A comparative analysis of futures contract margins

A Comparative Analysis of Futures Contract Margins Gerald D. Gay* William C. Hunter** Robert W. Kolb***

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n recent years, futures markets have received an increasing amount of attention from both the trading public and from finance scholars. One important characteristic of the futures market continues to stand out as an area that has not received sufficient attention-the establishment, management, and function of margins on futures contracts. This lack of attention to futures margins probably stems from the fact that futures margins behave very differently from margins in the stock market. In contrast to the operation of credit margins in the stock market, a futures margin is not a partial payment for the position being undertaken. Instead, the futures margin is a performance bond which serves as collateral or as a good faith deposit given by the trader to the broker. Also, in contrast to the stock market, futures margins are not set by any external agency, such as the Federal Reserve Board that sets margin policy for stock trading. Instead, futures margins are set by the futures exchanges and by brokers. Furthermore, there are several different kinds of margins in the futures market. These include the initial margin, maintenance margin, hedging margin, and spreading margin. This article seeks to explain margin setting and management behavior by the futures exchanges and to contribute to the theory of margins by building on the previous work of Bear (19721, Telser (1981a, 1981b), Figlewski (1984), and Kahl,

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Research support from the College of Business Administration, Georgia State University is gratefully acknnwledged. We have benefited from the research assistance of Tae-Hyuk Kim. 'The Commodity Futures Trading Commission (CFTC) is empowered to review exchange behavior regarding margins and other matters of public interest.

Gerald D. Gay is an Associate Professor of Finance at Georgia State University. William C. Hunter is a Professor of Finance at Atlanta University. Robert W. Kolb is a n Associate Professor of Finance at the University of Miami.

The Journal of Futurrs Markets, Val. 6, No. 2. 307-%24 11986) 0 1986 by John Wiley 8 Sons. Inc.

CCC 0270-73 14/86/020307-IRS04.00

Rutz, and Sinquefield (1985). Section I of the article explores the institutional background of margin setting and management and summarizes the previous literature. Section I1 formalizes the intuitive discussion of margins presented in Section I and develops testable hypotheses regarding levels and revisions of futures margins. The statistical tests of these hypotheses are presented in Section 111. The tests utilize data consisting of the daily prices of 10 different commodities traded on the Chicago Board of Trade during IV 1979-1983 along with the complete margin history of these contracts. Section IV concludes with a brief summary and a discussion of the normative implications of this research. 1. INSTITUTIONAL BACKGROUND AND RATIONALE OF MARGINS

The imposition of margin requirements is a virtually universal feature of futures trading, yet it has not been mandated by any regulatory agency. As Telser (1981a) emphasizes, this implies that the use of margins has emerged from the market forces that exist in the very nature of futures trading. In the futures markets there is a hierarchy of legal obligations, with the futures exchange and its clearing corporation standing at the pinnacle. The futures exchange holds its clearing members responsible for all trades that they execute, whether these trades are initiated for their own account or executed in their role as a broker (or futures commission merchant) for customers. The brokers hold their customers responsible for all gains or losses incurred in the customers’ trading activities. In these respects, the position of the broker relative to the exchange is analogous to the position of the customer relative to the broker, except that the broker has obligations to the exchange and also impose obligations on the customer. In executing a trade for a client, the broker assumes a position of risk. If the trade loses money and the client refuses to honor the loss, the broker must still make good the loss to the exchange. The broker may then proceed against the customer to re-capture what is due. However, such proceedings are likely to be costly and the outcome uncertain, so the broker‘s risk position remains. In fact, the broker can eliminate his risk only by demanding significant deposits from the customer as a condition of executing the trade. For example, for a customer’s purchase transaction, the broker could demand a deposit equal to the delivery price of the good. For a sale transaction, the broker could eliminate his risk by requiring the customer to deposit the deliverable good. Obviously, such requirements, which are tantamount to margins of loo%, would be sufficiently onerous to virtually eliminate futures trading. By the same token, the exchange assumes a risk position by allowing a broker to trade with a margin of less than 100%. Consequently, the position of the exchange relative to the broker is analogous to the position of the broker relative to the broker’s client. In neither case can there be perfect safety if trading is to be possible. Because the positions are formally similar, the analysis of margins presented in this article focuses on the exchange’s imposition of margin requirements on the broker. Instead of operating without risk, the exchange is faced with the following problem. If the margin requirement is too low, the exchange’s risk position may be intolerable. If 100% margins are imposed, the trading costs imposed on brokers and customers will destroy the market. As a consequence, the exchange must choose a level of margin that balances the benefits to be received by attracting trading customers and executing transactions against the risk exposure that is involved.

