SHORT RUN PRICE CYCLES IN THE SYDNEY WOOL FUTURES MARKET B. F. HUNT*
University of Adelaide Evidence of systematic shart mn price movements in Sydney wool futures prices is presented. Traders’ reaction to market uncertainty is suggested as a rationale of wool futures price periodicity. There is also a discussion of the significance of the cycle with regard to the efficiency of the market.
An increasing number of economists believe that price formation in efficient futures markets is best described by what is known as a random walk.’ The existence of price cycles constitutes evidence contrary to the random walk theory, In this study we present evidence of short run cycles in Sydney wool futures prices, We also offer an explanation of the cause of these short term cycles and examine the significance of the empirical cycles with regard to the efficiency of the Sydney wool futures market. Sydney Greasy Wool Futures Exchange Transactors in the Sydney wool futures market buy and sell a transferable contract to supply 1,500 kilograms of clean average 64’s wool on a prescribed date.2 Eight different contracts, distinguished by and named after the different delivery dates, are traded simultaneously. For exampIe, the July future refers to the contract to deliver wool in the last week in July. As the contracts are transferable, it is possible for a trader to satisfy a contractual obligation through the undertaking of an opposite position. That is, if a trader has sold a contract to deliver wool, he may close the transaction by buying a contract to accept 1,500 kilograms of wool. Similarly a trader who has previously bought a contract may close out his market commitment by selling. The Sydney wool futures market also has intimately associated with it a Clearing House that coordinates transactions, settles profits and losses and oversees deliveries of contracts.
* The author wishes to acknowledge that valuable advice and assi5tance was obtained from F. G . Jarrett, T. J . Mules and two anonymous referees. The contents of this article are part of a general statistical study of the Sydney wool futures market. 1The relationship between the random walk model and the theory of efficients markets is presented in, E. Fama, ‘Efficient Capital MarketsA Review of Theoretical and Empirical Work‘, Journal of Finance, 25 ( 2 ) : 383416, 1970; A comprehensive list of random walk studies is given in P. D. Praetz, A Smisrical Study of Fluctuations of Australian Share Prices, unpublished Ph.D. thesis, Adelaide, 1971. 2This passage is but a very brief description of the Sydney wool futures market. For more detail on the Sydney futures market and futures markets in general see John Phillips, ‘The Theory and Practice of Futures Trading’, Review of Marketing and d4gricultural Economics, 23 ( 2 ) : 4363, 1966, Roger W. Gray. Wool Futures Trading in AustraliaFurther P Iospects, University of Sydney, Department of Agricultural Economics: Research Bulletin No. 5 ; R. W. Gray and D. J. S . Rutledge, ‘The Economics of Commodity Futures Markets: A Survey’. Review of Marketing and Agricultural Economics, 39 ( 4 ) : 57108, 1971. 133 Dl
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Participants in a futures market can, for ease of exposition, be split into two main groups, hedgers and spec~lators.~ Traders are divided into these two groups, not because their transactions are essentially different from one another, but because of the different way the two groups view the futures market and the different benefits they expect to derive from a futures market transaction. A hedger is a trader already committed to the commodity market, for example, a wool grower or tops manufacturer. A hedger expects n futures market transaction to reduce his price risk. On the other hand the speculator’s aim is simply to profit from his futures market trade. A hedger is less sensitive to price changes in the futures market than is a speculator, as the hedger can expect any futures price change to be offset by a price change in the commodity market. The division of traders into hedgers and speculators while only being a halftruth does facilitate the rationalization of market phenomena such as price cycles. A hedger is one who holds a position in the futures market opposite to that he holds in the commodity market. A hedger may make a short hedge or a long hedge. A short hedge involves initially selling futures and purchasing them at a later date. A long hedge requires one to buy futures first then sell them later. An example of a short hedge is a wool grower who sells futures contracts to cover his entire anticipated wool clip. After his clip is auctioned, he then cancels his position in the futures market by purchasing futures. The hedge is perfect if, at the time of selling, any loss due to a price drop in the commodity market is recouped by the profit on his futures transaction. It is this compensatory aspect of the futures market that enables the hedger to reduce his price risk. A speculator in the futures market is the same beast that speculates in any other area of uncertainty. He, by virtue of his expertise and willingness to shoulder risk, aims to make an uncertain profit from his transactions. The Random Walk Model The theory of efficient markets states that prices should reflect all available information. In this paper the information set is historical prices, ‘thus we are subjecting the Sydney wool futures market to a ‘weak form’ (to use Fama’s terminology) test of effi~iency.~ A market that exhibits ‘weak form’ efficiency is a fair game in that abnormal (excessive) profits cannot be generated solely from information contained in past prices. The random walk model is a special case of the fair game, efficient markets model.6 The random walk model of price formation in a futures market makes two basic assertions. First, price changes conform to some stable probability distribution. Second, price changes should be independent of one another. This second assertion of the random walk model denies any cyclical pattern in prices. 3 A fuller rescription of transactor types is presented in B. A. GOSS,The Theory of F u m e s Trading, Routledge & Kegan Paul, London (1972). 4 See Fama, o p . cif.,pp. 387388. SIbid., p. 386387.
