BACKWARD TO THE FUTURE: A TEST OF THREE FUTURES MARKETS. by: D.E.Allen 1 School of Finance and Business Economics Edith Cowan University

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1 BACKWARD TO THE FUTURE: A TEST OF THREE FUTURES MARKETS by: D.E.Allen 1 School of Finance and Business Economics Edith Cowan University S. Cruickshank School of Finance and Business Economics Edith Cowan University N. Morkel-Kingsbury School of Accounting and Finance Monash University and N. Souness W.A. Treasury Abstract Normal backwardation, first discussed by Keynes (1923), (1930) and Hicks (1946), is a fee paid by a seller of a security to the buyer for the privilege of deferring delivery. It implies that a risk premium exists so that the futures price falls short of the expected future spot price. The reverse case, contango, implies that the futures price exceeds the expected future spot price. This paper applies tests for the existence of normal backwardation to daily closing prices on the Sydney Futures Exchange (SFE), London International Financial Futures and Options Exchange (LIFFE) and the Singapore International Monetary Exchange (SIMEX). By applying a series of tests after Kolb s (1992) study of US commodities, it is found that few of the contracts studied consistently exhibit normal backwardation while many show evidence of contango. Keywords: Futures Prices; Normal Backwardation. JEL classification: G13. 1 D.E. Allen Professor of Finance Edith Cowan University School of Finance and Business Economics Joondalup Campus JOONDALUP WA 6027 Ph Fax d.allen@cowan.edu.au

2 1. Introduction The following paper presents the findings of an investigation into normal backwardation on the Sydney Futures Exchange (SFE), London International Financial Futures and Options Exchange (LIFFE) and Singapore International Monetary Exchange (SIMEX) using a method of analysis which parallels the methods used by Kolb (1992) in his US study. Under the theory of normal backwardation developed by Keynes and Hicks, futures prices tend to rise over the life of a futures contract because hedgers tend to be short in the futures market. That is, hedgers hold short positions as insurance against their cash position and must pay speculators a return to hold long positions in order to offset their risk. Markets are therefore considered to be in normal backwardation when the futures price is less than expected future spot price. In other words, Keynes and Hicks saw normal backwardation to be the equivalent of a positive risk premium. Keynes (1930, p.144), therefore suggested that The quoted forward price, though above the present spot price, must fall below the anticipated future spot price by at least the amount of the normal backwardation. This theory follows essentially from the view that hedgers as a group take a short futures position whilst speculators collectively adopt a long position. Hicks suggested that this leads to a constitutional weakness in the market. Keynes and Hicks explained this in terms of technical conditions in production and consumption. Producers have to look further to the future than consumers, the former are committed to maintaining production whilst the latter have a more liberal choice 2

3 about their consumption. This leads to a stronger demand to cover planned production (supplies) than to cover planned consumption (demand). Thus, producers are net short in futures and speculators have to be induced to go net long. A positive risk premium, or normal backwardation, emerges to induce them to do this. This explanation applies to commodity markets but does not necessarily fit the case of financial futures. Kawai (1987) provides the following explanation. Consider the following equilibrium conditions in spot and futures markets at time 0. Q 0,0 + Z -1 = C 0,0 + K 0 (Spot Market Equilibrium) Q 0,1 + K 0 - C 0,1 = Z 0 (Futures Market Equilibrium) The variables Q, C, K, and Z refer to output supply, consumption, storage and futures speculation and their subscripts represent time. For example, Q t,s is output planned at time t and delivered at time s. K 0 is the amount carried from time 0 to time 1, whilst Z 0 is the amount of speculative futures contracts purchased if Z 0 > 0 or sold if Z 0 < 0 at time 0 for delivery at time 1 (Kawai ignores storage from the previous period). The market clearing conditions yield: Z 0 = Q 0,1 + K 0 - C 0,1 = C 1,1 + K 1 - Q 1,1 The arguments suggested by Keynes and Hicks posit that production is mostly planned and consumption is more flexible, therefore Q 0,1 > C 0,1 and C 1,1 > Q 1,1. The 3

