Analyzing the Arbitrage Opportunities and their Determinants in Deliverable Futures Contracts: Evidence from Pakistan

This study explores arbitrage opportunities in Deliverable Futures Contracts (DFC) that arise due to mispricing and also examines the factors affecting it. The cost of carry model is used to calculate the fair prices of futures. Mispricing is taken as a direct measure of arbitrage opportunities. With one-year daily data, collected from data portal of Pakistan Stock Exchange, mispricing is calculated in DFCs on 22 stocks. Summary statistics of mispricing confirms the presence of arbitrage opportunities in selected stocks. Random Effect Tobit regression results indicate that time to contract expiry, volatility in underlying stock, trading volume of ready market, and trading volume of future market significantly explain mispricing .


Introduction
A large number of studies have been devoted to check the pricing efficiency of futures, being traded on various stock markets worldwide. These studies have used the famous cost of carry model, developed by Cornell and French (1983), to arrive at fair prices of futures contracts. Any difference of fair price of futures contract from its actual price i.e. mispricing, is actually an arbitrage opportunity. Earlier studies also examined the mispricing in relation to some factors. These factors mainly include time to contract expiry, volatility of underlying stock, liquidity, and open interest, etc. Many researchers confirmed the existence of arbitrage opportunities in derivatives and the significant effect of the aforesaid factors.
In the context of Pakistan, these derivatives are studied for their role in pricing and volatility of the underlying stock (Awan & Shah, 2014;Jamal & Fraz, 2013;Khan, Shah, & Abbas, 2011;Khan & Hijzi, 2009;Ullah & Shah, 2013). However, the presence of arbitrage opportunities due to mispricing in SSF at Pakistan Stock Exchange (PSX) and the factors affecting these opportunities are yet to be confirmed. This research contributes to the existing literature first by calculating arbitrage opportunities, as indicated by mispricing in DFCs being traded at PSX, and then by relating mispricing with the factors affecting it. The outcomes of this study have implications for PSX investors and regulators.
The remainder of this paper is structured as follows. Section 2 presents the literature review and the theoretical framework. The research methodology is discussed in section 3. Section 4 provides results and discussion. Conclusions are stated in section 5. Recommendations are made in section 6. Section 7 discusses the limitations of this study.

Problem Statement
Futures contract provide arbitrage opportunities if not fairly priced. This attribute of the futures contract is not examined in the context of Pakistan and these contracts are generally assumed as risk hedging instruments only. A study from Pakistan is needed to examine the arbitrage opportunities in single stock futures and the factors affecting these opportunities.

Research Objective
The main objective of this study is to examine arbitrage opportunities in DFCs at PSX with respect to time to maturity, price volatility

Futures in the Context of Pakistani Stock Market
Single stock futures were introduced in Pakistan in the year 2001. The futures market of Pakistan could not get much attention from the researchers. A few studies have examined futures-spot relationship to check the spot price volatility (Awan & Shah, 2014;Khan et al., 2011;Khan & Hijzi, 2009) and as spot price discovery function (Jamal & Fraz, 2013;Ullah & Shah, 2013).While discussing numerous other ways to invest in stock market, Khan and Hassan (2013)also talk about trading in futures. But no study has checked the presence of arbitrage opportunities in single stock futures.