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Working6 and Samuelson7 have provided the theoretical underpinning of the random walk model. ‘The basis of their rationale is that an efficient market is characterized by many highly informed participants who incorporat: into their notion of the worth of the traded asset all relevant available knowledge. To use the terminology of Working and Samuelson, the niarket price is anticipated in that all existing informtion gleaned from the past and all that can be perceived about the future is discounted in today’s price. The price of the traded asset will thus only change in response to truly new information. This new unanticipated information must necessarily arrive randomly producing random price changes. The random walk model of futures price formation can be symbolically expressed as P t + l = pt t z t u, (la> where Pt is price of the future at tinie t and U, is a stable random variable such that
aut and 2 is a constant term that represents the opportunity cost of investing
funds in the futures market.R The expected price change between periods 1 can be represented as
t and t
+
In a random walk market there can be no cyclical pattern to prices as this violates equations ( l b ) and ( l c ) . We tested Sydney wool futures prices for periodic dependencies using the techniques of spectral analysis and cyclical indices construction.
Data The data consisted of eight futures price series, made up of four seven times per day price series and four daily price series. The seven times per day series consisted of observations, at seven times during the day, upon the July, October, March and New July futures from 7 / 5 / 7 2 to 31/5/72. The daily series were produced from futures prices during the period 4/1/72 to 31/7/73. The daily futures price series are described by and named after the distance of the futures contract from maturity. Prices for the days when the market was shut were imputed by lincar interpolation. Techniques Spectral analysis was the tool employed to check if the independence criterion of the random walk model (equation ( 3 ) ) was met in our daily and seven times per day futures price series. We aIso constructed 8Holbrook Working, ‘New Ideas and Methods for Price Research’, Journal of Farm Economics, 38 ( 5 ) : 142736, 1956. 7 Paul A. Samuelson, ‘Proof that Properly Anticipated Prices Fluctuate Randomly’, Industrial Management Review, 6 ( 2 ) : 4149, 1965. 8 The model described by equations (1) is not strictly speaking a pure random walk, but is a random walk with drift. A pure random walk requires that 2 (equation ( l a ) ) equals zero. D2
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indices of cyclical variation to quantify any periodic movement detected by spectral analysis. Spectral analysis9 is concerned with decomposing time series into a number of components, each associated with a frequency or period.") This spectral decomposition of a time series yields a spectral density function and measures the relative importance of each frequency band in terms of its contribution to the overall variance of a time series. Spectral analysis produces an output which consists of the logarithm of the spectrum, y axis, graphed against the number of estimation lags, x axis. The x axis is very simply converted to period using the simple formula paiod = 2m/j (2) where m represents the maximum number of estimation lags and j equals the particular estimation lag. For all the empirical spectra, m 6 35.l' Thus a lag of 5 is associated with a period of 14 time units.12 Any significant price cycle will show itself as a peak in the log spectrum at the appropriate lag. For instance, a weekly price cycle (5 trading days) would impart to the spectrum of daily prices a peak at lag 14. Five and ten per cent confidence intervals for the theoretical spectrum were calculated by Jenkins and reprinted in Granger and Hatanaka.13 The confidence intervals can be superimposed upon the empirical spectra as horizontal lines. The construction of indices of empirical variation was identical to that described by Karmel.'' A matrix of ratios of empirical observations to the moving average of Iength equal to the cycle period was formed for each series. The ratios were then averaged and adjusted to produce indices of periodic variation. The indices were then transformed by subtracting one so that they were given a mean of zero. Finally, the transformed indices were multiplied by 1,000 to emphasize the periodic variation.
