Essay on Financial Futures

Introduction

Financial forward and futures contracts represent a commitment by one party to make delivery of the underlying asset to the contract's counterparty for a cash payment in the future date. Besides being the hedging instruments, forward and futures are used by market speculators and arbitrageurs to enhance their returns margin. Although no initial cash transfer between parties is required for both forward and futures contracts, certain distinctive features between them should be noted. The terms and conditions in the forward contract are set by the parties to the contract through negotiation. The delivery date and forward price are predetermined at the time the contract is entered into. The futures contract's terms and conditions, on the other hand, are more standardized than those specified in the forward contract with four special features. First, the exchange (e.g., the MERC) who acts as counterparty to futures contracts prespecifies the maturity date, delivery location, quality and quantity of the security to be delivered per contract. Second, the exchange guarantees the performance of both clearing firms involved in the futures trade. Third, positions in futures contracts can be liquidated prior to the maturity date of the contract by taking an offsetting position in the identical contracts. And fourth, the gain or loss on a futures position is marked to market, settled, and cleared through daily cash payments. These four special characteristics provide added protection against illiquidity, default (or credit risk), and settlement risks for futures contracts over forward contracts.

Theoretical Basis for Futures Pricing Back to Top

The simple futures pricing model is based on the principle of arbitrage-free, forward-expected spot prices relationship. Other more empirically relevant models include the capital asset pricing model (CAPM), the net hedging pressure (NHP) theory, and the cost of carry model (CCM). Theoretically, the forward price at which arbitrage opportunity cannot occur is:

FW_t = S_t(1+i)^T = E[S_t+T]
where: FW_t = market value of forward contract at time t; S_t = spot or cash price of the underlying security at time 0; i = rate of return of the risk-free security, i.e., interest rate; T = time to maturity of forward contract; E[S_t+T] = expected future spot price of the underlying security at time t+T

Haugen (1986) suggests that since futures contracts are traded on the exchange, there exist some discrepencies and relationship between forward and futures contract prices. The difference in the cash flows results in a divergence between the two prices:

F_t = FW_t + RP - DP

where: F_t = futures contract price at time t; RP = reinvestment premium; DP = delivery premium

Reinvestment premium depends on the relationship of the covariance between the spot price of the underlying security and the level of risk-free interest rate. If the relationship is positive, then RP will be positive, and vice versa. If the underlying security is T-bond, then RP will be negative since T-bond price and interest rate are inversely correlated. The delivery premium is negative because the futures provides the contract seller the options with respect to the exact nature of the underlying security that can be delivered to the buyer. The contract buyer, therefore, demands a discount on futures price, i.e., the negative DP, which depends on the degree of latitude the seller has in terms of delivery and the extent to which the futures price can be adjusted on delivery to fit the character of the underlying security.

Based on the CAPM, a change in the futures price is proportional to the changes in the term premium of the risk-free rate and the market risk premium. If this relationship holds, futures price is considered an unbiased estimator of the expected future spot price. However, it is found through empirical studies by Dusak (1973) and Bodie and Rosanksy (1980) that the betas of commodity futures contracts approach zero. Hence, this implies that the market risk premium on commodity futures is also zero. Nontheless, Bodie and Rosanksy observe that commodity futures have positive returns. This contradiction occurs because the stock market beta is not an appropriate measure of risk for commodity futures since it cannot capture idiosyncratic risk of each kind of commodities. They, therefore, conclude that stock-maket-based CAPM cannot be used to value commodity futures contract accurately.

The NHP theory postulates that futures returns are biased against the net hedging position in favor of the net speculative position. Following Keynes (1930), Hicks (1946), and Houthakker (1957), if the futures are underpriced, creating excess returns for long speculators, then there exists a situation known as normal backwardation. In this situation, net short hedging exceeds net long speculation. If, on the other hand, the futures are overpriced, the opposite situation occurs. This situation is called a contango where net long hedging exceeds net short speculation. Both of these two NHP situations are rejected by many empirical studies by Rockwell (1967), Fama and French (1987), Hartzmark (1987), Murphy and Hilliard (1989), Phillips and Weiner (1991), and Kolb (1992) which shall be discussed later. Therefore, NHP theory is not empirically powerful enough to serve as accurate pricing basis for futures contracts.