Futures in the Context of Foreign Stock Markets
Since the introduction of stock index futures in the US market in 1982, relative pricing of futures and the underlying asset has been a great interest of researchers. Along with other motives, academicians and practitioners had checked the future spot price relationship to look for arbitrage opportunities as well that arise due to mispricing in futures. Brenner, Subrahmanyam, and Uno (1989) studied the behavior of prices of Japanese stock as represented by Nikkei Stock Average (NSA) index and NSA futures. Theoretical fair prices were obtained using the cost of carry model and after comparison with 97 Chuhdary,M.,& Ismail,A. Volume 1 Issue 2; August 2019 actual prices, the presence of mispricing was confirmed in NSA futures. The study concludes that future contracts are generally sold at a discount rate. Stoll and Whaley (1990) checked the temporal relation between price movements of S&P 500 and MM index futures and underlying stock indices. The study checks the volatility of index futures against the stock indices and the deviation of futures from their true values. Results indicate that returns from futures indices lead the stock indices by five minutes on average. The study found pieces of evidence that new information circulates in futures market first and then it is transmitted to the stock market. Arbitragers then come into action and trade to bring futures prices back to equilibrium. Yadav and Pope (1990) analyzed the pricing efficiency of UK FTSE-100 contracts traded on London International Financial Futures Exchange (LIFFE) before and after the big bang. While accounting for relevant transaction costs, separate results for the different types of investors were reported. The average of mispricing returns was significantly positive when these contracts were initially underpriced and vice versa. Among various other determinants, only time to contract expiration was found to be significantly relevant in explaining percentage mispricing. Both inter-day and intraday volatility were found to be relatively greater in the futures market.
The number and size of pricing violations in S&P 500 index options before and after the introduction of SPDRs 3 at AMEX were examined by Ackert and Tian (2001).The study stated that arbitrage trading is vital to bring efficiency in the market as it moves the prices back to their fair values. Empirical results supported that SPDRs improved the connection between index and options market. Liquidity and stock index volatility were found to be important determinants for mispricing in index options. Misra, Kannan, and Misra (2006) confirmed the violation of spot-futures parity theorem in the case of NSE Nifty futures and also considered the determinants of these violations in the Indian stock market. Price violations were estimated in Nifty futures 4 for a period of one year. Significant mispricing, providing an average profit of 2422 Indian rupees per contract, was found. According to this study, mispricing was greater in extent for far the month futures contracts than for the contracts which are going to expire soon. Mispricing band was larger for the contracts with negative price deviations and more liquidity. Open interest was another significant and positive determinant of mispricing. Arbitrage opportunities were not changing due to rising or declining trends in the market. Vipul (2008) found mispricing in 6 highly liquid single stock futures in the Indian stock market. After accounting for 0.35 % and 0.70 % transaction cost for NSE members and financial institutions respectively, the study confirmed the existence of arbitrage opportunities. Using VAR framework, the study checked if certain factors (mispricing, change in open interest, change in volume of underlying stock and future contract and change in volatility of underlying stock and futures contract) have the ability to predict each other. Evidence of strong autocorrelation among these variables was found and each one could be explained by its past values. Mispricing didn't lead or lag any other variable. Fassas (2010) investigates the pricing efficiency of FTSE/ATHEX-20 index futures by using the cost of carry model and found that significant profit-making opportunities for arbitragers exist even after considering the roundtrip transaction cost. A significant relationship between mispricing and dividend payments, shortselling restrictions, implied volatility and, the volume of the ready and future market is also seen. Bialkowski and Jakubowski (2012)found that trading activity in SSFs is explained by different determinants. The study states that in order to determine the efficiency of the futures market, spotfuture mispricing is often used as a benchmark. It can be expected that magnitude of mispricing is negatively correlated to trading activity as indicated by trading volume or open interest. Conversely, mispricing at some level encourages arbitrager to trade and make a profit, therefore, a positive association is also expected between the magnitude of mispricing and trading activity. SSFs, by this study, are found to be more efficiently priced around ex-dividend dates. Nandan, Agrawal, and Bhargava (2014) confirmed the deviation from fair prices of CNX Nifty futures. Negative mispricing is greater in frequency and magnitude. However, mispricing trend was found to be different for different sub-periods across the study period. Deville, Gresse, and De Séverac (2014) investigated the direct and indirect impact of the introduction of index security (ETF) on underlying-index spot-futures pricing. The study found significant improvement in the no-arbitrage price relationship in post ETF period. Index-futures mispricing was found to decrease, at first, in a multivariate analysis that controlled the factors affecting spot-futures price relationship. The VAR analysis then indicated that index futures mispricing did not invite ETF trading and that ETF trading did not contribute to reducing index-futures mispricing. These findings failed to support the assumption that the improvement of noarbitrage price relationship is mainly due to the introduction of ETF. However, some findings suggested that efficiency improvement, after ETF introduction, probably arose from a long-run indirect effect of structural change in the way traders distribute across index markets.
By using equity data from Taiwan Stock Exchange Corporation (TWSE) and futures data from Taiwan Futures Exchange (TAIFEX), Chang and Lin (2015)examined the cash futures basis to find arbitrage opportunities in Taiwan stock market. The magnitude of basis spreads was further related to the liquidity, volatility and informed trading and results for the period near to expiration and far from expiration were compared. Regression results indicated that increased trading and higher volatility tend to increase the spreads and market is dominated by the speculators. Aggarwal (2015) arrived at the futures basis of 141 stocks using the cost of carry model to explore the arbitrage opportunities. These bases were then related to the basis risk, liquidity risk, liquidity cost, and stock volatility to find the limits to arbitrage.  Rambabu, Chaudhari, Sangishetty, and Naidu (2017) found profit-making arbitrage opportunities in futures and options using NIFTY 50 stocks as the underlying asset. It was noticed that these mispricing opportunities were due to market inefficiencies resulting from various factors such as fundamental risks, noise trader risk, information gap, financing issues, higher implied volatility, portfolio management problems, lesser liquidity of the markets and trade accompanied implementation cost. Shankar, Sankar, and Kiran (2019) examined SSFs trading at NSE India. The study used multi-regime models to calculate mispricing bounds for over one hundred stocks that were further related to liquidity and volatility. Study concluded that an increase in mispricing is associated with a decrease in liquidity. However, even after controlling for the effects of liquidity, mispricing increased with increasing volatility.