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This amount that must be deposited to buy or sell short one futures contract is referred to as the initial margin for that contract. As an example, for the Chicago Board of Trade Treasury Bond futures contract with a $100,000 face value amount, the Board of Trade required an initial margin of $3,000 per contract as of March 30, 1983. Contracts for each particular commodity have their own margin requirements. This initial margin must be posted in cash or in the form of short-term U.S. Treasury securities with letters of credit for commercial customers accepted as well. Brokers may impose higher requirements on their customers if they wish, but they must adhere to the minimum requirements set by the exchange. The broker is also free to vary the margin requirements across his customers. After the initial margin is posted and the trade is executed, the trader’s gains and losses depend on the change in the futures price. If the trader sustains a loss, the value of the margin account held by the broker falls, as does the value of the broker’s deposit with the exchange. When the value of the margin account falls below a certain level, called the maintenance level, the exchange requires the payment of additional margin in cash sufficient to restore the margin account to its initial level. For example, on March 30, 1983 the maintenance margin for the Treasury Bond futures contract was $2,000. In this case, assume that a trader had deposited the initial margin of $3,000 and purchased one contract. Subsequently, the futures price fell by $1,500, driving the value of the customers’ account below the maintenance margin level of $2,000. The trader would be required to deposit $1,500 maintenance margin in cash to restore the value of the margin account to its initial level of $3,000. The preceding description of margins applies to outright positions in a single futures contract. Other rules exist to cover hedging and spreading transactions. In a hedge, the spot value and the futures value of the commodity are highly correlated, so for the combined position the two price changes should be closely offsetting. Because of the lower risk involved, the hedging margin, which is the initial margin for one qualifying as a hedging account, is typically lower than the initial margin for an outright position. For example, the hedging margin for T-bond futures was $2,000, as opposed to the $3,000 initial margin level on March 30, 1983. (Although conceptually distinct from the maintenance margin, hedging margins at the CBT are typically set at the same level as the maintenance margin). Much of the speculative activity in the futures markets involves simultaneous positions in two or more delivery months for a specific commodity (intracommodity spread), or positions in similar maturities but between two different commodities considered to be close substitutes (intercommodity spread). These types of spreads have their own margin requirements. For instance, in the case of an intracommodity spread in Treasury Bonds, the spread margin was $2,000 per two contract spread position as of March 30, 1983. Also, on March 30, 1983 the margin for the intercommodity spread of one Treasury Bond contract against the 2 year Treasury Note contract was $1,500 per two contract spread position. This compares with the initial margin of the two contracts of $3,000 each. Each futures exchange appoints a committee that is responsible for setting margin requirements. Members of the margin committee are exchange members and are chosen to represent a cross-section of interests and trading areas. Margin committees meet on a regularly scheduled basis and may also meet on special occasion as the situation warrants. From conversation with the exchanges, principally the Chicago