One other model remains which is the cost of carry model. The CCM is used to measure the relationship between the spot price of the underlying security and its futures price. It assumes that the short-positioned futures arbitrageurs borrow funds to purchase the underlying security in the spot market and deliver it when the futures contract matures. The CCM is similar to the forward pricing model as follow:

FV_t = S_t(1+i)^T = F_t = E[S_t+T]

where: FV_t = theoretical value of futures contract at time t; F_t = market price of futures contract at time t; S_t = spot price of the underlying security at time t; i = rate of return on risk-free security, i.e., interest rate; T = time to maturity of futures contract

The theoretical value and the market price of the futures contract are assumed to be equal under the perfect capital markets' conditions which include perfect competition, frictionless markets, complete information, homogeneous beliefs, and individual rationality. When the conditions of perfect markets are relaxed, arbitrage opportunities exist. If FV_t = S_t(1+i)^T < F_t, an arbitrage position can be set by selling (short) the relatively overpriced Ft and buying (long) the fairly priced security in the spot market with S_t amount of lending (short) at i to be paid back in T periods. The net cash position is zero, since the arbitrageur is long in security while being short in the loan with identical amount. The riskless profit is locked in at time t and to be paid off at the marutiry date t+T. If FV_t = S_t(1+i)^T > F_t, then the opposite positions are required in futures (long), spot (short), and borrowing (long) transactions to lock in the profit at time t. Yet, these arbitrage opportunities exist in a very short-time horizon due to certain impediments to riskless profit including transaction costs, short-selling restrictions, borrowing/lending limitations and rates divergence, and the volatility of the risk-free interest rate.

There are certain relationships among FV, F, and i which are worth discussing. Cox, Ingersoll, and Ross (1981) infer the relationship between FV and F from the correlations between F and i. If i and F are positively correlated, then F should be greater than FV. In case of FV = F and when i and F rise together, the long futures position gains and the short loses. The short futures pays long futures in cash at day's end. The long, in turn, lends this cash amount at relatively high interest rate. When i and F fall together, the long position loses while the short gains. The long pays cash to the short and borrows the amount she pays at a relatively low interest rate. The reverse of these positions is true if the correlation between i and F is negative. That is, F should be less than FV when i moves in the oppositie direction to F. At market equilibrium when FV = F and when i rises (falls) and F falls (rises), the short futures position gains (loses) and the long loses (gains) at day's end. The short futures position receives (pays) cash from (to) the long and lends (borrows) it at a relatively high (low) interest rate.

Some Futures Trading Strategies Back to Top

Stock Index Futures Arbitrage

The futures contracts on stock indices offer some arbitrage opportunities to those traders who could discover price discrepency between FV and F. The main source of price differential can be attributed to the presence of dividends received from holding stocks in the index and the financing costs incurred in either lending or borrowing transactions. Thus, the theoretical value of stock index futures is given by:

FV_t = S_t(1+i)^T - D = F_t

where: D = dividends received from holding stocks in the index up to t+T

In setting up the arbitrage positions for stock index futures, the net financing costs (NFC), i.e., the difference between dividend yield and interest rate, must be taken into account. The stock index futures is overpriced when F - S > NFC, and underpriced when F - S < NFC. The arbitrage positions can be set accordingly following the logic discussed earlier in the previous section. For example, the short futures arbitrage takes place when F is overpriced. This is accomplished by selling (short) stock index futures, buying (long) stock index spot, lending (short) the cash amount equal to stock index price, and receiving cash dividends. Since the profit from short position in futures and long position in spot exceeds the NFC, riskless arbitrage results. In contrast, the long future arbitrage occurs when F is underpriced. The positions are set up as follow: buying (long) stock index in the futures market, selling (short) stock index in the spot market, borrowing (long) the amount equivalent to the index price, and forgoing the cash dividends. As a result, the NFC must be greater than the profit made from the difference between the futures and spot index prices.

The difficulty in determining the NFC poses certain risk in setting up the stock index arbitrage positions. This risk is caused by the timing and the stream of dividends which cannot be determined as easily as the more certain interest rate. Another difficulty stems from the fact that stock index futures price sometimes leads the spot price of the index itself. This further complicates the identification of the futures contract's mispricing. Moreover, the perfectly hedged positions between stock index spot and leveraging may not be achievable due to dividends' uncertainty and increased transaction costs.

