Simulation of moving average hedging strategies for winter wheat
by Al Stevens Brogan
A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE
in Applied Economics
Montana State University
© Copyright by Al Stevens Brogan (1977)
Abstract:
This research is an investigation of hedging alternatives for Montana winter wheat producers. Various
moving averages are used to make hedging decisions. The results of implementing various
decision-rules are simulated using a General Purpose Discrete Simulator program.
The Great Falls, Montana winter wheat basis is analyzed as a function of days remaining to contract
maturity for futures contracts on both the Chicago Exchange and Kansas City Exchange. The Kansas
City basis is found to be more predictable. It is indicated that within a crop year the December and
March bases narrow as contract maturity approaches. This is not true for the September basis. The May
basis tends to narrow until December and then widen. These results are incorporated as returns to
hedging. The distribution daily price changes is analyzed in a time series framework. Estimated
autocorrelation functions indicate that daily futures price changes follow a random walk.
The results of the simulation of moving average decision rules are generally negative. It is concluded
that moving averages are not a good criterion for hedging decisions by Montana producers. STATEMENT OF PERMISSION TO COPY
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It
is understood that any copying or publication of this thesis for
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Signature
Date
'T
'
-
SIMULATION OF MOVING AVERAGE
HEDGING STRATEGIES FOR WINTER WHEAT
by
AL STEVENS BROGAN
A thesis submitted in partial fulfillment
of the requirements for the degree
of
■ MASTER OF SCIENCE
in
Applied Economics
Approved:
Chairperson, Graduate Committee
Heai
[ajor Department
Graduate Dean
. MONTANA STATE UNIVERSITY
Bozeman, Montana
June, 1977
ill
ACKNOWLEDGEMENTS
I
am grateful to my major advisor. Dr. R. Clyde Greer, for his
support and guidance.
I am also grateful to Drs. Oscar Burt, John
Marsh, Edward Ward and Professor Maurice Taylor for their advice, and
assistance.
I would like to thank Farmers Union GTA for the graduate scholar
ship which funded this work.
I would also like to thank Mr. Gale
Hansen of Farmers Union GTA in Great Falls and Mr. Kent Norby of
Cargill, Inc. in Great Falls for their aid in gathering data.
I am appreciative of the efforts of the typists, June Freswick
and especially Evelyn Richard.
I also wish to express my gratitude to my wife, Laura, whose ,
support and encouragement smoothed the rough spots.
iv
TABLE OF CONTENTS
Chapter
Page
Vita...............................
Acknowledgement..........
Table of Contents ...............................
List of Tables.......... : ......................
List of F i g u r e s ................................
Abstract. .......................................
ii
iii
iv
v
vii
viii
1
INTRODUCTION....................................
Introduction. . . . ..........................
Objectives....................................
I
I
3
2
THEORETICAL CONSIDERATIONS. ....................
Hedging Theory................................
Price Change Theory ...........................
5
5
9
3
THE B A S I S ......................................
Methodology..................................
Conclusions.......... ......................
14
14
28
4
SHORTRUN FUTURES PRICE CHANGES. . .......... .. .
30
5
THE SIMULATION MODEL............................
The Simulation Program. .......................
34
36
6
RESULTS AND CONCLUSIONS ........................
Simulation Results............................
Conclusions.........................
40
40
54
Estimated Autocorrelation Functions for Daily.
Price Changes of Wheat Futures Contracts of
the Kansas City Boardof Trade.................
56
GPDS Computer Program
"Simul"
Subroutine "Average” .. . , ...................
62
APPENDICES
A
B
REFERENCES
77
V
LIST OF TABLES
TABLE
1
2
3
4
5
6
7
8
9
10
11
PAGE
Estimation of the Basis Model for the September
■ Contract During theAugust-September Period . . .
18
Estimation of the Basis Model for the December
Contract. ......................................
20
Estimation of the Basis Model for the Chicago-March
Contract........................................
22
Estimation for the Basis Model for the Kansas CityMarch Contract. . .; ....................
23
Estimation of the Basis Model for the Chicago-May
Contract During the Periods of August-May and
September^-May..................................
24
Estimation of the Basis Model for the Chicago-May
Contract During the Periods December-May and
March-May .............. ■......................
25
Estimation of the Basis Model for the Kansas CityMay Contract During the Periods August-May and
September-May ..................................
26
Estimation of the Basis Model for the Kansas CityMay Contract During the Periods December-May and
March-May......................................
27
Distribution of Daily Price.Changes of Kansas City
Wheat Contracts ..........................
33
Simulation Results of Simple Three Day and Simple
Ten Day Moving Average Decision Rule Over Twenty
Years '..........................................
41
Simulation Results of Simple Five Day and Simple
Fifteen Day Moving Average Decision Rule Over
Twenty Y e a r s , ...........
44
vi
TABLE
12
13
14
PAGE
Simulation Results of Simple Ten Day and Simple
Thirty Day Moving Average Decision Rule Over
Twenty Years..................................
47
Simulation Results of Simple Five Day and Expon­
ential Thirty Day Moving Average Decision Rule
Over Twenty Y e a r s .......................
50
Simulation Results of Exponential Five Day and
Exponential Thirty Day Moving Average Decision
Rule Over TwentyYears........................
53
vix
LIST OF FIGURES
FIGURE
I
PAGE
A Simplified Flow Diagram of the Simulation
P r o g r a m ......................................
35
viii
ABSTRACT
This research is an investigation of hedging alternatives for
Montana winter wheat producers. Various moving averages are used to
make hedging decisions. The results of implementing various decisionrules are simulated using a General Purpose Discrete Simulator program.
The Great Falls, Montana winter wheat basis is analyzed as a
function of days remaining to contract maturity for futures contracts
on both the Chicago Exchange and Kansas City Exchange. The Kansas ■
City basis is found to be more predictable. It is indicated that
within a crop year the December and March bases narrow as contract
maturity approaches. This is not true for the September basis. The
May basis tends to narrow until December and then widen. These
results are incorporated as returns to hedging. The distribution
daily price changes is analyzed in a time series framework. Estimated,
autocorrelation functions indicate that daily futures price changes
follow a random walk.
The results of the simulation of moving average decision rules
are generally negative. It is concluded that moving averages are
not a good criterion for hedging decisions by Montana producers.
Chapter I
Introduction
Agriculture is an important industry to Montana.
of Montana’s income is derived from agriculture.
Over 40 percent
Within the agri­
cultural sector, winter wheat holds an important place.
For the four
crop years from 1973/74 to 1976/77 the average annual winter wheat
production has been 84.2 million bushels.
For many producers winter
wheat is the most important source of income.
Yet these producers
can not be sure in advance what return their crop will bring.
From
1972 to 1976 prices have fluctuated between $2.00 and $6.00 a bushel.
Because of this instability, a few producers have adopted futures
trading as part of their marketing activities.
During this period of price volatility many authors, in trade
publications, recommended that farmers should hedge.
then presented a simplified example of hedging.
These articles
In this classical
sense, hedging involves selling futures contracts to match production
and.then lifting the hedge when the grain is marketed in the spot
market.
However, work by Wayne Purcell (1976) indicates that returns
can be increased by using a trading hedge based on moving averages.
The mechanics of a trading hedge are simple.
A producer hedges
grain when a short term moving average is below a longer term moving
average and lifts the hedge when the short term average moves above
the long term.
2
Inherent in the consideration of a trading hedge is an assumption
about the motive for hedging.
ducer hedges to reduce risk.
Classical hedging assumes that a pro­
This view requires that variability of
spot market price be greater than the variability of the difference
between futures price and spot market price.
that a producer hedges to maximize return.
Trading hedging assumes
In this case, stability
of a price difference, or basis, is less important than the predict­
ability of the change in the basis and of the direction of price move­
ments.
These concepts have been examined in the professional literature.
Holbrook Working (1953a; 1953b) and Roger Gray (1960) have demonstrated
the faults associated with classical hedging.
However, their work is
not generally applicable to the special problems encountered by a.
producer who is spatially separated from a futures market and whose
product does not generally move toward the delivery points of a futures
••
contract, the position in which a Montana producer finds himself. All
wheat futures delivery points are east of Montana.
Ochsner (1974) con­
cluded that in recent years over 50 percent of Montana's wheat crop
has been exported from the west coast.
shipped east.
Very little Montana wheat is
Montana producers do not have the information needed
to determine the applicability of new concepts in hedging to their
situation.
3
Objectives
The general purpose of this study is to investigate some of the
specific opportunities and problems faced by a Montana producer who
wishes to use the futures market.
Specifically the study is addressed
to:
■
1.
'
.
■/
describing the theory of hedging,
2 . reviewing the theory of speculative price changes,
3.
choosing a futures market appropriate for Montana winter
wheat producers,
4.
determining a distribution of daily future price changes,
and
5.
simulating the results a producer might expect for moving
average trading strategies.
\
The theoretical considerations are presented in Chapter 2.
development of the theory of hedging is discussed.
The
Some ideas and
evidence concerning price changes in. speculative markets are presented.
The choice of a market is investigated in Chapter 3.
ability of basis movement is stressed as a criterion.
Predict­
Basis is
analyzed as a function of time.
The distribution of daily price changes is the subject of Chapter
4.
Time series analysis is applied to price changes, and the results
are presented.
The simulation model used to test hedging strategies is described
4
in Chapter 5.
Moving averages are used as a decision criterion,
The
results of Chapters 3 and 4 are implemented in the simulation.
The results of the simulation model are presented in Chapter 6 .
The conclusions of the study and suggestions for further research
are discussed.
Chapter 2
THEORETICAL CONSIDERATIONS
Hedging Theory
There are four concepts of hedging, each based on differing
assumptions regarding hedgers' motives.
These concepts are classified
as risk elimination, risk reduction, arbitrage, and portfolio manage­
ment.
These, concepts are examined individually.
The risk elimination concept of hedging holds that hedging is
effective only if all risk associated with price fluctuations of a
commodity is eliminated.
In other words, any gains or losses in the
cash market due to price changes are exactly offset by respective
losses or gains in the futures market.
This view of hedging is very
naive and is characteristic of much of the work done in the early part
of the twentieth century (Hardy and Lyon, 1923; Taylor, 1913;.Boyle,
1920) .
Obviously, the risk elimination criterion requires a constant
spread between cash and futures prices for hedging to be effective.
Even cursory examination indicates that cash and futures prices do not
move exactly in parallel.
This observation, coupled with the
.
fact that successful business operations do hedge leads to the next
concept of hedging, that of risk reduction.
The risk reduction concept of hedging is an outgrowth of the
earlier, naive view.
The examination which indicates that cash and
6
futures prices do not move exactly parallel does show a similarity
of price movements (Gruen, 1960).
A simple test of hedging under this
view is to calculate the ratio of expected changes in the cash pricefutures price difference to the expected changes in cash price.
If
this ratio is less than one, then.hedging can be deemed to be effective
(Snape and Yamey, 1965).
This test was used in several studies before
and after Snape and Yamey’s article (Howell, 1948, 1962;
Watson, 1938;
Graf, 1953; Brogan, 1973).
that the returns to hedging were negative.
Howell and
Graf, especially, concluded
Again, the results of this
risk reduction concept of hedging were in conflict with the business­
man's view of hedging.
This disparity led directly to Holbrook
Working's formulation of the third concept of hedging, arbitrage
hedging.
The arbitrage concept of hedging rests on Working's contention
that hedging is done for at least one of four reasons.
These are that
hedging:
1.
facilitates buying and selling decisions;
2 . gives greater freedom;
3.
provides a reliable basis for conducting storage; and
4.
reduces risk (Working, 1953a, p. 560-561).
According to Working this view of hedging changed the criterion for
effective hedging from minimum basis fluctuation to predictable basis
fluctuation (Working, 1953b).