R em1ts The two sets of price series were transformed into log first differences. The spectrum for each series was estimated at m = 35 frequency points. Two of the empirical spectra are presented in Figure 1 and Figure 2. Each consists of the log of the estimated spectrum plotted against the number of estimation lags j . The periods associated with the important spectral peaks are given in parentheses.I5 Confidence bands have been drawn on Figures 1 and 2 at the 95 per cent level.IR Q A detailed exposition of spectral analysis is given in C. W. J. Granger and M. Hatanaka, Spectral Analysis of Economic Time Series, Princeton University Press, Princeton, New Jersey (1964). 10 Period is the inverse of frequency and vice versa. 11 The numlber of estimation lags, m, was chosen using the criteria set out in Granger and Hatanaka, o p . cit., p. 61. 12The time units refer to the interval between data observations, i n our case daily and seven times per day. 13 Granger and Hatanaka, op. cit., p. 63. 14 P. H. KarmeI, Applied Statistics for Economists, I. Pitman & Sons, Melbourne ( 19671. 15The relationship between the period ( l / w ) , the frequency (w) and the number of lags ( j ) is given, in equation ( 5 ) . 1eCare must be taken when using confidence intervals as any departure from normality in the data will impart a downward bias to the confidence intervals.
(5.0
0
8
days)
16
24
32
Kumber of L a g s
FIGURE1Spectrum
of daily futures price changes, twelvemonth series.
The Twelve Month daily price spectrum (Figure 1) provides graphic evidence that a weekly cyclical pattern exists. The spectral peak associated with a period of 5 days (a trading week) transgresses the 95 per cent confidence limits. There is also evidence of a harmonic of this cycle at a period of 2 . 6 days." The spectrum of the October seven times per day series (Figure 2 ) has some spectral peaks characteristic of a nonrandom prices series. There is, however, little or no evidence of a daily cycle (period of 7 time units). Table 1 presents in summary form the results of spectral analysis of the eight futures prices series. Table 1 lists the number of spectral estimates outside the 90 and 95 per cent confidence limits, also the major period components of the empirical spectra are listed. The major period components are an enumeration of the important peaks contained in the empirical spectra. For example, a glance at Figure 1 and Figure 2 reveals the major pzriod components of the October sevefi times per day series to be 2 . 3 and 3.2 time units, and similarly the Twelve Month spectrum has major period components of 2 . 6 and 5.0 days. Finally, Table 1 contains our classification of each series into one of three categories. The series are listed as being either random (R), almost random (A.R.) or nonrandom (N.R. ) . The classification was per'7 Harmonics of a fundamental frequency strengthen the case for the existence of the fundamental frequency. Granger and Hatanaka, o p . d., pp. 4647.
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5.20
5.3G
2
+ U
5*52
a C3
u)
il:*
5.G
5.84
6.OC
I
1
I
a
16
24
I
32
Number of Lags
FIGURE. 2Spectrum
of seven times per day futures price changes, October series.
formed subjectively and is only partly determined by the number of points outside the confidencc limits. If, for example, there existed a
spectral peak at a logical cycle length, such as a day, then we would not consider the series to be random. In our opinion this is so even if the spectral peak does not transgress the particular confidence interval. The resuIts in Table 1 appear contrary to the random walk assertion that price changes in the Sydney futures market are independent of one another. This is particularly true for the daily futures price series where spectral analysis revealed some significant periodic components replete with accompanying harmonic peaks. The daily price spectra contained very strong evidence to support the proposition that a weekly cycle exists in the Sydney futures market. The evidence for a daily cycle was less impressive. Only the spectra of New July prices possessed a daily cyde peak. It was, however, within the 5 per cent confidence limits. We thus concluded there was no reason to suggest that prices in the Sydney wool futures market contained a daily cycle. However, the seven times per day spectra did provide evidence to support the weekly cycIe proposition. Two of the spectra had 35 time units (one week) as one of their major frequency components. Once we had established with the spectral technique that there existed a strong weekly cycle and a less strong daily cycle, the next step
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TABLE 1 Resrilts of Spectral Analysis Time Interval
Series Name
Smctral Estimatcs outside confidence limits ' 5% 10%
~~
Seven Times/Day
,, Daily
,>
Maior Period Components
Classihcatioii 
~

July October March New July
0
oi
3 0 01
10
2 0
3.2, 2.3 35, 4 4, 2 . 3 35, 7, 31 5 , 2.3
R. A.R. R. A.R.
Near Four Months
0 3
0
10, 5 4, 2 7 5, 2 6
R. N.R.
~
5
4.4. 3.0, 2 1
I
I
I
I
Twelve Months
3
8
5, 2 6
N.R.