Dynamic Portfolio Insurance

Dynamic portfolio insurance can be viewed as an alternative strategy to stock index futures arbitrage that is used to protect the capital gains of the current portfolio without conceding the opportunity for future capital gains when the prices or the indices rise. It effectively guarantees the minimum selling price of the portfolio or stock index should the markets decline while allowing unlimited gains on the up-side should the markets rally. The price risk in the spot markets can be hedged by taking a short portfolio futures position while going long in spot portfolio position. The short futures position serves as an insurance against the down-side price risk without making any initial cash outlay. Portfolio insurance can be obtained through taking the long positions both in the underlying security and the put option. However, this option-based strategy incurs initial cash payment in the form of put premium whenever the put contract is entered into. It is noteworthy that during the stock market crash of 1987, dynamic portfolio insurance activities and program trading (i.e., simulataneously buying and selling large number of stocks to adjust or reblance the current portfolios in a single execution to exploit timing advantage and save transaction costs) were blamed as being its primary causes since there had been more short portfolio positions than long in both futures and spot markets which put more pressure to sell and result in prices to cascade downward even furtuer very rapidly. The phenomenon experienced then can be perceived as being either the market prices adjustment toward their fundamental values or the overreaction in both the underlying securities and the derivatives markets. It leads researchers and market regulators to ponder the empirical evidence with respect to the issues of derivatives mispricing and the need for price adjustment mechanisms (e.g., circuit breaker) and the issue of lead-lag effects between the spot and futures markets.
Empirical Evidence of Futures Trading

Futures Mispricing Effects Back to Top

The studies conducted in this area have focused on the cross-sectional price discrepencies between the theoretical value of futures derived from the spot price of the underlying security and the market value of such futures contract. Dusak (1973) and Bodie and Rosansky (1980) base their studies on the CAPM to determine the betas of commoditiy futures market in relation to the stock market. They find that commodity futures betas approach zero with positive intercept. Breeden (1979, 1980) uses his consumption-based CAPM to test the futures-spot price relationships of a basket of commodity goods. He finds that the betas are positive for livestock but negative for grains, which imply the absence of common measure of commodity-market risk premium from which mispricing can be determined. Fama and French (1987) test the normal backwardation hypothesis under the NHP theory and find more evidence against it. Murphy and Hilliard (1989) observes the disappearance of underpriced commodity futures after the first oil shock of 1973. Hartzmark (1987) studies the aggregate profits of futures speculators and arbitrageurs and finds weak evidence to support the existence of normal backwardation or contango. Phillips and Weiner (1991) conducts similar test to Hartzmark using intraday trades in the petroleum forward markets and concludes that no group of oil traders, except the Japanese trading firms, can make substantial profits on the daily basis. Kolb (1992) shows that only 7 out of 29 futures contracts have the evidence of mispricings (both contango and normal backwardation), based on one million daily futures prices. He concludes that currency and bond futures have provided unbiased estimates of their expected spot prices.

Lead and Lag Effects

The lead-lag effects of futures prices on spot prices are concerned with the timing differences between the two which result in the price discovery when futures lead spot and the mispricing when they lag. Since futures contracts trading are less expensive than spot transactions, futures markets seem to be more efficient than and tend to lead the underlying assets markets. However, the spot prices of smaller and less-frequently traded stocks may not be timely reflected in the futures market which cause the lag effect and mispricing. As hedgers and speculators are trading in both markets, their activities and information tend to be more fluid in the futures markets than in the spot markets. Most empirical evidences support the lead effect more than the lag effect. Finnerty and Park (1987) discover a significant lead-lag relationship between futures and spot prices. Kawaller, Koch, and Koch (1987) find that futures contracts lead the spot index by as much as 20 to 45 minutes while Herbst, McCormak, and West (1987) observe that the S&P 500 and Value Line futures lead the spot index between 0 to 16 minutes. However, Laatsch and Schwartz (1988) find no lead-lag effect in the IMM. Swinnerton, Curcio, and Bennett (1988) conclude that a lead time of 5 minutes is the best predictor of the cash index with up to 30-minute range of predictability. Stoll and Whaley (1990) find that futures prices lead spot prices on average of 5 minutes. Swinnerton, Curcio, and Yonan (1995) note that Nikkei stock index futures do not lead the spot prices. Chang, Jian, and Locke (1995) find the weekend lead effect on the S&P 500 futures prices such that the Friday close to Monday open negative effect appears to be anticipated in the last minutes of Friday's trading. They also extend the time frame of the weekend by 5 minutes at the close and open and find a doubling of the weekend effect.

