Digest (December 2001) January 2001 to December 2001 Yearly 4. Empirical Results 24 The KLSE CI futures started to trade on December 15, However, it has only 10 trading days in 1995 and hence is not considered in this study. 1043

20 Hsinan Hsu et al. 4.1 Arbitrage Opportunities of the Cost of Carry Model From Table 4, noted that the occurrence of negative basis was very frequent during the sample period from January 1996 to March In overall, it has amounted to 671 observations or 43.7% of the total 1535 observations. As we learned from Section 2 that this could not be true given that the futures prices must always greater than the spot prices by applying equation (1) as the risk free rates are always greater than the dividend yields. In the sample period, the average risk free rates are % which is higher than the dividend yields of % used in this study. Many studies done on other futures markets found similar results, some have argued that this deviation is due mainly to the existence of transaction costs in an imperfect market that we have. But could that substantial and frequent occurrences are due solely to the transaction costs? Some also argued that this deviation was merely a transitory phenomenon. However, in the context of KLSE CI futures market, the negative basis occurred in the early trading days (1996 to 1998). It does not diminish as time goes by but remain in the later stage of the market trading days (2001). The adequacy of the cost of carry model is further examined with the consideration of transaction costs. If the model is adequate, the basis should remain in the no-arbitrage bounds as identified in equation (4). However, as shown in Table 4, there are many instances where the basis violates the lower and upper bounds of the no-arbitrage bounds during the sample period. In overall, at the same level of transaction costs, the basis violates the upper bound more often than the lower bound. Violations of upper bounds are 9.4%, 6.4% and 4.0% at transaction cost level of 2.0%, 2.5% and 3.0% respectively as opposed to violations of lower bounds of 6.1%, 4.2% and 3.3% respectively. Note from Table 4 that the lower bound violations are happened mainly in 1997 and 1998, while upper bound violations are concentrated in 1998 and At the transaction cost level of 2.0%, the lower and upper bounds violations in the period of 1997 to 1998 and 1998 to 1999 respectively, are further examined and documented in Table 5. From Table 5, it is clear that the lower bound violations are most frequent within the period from September 1997 to September While the upper bound violations happened mainly during September 1998 to December This seems to be closely related to the 1997 Asian Financial Crisis and the economic recovery thereafter. 1044

21 Asia Pacific Management Review (2004) 9(6), Table 4 Arbitrage Opportunities of the Cost of Carry Model Sample Period and Transaction cost level (b) % 2.5% 3.0% % 2.5% 3.0% % 2.5% 3.0% % 2.5% 3.0% % 2.5% 3.0% % 2.5% 3.0% % 2.5% 3.0% Total 2.0% 2.5% 3.0% No. of observations Negative basis Below lower (%) a bound (%) b (49.2) (66.1) (46.7) (18.1) (33.6) (56.4) 58 6 (10.3) (43.7) 0 (0.0) 0 (0.0) 0 (0.0) 39 (15.7) 32 (12.9) 26 (10.5) 48 (19.5) 31 (12.6) 24 (9.7) 1 (0.4) 1 (0.4) 0 (0.0) 1 (0.4) 0 (0.0) 0 (0.0) 5 (2.1) 1 (0.4) 1 (0.4) 0 (0.0) 0 (0.0) 0 (0.0) 94 (6.1) 65 (4.2) 51 (3.3) a Being AF t - S t < 0. b Being AF t - S t less than the lower bound of equation (4). c Being AF t - S t greater than the upper bound of equation (4). Above upper bound (%) c 0 (0.0) 0 (0.0) 0 (0.0) 3 (1.2) 1 (0.4) 1 (0.4) 44 (17.9) 37 (15.0) 27 (11.0) 79 (31.9) 54 (21.8) 33 (13.3) 10 (4.1) 5 (2.0) 1 (0.4) 0 (0.0) 0 (0.0) 0 (0.0) 8 (13.8) 1 (1.7) 0 (0.0) 144 (9.4) 98 (6.4) 62 (4.0) Maximum number of successive violations The Asian financial crisis surfaced on July 2, 1997 when the Bank of Thailand abandoned its policy of pegging the Baht against the US Dollar. This was followed by the Central Bank of Malaysia giving up the defense of the Ringgit on July 14, On July 26, 1997, the prime minister of Malaysia, Datuk Seri Dr. Mahathir Mohamad, named George Soros as the man responsible for the speculative attack on the Ringgit. The two men had a 1045

