An Alternative Test of the Performance of Futures Markets:A note - 政大學術集成

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(1)54. Journal of Financial Studies VoLl No.2 January 1994. An Alternative Test of the Performance of Futures Markets A Note 1. Introduction. The central feature of an capitalist economy is that the prices of and services are allowed to fluctuate freely according to the laws of and supply. As such, the scarce resources of the economy can be UUUl;iUfII1 efficiently and optimally. However, the major disadvantage of such an omy is also exactly these prices fluctuations, especially the uncertain future prices. With the deregulation of financial markets after late 1970s, price volatility has become even greater. As a result, futures contracts other derivative instruments have emerged. Although these new markets are accepted with warm welcome and experience dramatic their economic functions are still hotly debated. Voluminous studies have been done on the evaluation of the p of speculative markets. Among them, the Efficient Market Hypothesis( test is the standard criteria. However, as Stein(1987;1991) points out, are deficiencies of the EMH test. Instead, he proposes a new measure which can overcome those deficiencies. Specifically, with the new ciency measure, we can compare and rank the performance of futures quantitatively. And by decomposition of the measure, we can also identify sources of poor market performance. This paper proceeds as follows. The ciencies of EMH tests are discussed and the new efficiency measure is in section II, section III is the empirical test of the performance of nine futures markets in five countries, and finally section IV is the conclusion. 2. Theoretical Considerations 2.1 The Inadequacy of Conventional Efficient Market Tests. The Standard method of evaluating the performance of speculative kets has been the tests of Efficient Market Hypothesis(EMH). EMH consists of four assumptions: A1) The price of an asset is the discounted expectation of the future. flows..

(2) Journal of Financial Studies Vol.l No.2 January 1994. 55. New information about cash flows is reflected immediately, without any lagged response, in the price of the asset; and the market uses it correctly in setting asset prices. New information arrives randomly. Market expectations are unbiased estimates of subsequently realized prices. When used in the futures market, EMH tests examine whether: (i) fu price is an unbiased estimate of the subsequent spot price and (ii) other abIes add significantly to the prediction offuture spot price. Denote qt+h(t) the price at time t of a futures contract maturing at time t + h, and Pt+h, the subsequent cash price. Then EMH implies. (1). fe(h) = Pt+h - qt+h(t) = €t+h. Where forecast error je(h) = €t+h should be i.i.d. with a zero mean. That futures price is the unbiased estimate of the subsequent spot price. When premium is accounted, the expectation of €t+h need not be zero, although is still i.i .d . EMH test is also often tested by the following form: n. Pt+h = a(h) +b(h)qt+h(t). +L. CiXi,t. + €t+h. (2). i=l. Where Xi ,t are all "other" economic variables which could possibly help . the subsequent price. The null hypothesis is that: a(h) = 0, coef '.<~l1\'H::!H:; b(h) = 1, Ci = 0. If the null hypothesis is not rejected, the researcher that the futures market is efficient. The futures price contains all rele available information about the subsequent spot -price. l There are limitations of EMH tests. First, EMH tests are only "pregnancy tests". They do not convey any order of magnitude for comparison of the per formance of futures markets. More specifically, EMH tests are incapable of quantitatively how well the futures markets are functioning. Mar r~' ''''"i:l are either efficient or they are not. If two markets both pass the EMH ;~itp.~ts, which market is performing better? Or if two markets both fait" to pass tests, can we tell which market is functing worse? Thus, one cannot rank lSee, for example, Rodrick and Srivastave(1987) and Chu(1993a).. .I.

(3) 56 . Journal of Financial Studies VoU No.2 January 1994. market performance on the basis of EMH. Second, The standard of optimal market behaviour is not established. As a result, the social benefit of futures markets can not be evaluated. Third, EMH tests have very little to say about the causes of the deviation between futures price and the subsequently real, ized cash price. "Time varying risk premium" (Fama(1984) and Hodrick and Srivastava (1987) is only a tautological term to describe this deviation. The logical and endogenous economic content of causes of the deviation need to be explained.. 2.2 New Quantitative Efficiency Measure Stein(1987;1991) proposes a new efficiency measure which can be applied to evaluate the performance of futures markets quant itatively. The effiCiency of a futures market is measured by the mean squared forecast error between futures price and the subsequently realized cash price. But to allow for the difference of individual market system and to avoid direct comparison of the deviations in absolute term, a standardizing procedure is employed by divid ing the mean squared forecast error by the variance of the cash prices of the under lying commodity. 2 In essence , the new efficiency measure is defined as:. SL(h) = MSE(h) var p Where MSE(h) = E[Pt+h - qt+h(t)J2 , is the mean square error of the deviation between fut ures price and cash price, and var p is the variance of cash prices of the underlying commodity.3 The larger the efficiency mt:<l')Ul is, the worse the futures market behaves relative to other markets. We can go one step further to decompose the MSE into three parts as following equation:. MSE(h). =. E[Pt+h - qt+h(t)]2 . + (]5 - q) - (q - qW (15 - q)2 + (1 - b)2cr; + (1 - r2)ci~ (Urn + Ur + Ud ) * MSE(h). E[(p - ]5). 2In original Stein's papers , this new efficiency measure is elaborated through the of social welfare loss. For detailed discussion, please see Stein (1987) chapter 6. n. 3In empirical calculations, MSE(h). = ~ L:(Pt+h -. qt+h(t)]2 ... t=l. I.. ________ .__ _. _ __ _ _____. _ _ _" U' .lI!H I I J IT rrn I,·.