Arbitrage Opportunities in Futures
The fundamental variable upon which the entire study is based is mispricing. Chang and Lin (2015) stated that the accessibility of a replicating portfolio identifies an arbitrage opportunity in a frictionless market if mispricing is not equal to zero. In order to determine arbitrage opportunities, as represented by mispricing, we first need to calculate the fair price of the futures contract. Cornell and French (1983) introduced the most reliable model for futures fair pricing.

Ft=St e (r-d) (T-t)
The price structure given by this model relates the spot and futures prices as a function of time to maturity. The difference between the spot and futures price is contributed by the "cost to carry" the asset until its maturity. The cost of carry model doesn't assume transaction cost, taxes, and short selling restrictions. This model further assumes that lending and borrowing rates are the same. results in mispricing (Vipul, 2008).The mispricing creates an arbitrage opportunity where trader simultaneously buys/sells the future and underlying asset to make a risk-free profit.

Determinants of Arbitrage Opportunities
Numerous factors are said to be responsible when explaining arbitrage opportunities in futures. Previous related works help to derive important determinants of mispricing.
Time to contract expiration/maturity, according to Yadav and Pope (1990),can be related to the higher absolute magnitude of mispricing due to uncertainty about dividends, relative pattern of interest rates, and stock prices. Theoretically, the price of an SSF is greater than spot price in the period far from contract expiration and gradually it starts declining until the expiration day arrives; at which the fair price of futures becomes exactly equal to the spot price.
Mispricing is also affected by spot volatility and there are different opinions of researchers about it. One opinion is that higher volatility is a result of greater price movements and consequently, it increases the mispricing.
The other is that market participants rebalance their portfolio due to higher volatility which changes the expected returns of futures and spot market. It attracts other participants to take advantage of this and increases the arbitrage activity, thus decreasing the mispricing. However, Chang and Lin (2015) found that volatility generally serves to increase the spread. Tu et al. (2016) suggested that even during the period of financial crises, concurrent or spot volatility is capable of explaining futures mispricing.
Liquidity of futures and spot markets, as indicated by trading volume, is another important determinant of mispricing. Different arguments are found behind the relationship between liquidity and mispricing in related studies. Fassas (2010)states that if arbitrage transactions are initiated by the arbitrager then it leads to narrowing of price deviations. Chang and Lin (2015), however, finds a positive relationship between liquidity of futures and mispricing and explained this effect as a result of speculator's trading who widen the spreads by dominating the market and exacerbating the arbitrage. Open interest is also used by Misra et al. (2006)and Vipul (2008)to check if the opening of new contracts or closing of older contracts affects mispricing.
Finally, a set of commonly studied determinates of mispricing is obtained that can be used to explain the mispricing in DFCs at PSX as well. Figure 1 illustrates it.