Evidence of Stock Index Futures Arbitrage

MacKinlay and Ramaswamy (1988) find that arbitrage violations are path dependent and it is less likely for the mispriced value to cross over to the opposite arbitrage boundary. Merrick (1989) notes that the effective transaction costs are about 70% of the originally expected costs when unwindings and rollovers are used as part of a complete arbitrage strategy. Daigler (1991) finds that arbitrage opportunities in futures contracts are caused by the lag effect of the cash index. Chung (1991) concludes that the size and number of mispricings are smaller than previously reported; arbitrage profits have declined over time. Chan and Chung (1993) discover a higher intraday volatility is followed by a decrease in the mispricing spread while an increase in the mispricing spread is followed by an increase in market volatility. Yadev and Pope (1994) find significant positive relationships between the magnitude of mispricing and the time to maturity and conclude that mispricings are profit opportunities and not risk premia. Kumar and Seppi (1994) observe that S&P 500 futures arbitrage has been less profitable gradually because of the growth in the number of arbitrage desks, a reduced level of rebalancing risk, and the greater cost of possessing information advantage over the market makers. Swinnerton, Curcio, and Yonan (1995) notice that index arbitrage activity for the Nikkei stock index futures has little impact on intraday price movements with the long arbitrage effect greater than the short especially in the afternoon. Board and Sutcliffe (1996) find that commodities listed in different markets have increased trading volume due to the manipulations of market participants. The lower the rate of mispricings, the more efficient the markets.

Conclusion Back to Top

From the perspective of corporate users, forward and futures contracts serve as their hedging tools to control or reduce their exposures to price risk and returns volatility. Individual investors view these kinds of financial derivative as being the vehicles for them to speculate or arbitrage in order to enhance their profits. Speculators may find it more risky to take an uncovered position in either spot or futures market, while arbitrageurs and calendar/cross spreaders are able to set up profitable positions in both markets and combine them with appropriately leveraged positions more effectively. No matter what the purposes and incentives are, all market participants obtain more investment flexibility and latitude from parallel tradings in both futures and spot markets than from naked transactions in the spot markets alone.

The arbitrage-free principle allows the equilibrium relationship between the futures and spot contract prices to hold. Arbitrage opportunities between the two markets arise when either the futures or spot price is mispriced cross-sectionally. It is also discovered empirically that futures prices sometimes lead spot prices within a shot period of time. This also allows investors to determine the level of spot prices through futures prices observation. There is one big precaution in the applications of financial futures amidst today's sophisticated and high-speed trading markets of which investors and firms should be aware. Since the relationship between futures and spot markets is normally positive, the insurance protection against the down-side price risk when both markets decline may lead to excessive net short positions and result in the market breakdown, as occurred in major financial centers throughout the world in October 1987. These positive implications and negative impacts are the products of the linkages between futures and spot markets. All rest upon the rational judgements of market participants to employ sound strategies to hedge against risks or enhance trading returns, and the proactive intervention of market regulators to formulate prudent policies and implement appropriate measures to stabilize the markets.

The balance between the short and long positions in the aggregate futures and spot contracts is of utmost importance to the healthy functioning of the two markets. Too little supply of spot securities for future delivery will cause the futures contract to be an ineffective hedging instrument. Too much heterogeneity among the supply of the underlying assets tends to make the futures contract a bad long hedging vehicle. Therefore, it is advisable that market participants trade futures contracts that are large in deliverable supply and homogeneous in characteristics such as government securities and foreign currencies.

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* Worapot Ongkrutaraksa is a lecturer in Finance and Strategic Management at Maejo University's Faculty of Agricultural Business, Chiang Mai, Thailand. He used to conduct his post-graduate research in financial economics at Kent State University and international political economy at Harvard University through the Fulbright sponsorship between 1995 and 1998.

E-mail: worapot@iname.com

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