(4) -. Journal of Financial Studies VoLl No.2 January 1994. 57. P = Pt+h is the realized cash price at time t + h, p is the mean of the cash prices over sample period, and is the variance of Pt+h; q = qt+h(t) price of futures contract which matures at time t + h, q is its mean, and the variance; b equals c~:~p~q) and is the regression coefficient of Pt+h on ; and finally 1'2 is the square of the correlation between'pt+h andqt+h(t) usually mentioned as the' quality oj hedging or hedging effectiveness.. 0';. The first component, Urn = (~~ll, is the fraction of MSE due to the between p and q. This is called the bias component. The second (l-b)20';. th f . from t h e d eVIatlOn . . 11'UUVUU, Ur = MSE IS e rac t'IOn 0 f MSE commg IIlItween b and unity. If the regression coefficient b of Pt+h(t) on qt+h(t) were source of MSE then Ur would be zero. Urn and Ur together are2 the , 2 from risk premium. The last component Ud = (l~S~O'p is .the prop'ortion 1'lIfo-IVIIJ.LJ that cannot be eliminated by the hedging of futures contract. Only futur es contract provides perfect hedging for the underlying commodity, this term become zero. 4 We therefore have a quantitative efficiency measure which can be used evaluate the performance of futures markets, and by decomposition of the measure, we can identify the sources of poor market perfor~ance.. 3. Empirical Results. The data we use are S&P 500 stock index, long term T -bond and gO-day futures in U.S., FT-IOO stock index and Long Gilt government bond in U.K., Nikkei 225 stock index and long term government bond futures All Ordinary Shares stock index futures in Australia, and Hang Seng index futures in Hong Kong. U.S. data are froin Wall Street Jc;>urnal, Reserve Bulletin, and the data bank of Columbia University Futures (CFC'). U.K. data are from GEeD Financial Statistics, CFe and daily Financial Times. Australian data are from GECD Financial Statistics, CFe. Japan data are from GEeD Financial Statistics, Quarterly Bulletin StatisticsjorAsia and the Pacific, Japan Economics Weekly(in Japanese) daily Nihon K ezai Shimbun. Hong Kong data are from daily Financial 4If Rational Expectation(RE) is assumed, then this residual is the unavoidable error of tic economic environment. But if Asymptotically Rational Expectation(ARE) is this residual is the sum of unavoidable error and.Bayesian error. See Stein(1987) 6..

(5) 58. Journal of Financial Studies VoU No.2 January 1994. Times and CFC. The futures prices we use are the monthly-end closing Pli of each contract . As for the realized cash prices of stock index futures ~es actual cash prices are used, and for the cash prices of interest rate instrurn~n~ we use the expiration date futures prices as realized cash prices. The period is from the beginning date of the transaction of individual contract December 1989(Nikkei 225 futures ends in June 1990). All data are natur ' log transformed and deflated by Producer's Price Index(PPI) .5. daJ. 3.2 Empirical Result. Table 1 is the empirical result. Row 1 in the table is the efficiency measu of the performance of individual futures market. Row 2-4 are the decompos~ tions .of MSE according to equation (4). h is the length of the month until t~ futures contract matures. In the calculations of efficiency measure, Nikkei 22~ and Hang Seng stock indexes have the largest SL, followed by Japanese goJ. ernment bond and All Ordinary Shares futures. This suggests that Japane: and Hong Kong markets have the poorer p'erformances t han other marke~ The result also shows that most futures have a larger SL in the longer ma~ turity contract relative to the nearby contract. This is quite consistent wit' the intuition. Since the further away the futures contract is from thematlli rity date, the more possible is the deviation between futures price and t subsequently realized cash price, and hence the larger SL will be. As for t~ decomposition of MSE, most deviations come from Ud , the fraction due ~ (1 ~ r2)var p which is the cash price variability that could not be eliminat by the hedging of futures contract. On the other hand, risk premium(Ur aDi Um)is not an important source of the MSE. However, t he importance of ri premium increases as the maturity date becomes longer. This is quite reasor able. Since the longer the maturity date, the more uncertain the future pric will be , therefore more risk premium is needed to compensate for thisunc tainty. Risk premium also plays an important role in Nikkei 225 and Ha Seng markets. Risk premium in Nikkei 225 futures even dominates foreca! error as the main source of MSE. 6 4. Conclusion There are deficiencies with the traditional EMH tests in the of the performance of futures markets. This paper applies a new 5Because PPI of Hong Kong is not avaliable, we use Consumer Price Index as sll 6Insufficient market liquidity and immature attitude towards futures trading are to be the reasons of high risk premium and poor performance of Japanese and Hong markets. For detailed discussions, please see Chu(1993b).. ,t,.