7
change in the basis was the size of the basis at the beginning of a. '
period (Working, 1953a).
He regressed the change in the basis from
September to December against the value of the basis on September I.
The resulting equation was Y = 0.861 X + 1 .87'.
approach seems to be begging the question.
Unfortunately,:this .
The futures price and
cash price must approach each other in the maturity month, differing
at most by the cost associated with making or accepting delivery of
the commodity.
If the futures price exceeds the cash price by more
than delivery costs, then a trader could sell a contract, purchase the
commodity, and deliver against the contract. An opposite set of
transactions would be to the trader's benefit if the cash price exceeded
the futures price by more than the acceptance costs.
Roger Gray adopted Working's concept of hedging and then main­
tained that the effectiveness of hedging depends upon a market being a
balance between traders desiring long positions and those desiring
short positions.
He maintained that a market was in balance if the
average value of the basis was equal to zero.
implied.a low cost of hedging (Gray, 1960).
A basis, equal to zero
It was argued that this
criterion was' similar to the previously discarded criteria of risk
.
reduction and risk elimination and did not receive further attention.
Two additional corollaries were developed by Working under the
arbitrage concept of hedging,
hedging.
anticipatory hedging and selective
Both of these concepts may be especially useful in the case
8
of primary producers. Anticipatory hedging consists of taking a
position in the futures market opposite of an anticipated position in
the cash market;
A wheat•farmer, for instance, may hedge a portion
of his crop before it is harvested or before it is planted, in
anticipation of having the crop in the future.
Selective hedging
involves a determination of the size of a futures position conditioned
on an expected price change.
That is, an individual may take a larger
futures position if the cash price is expected to move unfavorably and
vice versa.
A fourth,. and less fully developed, concept of hedging is that of
portfolio management.
The portfolio management concept of hedging is
a relatively new point of view.
This concept stems from investment
analysis where the purpose is to balance assets which have various
returns and risks associated with them.
The original formulation of
a mathematical model for portfolio selection was done by Markowitz
(1952). • This.approach has been applied to commodities and commodity
futures by Johnson (1960), Telser (1955), and Stein (1961) with
varying results.
•
'
'
, ;
The basic model consists of a column vector of expected returns
'
and a matrix of variances and covariances.
The total position can be
described by a row vector of amounts held of each asset.
The problem
then be expressed in either of two ways, to maximize, expected returns
subject to a given level of risk or to minimize risk subject to a
9
given level of return.
If X is the expected return matrix, V the
variance-covariance matrix, and A the asset matrix, then the first
alternative can be expressed as the problem:
Maximize AX subject to
<
'
’ ' AVA' - C .
while alternative two is expressed as
Minimize AVA 1 subject to.
AX-D
In the case of commodities, the possible assets are unhedged stocks,
hedged stocks and stocks marketed by forward sale.
While the model
seems to be ah especially neat formulation of hedging, certain problems
exist;
First, the variance-covariance matrix must generally be of a
subjective nature.
to determine.
Secondly, the expected return vector is difficult
A final problem arises from the inherent assumption that
variance is the best measure of risk.
This approach seems to be a
step backwards emphasizing risk to the neglect of the other factors
developed by Working.
Price Change Theory
Futures prices change daily and even within the trading day.
These
short run price movements have long been a subject of study by econo­
mists and statisticians and an area of conflict between academicians and
10
traders.
This section presents summaries of the various theories and
the evidence which has accumulated, dealing particularly with random
walk, anticipatory prices,. and random shock hypotheses.
The random walk hypothesis is the take-off point for most analyses
of the behavior of short run price movements.
This hypothesis was
first presented by.Louis Bachelier in 1900 (Bachelier, 1900).
Accord­
ing to Bachelierj, the price of a commodity in time period t was equal
to the price in period (t-1) plus a random element, i.e.,
pt " pt - i + = f
It is the distribution of e
which is important.
first contention was that E(e ) = 0.
contention is straightforward.
Bachelier's
The argument to support this .
If the expected price change is other
than zero, then traders would take positions appropriately.
For
example, if the expected price change is,greater than zero, then
traders would buy, confident that they could sell at a higher price in
the future.
However, this buying activity in period (t-1) would
force the (t-1) price to that level where the expected price change
was zero.
A similar analysis holds for expected price changes less
■
than zero.
Bachelier's second contention concerning the e 's was that they
were independently distributed and normal.
This conclusion was
reached by solving the. integral equation of the probability of any
price in period t given the price in period (t-1) .
This solution is
.
11
dependent upon three assumptions concerning the.probability density
function:
a.
it is differentiable with respect to t,
■b.. it has first and second partials with respect to price in
period t, and
c.
it has finite mean and variance (Cootner, 1964, p. 4.)•
As a. consequence of Bachalier's work, many economists have studied .
and tested price series for randomness with mixed results. While
Kendall (1953) and Alexander (1961) concluded that price changes were
random, Lirsoh (1960) found that price changes followed a moving
average process.
Smidt (1965) and Stevenson and Bear (1970) rejected
random walk as an explanation of futures price behavior.
Two alter­
natives, martingale and stable paretian, to the random walk hypo­
thesis have been developed but the evidence is far from conclusive.,
The martingale and stable paretian models each disregard one of the
assumptions of random walk.
The martingale model assumes E (e^) = 0 ■
but does hot assume, independence of the s 's.
t .
The stable paretian
hypothesis does not assume that the distribution has a finite variance.
The lack of a second moment has serious implications.
If the second
moment does not exist, then standard statistical techniques are not
appropriate.
Further discussion of these problems can be found in
articles by Mandelbrot (1963, 1966), in Cootner's book (1964), and.in
a U.S.D.A. bulletin by Mann and Heifner (1976).
The latter, especially.
12
rejected random walk and martingale models as well as the Gaussian
hypothesis.
It is evident that the random walk model is not a completely
satisfactory explanation of futures price movements.
An alternative
explanation was offered by Holbrook Working (1958) ., Working developed
an anticipatory, market model based on classes of traders which explained
the gradual effect of new information on prices.
The e in any period
t
is affected not only by the new information but also by the series of
past information.
Donald Gordon in a discussion of Working's paper
objected to the division of traders into classes and then demonstrated
that such a division was not a necessary component of the theory of
anticipatory prices.
Working's theory can be put into the framework of time series
analysis according to the following finite random shock formula:
*t
where
"t + *1 \ - l + V t - 2 +
+ Vt-n
is the price change and the p^'s are random variables which
are measurements of new developments and new information.
To apply time series analysis it is necessary to assume that the
p 's are independently, identically distributed. With this assumption,
1
.
'
the process becomes a linear discrete stochastic process (Nelson,
1973).
This can be approximated as an autoregressive process of order
p as follows:
13
8t ' " A - i + V t - 2 +
+ ^P^t-p + Pt
where the ir^'s are functions of the original Y^'s, and the
(I)
^ ’.s are
previous observations.
It is apparent that a theory of the behavior of futures price
’\
'
changes can be devised which is consistent with, concepts.of market
efficiency but does not require the independence of successive price
changes.
A later section will be devoted to the approximation of
equation I from observed futures market- price c h a n g e s .
Chapter 3
THE BASIS
No. examination of futures market can be deemed adequate without
an investigation of the basis.
However, this necessary introduction
of basis also introduces confusion.
Arthur (1971, p 64-69) identifies
four concepts of basis ranging from, the general "a spread or difference
of the price relating to actual grain, above or below the price of a
futures contract for such product." to the specific opportunity basis
which "calls for the quotations at which I either close out my position
on both sides or have the opportunity to close out my positions."
Technically, then, basis even in the general sense
refers to the.
difference between a specific futures contract price and a cash price.
In this exposition, however, the term basis is used to refer to the
price difference between any futures price and a Great Falls, Montana
cash price.
When.a more specific interpretation is needed, the general
term will be modified by including market and contract maturity month
such as Kansas City - July basis or Chicago r- May basis. When there is
no room for ambiguity, the market designation may be dropped.
Methodology
As Working's, view of hedging emphasizes, it is the predictability
of basis movements which is important.
A concentric idea, however,
is that a hedger should only be interested in the predictability of
15
the basis when he is in a position to take advantage of favorable basis
movements.
Thus, the Montana producer is interested in basis predic­
tion only for that period after probable harvest or from August to
contract expiration dates within a crop year.
While the results of
this study may have implications for the timing of sales within a
crop year,, the optimum selling date is a question beyond the scope of
this study.
The producer cannot gain from favorable basis movements
unless the crop is in hand and can be sold.
Thus, for Montana produc­
ers, there are four relevant contract months, September, December,
March and May.
July is excluded on the presumption that the crop
harvested in any year will not be held beyond the date beginning of the
next harvest season.
It is.further assumed that a producer will
not maintain an open position beyond the first trading day in the month
of contract termination.
Some authors argue that it is important for a producer to predict
the value of the basis.
It is their contention that a producer should
hedge only when the futures price adjusted by the predicted basis
represents a return great enough to cover all costs.
This attitude
is consistent with risk reduction, but is a step away from dynamic
hedging and aggressive marketing by the producer.
TwO situations
clearly illustrate the fallacy inherent in such a static strategy.
In the first case, commodity prices may be so low that costs cannot
be covered and still be dropping.
In this situation, it is obvious
16
that a producer may hedge to minimize a loss.
In the second case,
commodity prices may be high enough to cover all costs, and yet
still be rising.
In this eventuality, it is clearly to the producer's
disadvantage to hedge.
Therefore, to effectively implement an
aggressive marketing program a producer must be able to predict the
direction of price movements and basis movements.
The former problem
will be dealt with in a later, chapter while the latter will be dealt
with here.
At any point in time the basis is made up of several components
including a constant term representing locational differences, a
yearly term representing peculiarities of a particular season or crop
year, a daily term representing storage costs from the present to
contract maturity, and an error term.
This suggests the following
linear model.
-
Bti = *0 + Gli?! + *2»t + =t
where
is the basis on day t of year i
g is a constant
o
is a vector (I x i) of coefficients
is a matrix (i x I) of zero - one values
@2 is a coefficient of daily change
is the number of days to contract maturity, and
e
is an error term.
This general model can be estimated using ordinary least squares
17
if there are (.1 + I) years- of data available.
As specified the
model parameters estimates have the following interpretation,
;
the location difference which is constant over time.
g
is
■■■
The S. ,'s are
Ii
inter-year differences representing a difference from the base year.
@2 is the expected daily basis change.
For each futures exchange there are ten possible contract-trading
period combinations when the Montana producer may hedge his crop and
expect to gain from basis change.
I;
The combinations are:
a September contract may be used in the August trading
period;
2.
a December contract may be used in the August and September
to December trading periods;
3.
a March contract may be used in the August, September to
December and December to March trading periods; and
4.
a May contract may be used in the August, September to
December, December to March, and March to May trading periods
Data used to estimate the model are Chicago and Kansas City wheat
futures closing quotations from July I, 1971 to June 30, 1976 and
prices paid for ordinary winter wheat at Great Falls, Montana for the
same period. ■The estimations results are discussed below.
Regression results for the September contract are presented in
Table I.
The starting date for this regression is the first trading
day in August and ending date is the first trading day in September.
18
Table I
.Estimation of the Basis Model for the September
Contract during the August-September Period..
Chicago
Kansas City
Variable
D .■
Y
-.1677 E-2 (.1241 E-2)*
-.3135 E-2 (.1542 E-2)
.9437 E-I (.3973 E-l)
-.3264
.1203 E-2 (.3946 E-l)
-.8265 E-I (.4160 E^l)
.4658 E-I (.4031 E-l)
.6199 E-I (.4149 E-l)
Intercept
.3938
.5410
R2
.1422
.5669
St. Error
of the
estimate
.1347
.1391
Y2
Y3
(.4072 E-l)
*The numbers in parentheses are the standard errors of the regression
coefficients.
