World Scientific Handbook in Financial Economics Series The World Scientific Handbook of Futures Markets

We outline several fundamental themes for the WPS Handbook of the Futures Markets. The Handbook as the others in the same series intends to be a definitive source for comprehensive and accessible information in futures markets. The emphasis is on the unique characteristics of futures markets that make them worthy of a special volume. In our judgment, futures markets are currently undergoing remarkable changes as trading is shifting from open outcry to electronic and as the traditional functions of hedging and speculation are extended to include futures as an alternative investment vehicle in traditional portfolios. The unique feature of this volume is the selection of five classic papers that lay the foundations of the futures markets and the invitation to the leading academics who do work in the area to write critical surveys in a dozen important topics. The WSPC Handbook of Futures Markets Part I: Introduction Chapter 1: Overview and Introduction Dating back to the 1800s (and in some ways, back to the earliest beginnings of commerce), the futures markets were initially developed to help agricultural producers and consumers manage the price risks they faced with harvesting, marketing and processing annual crops. The futures industry still serves those markets, but has also broadened along with the expansion of our economy beyond its agricultural roots. The need for efficient forward pricing and risk management mechanisms is the reason for the tremendous growth in futures markets. Futures markets enable raw material producers and users, financial intermediaries, and international trading firms to manage their price, interest rate, and exchange rate risk. And speculators throughout the world can interpret the information that converges on exchange floors to enter the futures markets as investors. Because of its ease of use and its many economic benefits, futures trading has expanded to include numerous and varied markets throughout the world. The increased importance of futures, which can be seen by the tremendous growth in terms of volume and number of contracts, makes their study an increasing necessity in today’s financial world. In the early 1970s, approximately 13 million futures contracts were traded in the United States—most of which were agricultural. By 1999, trading volume exploded to more than 593 million, with only 11 percent related to agricultural products. During 2006, over 3.5 billion futures contracts were traded globally. Today, there are futures contracts for interest rates, stock indexes, manufactured and processed products, nonstorable commodities, precious metals, as well as foreign currencies and foreign bonds. And the number of proposals for new contracts continues to grow. This introductory chapter will review in detail the special characteristics of futures markets, discuss its evolution and highlight and contrast these markets to other financial markets. Written by the editors Malliaris and Ziemba Part I. Classical Contributions Chapter 2 Samuelson, Paul. "Proof That Properly Anticipated Prices Fluctuate Randomly". Industrial Management Review, 1965 volume:6: 41–49; By posting a rather general stochastic model of price change, the paper deduces a fairly sweeping theorem in which next period’s price differences are shown to be uncorrelated with (if not completely independent of) previous period’s price differences. This martingale property of zero expected capital gain will then be replaced by the slightly more general case of a constant mean percentage gain per unit time. The paper concludes that one can never get something for nothing. From a non empirical base of axioms you never get empirical results. Deductive analysis cannot determine whether the empirical properties of the stochastic model posited in the paper come at all close to resembling the empirical determinants of real world markets. That question is not investigated. Instead the author goes about proving that prices move in a random walk. Chapter 3 Benoit Mandelbrot, 1963."The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394-. Broadly speaking, the predictions of the main model seem to me to be reasonable. At closer inspection, however, one notes that large price changes are not isolated between periods of slow change; they rather tend to be the result of several fluctuations, some of which "overshoot" the final change. Similarly, the movement of prices in periods of tranquility seems to be smoother than predicted by my process. In other words, large changes tend to be followed by large changes-of either sign-and small changes tend to be followed by small changes, so that the isolines of low probability of [L(t, 1), L(t 1, 1)] are Xshaped. In the case of daily cotton prices, Hendrik S. Houthakker stressed this fact in several conferences and private conversation. Such an X shape can be easily obtained by rotation from the "plus-sign shape" which was observed in Figure 4 to be applicable when L (t, 1) and L(t 1, 1) are statistically independent and symmetric. The necessary rotation introduces the two expressions: S(t) = (1/2)[L(t, 1) + L(t 1, 1)] = (1/2) [loge Z(t + 1) loge Z(t 1)1 and D(t) = (1/2) [L(t, 1) -L(t1, 1)] = (1/2) [loge Z(t + 1) 2 loge Z(t) + loge Z(t 1)]. It follows that in order to obtain the X shape of the empirical isolines, it would be sufficient to assume that the first and second finite differences of loge Z(t) are two stable Paretian random variables, independent of each other and naturally of loge Z(t) (see Fig. 4). Such a process is invariant by time inversion. It is interesting to note that the distribution of L(1, 1), conditioned by the known L(t 1, 1), is asymptotically Paretian with an exponent equal to 2a + 1.1' Since, for the usual range of a, 2a + 1 is greater than 4, it is clear that no stable Paretian law can be associated with the conditioned LQ, 1). In fact, even the kurtosis is finite for the conditioned L(t, 1). Let us then consider a Markovian process with the transition probability I have just introduced. If the initial L(TO, 1) is small, the first values of L(t, 1) will be weakly Paretian with a high exponent 2a + 1, so that loge Z(t) will begin by fluctuating much less rapidly than in the case of independent L(t, 1). Eventually, however, a large L(t0, 1) will appear. Thereafter, L(t, 1) will fluctuate for some time between values of the orders of magnitude of L(t0, 1) and -L(t0, 1). This will last long enough to compensate fully for the deficiency of large values during the period of slow variation. In other words, the occasional sharp changes of L(t, 1) predicted by the model of independent L(t, 1) are replaced by oscillatory periods, and the periods without sharp change are less fluctuating than when the L(t, 1) are independent. We see that, for the correct estimation of a, it is mandatory to avoid the elimination of periods of rapid change of prices. One cannot argue that they are "causally" explainable and ought to be eliminated before the "noise" is examined more closely. If one succeeded in eliminating all large changes in this way, one would have a Gaussian-like remainder which, however, would be devoid of any significance.