D i 5 t a nt
1
3
5
A.R.
was to quantify the regular price movements through the construction of indices of cyclical variation. The indices of weekly variation (Table 2) show clearly the extent of the cycle. The prices of Sydney wool futures are on average high at the beginning and end of the week and low on Tuesday, Wednesday and Thursday. The cycle represents approximately 1.5 per cent of the price of the futures contract.ls The indices of daily variation (TabIe 3 ) show up the insignificance of the daily cycle. The daily cycle is a minor perturbation representing only 0.2 to 0 . 4 per cent of the futures price. The results are presented in Table 2. Rationale of Weekly Price Cycles
The results of our investigations clearly show that wool futures prices follow a regular weekly pattern. An explanation of this strong weekiy cycle is to be found upon examination of the rational reactions of the different futures market traiisactor groups to uncertainty. Thc weekly pattcrn ccnsists of prices being typically high on Monday, falling away during the week to bottom on Wednesday and finally rising to be high again on Friday. To explain such a cycle it is necessary to examine the mechanics of trading and the nature of the traders. If a trader has not yet completed a futures market transaction. that is, he has bought but not sold a contract or vice versa, he is said to be maintaining an open position in thc market. There is associated with every futures transaction a buyer and a seller. It thus follows that for every long open position, there is necessarily a short open position, where l * T h e extent of the cyclical variation (in percent) is obtained by subtracting the lowest index from the highest index and dividing by ten, for example the Near futures cyclc represents a weekly fluctuation of 1 2 per cent.
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TABLE 2 Indices of Weekly Variation (minus one, multiplied b y 1000)
Tuesday
0
1
0
Wednesday
8
10
10
Thursday
2
3
3
Friday
~
5
.
 4.
0
i
7
3 3
. . ..
I
I
5 ~~
~
TABLE 3 Indices of Daily Variation (minus one, multiplied by 1000) ~
~
~~
Seven Times per Day Futures Price Series .. . . . . .~~
~~~~~
.
~~~~~
October
11.00 a.m.
2
2
12.00 noon
0
1
12.30 p.m.
1
0
3.00 p.m.
0
1
4.00 p.m.
1
4.20 pm.
1
4.30 p.m.
1
~
March
New July
0
1
0
1 0
1
1 1
1
2
~
long and short refer to the different approaches to a completed futures transaction. A long transaction involves initially buying a contract, while a short transaction requires that the trader initialIy sells a contract. The equivalence of open long and short contracts can be symbolically expressed as CL = cY , (3) where CI,rspresents the long contract and C8 the short contract. As mentioned before, there are broadly two types of transactions, the risk reducing hedge and the profit seeking speculation. The open positions can thus be divided into hedging and speculative transactions. Hence equation (3 ) becomes HL SL = H s Sg (4) where the subscripts L and S refer to long and short and H and S designate the number of open transactions concerned with hedging or speculation respectively.
+
+
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The hedger, to reduce risk, takes the opposite position in the futures market to his commitment in the commodity market. The producers of wool, the farmers, are long in the commodity market and hence to reduce price risk they take up a short position in the futures market. The users of wool, top makers, spinners, weavers, etc., having perhaps soId their products forward, are short in the commodity market, thlerefore they go long in the futures market. H s of equation ( 4 ) is identified with the producers of wool and HT, with the users of raw wool.'" . . . the majority of hedgers at Sydney may be long rather than short. Certainly there appears to have been little hedging by growers; and it is significant that the move for the establishment of the Sydney market came mainly from those who would be more likely to sell wool forward (and be long hedgers when hedging) than to hold stocks of actual This opinion was reinforced during private communication between the author and the secretary of the S.G.W.F.E. Long hedging transactions exceed short hedging transactions, that is HL > (5) referring to equation ( 4 ) it is possible to deduce that
s, > S L and therefore,
s,
s, >
0 (4) that is speculation is net short. The cyclical behaviour of futures is a direct result of speculators being on average short transactors. The speculator whose aim is an uncertain profit is far more sensitive to the nuances of the market than is the hedger who is merely reducing risk by maintaining a position in the futures market. It is apparent that the maintenance of an open futures market position during the weekend involves a considerable amount of risk. Price changing events do take place over the holiday period. The potential consequences of a major price changing event to speculators are much greater during the weekend because the speculator cannot alter his position until Monday. It is our proposition that many speculators regard the risk of holding a position over the weekend as intolerable. For this reason they close out their market position on Friday. As speculators are net short, they must buy back futures to liquidate their position in the market. This increased buying pressure means prices rise on Friday. Such a hypothesis explains why futures prices are high on Friday, but it does not explain why prices remain relatively high on Monday after the weekend period has passed. Monday's high prices are again the result of risk averse speculators leaving the market prior to a period of uncertainty. The major price changing influence upon wool future prices is the auction price of wool. Auctions in Australia generally commence on a Tuesday. This means Monday becomes a period of gross uncertainty for a speculator in wool futures. Thus some speculators prefer to vacate the futures market on Monday forcing prices to a weekly high. 