19
For both exchanges the estimated coefficient on days remaining
to contract maturity is negative.
coefficient is insignificant.
In the Chicago equation, the
The most probable explanation for
these.coefficients being negative is that prices offered Montana
producers are being depressed during a harvest "glut" while Midwest
prices have achieved post, harvest stability.
The estimated coef­
ficients on the year dummy variables represent a difference from the
base year contract of September 1971.
A standard error of the estimate criterion would favor the
Chicago market while an R-squared criterion would favor Kansas City.
In either case, the producer should expect an unfavorable basis
movement through the month of August for the September contract.
The December basis was estimated for trading period beginning
in August, after harvest, and September, after the September contract
expired.
The results are presented in Table 2.
■ In all four cases, the coefficient on
days remaining to contract
maturity is significant and has the expected sign.
The coefficients
on the year dummy variables indicate a difference from the base year.
While these results are useful for estimating basis predictability,
they are not useful for estimating the absolute value of the basis.
These results suggest that there are significantly different inter­
year demand and/or supply forces which determine the absolute value of
the basis.
Identification of these latter forces is beyond the scope
Table 2
Estimation of the Basis Model for the December Contract
August-Deceiriber
Chicago
Sep tember-December
Kansas City
Chicago
Kansas City
Variable
Dt
Y1
Y2
Y3
Y4
Intercept
R2
Std., Error
of the
estimate
.1126 E-2 (.1832 (E-3)*
.1148 E-2 (.1739 E-3)
.1871 E-2 (.2339 E-3)
.1853 E-2 (.1680 E-3)
.2593 E-I (.2068 E-l)
.9814 E-I (.1956 E-l)
-.9400 E-2 (.1974 E-l)
.6814 E-I (.1395 E-l)
-.1356
(.2056 E-l)
-.6948 E-2 (.2063 E-l)
-.1705
(.1939 E-l)
-.1085
(.1966 E-l)
-.1025
(,.1384 E-l)
.2705 E-I (.1944 E-l)
-.6560 E-I (.1958 E-l)
-.3504 E-I (.1378 E - D
.7756 E-3 (.2056 E-l)
.1510 (.1939 E-l)
-.7193 E-I (.1936 E-l)
.9178 E-I (.1373 E-l)
.3773
.2948
.3786
.2182
.4645
.2542
.1336
.1260
.1095
.2837
-
.
-
*The numbers in parentheses are the standard errors of the regression coefficients.
.5523
.0771
ts3
O
21
of this work.
For both contract-trading period combinations, the Kansas CityDecember basis model has a lower standard error of the estimate
higher R-squafed than the Chicago-December basis model.
and
This implies
that if. a producer is to use a December contract to hedge he should
choose the Kansas City exchange.
The results of the March basis model estimations are presented in
Tables 3 and 4.
In five of the six cases
the coefficients on days
remaining to contract maturity are positive and significant.
For the
sixth case, the Chicago-March basis for the period December to March
the coefficient is not significantly different from zero.
This is also
the only case where the Chicago basis model has a higher R-squared
than the Kansas City model.
However, in every case the Kansas City-
March basis model has a lower standard error of the estimate than the
Chicago-March basis model.
The implications of these results are similar to those of the
December models.
A producer who chooses to hedge with a March contract
should also choose the Kansas City exchange.
Furthermore, depending
upon the period, the producer can expect to benefit by a cent per
bushel move in the basis every five to twenty days.
In a like manner, the May basis was estimated for both Chicago and
Kansas City.
The results of these regressions, with starting dates of
August, September, December and March are presented in Tables 5, 6 , 7,
22
Table 3
Estimation of., ttie Basis Model for the- Chicago-March Contract
August-March
.
September-March
December-March
Variable
.9903 E-I (-.8764 E-4)» ,.1065 E-2 (.9547 E-4) .1864 E-3 '(. 1497 E-3) '
Dt
Y1
.
Y
' ■
Y3
■
Y4
-.3530 E-I (.172.7 E-l)
-.6747' E-I (.1607 E-l) -.1724
-.1945.
-.1664
.,(,1258 E-l) '
(.1604 E-l) -.1132
(.1258 E-l)
-.2318 E-I (.1712 E-l)
-.6907 E-I (.1587 E-l) -.2557
(.1236 E-l)
-.2254 E-2 (.1711 E-l)
-.6842 E-I (.1587 E-l) -.2132
(..1241 E-l) ■
Intercep t
R2
St. Error
of the I
estimate
(.1721 E-l).
.3618
.3004
.1457
.
.3792
'
; ■
.2809
.1247
.4994
'
.6392 ..
.0688
'
' '
*The numbers in parentheses are the standard errors of the. regression
coefficients.
I
23
Table 4
Estimation for the Basis Model for the Kansas City-March Contract
August-March
Sep teiriber-Mar ch
December-March
Variable
Dt
Y1
. Y2
Y3
Y4
.1068 E-2 (.8166 E-4)*
.1195 E-2 (.8018 E-4)
.4050 E-I (.1603 E-l)
.1096 E-I (.1344 E-l) -.7371 E-I (.1191 E-l)
-.2045
(.1593 E-l)
(.1336 E-l) -.1540
(.1186 E-l)
.4987 E-I (.1589 E-l)
.3742 E-2 (.1327 E-l) -.1395
(.1171 E-l.)
.1431
.9517 E-I (.1333 E-l) -.2004 E-I (.1186 E-l)
(.1595 E-l)
Intercept.2545
R2
.5362 .
Std. Error
of the
estimate
.1353
'
-.1934
.5183 E-3 (.1430 E-3)
.2607
.3534
.5505
.4941
.1043
.0652
'
*The numbers In parentheses are the standard errors- of the regression
coefficients.
,
24
Table 5
Estimation of the Basis Model for the Chicago-May Contract
During the Periods of August-May and September-May
August-May
September-May
Variable
A
'
Y1
Y2
Y3
Y4
Intercept
R2
Std. Error of
the estimate
.7255 E-3 (.7961 E-4)*
.7124 E-3 (.9244 E-4)
-.6932 E-I (.2016 E-l)
-.9815 E-I (.2070 E-l)
-.3233.
-.2925
(.2010 E-l)
(.2067 E-l)
-.3079 E-I (.2007 E-l)
-.6196 E-I (.2057 E-l)
.4798 E-I (.1999 E-l)
.3566 E-2 (.2048 E-l)
. .3288
.3466
.3516
.2925
.1936
.1866
*The numbers in parentheses are the standard,errors of the regression
coefficeints.
25
Table 6
Estimation of the Basis Model for the Chicago-May Contract
During the Periods December-May and March-May
.
March-May
December-May
Variable
Dt
Y1
Y2
Y3
Y4
-.1358 E-3 (.8147 E-4 )*
-.3544 E-3 (.2643 E-3)
-.1799
G 1122 E-l)
-.2015
-.2280
(.1122 E-l)
-.2228
(.1116 E-l)
-.8359 E-I (.1111 E-l)
'
-.1905
-.2459
(..1514 E-l)
(.1514 E-l)
'
(.1533 E-l)
-.9852 E-I (.1505 E-l)
Intercept
.4517.
.5683
R2
.5552
.6164
.0801
.0702
St. Error of
the estimate
.
*The numbers in parentheses are the standard errors of the regression
coefficients.
26
Table 7
Estimation of the Basis Model for the Kansas City-May Contract
During the Periods August-May and Septemher-May ■
:
August-May
Sept ember-May
Variable
.5718 E-3 (.5800 E-4)*
Dt
'
Y1
’
Y2
Y3
Y4
Intercept
R2 .
St. Error of
the estimate
.5540 E-3 (.5870 E-4)
-.5759 E-I (.1468 E-l)
-.9362 E-I (.1315 E-l)
-.4113
-.3672
(.1460 E-l)
-5816 E-2 (.1462 E-l)
01308 E-l)
-.3747 E-I (.1306 E-l)
.1671 < . (.1456 E-l)
.1420
.2680
.2790
.6608
.6801
.1410
.1185
(.1300 E-l)
*The numbers in parentheses are the standard errors of the regression
coefficients.
27
Table 8
Estimation of the Basis Model for the Kansas City-May Contract
During the Periods Decemher-May and March-May
Decembef-May
March-May
Variable
-.4677 E-3 (.8466 E-4)*
Dt
' Yi
.
Y 2.
Y3
■
Y4
■
-.1953 .
I
(.1165 E-l)
-.3229
' -.1467...
■
Intercept
R2
Std. Error of
the estimate
-.1262 E-2 (.2334 E-3)
,
-.2435
(.1328 E-l)
(.1162 E-l)
-.2497
(.1328 E-l)
(.1159 E-l)
. -.1852
(.1354 E-l)
.8827 E-I (.1153 E-l)
■■ V
.3880
.1168
.7580 '
.8564
.0832
.0616
C 1321 E-I).'
.4184
,'
'
■
*The numbers in parentheses are the standard errors of the regression
coefficients.
28
and 8 .
These results show that in three of the four cases the Kansas City
market is clearly preferable using either the R-squared or the standard
error of the estimate criterion.
In the fourth case, the period
beginning in December the Chicago-May basis has a slightly lower
standard error than that of Kansas City.
market is to be preferred.
Overall, the Kansas City
Far more important, however, is the fact
that the coefficient on days to contract maturity is negative and
significant for Kansas City for the periods beginning in December and
March.
A possible cause of this is that while prices are rising through
the crop year, new crop expectations are affecting the May futures
price.
This is especially plausible when it is remembered that harvest
in the extreme southern portion of the winter wheat producing area
begins in early May.
The implication of this is that while a producer
who chooses to hedge with the Kansas City-May contract may expect 'a
favorable basis movement of between five and six thousandths of a cent
per day in the period August through December, that producer should
also expect an unfavorable basis movement of between four and twelve
thousandths of a cent per day in the December through May period.
Conclusions
In nearly all cases the Kansas City market is preferable to
Chicago.
Therefore, the time series analysis in the next "chapter will
29
focus on the Kansas City futures market.
Furthermore, the December
and March contracts offer the greatest probability of a favorable
basis movement for any period after August.
These expected movements
will be'incorporated as a return to hedging in the simulation model
■described in Chapter 5.
Chapter 4
SHORTRUN FUTURES PRICE CHANGES •
The various theories of price changes in speculative markets
were discussed in Chapter 2.
The results of applying these theories
to the Kansas City Board of Trade wheat contracts for the period
July 1971 through June 1976 are presented in this chapter.
Specific­
ally, if the price changes follow an autoregressive, moving average
framework, the series can be identified through the autocorrelation
function and the partial autocorrelation function.
For instance, if
the series is a moving average process of order q so that 2^ =
+
¥-,y - + ...'Py
, then the autocorrelation function will have
■ I t-1
q t-q
spikes at lags I through q and then be cut off.
The partial corre­
lation function will decrease gradually to zero (Nelson, 1973, p. 89).
If the series is from the autoregressive process of order p such that
2 .= y + <)).,2
+ ... <j> 2
, then the autocorrelation function will
t
t
JL t I
p t p
tail off according to the Yule-Walker equations while the partial
autocorrelation function will have spikes at lags I through p and then
be cut off (Nelson, 1973, p. 89). ' Similarly, the most complicated
possibility, a mixed autoregressive-moving average process of orders
p and q can be identified through the autocorrelations and partial
autocorrelations.
In this case the model is 2^ = y^ + <j)^2t__^ +
(J)12 - + ... +<j) 2^
+xP1Il 1 +. ... + xP 'p. .