4 above implies that Z 0 > 0 follows and there exists a positive risk premium or normal backwardation. However, in some markets such as those for foreign exchange and financial instruments the technological distinction between production (Q) and consumption (C) is not pronounced and storage could be negative (K<0). It follows that normal backwardation is not guaranteed. Thus, for the commodities considered in this paper the issue becomes an empirical one. The paper is divided into five sections which include a review of previous findings in section 2, with a description of the data and methods adopted in the next section, a presentation of the results in section 4 and concluding comments in section Previous Evidence Regarding Backwardation. There is no consistent evidence about the existence of normal backwardation despite a long tradition of research which dates back to Keynes (1930), Hardy (1940), Working (1948, 1949), Houthakker (1957), Telser (1958, 1967), Cootner (1960, 1967), Rockwell (1967) and Dusak (1973). Some of the early work focussed on whether hedgers were net long or short as a whole and whether they earned profits. Houthakker (1957) reported results consistent with backwardation but Rockwell (1967) using a similar approach but larger data sets reported no consistent evidence of it. Dusak (1973) approached the issue from a CAPM framework and suggested that futures contracts had zero systematic risk and 4

5 zero returns. Bodies and Rosansky (1980), Carter, Rausser and Schmidt (1983), and Fama and French (1987) all reported evidence in support of backwardation. The notion of a convenience yield as suggested by Kaldor (1939) and Working (1948) is often used as an explanation for backwardation in futures prices of storable commodities. Litzenburger and Rabinowitz (1995) analyse backwardation in the oil futures markets where it is prevalent and find that it is linked to oil price volatility. The most comprehensive recent study of backwardation in US markets is by Kolb (1992). He studied 29 commodities for the period Only four contracts, feeder cattle, live beef, live hogs and orange juice conform well to normal backwardation. Another five, copper, cotton, soy beans, soy meal, and soy oil partially conform to it. The remaining 20 commodities did not display evidence of backwardation and three of these (crude oil, heating oil and lumber) appear to be in contango. This work was followed by Deaves and Krinsky (1995) who reassessed the contracts that Kolb (1992) found to exhibit evidence of normal backwardation, but with 5 additional years of data. They found that fewer of the contracts then produced evidence of increasing futures prices over time and concluded that market participants would be better off viewing futures prices as reflective of market expectations of future spot prices. The current paper, however, re-applies Kolb s (1992) tests to commodity futures listed on the Sydney Futures Exchange (SFE), London International Financial Futures and 5

6 Options Exchange (LIFFE) and the Singapore International Monetary Exchange (SIMEX). 3. Testing Methodology and Data. No arbitrage conditions between cash and futures markets mean that the futures price must converge to the cash price as expiration approaches. Black (1976) sets out these conditions very clearly. If we follow Kolb (1992) and let F i,t represent the price of a futures contract i with t days remaining until expiration. Similarly P i,t stands for the cash price t days before the expiry of contract i. We know that at expiry the two prices must be equal to one another to prevent arbitrage. It follows that: P i,0 = F i,0 for all i (1) Given this identity, this study uses the price of the futures contract at expiry, F i,0 as a proxy for the cash price at the expiration of the contract. It is further assumed that the market forms unbiased expectations of the spot price expected to hold at expiry and that the observed spot price is a proxy for the expected spot price. Thus, F i,0 is regarded as the spot price expected to hold when contract i expires. If backwardation holds, then futures prices should rise over the life of the contract to the expected spot price at expiry. Kolb (1992) demonstrates that this implies: 6

7 E[ln(F i,t / F i,t+1 )] > 0 and E[F i,t / F i,t+1-1] > 0 (2) This suggests a straightforward test involving the computation of simple and logarithmic returns across all contract maturities (I) and across all days from inception until expiry T. The mean return on any given contract is given by the equation below: T I RETi, t= i= µ = 1 1 (3) I T t In (3) above RETi, t = F i,t / F i,t+1-1. In effect, the existence of normal backwardation suggests that the daily returns on futures contracts must be positive. All contracts are examined to see whether the daily mean return is positive. Kolb (1992) further demonstrates that futures prices before expiration should lie below the expected future spot price at expiration. E(F i,t - F i,0 ) < 0 (4) This can be examined by analysing the relative differences between all futures prices at time t, and all futures prices ultimately observed at expiry. Kolb (1992) recommends the examination of the relative price differential D i,t, defined in (5) below, on the grounds that this metric will not be affected by the units in which the contracts are denominated or by absolute level of all prices examined. 7

8 D i,t = (F i,t / F i,0 ) - 1 (5) The expected value of D i,t should be negative for any day prior to expiration of the contract if normal backwardation holds. E(D i,t) < 0 for t > 0 (6) The following metric is compared across all contracts. M t = I i=1 Di I, t (7) Given normal backwardation Mt should be negative for all days prior to expiry. In effect E(M t+k ) <... < E(M t )... < E(M o ) (8) The expression in (8) can be tested by running the following regression. D i,t = α i + β i t + ε t (9) To avoid serial correlation Kolb randomly selects contracts i and time to maturity t. We follow suit. The hypothesis is that if normal backwardation holds, β i < 0. 8