op. cit., pp. 1822; Phillips, op. cit., pp. 6163. Snape, 'Price Relationships in the Sydney Wool Futures Market', Econumicu, 35 (138) : 169178, 1968. 1 9 Gray, 20 R. H.
142 AUSTRALIAN JOURNAL O F AGRICULTURAL ECONOMICS AUG. The low prices on Tuesday, Wednesday and Thursday are a manifestation of speculators resuming their net short position. Selling pressure drops the futures price as speculators come back into the futures market. Irnplications of Weekly Price Cycles The discovery of a regular pattern of any description necessarily eliminates the random walk model as a description of Sydney wool futures prices. However, the presence of a weekly cycle is not sufficient in itself to invalidate the notion of an efficient market. For instance, a weekly cycle may be well known but continue to exist in an efficient market because the cost (to speculators) of a transaction varies during the week. An efficient market containing price cycles can be described by modifying equations ( 1 ) to
= pt
+ Z(t) +
(7a) where Pi is the price at time t, and U t is the same stochastic variable described by equations ( l b ) and ( I c ) . The essential difference between equation ( l a ) and equation (7a) is that in equation (7a), Z ( t ) , the opportunity cost of investing funds is no longer a constant but is a function of the time of the week. Thc expected normal price change 1 is given by between periods t and t Pt+l
ut
+
This model remains a fair game, E [ U t ] = 0, but the price series is n o longer a random walk as Z ( t ) is not constant for all t . It can be seen from equation (7b) that a weekly cycle can be built into profit expectations. In a market described by equations ( 7 ) it is not possible to make excess profits by operating upon the price cycle. We have shown that it is not sufficient to demonstrate that the Sydney wool futures prices contain weekly periodicity but that it is necessary to show that the periodicity generates abnormal profits before a conclusion of market inefficiency is validated. We do however believe the weekly price cycle in the Sydney wool futures market does produce opportunities for easily won (abnormal) profits. The weekly price cycle (Table 2) in the S.G.W.F.E. is of the order of 1.2 to 1 8 per cent. The cost of a complete transaction in the S.G.W.F.E. is made up of two separate charges. 'The brokerage is $40 per contract and the Clearing House charge $2.50. The total cost of a transaction is thus $42.50. The value of the 1 . 2 to 1 . 8 per cent weekly cycle is a function of the transaction price. The approximate average price over the period was 350 cents/kilo and thus the weekly cycle represents a fluctuation cf $63 to $94 per contract. A trader should therefore be able to make a profit solely from the knowledge that prices are high on Monday and low on Wednesday. We have argued that at least some of the potential profit deriving from weekly price fluctuations is foregone by speculators in order to decrease price risk. However the proposition that Z ( t ) is not constant while being valid for speculators does not hold true for hedgers. Hedgers are committed to the futures market by their commodity market positions and are by the assumptions of the introductory section very much less sensitive to futures price changes than speculators. Thus it would
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seem rational for hedgers to operate on the weekly cycle as they enter and leave the futures market, that is, buy on Wednesdays and sell on Mondays. If, in fact, hedgers did take advantage of the weekly price fluctuations their actions would remove the price cycle. We believe the continued existence of a significant weekly cycle in the Sydney wool futures prices demonstrates that the market is inefficient, at least in the short run.