COMPARATIVE ANALYSIS OF MARGINS

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Board of Trade, the committees examine four major factors regarding each of the traded commodities: price volatility, liquidity, current and expected cash market conditions, and margins at other exchanges. Prior to each meeting the economics department presents a price volatility report which shows the three-month history of close-to-close prices and the high-low price range for each day’s trading for each commodity. While the price variability issue appears to be the most important, the committee also considers the liquidity in the market. For those contracts with low liquidity, generally less than 2,000 contracts of volume, there may be a tendency to keep the margins somewhat higher. Traders on the committee also report their views of current and expected cash market conditions in each commodity. Because the level of margin is a trading cost, it is also a competitive factor across exchanges. As a result, the margin committee also gives some consideration to the level of margins at other exchanges, although this is reported not to be a major factor in the determination of margins. In summary, price variability seems to be the major factor, with some consideration given to market “tone”-the liquidity available in the market and developments in the cash market a5 well.’ The margin committee, like the broker, must also be sensitive to the tradeoff between keeping trading costs low and the desire to protect the exchange from unnecessary risk exposure. Because initial margins of less than 100% expose the exchange to some risk of default by the hroker and expose the broker to some risk of default by the customer, the margin rules must be established to balance the benefit from inducing trading against the risk of financial loss in the case of default. The balancing of expected return (the expected income from commissions and other services that might be provided) and risk (the chance of capital loss due to default) depends on the utility function of the principals. Because the margin committee is selecting minimum margin levels for all participants, it also has the job of aggregating the utility functions of diverse market participants in order to find an optimum. According to Telser (1981b), this minimum margin requirement is rational in that the exchange has a self interest in maintaining the reputation of its members so that doubt will not be cast upon the exchange and its integrity. Since the exchange could in effect provide a safety net for its members, they might be prone to take more risk-i.e., accept lower margins-than would ordinarily be the case. To the extent that the exchange stands ready to rescue members in financial difficulty, minimum margins act as constraints on imprudent behavior. There are three conditions under which one can justify the assumption that the margin committee operates to maximize the aggregate utility function of the futures exchange membership: (1) all exchange members have preferences which are not too dissimilar, (2) all members have identical expectations about the future, or (3) all exchange members have single-peaked preferences. While it is difficult to accept Condition (2), Condition (1) is certainly plausible. Given that the members of the futures exchange are in effect agents of the other members in the sense of engaging in transactions which directly bear on the reputation and integrity of the exchange, ‘Given the importancr of the price variability factor, the model we derive in the following section focuses on this aspect in the margin setting process. ’In simple trrms, the single-peaked preferences condition means that a group of decision-makers can use majority rule as an agreed upon means to make a determinant choice when choosing among a finite set of alternatives as long as the number of voting decision-makers is odd. For a rigorous discussion of the single-peaked preferences condition, Arrow, (1951).The fact that the exchange margin Committee has an odd number of voting members is consistent with the notion of single-peaked preferences.

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Ross’s (1974) principle of similarity can be used to support the conjecture that the preferences of exchange members are not too d i ~ s i m i l a rSince .~ the actions of each exchange member can clearly affect the wealth of other exchange members, exchange membership serves as a signal that the preferences of the members are not too dissimilar. According to this view, the members of the exchange constitute the margin committee so that it expresses preferences similar to their own. Thus, the margin committee must select the correct level of margins to achieve the optimum combination of expected return and risk. Furthermore, from the point of view of the futures exchange, margins should be set such that the marginal change in utility as a function of the margin is the same across contracts, just as the multi-product firm should set prices so that marginal profits from all products are the same. Because the margin committee has no specific information about individual traders, it can know nothing about different default probabilities among different traders and across contracts.’ Under these conditions, the margin committee should choose levels of initial and maintenance margins that keep the probability of risk exposure constant across contracts. The broker or the exchange is subject to a positive probability of loss only when the value of the trader’s margin account is below zero or has a chance of falling below zero. Under this argument, the margin levels should accordingly be set to give equal probability of that occurrence across contracts and across traders. A precise model of margin setting behavior would require detailed knowledge of the relationships among the margin level, the risk level, and expected profitability, as well as knowledge of the aggregate utility function that the margin committee is attempting to maximize. Nonetheless, as the next section shows, there are a number of implications of the informal model developed in this section that are empirically testable.

