Review of Hedging Theory

Hedging is a multivariate process for managing risks and achieving objectives. The process of hedging is not the simple buying or selling of futures and options against physicals. It is the prudent selection process whereby regulatory, financial, operational, supply and demand, and other factors must be continually evaluated in order to derive the maximum benefits from the process.

There are a broad variety of hedging theories available, which provide a decision rule for people to hold the futures contracts and spot commodity. First of all, Gray and Rutledge (1971) categorized hedge theory into four groups by means of the purpose of hedging, including risk elimination, risk reduction, profit maximization, and portfolio approach. Ederington (1979) showed that the future hedging theories could be classified as three groups: traditional hedging theory, selective hedging theory, and portfolio hedging theory. The traditional hedging theory was inconsistent with reality situation and selective hedging theory not only concerned hedging strategy but also involved in speculative strategy. In general, most of financial assumption took minimizing risks as investors’ hedging strategy. Therefore, the portfolio hedging theory was the most common method to be used nowadays. Among those, Junkus and Lee (1985) adopted profit maximization, risk elimination, risk minimization and utility maximization as the hedging strategy in an empirical study. Cecchetti, Cumby and Figlewski (1988) used risk minimization and maximized expected utility theory to estimate the optimal futures hedge strategy with spot and futures prices dynamic distribution. The remainder of this section describes the three measures of hedging theories from Ederington’s viewpoints.

2.2.1 Traditional Hedging Theory

Traditional hedging theory focuses on the ability to reduce risk by using futures contracts. If people are long in the cash market, they take a short position in the futures market and vice versa, because they counteract price changes in the two markets against one another. This traditional view suggests that hedging is carried out to reduce price risk (Cootner, 1967). The equal and opposite hedge strategy assume implicitly that the hedger is unskilled or uninterested in forming expectations on the movements of spot price, and that he derives his profits solely from subjecting the transformation of another commodity (Ward and Schimat, 1979). Thus, this hedger has been viewed as a sort of insurance (Samuelson, 1973) against price risk, and the evaluation of its effectiveness is related to risk elimination.

In other words, the traditional approach is to hold equal and opposite positions in the futures market whenever a cash position is held. The positions are supposed to be equal in size and adverse direction. Since it is presumed that cash and futures prices of identical products will nearly be perfectly correlated, losses on one position will be compensated for other position profits. As a result, the traditional approach expects that hedging will virtually eliminate price risk during the investment process.

Unfortunately, not all risks are eliminated by traditional hedging method.

Under the traditional theory, only the basis risk is zero and can be getting rid of the price risk of the spot position. Therefore, this theory deviated from the truly circumstances in reality.

2.2.2 Selective Hedging Theory

Holbrook Working (1953) modified the traditional view of hedgers by arguing that the essence of hedging is speculation on the basis. He argued that expected profit maximization, rather than pure risk minimization, is the objective of hedgers.

Working’s Hypothesis took a different perspective of futures hedging. He challenged the view that hedgers are pure risk-minimizers. Instead, he believed that hedgers behave much like speculators who decide to hedge or not to hedge according to their expectation of the change in spot-future price relation.

Therefore, in the 1960s Holbrook Working categorized alternative motives for the futures hedging and these viewpoints continue to be valid in the 1990s. The three categories are arbitrage hedging, operational hedging, and anticipatory hedging. Arbitrage hedging means that people use the inconsistent of securities value to trade, obtain the risk-free premium through the basis change that has already been anticipated. Operational hedging facilitates commercial business by allowing firms to buy and sell on the futures markets as temporary substitutes for subsequent cash market transactions. Anticipatory hedging involves buying or selling futures contracts by commercial firms in “anticipation” of forthcoming cash market transactions. Price expectations play an important role in this hedge.

The selective hedging theory made it clears the speculative aspect of hedging: Price changes will not be offset perfectly in any cash and futures combination. The hedger is trading the risk of holding a commodity unhedged for the smaller risk of changes in the basis (Cootner, 1967). In Working’s model, this speculative aspect of hedging is taken limited, and the positions in the futures and cash markets are determined simultaneously in order to capture increased return arising from relative fluctuation in spot and futures prices.

Working used an examination of the year-to-year constancy of the relation between the size of the “spot premium” (means basis) and the gain or loss from subsequent storage with hedging in wheat. At last, the theory detected that a large negative basis (cash price subtract futures price) was likely to be followed by a large positive change in the basis, and that a large positive basis was followed by a large negative change in the basis.

2.2.3 Portfolio Hedging Theory

The traditional hedging theory emphasized on risk reduction, while the selective hedging theory considered making the expected utility maximization.

The approaches above were partial and cannot be represented the reality financial markets. However, the portfolio hedging theories integrate these concepts and believe that both reduce the risk and maximize the expected utility should be considered together while hedging. This kind of hedging behavior will also be accordant with common people's behavior.

A portfolio explanation of hedging was first strictly presented and developed by Telser (1958), Stein (1961), and Jahnson (1960), who used the Markowits (1959) conceptions of portfolio management. With this approach a hedger is viewed as being able to hold several different cash and futures assets in a portfolio and is assumed to maximize the expected value of his utility function by choosing among the alternative portfolios on the basis of their means and variances. Serveral researchers have drawn on this framework such as Johnson and Steim (1960), Anderson and Danthine (1981), and Howard and D'Antonio (1984).

The early researches about portfolio hedging theory can be taken as

"minimum variance hedge approach". Johnson (1960) and Steim (1961) applied the Markowitz two-product portfolio model to spot and futures markets. Their approach has been widely used because it provides a method to identify the

minimum-variance portfolio for each level of return. In this model, the hedger is essentially infinitely risk-averse, and defines risk in terms of the variance of his total position in the spot and futures markets. The variance of the return on a hedged portfolio is minimized and the hedge ratio is expressed in terms of expectations on the variation of price changes in the spot and futures markets.

Johnson's model differs from Working's in that the objective is to minimize risk and that the position is defined in terms of absolute rather than relative price changes.

Anderson and Danthine (1981) proposed the maximized expected utility hedging model. A mean-variance utility formulation is used to obtain operational results to generate the optimal hedge ratio. The framework is equivalent to expected-utility maximization where net revenues are distributed normally and agents' utility functions are exponential. Under the maximization utility model, the theory obtained the following conclusion. First of all, the optima positions of spot and futures are determined simultaneously and the existence of hedge opportunities will influence decision. Secondly, a perfect hedge strategy can be reached by using the multiple-contracts portfolios. Thirdly, a hedger's strategy is depended on the correlation of expected spot and futures price. At last, the optimal hedging strategy concerns not only the minimized risk but also maximized expected utility for the portfolio hedging.

Howard and D'Antonio (1984) considered that previous researches did not submit appropriate risk-return measurement criterions about hedging effectiveness. However, Howard and D'Antonio proposed that hedging effectiveness was seen as comprising both risk and return components. The major foundation of this theory is to utilize the mean-variance analysis to maximize excess return of per unit risk. This theory indicated that hedging effectiveness does not always improve as the spot-future correlation coefficient increases, but depends heavily on the risk-return relative. It was found that this

futures market conditions, the other affected by both cash and futures markets as well as the hedger's cash portfolio. As the result, the model illustrates that when the risk-return relation is equal to the spot-future correlation coefficient, there is no benefit to holding futures.