(6) t,. Journal of Financial Studies VoU No.2 January 1994. 59. in Stein(1987; 1991) to evaluate the performance of nine financial in five countries. The result shows that different futures market be differently in different countries. Among them, Japanese and Hong Kong have the poorest performance, followed by Australian market, U.K. and U.S. markets. In tracing the sources of the deviation between fu price and subsequently realized cash price, forecast error that can not be away by the futures contract is found to be the major cause. However, premium also plays an important role in the Nikkei 225 and Hang Seng index futures markets.. ~.

(7) 60. Journal of Financial Studies Vol.1 No.2 January 1994. ". TABLE 1 Efficiency Measure and the Decomposition of M8E h=rnonth 8&P 500. h=l. h=2. h=3. h=6. 8L. .0116. .0368. .0961. .1912. Urn. .0001. .0256. .0000. .0018 ' '. Ur. .0059. .0013. .0023. .0097. Ud. 1.0275. 1.0054. 1.0491. 1.0222,. I. T-bond. h=l. h=2. h=3. h=6. 8L. .0185. .0575. .1267. .2550. Urn. .0003. .0074. .0167. .0075. Ur. .0561. .0607. .1451. .1676. Ud. .9632. .9517. .8606. .8265. -. T-bill. h=l. h=2. I. h=3. 8L. .0028. .0089. I. .0248. Urn. .2053. .1770. .1973. .0143. .0197. .0545. .1263. .7963. .8169. .7622. .6258. Ur Ud. 4. I. 1.

(8) •. Journal of Financial Studies VoU No.2 January 1994. FT-100. h=l. SL. Urn Ur Ud. 61. h=2. h=3. h=6. .0523. .1031. .3076. .8074. .0766. .0030. .0001. .0022. .0000. .0005. .1120. .3020. .9653. 1.0437. .9607. .8014. Long Gilt. h=l. h=2. h=3. h=6. SL. .0395. .0905. .0977. .1674. Urn Ur Ud. .0056. .0287. .0537. .0690. .0112. .0047. .0069. .0003. 1.0285. 1.0108. .9824. .9077. :.,.. ,.. L. -. Nikkei 225. h=l. h=2. h=3. h=6. SL. .1175. 1.4174. 2.0209. 4.1124. Urn Ur Ud. .1541. .0162. .0269. .0117. .0238. .7111. .7693. 1.0020. .9631. .4367. .3660. .2379. -. I.

(9) 62. Journal of Financial Studies VoLl No.2 January 1994. Japan Bond. h=l. h=2. SL. .0567. .2053. .6524. Urn. .0213. .0069. .0190. .0376. Ur. .1141. .2776. .1613. .4318. Ud. .9259. .7775. 1.1345. .8330. Ordinary Shares. h=l. h=2. h=3. h=6. h=3. h=6. ~. .. 1.1737 .. SL. .0410. .0808. .4611. .7453. Urn. .1502. .0004. .0003. .0006. Ur. .0118. .0402. .1567. .2571. Ud. .8782. 1.0628. .9188. .8524. , I. ~. .;. Hang Seng. h=l. h=2. h=3. SL. .6120. 1.3161. 1.0810. Urn. .0182. .0100. .0040. ,. Ur. .1580. .3674. .2301. .. Ud. .8566. .6411. .7754. •. -. ,.

(10) Journal of Financial Studies VoLl No.2 January 1994 . 63. References. Bailey, W. 1989, "The Market for Japanese Stock Index Futures: Some Preliminary Evidence," Journal of Futures Markets 9, 283- 95. 2. Brenner, M., Subrahmanyam, M.G., and Uno, J., 1989, "The Behavior of Prices in the Nikkei Spot and Futures Market," Journal of Financial Economics 23, 363-83. 3. Britto, R., 1985, "Futures Trading and the Level and Volatility of Spot. Prices: A Survey," Working Paper No.112, Columbia University.. 4. Chu, H., 1993a, "An Evaluation of the Performance of Financial Futures Markets: A Cross Country Study," Working Paper, The Center for the Study of Futures Markets, Columbia University. 5. - - - , 1993b, "An Evaluation of the Performance of Financial Futures Markets: A Cross Country, Cross Market Study," The Review of Futures Markets (forthcoming). 6. Edwards, F.R., 1988, "Futures Trading and Cash Market Volatility: Stock Index and Interest Rate Futures," Journal of Futures Markets. 8,421- 39. 7. Fama, E., 1984, "Forward and Spot Rates," Journal of Monetary Eco nomics 14, 319-38. 8. Rodrick, R.F. and Srivastava S., 1987, "Foreign Currency Futures," Jour nal of International Economics 22, 1- 24. 9. SamuelsoIl, P.A., 1965, "Proof that Properly Anticipated Prices Fluctu ate Randomly," Industrial Management Review 6,41-9.. 10. Stein, J.L., 1987, The Economics of Futures Markets, (Oxford, Basil Black well). 11. ----, 1991, International Financial Markets: Integration, Efficiency and Expectations, (Oxford, Basil Blackwell)..

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