. I t-1
p t-p
I t-1
q t-q..
The .autocorrelation
31
function will have an irregular pattern at lags I
tail off according to Yule-Walker equations.
through q and then
The partial autocorre­
lation function will gradually decrease to zero (Nelson, 1973, p. 89).
The identification of a time series model is hampered by the fact
that the autocorrelation function and the partial autocorrelation
function are unknown. However, these functions can be estimated..
An
estimate for the jth coefficient of the autocorrelation function is
*
rj
V . <at+d
T h -i v 2]
A
t=l
J 1
(Nelson, p. 71).
Once a model has been identified and estimated, the adequacy of
the model can be tested using a portmanteau test (Box and Jenkins, 1976,
p . 290-291).
A special case of this test can be applied to check
whether the series is white noise.
If daily futures price changes
comprise a series of independent random variables then
K
I
3=1
where n is number of observations and r. is the sample autocorrelation
3 •
2
of the jth lag, will be distributed approximately x (K) where K is
the number of autocorrelations (Box and Jenkins, 1976, p. 291).
If Q
is larger than the tabled Chi-square value at a selected confidence
32
level the series is not white noise.
The autocorrelation function for twenty-five Kansas' City wheat
contracts was estimated using the above formula.
The calculated
autocorrelation functions are presented in Appendix A.
The estimated
means, standard deviations, and Chi-square statistics for 24 degrees
of freedom are presented in Table 9.
At the 97.5 percent confidence
level, the Chi-square coefficient for 24 degrees of freedom is 39.4.
For 17 of 25 contracts the Chi-square statistic is below this level.
Therefore, in these cases, a conclusion of independent random price
changes with mean zero is not rejected".
Since, in all contract
months, the most recent contract is characterized by white noise this
distribution will be used in the simulation model.
The above conclusion is at odds with the conclusion of Mann and
Heifner (1976).
In their work, nonparametrie tests indicate serial
dependence in futures price changes.
Kansas City wheat contracts.
However, they did not deal with
Furthermore, while such serial dependence
may exist, the results of this study suggest that the dependence is so
weak that the information content is trivial and is not useful for
decision making.
33
Table 9
Distribution of Daily Price Changes of Kansas.City Wheat Contracts
Contract
March
March
March
March
March
May
May
May
May
May
July
July
July
July
July
1972
1973
1974
1975
1976
1972
1973
1974
1975
1976
1972
1973
1974
1975
1976
September
September
September
September
September
December
December
December
December
December
1972
1973
1974
1975
1976
1971
1972
1973
1974
1975
Mean
Standard Deviation
Chi-Square
1048E-3
.4495E-2
.1668E-1
2143E-2
.1595E-2
.7189E-2
.4094E-1
.1226
.1216
.687IE-I
19.81
14.92
53.59
27.96
,30.92
.1017E-3
.3823E-2
.5749E-2
6095E-2
.9080E-3
.7523E-2
'.3923E-1
.1329
.8649E-1
.7060E-1
23.28
26.48
40.41
43.95
29.18
.3318E-3
.3410E-2
.,6031E-1
6283E-2
-.5217E-3
.8938E-2
.4570E-1
.1289
.7375E-1
.6078E-1
23.30
56.78
31.78
' 21.32
20.95
.2784E-2
.1290E-1
.3125E-2
3947E-2
.6207E-3
.1689E-1
.7772E-1
. .1193
.7286E-1
.5487E-1
67.84
57.39
26.14
13.45
19.38
2024E-3
.4922E-2
•1260E-1
1094E-2
1952E-2
.7778E-2
.2328E-1
.1039
.1093
.7005E-1
18.43
. 116.52 '
41.63
33.07 .
. 25.07
Chapter 5
THE SIMULATION MODEL
Introduction
In this chapter the results of the previous two chapters are
combined into a simulation model.
The model will be used to test wheat
hedging strategies which are based on moving averages.
The output of
the simulation program will satisfy the original goal of this study,
that is, to estimate a distribution of returns for hedging activities
which incorporate various trading rules and stopping or marketing
dates.
A simplified diagram is presented in Figure I.
The program is
found in Appendix B.
The simulation will be done using a General Purpose Discrete
Simulation (GPDS) model which interfaces with a Fortran subroutine.
This program first generates a price change according to an assumed
white noise distribution.
is determined.
From the price change a new daily price
Following this the program calculates a pair of
moving averages for each decision strategy.
At this stage, the pro­
gram initiates or maintains a hedged position if a short term moving
average is less than a corresponding long term moving average.
After
a hedge has been initiated, the program closes the position when the
relationship of the moving averages is reversed.
When a hedge position .
is closed the program calculates the returns to the hedging activity .
35
Calculate a
price
change
Calculate
new price
Call Fortran
Subroutine
Calculate
Moving Averages
Wait for
Price
Change
Pause to
check for
trading
action
Terminate
transaction
,✓ /is'X
his last
iarketing
STOP
Generate a
trading
transaction
/ShoulJNl.
hedge b e ^ ^ f
solaced*'/
Place
Hedge
Lift
Hedge
Calculate
and tabulate
return
Figure I.
A Simplified Flow Diagram of the Simulation Program
36.
The Simulation Program
To generate price changes the program uses a random number
generator, which is intrinsic to GPDS.
The program picks a random
number which is internally converted so that it is from a distribution
which is Normal with P = O
and
2
a = I.
Externally, this is converted
to a number from a distribution which is Normal with y = 0 and
$.49.
a
2
=
This, and all other money values, are expressed in terms of
fourths, of a cent.
This is necessary because GPDS requires that ■
numerical values be integers.
The price change generated is then
added to the previous day's price.
The program then calls on a Fortran subroutine to calculate five
pairs of. moving averages.
These pairs are:
1.
Simple 3 day. Simple 10 day
2.
Simple 5 day, Simple 15 day
3.
Simple 10 day. Simple 30 day
4.
Simple 5 day. Exponential 30 day
5.
Exponential 5 day. Exponential 30 day
A simple moving average is one in which all days are given the same
weight.
The weight is equal to one divided by the number of days in
the average.
An exponential moving average is one in which all days
are given different weights.
The weight assigned to any one day is
calculated by dividing the number of days from the first day not
included in the average by the sum of the number of days in the average
37
To illustrate, the most recent day in a thirty day exponential moving
30
average would have a weight equal to 30/1 i. The earliest day included
i=l
in a five day exponential moving average would be assigned a weight
5
of 1/E i,
i=l
At this point the program checks to see if any hedges are in
effect.
If there is a hedged position, the program determines whether
the hedge should remain or be lifted.
Should any hedge be lifted, the
program calculates and tabulates the returns to that trade.
The
program automatically lifts any hedges in existence on the predeter­
mined stopping date.
For strategies in which there is no an existing
hedge, the program decides if one should be placed and places it if
necessary.
An assumption inherent in this model is that trades take
place at that day's price which triggered the decision rule.
For each hedging strategy returns are calculated by two methods.
One assumes that hedges after harvest (assumed to be mid-August) are
placed in the nearest contract month.
The second method assumes
that hedges placed after harvest are in the contract month which has
"the most favorable expected basis movement.
Under both methods, the
returns to hedging from the beginning of the marketing activity, the
November preceeding harvest when the crop is seeded, to harvest are
calculated in the same manner.
For this latter period the returns are
determined by the formula (Price Sold - Price Bought)(5000) - Costs.
Costs include commissions of $43.00 per round turn.
38
In addition to commissions, the interest on margin money is a
significant cost.
Interest should be charged from the beginning of
the marketing period to its termination.
calculate the interest charge.
The program does not
The reader should be mindful of this
cost when analyzing the simulated returns.
.
For periods after harvest the return includes an expected basis
change.
In these cases returns are calculated by the formula
(Price
Sold - Price Bought) + Expected Daily Basis Change x Days of Hedged
Position)
5000
- Costs.
The expected daily basis change is deter­
mined from the equations estimated in Chapter 3.
The program then
tabulates the returns.
Five terminations are considered in the program.
August, December, January, March and April.
sents a sale at harvest.
movements, are favorable.
of a crop year.
The August date repre­
The December and January dates represent
sales dates because of tax considerations.
a sale in early spring.
These are
The March date represents
It is the last date at which expected basis
The April sale represents a sale at the end
Months are assumed to consist of twenty-one trading
days and a year consists of 252 trading days.
A final assumption in the model is that the generated price
change applies equally to all contract months.
Since: the contract
months are considered to be in a single crop year, and since price
39
changes in this case appear to be highly correlated, the error
resulting from this assumption is probably negligible.
Chapter 6
RESULTS AND CONCLUSIONS
Simulation Results
The simulation program was run twenty times and the results o f .
each run were combined to obtain estimates of the mean return and
standard deviation.
These results are presented below.
The first trading rule used was to place a hedge if a three day
moving average was less than a ten day moving average and to lift the
hedge when the three day moving average moved above the ten day moving
average.
The results of this strategy are summarized in Table 10.
This strategy generated an average of ten trades per year between the
beginning of the marketing period and harvest.
If hedges, after the
beginning of August, were placed in the near contract, September, the
average annual return was $1,015 with an estimated standard deviation
of $1,139.
The yearly returns were split equally with ten losses and
ten gains, ranging from a maximum loss of $3,980 to a maximum gain of
$20,208.
If hedges after August I were placed inthe contract with
the most favorable expected basis movement, December, the average
annual return rose to $1,025.
In this case the estimated standard
deviation was $1,150, and the range was from a loss of $3,912 to a
gain of $20,234.
Eor a marketing period which ends in December, hedging based on
three and ten day moving averages resulted in ten years with gains
Table 10
Simulation Results of Simple Three Day and Simple Ten Day
Moving Average Decision Rule Over Twenty Years
Near
Contract
January
December
August
Favorable
Contract
Near
Contract
Favorable
Contract
Near
Contract
March
Favorable
Contract
Near
Contract
April
Favorable
Contract
Near
Contract
Favorable
Contract
Average Annual
Return
$1,015
$1,025
$1,723
$1,778
$2,126
$2,181
$1,967
$2,022
$2,417
$2,472
Standard
Deviation
$1,139
$1,150
$1,253
$1,252
$1,328
$1,327
$1,311
$1,310
$1,424
$1,422
Number Years
Positive
10
10
10
10
11
12
11
11
11
11
Number Years
Negative
10
10
10
10
9
8
9
9
9
9
Maximum Annual
Return
$20,208
. $20,234
-$21,159
$21,186
$23,187
$23,214
$22,453
$22,480
$23,684
$23,711'
Minimum Annual
Return
-$3,980
-$3,912
--$4,085
-4,001
-$3,772
-$2,688
-$4,041
-$3,999
-$7,395
-$7,353
Average Number
of Trades per
Year
10
10
14
14
16
16
18
18
20
, 20
'
42
and ten with losses.
period.
There was an average of fourteen trades over the
The average return calculated for always hedging with the
near contract was $1,723 with an estimated standard deviation of
$1,253.
The yearly returns ranged from a loss of $4,085 and a
gain of $21,159.
For hedging always done with the most favorable
contract, the mean return was $1,778.
estimated to be $1,252.
The standard deviation was
The range of returns was from a loss of
$4,001 to a gain of $21,186.
Including another one and a half months in the marketing period
improved the apparent results from using three and ten day moving
averages to make hedging decisions.
trades was increased to sixteen.
However, the average number of
During this period, hedging with
the near contract resulted in gains in eleven years and losses in
nine.
The average return was $2,126, and the estimated standard
deviation was $1,328.
The returns varied between a loss of $3,772
and a gain of $23,187.
The returns to hedging with the most favor­
able contract were even better with gains in twelve years and losses
in eight.
With this type of hedging, returns averaged $2,181, and
the standard deviation was estimated to be $1,327.