9 As previously mentioned, in contrast to Kolb's (1992) study of commodity futures markets in the United States, this paper examines those in Australia, Singapore and the United Kingdom. Table 1 summarises the data used in the analysis. We recovered daily settlement price data from the Datastream International database for 5 contracts listed on the LIFFE, 6 listed on the SFE and the single SIMEX commodity contract. In total, 454 contracts with 138,278 daily observations are analysed. Although substantially less than the sample used by Kolb, this is still sufficient to draw confident conclusions. The largest data series was provided by LIFFE cocoa futures which began in 1979 and involved a total of 103 contracts. The smallest data sets were those of the broad wool and fine wool contracts on the SFE. Having only commenced trading in 1998, data for each of these commodities was available on only 6 contracts. 9

10 4. Results The first procedure is a complete test of mean daily futures returns, both simple and logarithmic 2. Results are displayed in Table 2 which includes the first four moments of the distributions, a significance test for the returns and a Bera & Jarque (1981) test for normality 3. Interestingly, of the 12 contracts included in the study, mean returns are negative in 8 contracts and positive for the remaining 4. Negative returns, consistent with contango, are evident in each of the SFE s wool contracts, LIFFE barley and cocoa futures, wheat contracts on both the SFE and LIFFE and SIMEX crude oil futures. Consequently, evidence of normal backwardation in the form of positive mean returns exists only in LIFFE coffee and sugar contacts as well as both of the SFE s electricity futures. The mean returns for all contracts are not significantly different from zero and nonnormal. Contrary to Kolb, there is no discrepancy between the results for simple and logarithmic returns. The results in Table 3 measure daily price observations before expiry relative to the terminal futures price, this time producing weaker evidence of normal backwardation. In fact less than 45% of the total sample observations are below the terminal price. The results show that futures prices tend to be below the expiry price for LIFFE sugar 2 As in Kolb (1992), return refers to the percentage change in settlement price or logarithmic price differences from one day to the next. 3 These tests were repeated after the removing the outliers, however the results did not alter significantly. 10

11 futures and both SFE electricity contracts, thus strengthening the previous findings for these commodities. LIFFE wheat contracts also show evidence of normal backwardation, although somewhat more marginal than that of the other three contracts. These findings are reinforced by the z-scores 4 displayed in Table 3 which provide another test for the proportion of observations below the expiry price. Again we see evidence of backwardation in the contracts outlined above, with the p-values shown to be significant for all but the LIFFE wheat contract. We complement Kolb's analysis by also presenting the results for the number of individual contracts that are in normal backwardation/contango. The criteria for classification as normal (contango) is a minimum of 60% of futures prices below (above) the terminal futures price. Contracts with between 40% and 60% of prices of each type were classified as mixed. Using this method, the evidence for normal backwardation in all but one case (SFE wheat) is reduced. While the LIFFE sugar contract now shows signs of being in contango, the SFE electricity contracts continue to produce evidence of normal backwardation. Table 4 presents an analysis of whether the relative price differentials D it are significantly different from zero across contracts on given days to expiry. The results here are shown for the 90 days prior to expiry and are much weaker than those of Kolb. There is not one daily return for any contract that is significantly different to zero as per a t-test of µ/σ. However, notwithstanding the lack of significance, a very 4 Z-score statistics are calculated as (2x-(N-1))/ n. 11

12 high proportion of daily futures returns relative to the terminal futures price are positive, strongly supporting contango. Only the barley and sugar futures on the London exchange produce evidence of normal backwardation with 78% and 84% of prices, respectively, being below the terminal price. The results of the regression specified in (9) are presented in Table 5. For each of the contracts we selected 5,000 observations (or used the full sample when fewer than this number of observations were available) on which this regression was estimated. We avoided serial correlation by randomly selecting these observations and used White s (1980) procedure to take account of possible heteroskedasticity. The results reinforce our earlier findings with negative betas for the electricity futures, again an indication of normal backwardation. The LIFFE s coffee contract is the only other commodity that exhibits a negative coefficient, strengthening the possibility of normal backwardation in this particular commodity first evidenced in Table 2. By applying White s procedure we were able to obtain heteroskedastic-consistent standard errors and consequently estimate more accurate t-statistics. It is vital to use such standard errors since this is the one consistently incongruent property of the data. It does not appear that Kolb did so and it has an important impact on the results. In our case beta is highly significant for all but the sugar and SIMEX crude oil futures. 12

