خطر گریزی و محدودیت قیمت در بازارهای آتی

Assuming that a representative trader is risk-neutral, Brennan [1986. Journal of Financial Economics 16, 213–233] shows that price limits, in conjunction with margins, may help reduce the default risk, lower the margin requirement, and decrease the total contract cost. We show that Brennan's result is true only when the trader's degree of risk aversion is low and the precision of additional information about the equilibrium futures price is also low. When the trader either is more risk-averse or can receive precise information, price limits become ineffective in either reducing the default probability, cutting down the margin requirement, or lowering the contract cost.

The use of price limits in futures markets has generated a great deal of discussion since the global market crash in October 1987. Several researchers have tried to examine the impact and effectiveness of price limits, either empirically or theoretically. In essence, price limits are designed to reduce the total cost for market participants by serving as a price stabilization mechanism to assure the proper operation of futures markets. Their impact on the operation of markets, however, is still under debate. Advocates and supporting evidence suggest that price limits prevent extreme price movements and provide a cooling-off period during events of overreaction (e.g., Ma et al., 1989 and Greenwald and Stein, 1991; and Arak and Cook, 1997). Furthermore, since price limits constrain the price change in a trading period, they may serve to reduce the potential default risk in futures contracts (Brennan, 1986). Opponents to price limits contend that the imposition of price limits, instead of stabilizing price changes, may actually impede the price discovery process by preventing the price from reaching its equilibrium level effectively. The view that price limits serve nothing, but merely slow down the price adjustment process, has also gathered many proponents and supporting evidence (e.g., Telser, 1981, Figlewski, 1984, Miller et al., 1987, Lehmann, 1989, Fama, 1989 and Kim and Rhee, 1997). It is also argued that price limits may impose additional risks on market participation, because they prohibit mutually beneficial trades at prices outside the limits (e.g., Ackert and Hunter, 1994). A final argument against price limits is that they may have a “magnet effect.” This is because traders, for fear of losing liquidity and being locked in a position, may rush to protect themselves through active trading. As a result, when the price is close to a limit, the trading volume will be heavy and the price limit rule will serve as a magnet that further pulls the price even closer to the limit (e.g., Lee et al., 1994 and Subrahmanyam, 1994; and Harris, 1997). Some researchers have tried to examine whether the use of price limits, in conjunction with margin requirements, can improve the efficiency of the futures markets. Telser (1981) and Figlewski (1984) point out that price limits cannot substitute for margins since they, though lengthening the time it takes to adjust to a new equilibrium, do not reduce the size of price change. On the other hand, Ackert and Hunter (1994) argue that price limits can decrease the margin that brokers and exchanges require since repressing prices reduces the probability of default resulting from unfavorable price movements and thus lowers the risks.2 Assuming that a representative trader is risk-neutral, Brennan (1986) shows that price limits, in conjunction with margins, may help reduce the default risk, lower the margin requirement, and decrease the total contract cost. Intuitively, price limits provide a mechanism that obscures the exact amount of the loss incurring to the trader when price limits are triggered. Being uncertain about the magnitude of the loss, a risk-neutral trader bases his decision on the expected loss, conditional on the information of a limit move. He will adhere to his position if the expected loss is less than the effective margin, and will renege otherwise. Thus, there exist conditions in which certain combinations of price limits and margin requirement may improve the operation of the market. However, Brennan also indicates that the effectiveness of price limits disappears when the trader can obtain precise information derived from other markets such as the spot market. He predicts that price limits are less effective and less popular in financial futures contracts where reliable information about true prices is generally more available. Brennan's model nevertheless only considers the risk-neutral investor who is indifferent to investment risk. When the trader is risk-averse, the utility of abiding by the contract is relatively lower in comparison with the risk-neutral case, other things being equal. Therefore, there is a higher probability for the risk-averse investor to renege in the event of a limit move in order to avoid subsequent potential losses. More formally, instead of solely relying his decision upon the expected loss as a risk-neutral trader does, the risk-averse trader bases his decision upon the expected loss plus a “certainty equivalent.” The certainty equivalent is a monotonic, increasing function of the degree of risk aversion. For traders with low-risk tolerance, price limits may exacerbate the incidence of reneging, and a relatively higher margin may be required in order for the trader to abide by the contract. As a result, in a risk-averse framework, price limits may increase the default probability, the margin requirement, and the contract cost. The remainder of this paper is organized as follows. The next section extends Brennan's risk-neutral model to a risk-averse framework. Section 3 demonstrates numerical results under normally-distributed price changes. Section 4 concludes the paper.

This study investigates whether price limits can reduce the default risk and lower the effective margin requirement for a self-enforcing futures contract under the risk-averse framework. Since price limits create uncertainty, risk-averse traders who are reluctant to take risk will have a lower utility than risk-neutral traders when a limit is hit. As a result, the margin requirement should be set higher in order for the risk-averse trader to adhere to the contract. Our results demonstrate that price limits can reduce the margin requirement and the contract costs only when traders’ levels of risk aversion are extremely low and the traders cannot receive precise additional information. More specifically, when either riskaverse traders can receive more precise information or they can take risk only to a certain degree, price limits are not only ineffective in reducing the contract cost and lowering the margin requirement, but also increase the default probability. This study concludes that price limits are generally not efficient in improving the performance of futures contacts for risk-averse traders.