Research Hypotheses
Based on the afformationed framework, the study poses the following hypotheses: H1: Number of days to contract expiry has a significant relationship with mispricing. H2: Price volatility of underlying stock has a significant relationship with mispricing. H3: Trading volume of the futures contract has a significant relationship with mispricing.

Futures Trading Volume
Open Interest Spot Volatility Spot Trading Volume H4: Trading volume of the underlying stock has a significant relationship with mispricing. H5: Open interest in the futures contract has a significant relationship with mispricing.

Research Methodology
This section describes the Variables,Data, and theEconometric model.

Variables and Data
Data for this research is available online at the data portal of PSX. Data is collected from January 2015 to December 2015 DFCs on daily basis for twenty-two stocks, selected through purposive sampling technique. Selected stocks are listed in Table 1. 1) Security must be currently eligible 5 for deliverable futures trading. 2) Contracts on each security must be available throughout the year 2015. Securities with at least twelve 6 one-month contracts are selected only. 3) Securities must have non-zero trading volume throughout the study period.
The year 2015 is selected in order to get an insight in to this issue with recent data. Observations for first five days or overlapping period of each new contract are dropped 7 Data on 252 trading days for 22 stocks was considered for further analysis. Detail of selected trading days of January 2015 to December 2015 DFC is exemplified in table 2. This gives rise to more than twelve contracts per stock in a year. However, trading period of such futures remains same as DFCs on other stock for that specific month. 7 Contract for the next month is opened a few days before the expiry of the near month contract. This, according to Vipul (2008),reflects that the open interest, volatility, and volume of future during this overlapping period belong to the existing or near month contract. Therefore, data on overlapping days need to be removed for new contracts. This also applies to the cum-dividend and ex-dividend contracts. A balanced panel dataset with 5544 observations is finally obtained. Variable wise details of collected data and methods of calculation are discussed here.

Mispricing M
It is deviation of fair price from the actual price of futures. Mispricing leads to arbitrage by simultaneously changing the positions in the ready and futures market. Vipul (2008) defined mipricing as the difference of actual price of futures from its theoretical fair price. Following Burger and Smit (1997) mispricing is estimated by the following formula:

M=FA-FTh
Where FA is the actual futures price and it is taken as the closing price 8 of a particular DFC on day t. FTh is the theoretical fair price calculated using the cost of carry model given by Cornell and French (1983).Following Ackert and Tian (2001),commission costs and short-selling restrictions are ignored to capture maximum violation of spot-futuresparity. Therefore, FTh or the Theoretical fair price of a futures contract is calculated as: FTh=(S-D) e r(t-T) "S" is spot price of the underlying stock and it is taken as the closing price of the stock on day t. D is the present value (PV) of cash dividends 9 expected on the underlying stock until the maturity of the contract. Dividends are excluded from contracts available on the cum-dividend 10 basis for which a company has announced its book closure dates. Khatri (2016) provides following formula to calculate fair price with dividend adjustments whenever a dividend is expected till the maturity time.

F=(S-PV of dividend)*e rt
Here the present value of the dividend is at the applicable rate for the duration at the end of which dividend is received or expected. Fassas (2010) also excluded the present value of dividends from the spot price to get the fair prices of futures. "e" is exponent and its value is 2.718. "r" is risk-free interest rate and taken as the daily KIBOR for one month tenure. By following Fassas (2010), interbank offer rate is used as the risk-free rate of interest. Time till maturity of the contract is taken in fraction of a year i.e. t-T/365. Where "t" is the day for which fair price of futures is to be calculated and T is the day at which contract will close. By following related studies (Fassas, 2010;Misra et al., 2006), absolute mispricing |M| is used for further analysis because mispricing on either side gives rise to an arbitrage opportunity.
Data on daily futures and spot prices (Last day closing price, Open, High, Low, and Close), days to contract maturity, dividend payments, and daily KIBOR published by State Bank of Pakistan for one month tenure is collected from the official data portal of PSX for the selected stocks. 9 As dividend payments are usually discrete events, it is not viable to use a constant dividend yield (Fassas, 2010;Vipul, 2008). 10 Contracts that are entitled to receive dividends. At PSX stocks are sometimes split on cum dividend and ex dividend basis, and a revised schedule for trading is announced. Whenever Deliverable Futures trading schedule is announced, it is also mentioned which contracts are entitled to receive dividends and which contracts will be traded on ex-benefit basis even if the company has announced its closure of books. This information is available under the PSX Notice & Updates section and the information on dividends and book closure dates is available under the financials of each stock.