The range of
returns was from a loss of $3,688 to a gain of $23,214.
Extending the marketing period to the first of March resulted in
an average Ofs eighteen trades per year and in gains for eleven years
and losses in nine.
For near contract hedging the average return was
■
43
$1,967.
The estimated standard deviation was $1,311, and the range
was from a loss of $4,041 to a gain of $22,453.
Hedging the most
favorable contract raised the average return to $2,022 with an
estimated standard deviation of $1,310.
The range of returns was
from a loss of $3,999 to a gain of $22,480.
Including the months of March and April in the marketing period
resulted in gains in eleven years and losses in nine.
The additional,
two months did raise the average number of trades to twenty.
Near
contract hedging resulted in a mean return of $2,417 with an estimated
standard deviation of $1,424.
$7,395 to a gain of $23,684.
Annual returns ranged from a loss of
The average return for hedging with the
most favorable contract was $2,472.
The estimated standard deviation
was $1,422 and the range was from a loss of $7,353 to a gain of
$23,711..
The second trading rule simulated was to place a hedge when a
five day moving average was below a fifteen day moving average and to
lift the hedge when the relative positions of the moving average.were
reversed.
The results of this strategy are summarized in Table 11.
During every marketing period the average annual return from this
strategy was negative.
The annaul loss increased as the marketing
periods became longer.
This strategy did result in three to four
fewer trades than the previously discussed strategy.
For sale at harvest near contract hedging, resulted in an average
Table 11
Simulation Results of Simple Five Day and Simple Fifteen Day
Moving Average Decision Rule Over Twenty Years
t
December
August
January
Favorable
Contract
Favorable
Near
Contract Contract
April
Favorable
Contract
Near
Contract
-$954
-$933
-$1,261
-$1,216
-$1,364
-$1,322
-$1,799
-$1,754
-$1,648
-$1,607
$1,049
$1,051
$1,135
$1,135
$1,153
$1,153
$1,111
$1,111
$1,145
$1,144
Number Years
Positive
6
8
5
5
5
6
4
4
5
5
Number Years
Negative
14
12
15
15
15
14
16
16
15
15
Near
Contract
Average Annual
Return
Standard
Deviation
Near
Contract
March
Favorable
Contract
Near
Contract
Favorable
Contract
Maximum AnnualRe turn
$14,842
$14,842
$16,236
$16,238
$16,515
$16,517
$16,129
$16,131
$15,267
$15,269
Minimum Annual
Return
-$8,523
-$8,523
-$10,375
-$10,373
-$10,375
-$10,372
-$9,397
-$9,394
-$11,346
-$11,343
Average Number
of Trades per
Year
7
7
10
10
12
13
13
16
16
12.
45
loss of $954 with a standard deviation estimated at $1,049.
returns ranged from a loss of $8,523 to a gain of $14,842.
Annual
Hedging
with the most favorable contract decreased the average loss of $933.
The standard deviation was $1,051 and the range of returns was
unchanged from near contract hedging.
The average loss for near contract hedging and a marketing period
ending in December was $1,261.
to be $1,135.
$16,236.
The standard deviation was estimated,
The returns varied from a loss of $10,375 to a gain of
For hedging done with the most favorable contract month the
mean loss was $1,216.
The estimated standard deviation was unchanged
and the range of returns was from a loss of $10,372 to a gain of
$16,238.
Extending the marketing period, to mid-January resulted in an
average loss of $1,364 for near contract hedging with an estimated
standard deviation of $1,153.
The returns ranged from a loss of
$10,375 to a gain of $16,515.
Placing hedges in the most favorable .
contract decreased the average loss of $1,322.
The standard deviation
was estimated to be $1,153, and the range was from a loss of $10,372
to a gain of $16,517.
For a marketing period ending the first of March the average loss
was $1,799 for near contract hedging and $1,754 for most favorable
contract hedging.
to be $1,111.
In both cases the standard deviations were estimated
For hedging in the nearest contract the returns ranged
46
from a loss of $9,397 to a gain of $16,129.
The range of returns for
hedging in the most favorable contract month was from a loss of
$9,394 to a gain of $16,131i
Including March 1and April in the marketing period decreased the
average loss.
For hedging in the near contract the average loss was
$1,648 with an estimated standard deviation of $1,145.
The lowest
return was a loss of $11,346* and the highest return was a gain of
$15,267.
Hedging in the most favorable contract resulted in an
average loss of $1,607.
The standard deviation was estimated to be
$1,144, and the yearly returns ranged from a loss of $11,343 to a
gain of $15,269.
The third trading strategy which was simulated was to place a
hedge when a ten day moving average was below a thirty day moving
average and to lift the hedge when the ten day moving average moved
above the thirty day moving average.
are summarized in Table 12.
The results of this strategy
This strategy resulted in an average
of five trades before harvest, six before December, seven before the
middle of January, eight before the first of March, and nine before
the end of April.
For all marketing periods the average return was
a loss ranging approximately from $2,000 to $4,000.
For the period
before harvest two of the twenty years had a positive return, while
for the remaining trading periods only one year had a positive return.
In all cases the estimated standard deviation of returns and the
Table 12
Simulation Results of Simple Ten Day and Simple Thirty Day
Moving Average Decision Rule Over Twenty Years
August
Near
Contract
Average Annual
Return
Standard
Deviation
January
December
Favorable
Contract
Near
Contract
March
t
April
FavorabIe
■Contract
Near
Contract
Favorable
Contract
Near
Contract
Favorable
Contract
Near
Contract
Favorable
Contract
-$2,051
-$2,051
-$3,280
-$3,257
-$3,629.
-$3,574
-$4,095
-$4,041
$951
$951
$1,035
$1,035
$1,055
$1,055
$1,126
$1,126
2
I
I
I
I
I
I
I
I
19
19
19
-$4,115
$1,090 '
-$4,060
$1,090
Number Years
Positive
2
Number Years
Negative
18
18
19
19
19
19
19
Maximum Annual
Return
$14,228
$14,228
$14,246
$14,246
$14,246
$14,246
$15,631
$15,631
$14,161
$14,161
Minimum Annual
Return
-$6,165
-$6,165
-$8,609
-$8,609
-$8,992
-$8,992
-$9,726
-$9,726
-$10,531
-$10,531
Average Number
of Trades per
Year
5
5
6
7
7
8
8
9
9
,
' 6 '
■
48
range .of returns were identical for near contract hedging and most
favorable contract hedging.
For marketing at harvest the mean return to hedging with the
near contract and to hedging with the most favorable contract was
a loss of $2,051.
The estimated standard deviation was $951.
The
returns ranged from a loss of $6,165 to a gain of $14,228.
Near contract hedging resulted in an average loss of $3,280 for
a market period ending in December.
For the same period hedging the
most favorable contract resulted in a mean loss of $3,257.
The
standard deviation was estimated to be $1,035, and the range was from
a loss of $8,609 to a gain of $14,246.
When the marketing period was extended to the middle of January
the average loss for hedging with the near contract month was $3,629.
The average loss for hedging with the most favorable contract was
$2,574.
The estimated standard deviation was $1,055.
Returns varied
between a loss of $8,922 and a gain of $14,246.
For a marketing period ending in March the mean return was a loss
of $4,095 for hedges placed in the near contract and $4,041 for hedges
placed in the most favorable contract.
estimated to be $1,126.
The standard deviation was
The lowest return was a loss of $9,726; the
highest return was a gain of $15,631.
Near contract hedging resulted in an average loss of $4,115 for
a marketing period ending in April.
For the same period hedging
49
with the most favorable contract resulted in an average loss of
$4,060.
The estimated returns ranged from a loss of $10,531 to a gain
of $14,161.
The fourth decision rule to be implemented in the simulation
program used a simple five day moving average and an exponential
thirty day moving average.. A hedge was placed if the five day moving
average was below the thirty day and lifted when the thirty day moving
average was below the five day moving average.
strategy are summarized in Table 13.
The results from this
This strategy resulted in fewer
trades than the strategy based on simple five and fifteen day moving
averages.
During the November-August period, there was an average of
seven trades; during the November-December period, there was an
average of nine trades; during the November-January period, there was
an average of ten trades; during the November-March period, there was
an average of eleven trades; during the November-April period, there
was an average of thirteen trades.
was a loss.
In all cases the average return
For the marketing periods ending in January, March, and
April one annual return was positive, and the remaining nineteen were
negative.
For the marketing period ending in December, two years
showed gains and eighteen showed losses.
The marketing period which
ended with harvest had two years of gains if hedging was done in the
near contract and four years of gain if hedging was done in the most
favorable contract.
Table 13
Simulation Results of Simple Five Day and Exponential Thirty Day
Moving Average Decision Rule Over Twenty Years
December
August
Favorable
Near
Contract ■ Contract
Average Annual
Return
Near
Contract
January
Favorable
Contract
-$1,377
-$1,344
-$2,121
$1,057
$1,058
$1,102
$1,101
Number Years
Positive
2
4
2
Number Years
Negative
18
16
Maximum Annual
Return
$17,028
Minimum Annual
Return
Average Number
of Trades per
Year
Standard
Deviation
Near
Contract
-$2,073 . -$2,391
March
Favorable
Contract
Near
Contract
April
Favorable
Contract
Near
Contract
Favorable
Contract
-$2,340
-$2,690
-$2,640
-$2,601
-$2,566
$1,106
$1,105
$1,168
$1,167
$1,215
$1,215
2
I
I
I
I
I
I
18
18
19
19
.19
19
19
$17,028
$17,014
$17,015
$17,014
$17,015
$18,399
$18,400
$18,590
$18,591
-$5,766
-$5,766
-$7,211
-$7,201
-$7,211
-$7,208
-$7,243
-$7,240
-$8,098
-$8,095
7
7
9
9
10
10
. 11
11
: 19
.
13
■
13
51
For the marketing period ending with harvest the average loss
was $1,377,. with a standard deviation estimated to be $1,057 for near
contract hedging.
The returns ranged from a loss of $5,766 to a gain
of $17,028. . The mean loss to hedging with the most favorable contract
was $1,344.
The estimated standard deviation was $1,058.
The range
was identical to the case of hedging the near contract.
A marketing period which ended in December had an average loss
of $2,121 for near contract hedging. ■ The standard deviation was
estimated to be $1 ,102, and the range of returns was from a loss of
$7,211 to a gain of $17,014.
Hedging with the most favorable contract
resulted in an average loss of $2,073 with an estimated standard
deviation of $1,101.
The returns ranged from a loss of $7,201 to a
gain of $17,015.
Near contract hedging resulted in a mean loss of $2,391 for a
marketing period ending in January..
The standard deviation was
estimated to be $1,106 and the returns ranged from a loss of $7,211
to a gain of $17,014.
The average loss from hedging with the most
favorable contract was $2,340 with an estimated standard deviation
of $1,105.
The lowest return was a loss of $7,208, and the highest
return was a gain of $17,015.
Extending the marketing period to March resulted in an average
loss of $2,690 for near contract hedging with an estimated standard
deviation of $1,168.
The returns ranged from a loss of $7,243 to a
52
gain of $18,399.
For hedging with the most favorable contract the
mean loss was $2,640.
The estimated standard deviation was $1,167
and the range of returns was from a loss of $7,240 to a gain of
$18,400.
Including March and April in the marketing period reduced the
average loss slightly.
The average loss resulting from hedging with
the near contract was $2,601 with an estimated standard deviation of
$1,215.
The lowest return was an $8,098 loss, and the highest return
was an $18,590 gain.
Hedging with the most favorable contract
resulted in a mean loss of $2,566.
was $1,215.
The estimated standard deviation
The returns ranged from a loss of $8,095 to a gain of
$18,591.