13 5. Conclusion It appears quite clear that normal backwardation does not prevail for a majority of the contracts examined. The SFE s electricity and LIFFE sugar contracts produced the strongest evidence of normal backwardation, satisfying three of the four testing criteria. While the former display significantly negative betas in the regression of relative price differentials on time and the latter negative price differentials, both show evidence of positive mean returns and more observations below than above the expiry price (even on an individual contract basis). Overall, for these commodities it can be concluded that futures price do indeed increase over time, that is, a positive risk premium does exist. The LIFFE coffee contracts also showed signs of normal backwardation, satisfying two of the test procedures. However as the other two criteria cannot be met, we can at best describe the evidence in favour of backwardation in this commodity as mixed. The remaining contracts can however clearly be classified as being in contango. While the LIFFE barley contract satisfies only one of the four tests for normal backwardation, not one of the other 7 contracts satisfies even one of these criteria but rather satisfy all the criteria in favour of contango. Therefore, while examining alternative markets with a smaller sample period, we are able to conclude in the same manner as Kolb: normal backwardation does not appear to be a feature of these commodity futures markets normal backwardation is not 13

14 normal. In other words, it does not appear that a positive risk premium exists in a majority of the markets studied. 14

15 Table 1 DATA DESCRIPTION Commodity Expiration First year Contracts Number of Months Of Expiration Analysed Observations LIFFE Barley 1,3,5,9, ,696 LIFFE Cocoa 3,5,7,9, ,858 LIFFE Coffee 1,3,5,7,9, ,768 LIFFE Sugar 3,5,8,10, ,600 LIFFE Wheat 1,3,5,7,9, ,240 SFE Greasy Wool 2,4,6,8,10, ,324 SFE Broad Wool 2,4,6,8,10, ,348 SFE Fine Wool 2,4,6,8,10, ,348 SFE NSW Electricity All ,059 SFE Victoria Electric. All ,062 SFE Wheat 1,3,5,7,9, ,814 SIMEX Crude Oil All ,161 Total ,278 15

16 Table 2 MEAN FUTURES RETURNS AND OTHER STATISTICS LIFFE-Barley LIFFE-Cocoa LIFFE-Coffee LIFFE-Sugar LIFFE-Wheat SFE-NSW Electricity SFE-Vic Electricity SFE-Greasy Wool SFE-Broad Wool SFE-Fine Wool SFE-Wheat SIMEX-Crude Oil Obs. Mean. (%) Stdev (%) t-stat Skewness Kurtosis Normality p-value Simple 13, ,648, Log 13, ,076, Simple 40, , Log 40, , Simple 14, , Log 14, , Simple 17, , Log 17, , Simple 15, ,798, Log 15, ,596, Simple 4, , Log 4, , Simple 4, ,235, Log 4, , Simple 8, Log 8, Simple 1, , Log 1, , Simple 1, Log 1, Simple 5, , Log 5, , Simple 11, Log 11,

17 Table 3 PRICE OBSERVATIONS ABOVE AND BELOW TERMINAL FUTURES PRICES Commodity Observations Relative to Terminal Futures Price Overall Contracts Above Below %Below Z-Score p-value Contango Normal B. Mixed %Normal LIFFE-Barley 6,905 6, % % LIFFE-Cocoa 26,333 14, % % LIFFE-Coffee 7,618 7, % % LIFFE-Sugar 7,901 9, % % LIFFE-Wheat 7,464 7, % % SFE-Greasy Wool 5,526 2, % % SFE-Broad Wool 1, % % SFE-Fine Wool % % SFE-NSW Electricity 1,360 2, % % SFE-Vic. Electricity 1,473 2, % % SFE-Wheat 3,611 2, % % SIMEX-Crude Oil 5,694 5, % % Total Sample 75,735 61, % % 17

18 Table 4 RELATIVE PRICE DIFFERENTIALS t DAYS BEFORE EXPIRY LIFFE-Barley LIFFE-Cocoa LIFFE-Coffee LIFFE-Sugar t Avge. t-stat Avge. t-stat Avge. t-stat Avge. t-stat