Time to Contract Expiry FMAT
FMATt is the time till maturity of the futures contract on day t. Theoretically, the price of an SSF is greater than spot price in the period far from contract expiration and gradually it starts declining until the expiration day arrives; at which the fair price of futures becomes exactly equal to the spot price. FMATt is calculated by taking the number of days until contract expiry in fraction of a year i.e. t-T/365 (Burger & Smit, 1997).T is the day on which a DFC is going to expire and this information is available in daily quotations and announcements on PSX data portal.

Volatility of Underlying Stock SV
The volatility of share price is a measure of uncertainty about future share price movements (Burger & Smit, 1997). Chang and Lin (2015) found that volatility generally serves to increase the mispricing spread. Tu et al. (2016) suggested that even during the period of financial crises, concurrent or spot volatility is capable of explaining futures mispricing. Following Vipul (2008), formula provided by Parkinson (1980)for calculation of variance with extreme value method is used to estimate volatility in the price of the underlying stock on day t as: WhereShtis the maximum price and Slt is the minimum price of a share on day t. 0.601 is random walk factor 11 . Extreme value 11 The diffusion constant D that characterizes that random walk for each stock is estimated by the extreme value method in Parkinson (1980). The study says that the extreme value method is very easy to apply in practice, since daily, weekly, and in some cases, monthly highs and lows are published for every stock. The change using D to measure variance V could be of specific significance in studies that assume the dependence of V upon time and to get a given precision in V. As compared to the traditional method, around 80% less data and as a result, 80% smaller time interval is required for extreme value method. The study concluded that the extreme value method is 2.5 to 5 times better than the traditional method. The diffusion constant estimated by this study is: Volume 1 Issue 2; August 2019 method is given by Parkinson (1980) to estimate the variance. According to this, if S is the price of a stock, then ln (S) will follow a random walk (at least to a very good approximation). Vipul (2008), used the formula for variance originally developed by Parkinson (1980).
Thus, volatility has been estimated using: Data on daily high low prices of the underlying stock is collected from the PSX data portal.

Volume of Underlying Stock SVOLU
In this study, SVOLU or trading volume of underlying stock is taken as a proxy for the liquidity of underlying stock. It is taken as daily trading volume in a fraction of the total number of shares outstanding for that stock. This method is used to check if liquidity of underlying stock has any effect on mispricing in SSF or not. Theoretically, the liquidity of underlying stock tends to widen or narrow the pricing spreads in speculators or arbitragers dominated market respectively.

Futures Market Volume FVOLU
FVOLU or trading volume of futures, taken as a proxy for the liquidity of DFC, is also a determinant of mispricing in it (Ackert & Tian, 2001;Fassas, 2010;Misra et al., 2006;Vipul, 2008).FVOLU is taken as the trading volume of DFC in the percentage of number of shares outstanding for the underlying stock. Hypothetically, in arbitragers dominated market, mispricing decreases due to increasing liquidity. However, this relationship inverses when the market is in control of speculators.

Open Interest OI
Open interest is defined as the number of unsettled futures contracts at any time. Open interest is taken in the percentage of the free float as provided by PSX. OI was used by Misra et al. (2006) and Vipul (2008)to check if the opening of new contracts or closing of older contracts can explain mispricing behavior. Misra et al. (2006) confirmed that mispricing in futures was increasing due to increasing in open interest. Vipul (2008), however, found that change in mispricing was not due to change in open interest.
Data for daily trading volume (in ready and futures market) the total number of shares outstanding and open interest in percentage of free float is available on PSX data portal.