22 Hsinan Hsu et al. Table 5 Occurrence of Lower and Upper Bounds Violations (b = 2.0%) Lower Bound Violations Upper Bound Violations January February March April May June July August September October November December Total further exchange of words in public on September 20, From then on, the Ringgit exchange rate went on a downward spiral from 2.57 Ringgit to a US Dollar on July 14, 1997 to a lowest point of 4.88 Ringgit to a US Dollar on January 7, The fall in the exchange rate was followed closely by the Malaysian stock market index. On September 1, 1998, several measures intended to stabilize the Ringgit were implemented. These include the new Exchange Control Mechanism (ECM) that imposes regulations on the cross-border flow of Ringgit in notes and coins and withdrawal of larger notes (RM500 and RM1000) from the market. In addition, a 12-month moratorium on repatriating foreign funds was also introduced. 25 As a result, 25 This was later replaced by an exit tax in February 4, With this new amendment, the principal of the foreign capital remitted into the country after February 15, 1999 will no longer be taxed while profits are still taxable. Prior to this amendment, both repatriation of capital and profits are taxable. 1046

23 Asia Pacific Management Review (2004) 9(6), foreign investors dumped their shares in the stock market heavily. The Malaysian stock market lost 13.27% in one single day and reached its bottom of on September 1, 1998 from its highest of on February 25, 1997, i.e % (or points) of the stock market wealth was completely wiped out. On September 2, 1998, the Ringgit was formally pegged at 3.80 to one US Dollar. On September 4, 1998, the Malaysian government announced that an amount totaling of 20~25 billions Ringgit were expected to flow back to the Malaysian financial market as a result of the stringent control of the ECM. All these factors together with the strengthening of currencies of all other neighboring countries have revitalized the Malaysian stock market. The Malaysian stock market gained 31.9 points (or 12.14%), 18.5 points (6.3%), 50.3 points (16.07%) and 81.7 points (22.48%) on 2 nd, 3 rd, 4 th and 7 th of September 1998 respectively. The KLSE Composite index closed at on September 7, 1998 with a total increase of points or 69.4% from its September 1, 1998 level. Meanwhile, with brighter prospect of the stock market, the KLSE CI futures market has recorded the highest basis of in its history on September 7, Thereafter, the Malaysian stock market has slowly recovered. 26 The results from Table 5 match closely with the sequence of events mentioning above. It seems that the market conditions are closely related to the pricing of stock index futures in the KLSE CI futures market. For the lower bound violations that concentrated in September 1997 to September 1998, it seems to associate with the financial crisis that became worse since September 1997 and hit the bottom in September Thereafter, the economy and the stock market in Malaysia are slowly recovered. This is then seems to relate to the upper bound violations of the no-arbitrage bounds of the futures. Thus, with the frequent occurrence of the negative basis and the violations of both the lower and upper bounds of the no-arbitrage bounds of the futures price, it places doubt on the adequacy and suitability of the cost of carry model in the context of KLSE CI futures market. On the other hand, the pricing of futures seems to be related to some other factors. In this study, it seems that the price expectation plays a significant role in pricing of KLSE CI futures. In a bear market, 27 the actual futures are priced at a discount to 26 Please refer to Appendix 1 on the movement of KLSE CI and KLSE CI futures from January 1996 to March The lower bound violations simply mean that the AF < (F-b*S). That is, the actual futures prices are lower than the theoretical prices. 1047