The final trading strategy simulated was based on an exponential
five day moving average and an exponential thirty day moving average.
Hedges were placed when the five day moving average was below the
thirty day moving average and lifted when the relationship between the
moving averages was reversed.
summarized in Table 14.
The results from this strategy are
This strategy resulted in more trades than
that based on simple five, day and exponential thirty day moving
averages but fewer trades than that based on simple five and simple
fifteen day moving averages.
There was an average of seven trades
before harvest, ten before December, eleven before January, twelve
before March, and fourteen before April.
For one year, for the
Table 14
Simulation Results of Exponential Five Day and Exponential Thirty Day
Moving Average Decision Rule Over Twenty Years
March
January
December
August
Near
Contract
Favorable
Contract
Near
Contract
Favorable
Contract
-$2,174
-$2,139
-$2,836.
-$2,787
-$2,894.
-$3,845
-$3,215
-$3,166
-$3,027
-$2,978
$388
$388
$414
$412
$397
$395
$409
$406
$470
$466
Wnnihpr Years
Positive
I
I
0
0
0
0
0
0
0
0
Number Years
Negative
19
"19
20
20
20
20
20
20
20
20
$400
-$635
-$637
-$676
-$672
-$702
-$698
-$79
-$76
-$8,164
-$7,846
-$7,835
-$8,340
-$8,329
11
12
12
14
14
Average Annual
Return
Standard
Deviation
Maximum Annual
Return
$396
Minimum Annual
Return
'-$7,037
-$7,037
-$8,140
-$8,129
Average Number
of Trades per
Year
7
7
10
10
.
-$8,175 '
11
Near
Contract
April
Favorable
Contract
Near
Contract
Favorable
Contract
Near
Contract
Tavorable
Contract
54
marketing period ending at harvest, there was a positive return.
all other years there was a negative return.
In .
The estimated standard
deviations of returns for this strategy.were the smallest of any
strategy ranging from $388 to $470.
The average returns ranged from
a $2,139 loss for sale at harvest and hedging with the most favorable
contract to a loss of $3,215 for'sale the first of March and hedging
with the near contract.
A more detailed presentation of the results
is foregone because of the absolute ineffectiveness of this strategy.
Conclusions
This study has reviewed the theoretical considerations involving
hedging and speculative price changes.
The Montana basis for both
Chicago and Kansas City markets has been investigated.
The investiga­
tion leads to the conclusion that a Montana winter wheat producer who
hedges should do so on the Kansas City.Exchange.
The distribution of
daily futures price changes of Kansas City wheat contracts has been
analyzed in a time series framework.
Estimated autocorrelation
functions indicate that price changes follow a white noise pattern.
The first conclusion which can be drawn from the simulation .
results is that a producer who is going to hedge should hedge with
the contract which offers the most favorable expected basis movement
rather than with the near contract.
From August to December a pro­
ducer should hedge with the December futures contract.
From December
55
to March a producer should hedge with the March futures contract.
It is obvious that of the five strategies investigated in this
paper, the strategy based on simple three and simple ten day moving
averages is preferable.
However, even in this case, only two of the
ten calculated average returns are significantly greater than zero at
the 95 percent confidence level.
Significant returns were realized
for a marketing period ending in April hedging either with a near
contract or with the most favorable contract.
A producer who decides
to use a moving average decision rule should remember that even the
most favorable rule results in,losses nearly one-half of the time.
Overall, for Montana winter wheat producers moving averages do not
appear to be good indicators of the direction of price movements.
This study has only scratched the surface of a major problem for
Montana wheat producers.
Far more reserach is needed in this area.
Specifically, the basis needs to be investigated structurally.
The
distribution of futures price changes should be examined further
perhaps in the context of semi-Markov processes.
Other types of
strategies, such as filter rules, should be looked at.
The entire .
concept of how much to hedge given production uncertainty needs study.
Finally, any trading hedging strategies should be compared with other
possible marketing activities such as forward contracting, hedging
until sold, and storing grain.
APPENDIX .
APPENDIX A
Table I
Estimated Autocorrelation Functions
.00 -.06 -.10
.05
.08 .08
.01 -.11 -.16 -.01
.08 .08 .08 .08
Lags 1-12
Standard Error
Lags 13-24
Standard Error
.09 -.04
.08 .08
.04 .07
.08 .08
Lags 1-12
Standard Error
Lags 13-24
Standard Error
.04 -.15
.07 .07
March, 1974
Lags 1-12
Standard Error
Lags 13-24
Standard Error
.04 -.15 -.07
.07 .07 .07
.21 .14 -.01
.08 .08 .08
March 1975
Lags .1-12
-.14 -.22
Standard Error .07 .07
Lags 13-24
-.01 .02
Standard Error .08 .08
March, 1972
March, 1973
March, 1976
.08
.08
.02
.04
.07 .07
.11 -.01 -.05 -.03
.07 .07 .07 .07
Lags 1-12
-.01
Standard Error .07
Lags 13-24
-.17
Standard Error .07
.08 -.07 .01 -.03
.08 .08 .08 .08
.05 -.02 -.11 .07
.08 .08 .08 .08
.01 -.06 -.01
.07
.02
.07
.07
.05
.07
.07
.11
.07
.03
.08
.06
.08
.11
.01
.09
.09
.04 -.02 .03 .02 -.07
.07 .07 .07 .07 .07
.02 -.04 -.02 -.03 -.01
.07 .07 .07 .07 .07
.07 .11 -.07 -.07 -.03 .12
.07 .07 .07 .07 .07 .07
.08 -.11 .06 .17 — .08 -.16
.08 .08 .08 .08 .08 .08
.08 -.06 -.14
.07 .07 .07
.09 .00 .01
.08 .09 .09
.04 -.12
.07 .07
.00 -.04 .05
.08 .08 .08
.04 -.01
.08 .08 .08
.06 -.09 .06
.08 .08 .08
.04
.07
.05
.08
.09
.07
.03 -.02
.07 .07
.03 -.10
.07 .07
.02
.07
.08
.08
.09 -.10
.07 .07
.13 -.01
.08 .08
.02 -.03
.09 . .04
.08 .08
.00 -.05
.08 .08
.08
.04
.08
.00
.00 -.05 -.01
.07
.12
.08
.05
.07
.06
.08
.07
.03
.08
.07
.03
.08
.07
.08
.08
.17
.07
.07
.07
I
APPENDIX A
Table 2
May, 1973
May, 1974
Lags 1-12
Standard Error
Lags 13-24
Standard Error
.06 -.07
.07 .07
.12 .06
.07 .07
.03 — .08 -.06
.07 .07 .07
.01 -.01 -.16
.07 .07 .07
Lags 1-12
.19 -.12 — .08 .02
Standard Error .08 .08" .08 .08
-.02 -.JQ5 -.09 -.09
Lags 13-24
Standard Error .08 .08 .08 .08
Lags 1-12
Standard Error
Lags 13-24
Standard Error
.03 -:17
.07 .07.
.14 .06
.07 .08
.06
.08
.01
.08
.09
.07
.03
.07
.05 -.06 .04 -.06
.07 .07 ..07 .07
.02 -.02 -.02 .15
.07 .07 .07 .07
.04 -.05
.08 .08
.10 -.04
.08 .08
---- !
.00 •
.07 .07
.06 .01
.08 .08
OLO
—
May, 1972
I
Estimated Autocorrelation Functions for DailyPrice Changes of Kansas City-May Contracts
.00
.11 -.11
.08
.06
.08
,08
.08
.06 -.01
.08 . .08
.01
.00
.01 -.02
.08
;os
.08
.02 .11 .08 -.01 -.03 .08 -.14
.07 .07 .07 .07 .07 .07 .07
.03 -.10 -.10 .09 .19 -.02 - H O
.08 .08 .08 .08 .08 .08 .08
May, 1975
Lags 1-12
-.09 -.26 -.01 . .18
Standard Error .07 .07 .07 .07
.03 -.07 .06 .00
Lags 13-24
Standard Error .08 .08 .08 .08
.04 -.08 .07 .06
.08 .08 .08 .08
.03 .08 -.06 -.06
.08 .08 .08 .08
May, 19 76
Lags 1-12
-.04 -.02 -.02
Standard Error .07 .07 .07
-.16 -.11 -.01
Lags 13-24
Standard Error .07 .07 .07
.09
.07
.00 -.03
.00
.07
.07
.07
.10
.02
.00
.11
.07
.08
.08
.08
.08
.04 -.01 -.04
.07 .07 .07
.12
.02
.00
.08
.08
.08
.03 -.09 .11 -.01
.08 .08 .08 .08
.09 -.11 -.12 .02
.08 .08 .08 .08
.13 -.03
.07 .07
.04 .04
.08 .08
.01 .03
.07 .07
.06 — .08
.08 .08
.13
.07
.12
.08
APPENDIX A
Table 3
Estimated Autocorrelation Functions for Daily
Price Changes of Kansas City-July Contracts
Lags. 1-12
Standard Error
Lags 13-24
Standard Error
July, 1972
.07 .00 .00 -.10 -.20 -.03 -.02
.07 ■ .07 .07 .07 .07 .07 .07
.01 -.02 .04 -.08 -.07 -.03 -.06 .07
.07 .07 .07 .07 .08 .08 .08 .08
.09 -.06 -.09
.07 .07 .07
.00 -.01
.07
.07
.11
.00
.07
.04
.08
.07
.03
.08
July, 1973
.26 -.19 -.12 .04 .12 .11 -.10 -.21 .05 .04 .10 — .08
Lags 1-2
Standard Error .07 .07 .08 .08 .08 . .08 .08 .08 .08 .08 .08 .08
-.15 -.01 -.10 -.04 -.06 .05 -.02 .00 -.03 — .08 -.02 .00
Lags 13-24
Standard Error .08 109 .09 .09 .09 .09 .09 .09 .09 .09 .09 .09
Julv
Lags 1-12
Standard Error
Lags 13-24
Standard Error
1974
‘
.03 -.15
.07 .07
.08 .01
.07 .07
.02
Lags 1-12
-.09 -.10
Standard Error ' .07 .07
.02 -.06
Lags 13-24
Standard Error .07 .07
.00
.09 .09 -.09 -.06
.07 .07 .07 .07
.02 -.09 -.10 -.02 . .14
.07 .07 .07 .07 .07
.07
.02
.07
.00 -.04
.07 .07
.07
.04
.07
.09
.07
.04 -.01 -.02
.07 .07 .07
.01 .00 -.03
.07 .07 .07
.01
.07
.04
.07
.07
.06
.07
.07
Lags 1-12
-.07 \02 -.09
Standard Error .07 .07 .07
-.15 -.13 -.05
Lags 13-24
.
Standard
Error
.07 !.07 .07
,W
•02
.07
.05
.07
• July, 1976
'
.11
.07
•01
.07
.03
.07.
.03
.07
.01
.07
.03 -.01 — .08
.07 .07 .07
.92 .05 .05
.07 .07 .07
.02 -.05
.01
.11
July, 1975
.02 .13
.07 .07
.04 -.09
.07 .07
.07 -.06
.07 .07 .07 .07
.08 -.02 -.03 .04
.07 .07 .07 .07
.02 -.02
.07 .07
.05 -.05
.07 .07
.06
.07
.04
.07
APPENDIX A
Table 4
Estimated Autocorrelation Functions Daily Price
Changes of Kansas City-September Contracts
September,
1972
September;
1973
Lago 1-12
Standard Error
Lags 13-24
Standard Error
.27 -.13 -.01 .17
.07 .08 .08 .08
.18. -.05 — •16 . .01
.09 .09 .09 .09
Lags 1-12
Standard Error
Lags 13-24
Standard Error
.24 -.17 -.06 .22 .27 . .09 .02 .17
.07 .07 .08 .08 .08 .08 .08 .08
.06 .00 .03 -.01 -.03 .02 -.02 -.05
.09 .09 .09 .09 .09 .09 .09 .09
.14 -.11 -.15
.08 ;08 .08
.10 .17 .12
.09 .09 .09
.07 .10 .07 -.08
.07 .07 .07 .07
.05 -.06 -.02 .02
.08 .08 .08 .08
September,
1976
Lags 1-12 .