Econometric Model
The relationship between mispricing and its determinants is modelled as follows: |Mit|=α+β1FMATit+β2SVit+β3FVOLUit+β4SVOLUit +β5OIit +εit Where |Mit| is absolute mispricing per share of a company i on day t and FMATit is the number of days remaining in contract expiry, SVit is the volatility in the price of the underlying stock, FVOLUit is the volume of a futures contract, and SVOLUit is the volume of the underlying stock. OIit is open interest in the futures contract and εit is error term. Random effect Tobit model is used because the dependent variable is censored or unobservable when a pricing relationship holds. Yadav and Pope (1990), Ackert andTian (2001), andFassas (2010)used Tobit censored regression to model the factors that explain mispricing.

Results and Discussion
Single stock futures are being traded in Pakistan since the year 2001. A five-year comparison of performances of ready and futures markets of PSX is provided in Table 3. Futures on stocks are settled both by cash and through physical delivery of the underlying shares. For this research, Deliverable Futures Contracts were selected because of their non-zero trading volume as compared to CSFs. The specifications of DFC are given in Table 4. Before explaining mispricing with respect to its determinants, the presence of mispricing in DFCs was confirmed by calculating the difference between their actual and theoretical fair prices. Summary statistics of absolute mispricing per share are given in the Appendix: A. Stock-wise minimum, mean and maximum absolute values of mispricing can be seen in percentage per share in this table. Magnitude and frequency of mispricing in positive and negative directions are also given in the next columns. Same is plotted in figure  2 and 3 respectively for a quick glimpse of the reader. In line with previous studies, mispricing is found to be common in Pakistani stock futures. With negative mispricing of 6.74% per share price, PTC stock futures are leading. On the other hand, lowest mispricing per share is observed in EFOODS futures where maximum mispricing is 0.65 % per share price on the positive side. FCCL, NCL, and NML also exhibit dominant mispricing pattern, with maximum mispricing of 5.27%, 5.20% and 5.07 % per share price respectively. Overpricing of DFCs is more frequent than under pricing. Results prove that all stocks involved in DFC trading provide sound arbitrage opportunities to the investors who can earn riskless profit by choosing appropriate arbitrage strategy. According to Stoll and Whaley (1990), when the observed futures price is above the theoretical price FTh a long arbitrage profit, equal to the difference between the actual and theoretical price of futures, can be earned by selling the futures and buying the index portfolio i.e. the underlying asset. An Index portfolio can be purchased by borrowing the money at riskless interest rate. Conversely, if observed futures price is below the theoretical fair price FTh short arbitrage profit equal to the difference between the actual and theoretical price of futures can be earned by buying the futures and selling the index portfolio. The amount received from selling the underlying asset can be invested at a risk-free rate of interest. Outcomes of the random effect Tobit model are given in Table 6 to confirm the relationship of mispricing with the factors affecting it.

Time to Contract Expiry FMATit
According to the results of the Tobit regression, FMATit is the most significant variable. Results are similar to Burger and Smit (1997), Misra et al. (2006), Fassas (2010, and Tu et al. (2016).The coefficient is positive and indicates that a one percent change in time to contract expiry increases the magnitude of absolute mispricing by2.76 . Mispricing starts decreasing when the contract is near to its expiry. This is just in line with the pricing theory behind futures i.e. the cost of carry model. When t=0, the fair price of the futures becomes equal to the spot price of underlying stock and mispricing becomes 0.

Volatility of Underlying Stock SVit
The volatility of the underlying stock price is positively related to absolute mispricing and highly significant too. A one percent change in volatility on either side leads to a change in the magnitude of absolute mispricing of 1.5 accordingly. Chang and Lin (2015) and Tu et al. (2016) also found a positive and significant effect of concurrent volatility on mispricing. Results are also in line with the findings of Fassas (2010) but are contrary to (Vipul, 2008).