11. TESTABLE HYPOTHESES CONCERNING MARGINS As argued in the preceding section, the optimal margin depends on the aggregate utility function the margin committee is attempting to maximize and the relationship between expected profitability and the risk of financial loss due to default. Although these relationships are not observable and are difficult to model directly, it is still possible to test a number of implications of this view of margins. To make the analysis more tractable, we begin by making simplifying assumptions. We assume that the futures price, F,, follows a Wiener process with zero drift. If futures prices follow a Wiener process, then the futures price path generates a normal density, zero mean, stationary independent increment process with a variance of d t . In economic terms, modeling the futures prices as following a Wiener process with zero drift implies that the expected change in the futures price is zero, that futures price changes are normally distributed with constant variance, and that the ‘The principle of similarity states that in markets characterized by the presence of imperfect information, principals choose agents with risk preferences similar to their own if the actions of the agent can materially impact the wealth of the principal. ’If this information were available, margins could be tailored for each customer to balance the expected costs and benefits associated with changing the margins and thus changing the likelihood of default and market failure. ‘Again we note that the exchange imposed margins are minimum margins. If brokers have more information about the specific default probabilities of their customers they do have the power to impose higher initial margins than those set by the exchange.

COMPARATIVE ANALYSIS OF MARGINS

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futures price is continuous. 7*8 Assuming that the Wiener process is stationary also implies that all relevant features of the price path are captured by the mean and variance of the process, so that considerations of the business cycle and market “tone” are not reflected in the model, except as these might affect the variability of the futures price. Under the assumption that futures prices follow a Wiener process, we can calculate the first passage probability that the margin will be exhausted during some interval through fluctuations in the futures price, and we label this probability Z . The value of the margin account at time t , which started with a value of M at time s, depends only on the difference in the futures price from time s to time t . For the Wiener process, the variance of the difference between two prices is proportional to the length of the time interval, t - s, while the differences are normally distributed with the following density function:

where f is a realization of the process, a‘ is the variance of the futures price differences, and exp(*)is the base of the natural logarithm raised to the power given by the term in parentheses. By rescaling the initial price to equal zero, for a given horizon of T , and a margin level (whether initial or hedging) of M , the probability of a zero or negative balance in the margin account during this interval, Z , can be stated as: Prob{F,

-M,

for at least one t(0

t G T)}

which also equals: Prob{F, 2 M ,

for at least one t ( O d t

T)}

(1)

This probability can be computed in several ways, such as by the method of images, by conditional expectations methods, and analytically.’ Therefore, Prob{F, 3 M , 2Prob{FT 3 M ,

for at least one t(0 d t d 2‘)) =

for all M 3 0)

(2)

Because F , is distributed normally, the right-hand side of Equation (2) can be evaluated as: 2Prob{FT 3 M } = 2{1 - Prob[FT < M I }

(3)

’Figlewski (1984) has derived a similar model of futures price movements i n which he models the natural log of the futures price as a Wiener process. If the futures price itself follows a Wiener process, there is a very small positive probability that the price could move below zero during any finite time interval. In practice, of course. this could not occur. Relative to the model presented in this article, Figlewski’s approach implies limited liability as it is inrpossihle for the model to generate futures prices below zero. However, we believe that the variable of greatest economic interest is the dollar price change in the futures contract and not the percentage price change used in Figlewski’s model. Furthermore, the practical difference between the two models is small over short time intervais (Figlewski. 1985). *In assuming normality we recognize that this may be an approximation due to the existence of minimum price fluctuations. the possibility of significant price jumps, and daily price limits which may induce platykurtosis and other complications into the daily return distributions. ’See Cox and Miller (1965) for a proof using the method of images

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Dividing both F T and M by aVT, in order to standardize the variables, gives:

{

2Prob{FT 2 M } = 2 1 - Prob

[a%