-.14 .07 -.04 ■ .02 — .15
Standard Error .08 .08 .09 .09 .09
Lags 13-24
-.14 -.06 -.11 .09 .00
Standard Error .09 .09 .09 .09 .09
..
.07
.03 -.02 -.01
.08 .08 .08
.07
.04
.08
.01
.09
.09
.00
.10
.01
.07 .03
.09 .09
.01 -.04 -.07
.09 .09 •09
.09
.06 ..03 -.07 — .09 .07
.07 .07 .07 .07 .08
.11 .00 .08 .03 -.02
.08 .08 .08 .08 .08
Lags 1-12
Standard Error
Lags 13-24
Standard Error
.07
.08
.08
.10 •
.04 .00 -.01
.07 .07 .07
.06 -.03 .06
.08 .08 .08
September,
1975
.11 -.05
.14 -.03 -.01
.09 .09 .09
.07 .14 .06
.09 .09 .10
.03
.07
.09
.08
Lags 1-12
-.08 -.16
Standard Error .07 .07
Lags 13-24
.02 -.01
Standard Error .08 .08
.07
.08
.07
.09
.00
September,
1974
.00 -.05
.12
.03
.09
.07
.09
.04 .13 — .08 .05
.07 .07 .07 .07 .07
.07 -.03 -.11 .07 -.01
.08 .08 .08 .08 .08
.05 .01 .04
.09 .09 .09
.07 -.04 -.04
.09 .09 .09
.05 -.06 -.05
.09 .09 .09
.02 -.11 .03
.09 .09 .09
APPENDIX A
Table 5
Estimated Autocorrelatin Functions for Daily Price
Changes of Kansas City-December Contracts
December
1971
Lags 1-12
-.11 -.14 -.05 -.06 -.08
Standard Error .10 .10 .10 .10 .10
Lags 13-24
.01 .10 .11 -.05 -.15
Standard Error .11 .11 .11 .11 .11
December,
1972
Lags 1-12
Standard Error
Lags 13-24
Standard Error
.28 -.17 -.06
.07 .08 .08
.18 — .08 -.21
.09 .10 .10
December,
1973
Lags 1-12
Standard Error
Lags 13-24
Standard Error
.14 -.19 -.04 .05 .06
.07 .07 .07 .07 .07
.15 .07 -.03 -.05 -.10
.08 .08 .08 .08 .08
December,
1974
Lags 1-12
-.07 — .18
Standard Error .07 .07
Lags 13-24
-.02 -.03
Standard Error .08 .08
December,
1975
Lags 1-12
Standard Error
Lags 13-24
Standard Error
.01 -.07
.04
.10
.01
.11
.11
.10
.11
.11
.07
.11
.02
.11
.26
.08
.03
.17 -.16 -.24
.08 .09 .09
.25 .14 -.01
.07
.09
.08
.16, -.08 -. 13 .02
.09 .09 .09 .09
.20 .10 -.18 -.07
.10
.10
.10
.10
.10
.05
.07
.05
.07
.10
.08 — .08 .04 .14
.07 .07 .07 .07
.07 .16 -.08 -.05
.08 .08 .08 .08
.08 .14 .07 -.14
.07 .07 .07 .07
.09 -.10 -.02 .00
.08 .08 .08 .08
.03
.07 .07 .07
.03 -.07 -.07
.07 .07 .07
.10 -.07 -.03 -.11
.10 .10 .10 .10
.07 .00 -.14 .06
.11 .11 .11 .11
.11
.11
.14 -.07 -.02
.08 .08 .08
.04 — .02 .00
.08 .08 .08
.05 .06 -.12 .04
.08 .08 .08 .08
.00 -.03 -.01 .02 -.05
.08 .08 .08 .08 .08
.05
.08
.05 -.07 -.04
.07 .07 .07
.14 -.06 .07
.07 .07 .07
.11
.06 .03 -.14
.07 .07 .07
.15 -.01 .00
.08 .08 .08
.11
.08
.11
.08
.01
.10
.07
.05
.08
.07
.02
.08
APPENDIX B
OEv
AE
*r
TRADE
RtTl
Rt T 2
KF A L L O C a Tl
RE A L L O C A T E
Rt A L L O C A T E
REALLOCATE
STARTVACkU
GATE U
T E S T NE
TEST G
LOGIC S
BUFFER
TRANSFER
TEST L
T F S T NE
LOGIC S
BUFFER
BI T , 9 0 0 , X A C , 4 J O 1 F A C 1 20 , S T O 1 O
C U E , 2 0 , L C G 1 2 r , T A B 1 GC
F U N , 2 ,V AC , Z C 1U V R f O 1F S V
H S V 1 O 1F V S 1P 1H M S 1 O 1C H A 1 , G R P 1 ?
advance
VJ
ENCNACRO
STARTMACRO
G A T E ES
ASSIGN
VAPK
SEIZE
G A T E LS
PFLFASt
LOGIC R
LOGIC R
ASSIGN
ENDMACRO
SI AC T M A C R n
*6
HA
fit
na
4A
E N O m ACPC
STARTMACRO
*A
Kt
RFTT
RE T 4
ENCYACKO
ST A R T v A C R O
IA
<A
ENr^ACcr
STARTVAfRC
?
*A,
'C1 o n , -F
*F« »T,, ^ F
tL
» »'!
* F , P G , "H
" C 1 fU , "I!
"A
"A
S R 1 ZC
«A
Aj
VA
6A
6D
*E, SC
VC
S D 1 SC
SE , *C
Zr, 9 C
SG, SC
CR, JC
V D 1 ZC
Z E 1 »C
S F 1 SC
ZB, ZC
ZD, ZC
"E , PC
>l , 'C
RFTc
it*
fc ND^ftCRP
STARTMACRP
»r
JWC
*6,*C
TAfal
TAB 2
TABT
TABE
TARS
* TnIS
J
2
3
4
'j
6
7
C
V
IO
11
I2
I?
I4
IS
IC
F K U M A C R rI
START>ACD
TAPULATf
T A P U L A TE
TABULATE
TABULATE
T ABULATt
E N D M AC RH
START MACRO
TABULATE
TABULATE
TABULATE
TABULATE
ENDMACRP
ST A R T M A C R U
TABULATE
TABULATE
TABULATE
fcKLwACRU
STAPTMACRU
TABULATE
TABULATE
E NDMACRP
*A
SR
*D
SE
6A
*r
»C
*U
*A
TE
fC
o\
SA
5B
STAPTMACFn
TABULATE
AA
FKDMACRC
ST«UL A IE
N E X T S F C T t PK r^ c r<iE c
T-A-1 LE S
TAfcLE
X 9 , - l 12,7,33
table
P?,- 7 0 0 , 2 0 1 , T 3
TABLc
P4,-700,200,33
table
PS,-700,200,33
T A p LE
P 6,- 700,2 00,3 3
P A , - 7 O D , ? u O , 33
t a « le
TAEiLE
P 3, - 7 UV , 2 CO , 3 3
T AP L r
P‘1 , - 7 0" ,2 0 , ? 3
TABLE
P d ,- 7 0 0 , 2 0 0 , 3 3
TABLE
P6,-700,200,33
D 7 , - 7 C O , 2 On , 1 3
T A B LE
T ABLE
P 3 , - 7 0? ,2 0; , 1 3
I A P lE
P t , - T C O , 2 ' ,33
TAP I •
P d , -7 CO , 2 . 0 , ) 3
TA-LE
P C , - T V? , 2 C ',1 3
T A ijLI
P 7 , - - *v .' ,2 v" ,: 3
USED
IN THf
PROGRAM
I7
18
19
20
21
22
23
24
25
26
27
28
29
30
il
32
33
34
35
36
37
3p
39
40
41
42
43
44
45
46
47
46
49
50
51
52
5J
54
5'
K/
* THIS
TfOLf
TfTU
TABLE
TABLE
TfhLE
TABLE
T f n LE
TABLE
T fPL ^
TfELC
TABLE
TABLE
TAELc
TfELE
Tfv Lt
TAPLE
TABLt
TABLE
TABLE
T A RL t
TABLE
TARLt
TAUE
TAELE
T f n LE
TABLE
TABLE
TABLE
TABLE
TABLE
TABLE
TSrEc
T A BL E
TAEl E
TfBLt
TAGl F
IAtLt
TABLE
TABLE
TABLE
P3,-700,200,33
84,-700,200,3 3
P 5 , - 7 0 0 , 2 0 ” ,33
P o , -7 C O , ? C O , U
P7,- TC0,200,33
P3,-700,200,33
P 4 , - 7 0 3 , PD 3 , D
P5,-700,200,33
P o ,- 7 c ,2 C 0,3 3
P 7 , -7 00 , 20 3 ,3 3
P 3,-7 D J ,200,33
P 4 , - 7 u 3 , 2 C O , 33
P O , -7 C O , 20 0 , 3 3
P t , -7 CO , 2 3 0 , 3 3
P7 .-7 0 3 ,20"' » 33
P3,-70(v,2v",33
P A 1--fOO , 2 0 0 , 3 3
P 5,- / O u ,200,33
P fc, — 7 0 0 , 2 0 0 , 3 3
P7,-700,200,33
P 3 . - 7 u J ,200,3 3
P 4 , - 7 C I ,2 C . , ? 3
P 5 , - 7 0 0 ,210 ,33
P6,-700,200,33
P 7 ,— 7 O J , 2 t O , 3 T
P3,-700,200,33
84,-700,200,33
P5,-700,200,33
P t , -7 0 0 , 2 0 0 , 3 3
° 7 , - 7 O 0 , 2 C O , 33
P3,-/00,200,33
P4,-70).203,33
85,-700,200,33
86,-7 3 P , 2 C v ,7 3
P 7, - 7 C O , 2 C j , 3 J
*1,1,5,33
liI fl, ot 33
wt1 , 1 , 5 , 33
*1,1,5,33
* 1 , 1 , 5 , 3n
SECTION OEFTNCS
ALL
CF
T^
V A R I A i jL t S
*
I
0
1
4
s
VARTARLE
VAPIAOLC
VAP TABLE
VAf-TrtsLE
V C R V 4n LL
C l w 3?
u X l C l , if)*' V t P D r
u X l C l ,V t ^ iP HE
E1I-I
vIXl (I , D - H X i C I, 3 0
U S Lu.
6
I
*
*
THTi
V AR I £ t'L I
MX1(I,P:)-^X1(1,V4)
1
I l l l l l l l l l l i i
1
1
S f C T l- TN D E F I N E S
TH t
FUNCTIONS
USED
IN T H E P R O G R A M
*
O N I , BN
I F D N C T IHf
.,CIS
fF U
uN
nC
cT
t iI oO nN
PDF
, .
, , 0 „ , —5
. .6./ —I . 5 , - 4 2
- l l 0 * - H / - T b 0 ^ - 1 4 / f s e a 4 / l . C , 2 f a / l .b ^ 2 / 2 . C , i 6' /• 2' 5 , 7 0
3.0,84/3.5,98/4.0,112
• T H I S S E C T I O N I N I T I A L U ES A L L M A T R I C E S A N D S A V f V A L U E S
1
2
MATOIX
MATRIX
INITIAL
INITIAL
IAITIAL
INITIAL
INITIAL
INITIAL
INITIAL
INITIAL
I M T I Al
I M TI 'L
INITIAL
INITIAL
X ,I , 3 O
MXI Cl
y X i ci
« XT Cl
M X 2 C I ,- i ) , c / M X 2 C i , 2 ) , o / y x ? c : , 3 > , o / " X 2 C i , < , ) , .