Futures Market Volume FVOLUit
The volume of the futures, taken as a proxy for liquidity, is also positively related to absolute mispricing. Results are significant and can be interpreted as a 1% increase in the liquidity of futures increases the mispricing in futures by 4.41 and vice versa. Results are similar to Misra et al. (2006), Chang and Lin (2015) and Tu et al. (2016) as they confirm a significant positive relationship between Liquidity of futures and mispricing.

Volume of Underlying Stock SVOLUit
The trading volume of the underlying stock is also taken as a proxy for liquidity. The coefficient is negative and indicates that absolute mispricing is high in futures with less liquid underlying stock. A one percent increase in liquidity decreases the mispricing by 4.27.
Results are in line with Tu et al. (2016) and Chang and Lin (2015)and confirms a negative relationship between the liquidity of underlying stock and mispricing. This is consistent with the argument that heightened levels of arbitrage trading would tend to lower spreads (Chang & Lin, 2015). Fassas (2010) found a positive association between liquidity of cash market and mispricing. (Vipul, 2008)did not find any such relationship.

Open Interest OIit
The coefficient of OIit is positive and indicates that a 1% change in open interest increases or decreases absolute mispricing by 0.47. However, the result is insignificant at both 5% and 10% levels. Contrary to Misra et al. (2006), the result of this study confirms the finding of Vipul (2008) that there is no association between absolute mispricing and open interest.

Conclusion
Single stock futures have never been analyzed for arbitrage opportunities since their introduction in Pakistan. This study was dedicated to fill the gap by analyzing arbitrage opportunities in futures in the context of Pakistan. The analysis in this study leads to some significant conclusions in this regard. It is found that DFCs at PSX are frequently mispriced and provide risk-less profit-making arbitrage opportunities. Overpricing of these futures is relatively more common than under pricing. However, negative mispricing spreads are found to be greater in magnitude in some stocks.
As per previous related studies time till contract maturity, volatility and liquidity were found as main contributors of mispricing in DFCs. Effect of open interest was also examined to explain mispricing in earlier studies. In order to explain the mispricing in DFCs at PSX, same variables are used. Apart from open interest, all of these variables have significant explanatory power for mispricing. The magnitude of mispricing is found to be greater during the period far from contract expiration and in the contracts with higher volatility. Negative relationship of spot liquidity indicates the dominance of arbitragers in this market who trade to narrow the mispricing spreads. On the other hand, positive relationship between futures liquidity and mispricing is due to speculators' dominance as they trade by widening these spreads. This indicates that speculatory mo-tives may also be a reason behind mispricing. It is possible that mispricing in these contracts is initiated by the speculators, and then arbitragers may start trading to make these spreads narrower.

Recommendations
Based on the conclusions of this study, some practical recommendations are made here:  Stocks for trading under the DFC market are selected through uniform selection criteria, approved by SECP. Exchange can select top 100 book-entry securities meeting these criteria. The actual number of securities, selected every six months, is less than even half of this number. It is recommended that keeping in view the benefits of trading under futures market; other listed companies should also try to enter DFC market. Exchange can also relax the criteria in order to gather more companies under the Single Stocks Futures umbrella, where applicable and feasible in the mutual interest of stockholders and stakeholders.  With a positive association, time to contract expiry is found to be the most significant factor of mispricing. The magnitude of mispricing is greater at the start of the contract when more time is left to contract maturity. PSX can introduce the DFCs with different maturity periods i.e. two months and three months future contracts etc. to attract the arbitragers.  Arbitrage is a healthy activity that brings efficiency in the market. Results, however, indicated that magnitude of mispricing was increasing with the increasing liquidity of futures. This phenomenon points toward the dominance of speculator's in this market. Speculators trading should be discouraged so that arbitrage is not exacerbated by widening these spreads.  Futures serve to hedge against the risk related to price fluctuation in underlying stocks. On the other hand, higher volatility in underlying stock tends to increase the mispricing band, as indicated by the results of this study. It is suggested that stocks with higher volatility can be introduced in stock futures trading to help the investors to hedge against the risk and to exploit the arbitrage opportunities as well.