19 LIFFE-Barley LIFFE-Cocoa LIFFE-Coffee LIFFE-Sugar t Avge. t-stat Avge. t-stat Avge. t-stat Avge. t-stat Avg Std Dev t-stat # Pos # Neg % Neg 77.78% 14.44% 28.89% 84.44% 19

20 LIFFE-Wheat SFE-Greasy Wool SFE-Broad Wool SFE-Fine Wool t Avge. t-stat Avge. t-stat Avge. t-stat Avge. t-stat

21 LIFFE-Wheat SFE-Greasy Wool SFE-Broad Wool SFE-Fine Wool T Avge. t-stat Avge. t-stat Avge. t-stat Avge. t-stat Avg Std Dev t-stat # Pos # Neg % Neg 38.89% 6.67% 10.00% 8.89% 21

22 SFE-Wheat SFE-NSW Electric SFE-Vic Electric SIMEX-Crude Oil t Avge. t-stat Avge. t-stat Avge. t-stat Avge. t-stat

23 SFE-Wheat SFE-NSW Electric SFE-Vic Electric SIMEX-Crude Oil t Avge. t-stat Avge. t-stat Avge. t-stat Avge. t-stat Avg Std Dev t-stat # Pos # Neg % Neg 2.22% 5.56% 4.44% 11.11% 23

24 Table 5 REGRESSION RESULTS a : D i,t = α i + β i t + ε i,t Commodity α HCSE (α) t-stat (α) β HCSE (β) t-stat (β) R-SQ D-W LIFFE-Barley LIFFE-Cocoa LIFFE-Coffee LIFFE-Sugar LIFFE-Wheat SFE-Greasy Wool SFE-Broad Wool SFE-Fine Wool SFE-NSW Electricity SFE-Vic. Electricity SFE-Wheat SIMEX-Crude Oil a Using a maximum of 5000 randomly selected observations and White's correction for heteroskedasticity. 24

25 References Bera, A. K. and C. M. Jarque (1981) An efficient large-sample test for normality of observations in regression residuals, Australian National University Working Papers in Econometrics, 40, Canberra. Black, F., 1976, The pricing of commodity contracts, Journal of Financial Economics 3, Bodie, Z. and V.I. Rosansky, 1980, Risk and return in commodity futures, Financial Analysis Journal 36, Cootner, P.H., 1960, Returns to speculators: Telser vs Keynes, Journal of Political Economy 68 (August), Cootner, P.H., 1967, Speculation and hedging, Food Research Institute Studies 7, Supplement, Deaves, R. and I. Krinsky, 1995, Do futures prices for commodities embody risk premiums, Journal of Futures Markets 15, pp Dusak, K.,1973, Futures trading and investor returns: an investigation of commodity market risk premiums, Journal of Political Economy 8, Fama, E.F. and K.R. French, 1987, Commodity futures prices: some evidence on forecast power, premiums, and the theory of storage, Journal of Business 60, Hardy, C., 1940, Risk and risk bearing (Chicago: University of Chicago Press). Hicks, J.R.,1946, Value and capital (2nd Edition, London: Oxford University Press). Houthakker, H.S.,1957, Can speculators forecast prices?, The Review of Economics and Statistics 39, Kawai, M., 1989, Normal backwardation (entry in The New Palgrave Dictionary of Finance, The Macmillan Press, London) Keynes, J.M., 1923, Some aspects of commodity markets, The Manchester Guardian Commercial reconstruction Supplement 29, March. Reprinted in The Collected Writings of John Maynard Keynes, Vol 7 (London, Macmillan; New York: St. Martin s Press, 1971). Keynes, J.M., 1930, A treatise on money, Vol 2. London: Macmillan: Reprinted in The Collected Writings of John Maynard Keynes, Vol 7 (London, Macmillan; New York: St. Martin s Press, 1971). Kolb, R.W., 1992, Is normal backwardation normal?, The Journal of Futures Markets 12, 1,

26 Litzenberger, R.H. and N. Rabinowitz, 1995, Backwardation in oil futures markets: theory and evidence, Journal of Finance 5, Rockwell, C., 1967, Normal backwardation, forecasting and returns to commodity futures traders, Food Research Institute Studies 7, Supplement, Telser, L.G., 1958, Futures trading and the storage of cotton and wheat, Journal of Political Economy 66 (June), White, H., 1980, A heteroskedasticity-consistent covariance matrix and a direct test for heterskedasticity, Econometrica 48. Working, H., 1948, The theory of the price of storage, American Economic Review 39 (December),

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