XL,o/x
*
♦ TTHHt1 S f U R T R A N N S U ri k n U T I N L IO 1C , U c U L A T E ^ f U V I NG A A VE ^ A GE S .
*
G E N r RATE
Li,,, * » r
V I , K C , ILr *
TtST F
1,30
ASSIGN
,BETA
Tc A N S F E P
I,Vl
ALPHA ASSIGN
PI , K l .5 t T A
Tt ST F
VfS;>VL V ALUC I , I , I , V 2
° ,V 2
SfVFX
9,V5
SAVE*
,GMM
TRANSFER
bF rfi
Gf MV f
an v'. r-Cl
MSAVL- VA LU F
SCVF X
SfVFX
ALVANCt
TAPULATp
HTLPF
I,I,P I,V '
a,v i
M 1V o
O
G P D F l , " X l ( I 1I)1P l 1M X 2 ( i ,I)
MACPO
MACAO
M A C pO
MfCiO
MACiC
MACRO
MACRO
MACRO
MA C a n
dec
macro
MSAVE VALUE
^ SAVE VAlUF
MS AyE V A L U E
w SAVt VAL Ut
MSAVEVALUt
MSAVtVALUE
MSAVEVALUr
terminate
GENERATE
AAAl
advance
T R A C E Mf C R u
TEST I
RETl
MACRC
MACRO
TABl
T R A flS p E 0
BBa 1 TEST L
KET I 'IAuRiJ
MfCPG
TCBl
TRANSFER
TEST L
CCCl
RE TZ M A C R O
MAC RO
TAB?
T R A N S r E0
TEST L
DDDl
RE T?
RCC 'O
TA=X? y A C jV
Tp ANSr I 0
TEST L
IEcl
, M X i ( I 1 O) , D C C 1Z 1 L
,MXZC I,4) , O C U , i ! 'i
,MXZ(I1S) ,JJJ1Of.
,w XZ(I 1T) , M M M 1H 1V
, M X Z C i 1T) , P P P 1 IOfO
, I) ,MXZCi , 3 ) f D O D D , 1 2 , 0
, 2 ) , " X E ( I , 4 ) , G C G G , 14,,3),VX2(1 ,5),
,2),MX2(I* 7 ) fM K M M ,lH ,p
, h ) , y X Z C l , T l 1P P P P 1ZJfC
I
O
i , i ,x a , ? , 2
C I 1K I T J 1B B s I
A S S I G N 1 J 1V ,
,7
2,3,4 , ^ 1A
, HHHl
C l 1K l P G 1C C C l
A S S I G N , ^ 1 V <»
2,3,4,S,6
,HHHl
C l t K l 9 9 ,ODD I
A S S I G N f A 1 V D , S 1A 1?
3,4 , S , 0
,HHHl
E l 1K Z b Z , F f E I
A S S I G N 1 -,VI A
3,4,S 1A
1 hHti I
C l 1K Z v 4,1 t
Tl
De C
DFC
DEC
DEC
Drf
DEC
DEC
DEC
DEC
-J
***
vx 2.
ThIS SFGTICN
Re T 3
T AB 3
FFF I
RETA
TABA
GGG I
RE 15
T AR 5
HHhl
M A C 'G
M A C jO
TRANSFER
IEST L
"AC = U
MACRO
TRANSFER
TEST L
MACRO
wfC'JO
T A B U L &Th
TPANSr ER
AAAl I
TRACE
RETl
TABl
BBBll
RETl
TABl
GENERATE
ADVANCE
MACRO
TEST L
MALRG
MACRO
TRANSFER
TEST L
MACRO
M AC RU
TRANSFER
CCC 11 T E S T L
RE T 2
MACpU
T AB 2
MACR O
TRANSFER
DDDll TEST L
RET?
"ACRO
TAB?
MACRO
EEEll
RET1
T AB 3
TRANbFE :
TFSt L
/ A C UJ
MACRO
TRANSFER
FFF I I
Rf TA
TAPA
GGGl I
R ET 5
T AB 5
HHHll
IiST L
MACRO
MACRO
Tc ANSt r i;
i
*A C R L
MACRO
T RANSPER
G E N E F : TC
AAA?
TRADE
AOVANCE
RETl
Tl ST I
M A C <L
"AC : O
A S S I G N , 5 , Vl I , 6 , 7
4,5,6
f HHHl
C l , 1 0 2 5 , GGGl
A S S I G N , G 1 VI I , 7
5, .
, HHi i l
C l , K 3 6 7 , Hr H I
A S S I G N , 7 , VI?
F
Sc
, AAAi
, , , I , 7, , T
O
11, 1, X i f i 2»2
C l lK l T H 1B e B l l
A S S I G N , 3,V o ,4,5,6,7
7,8,3,10,11
, HHHl I
Cl, K l a 9 , C C C 11
ASSIGN,3,V13,4,5,o,
7 , a , J , 1 0, I T
, HHHl l
Cl , K l 99 ,Ij D O 11
A S S I G N , 4 , V l J , 5,6,7
E, 1 , 1 8 , 1 1
,Ii HH I I
C I , K ? 6? ,E EL 11
ASSIGN,4,V l 4,5,6,7
8,9,10,11
, h M H 11
C I, < 2 9 4 ,FhF II
A S S I G N , r ,V 1 5 ,6 , 7
1, 10,11
, Ho' H I I
v * t K 3 2 5 ,Gt-GJ I
AS S I GN, 6 , V I S , 7
10,11
, HHH I I
C l , K 3 o 7 , FHH I I
A S S I G N , 7, Vl 2
11
AAl I
,,,1,7,,'
, M
G
! I - , Xi , 4 , c
C l , K I 7 3 , 2 G'i 2
A S s i G N i ?V # •I
I -i '
OO
tab
i
BPB2
RETl
TflBl
CCC 2
RET?
TAB?
ODD 2
RE T 2
TAB?
EE E 2
RE T 3
TflB I
FFF 2
Rf T4
T A 84
GGC ?
RETb
TflBb
HHH2
Afl A 2 2
TRADE
RE T I
TflBl
BRB 2 ?
RFTl
TflBl
C C C 22
RET?
TAB2
00022
RET?
TAB?
EEE22
RET3
-v A l K U
TRANSFE v
TEST L
WACPC
MACRO
TRANSFER
TEST L
MflCPC
macro
TRANSFER
TEST L
M flCRC
MACRO
TP A N S E ER
Tl SI L
M A C 0O
wflCRO
T h ANSFfP
TEST I
MACRO
MACRO
T F fl NS FE P
TEST I
M A C PO
,MACRO
TABULATE
TRANSFER
GENERATE
ADVANCE
MACRO
TEST L
MACRO
MACRu
T R ANSFER.
TEST I
MACRO
MACRO
T P ANSFER
TEST L
wflCRD
MACRO
T R A N S p ER
Tt ST L
MACRO
MACRO
T? S S p ER
TEST L
MACRO
12,13,14,15,16
I HF H 2
C l , Kl B R , C C C 2
A S S I G N , 3 » V S , 4 , 5 , 0 ,!
1 2 , 1 3 , 1 4 , 15 , 16
,HHH2
Cl,K l 99,DCC2
A S S IG N , 4 , V 9 , 5 , 6 , 7
1 3 , 1 4 , IS, 16
,UHH2
C I,.< 2 6 2 , C L E 2
ASSIGN,4,710,5,6,7
!3,14,lb,lo
• iiHh 2
fl,K294,FFF2
ASSIGN,5,711,6,7
I t , 15,16
,HH H 2
C1,K325,GGG2
A S S I G N , 6, V I I, 7
15,16
, HH H 2
C 1 , K 3o / , H H H 2
ASS I O N, 7 , V l 2
I6
53
»AA A2
»,»1,7,,F
O
1 3 , 1 , X b , I 4,2
Cl,K l 78»Bb822
ASSIGN,3,VE,4 , 5,6,T
l ? » l o , 19,20,21
,HHH22
C I , K I 8 9 , C C C 22
A S S I G N , 3 , V 1 3 , 4 , 5, 0 , /
1 7 , I d ,19,23,21
,HUH? 2
C l fK l 99,00022
ASS If-N, 4, V 1 3 , 5 . 6 , 7
16,19,20,21
,HHh 2 2
Cl , K 2 6 2 ,1 L T 2 2
ASSI G N , 4 , V l 4,5,6,?
IE,ll,2i,21
,HHU22
Cl , K 2 , 4 A Ir 12
A S S I G N 1 S t V l b 1O,?
VO
MACRO
TRANSFER
F F F 22 T E S T L
RET4
MACRO
MACRO
TABA
TRANSFER
GGU22 TFST L
RFTS
-ACRD
MACRO
TABS
H H H 2 2 TE A N S F t R
GENERATE
ADVANCE
A A A3
t r a d e MACRO
TEST I
-ACRC
RFT ]
MACRO
TABl
TRANSFER
TEST L
BBB 3
MACRO
RETl
MACRO
TABl
TRANSFER
CCC 3 TEST L
MACRO
RFT2
MACRO
T AB2
TRANSFER
TEST L
ODD 3
MACRO
RF T 2
MACRO
T AB2
TRANSFER
TEST L
EEE 3
MftCRO
RF T3
T AB 3 w f C R O
TRANSFER
TEST L
FFF 3
RE T 4
MACRO
macro
TARA
TRANSFER
TEST L
GGG3
MACRO
RFTS
MACRO
TABc
I A R U L ATE
HHH 3
TPANSrFC
GENERATE
A A A 3 3 A D V "NCE
TRADE -ACRG
TEST L
macro
RFTl
T AE l
MACRO
TABS
I S , S C ,21
,HHM2 2
C I , K 3 25 ,G G G 22
A S S I G N , 6, V I S , 7
20,21
,H HH2 2
C I , K 3 6 7 , H H N 22
A S S I G N , 7 , V 12
21
,AAA22
,,,1,7,,
O
5,1 , X 9 , 6 , 2
C l , K l 79 , B B B j
A S SI G N , 3,Vd,4,5,6,7
22,23,24,25,26
,HHHi
C I,K I 89,C C C 3
A S S I G N , 3,V S , 4 , 5,o, I
22,23,24,25,26
,HHH 3
C I,K l 9 9 , D C u j
A S S I G N , 4 , V 9 , 5,6,7
2 3 , 2 4 ,2 5 , 2 6
,HH H 3
C I ,K 2 62 , ELE 3
A S S I G N , 4,V I 0,5,6,7
23,24,25,26
IHHH 3
G I * K2 94 » P F F 3
A S S I G N , 5 , Vl 1 , 6 , 7
24,25,2 N
i HH H 3
C 1 , K 3 2 4 , Go G 3
A S S I G N , 6 , Vl I ,7
25,26
,H H H 3
C I, K 3 6 7 , H h h 3
A S S I G N , T , Vl 2
26
54
,AS A3
, , , I , 7,,r
O
1 5 , I , X % , I 6,2
C I, K I 78 , I d G S 1
A S S I G N , L , V o , 4, 5 , 6 , 7
27,28,29,30,31
"U
O
TFflNSHn
BERlB
RFTl
TEST
L
Mf l CRU
y c Rc
TPflNSFE?
CCC 2 3 TEST I
RE T 2
wf l C R D
Tfl R?
MflCRG
TRANSFER
TflBl
DDD 3 3
RET?
T AR 2
EFF 3 3
RF T 3
Tf l RB
T ! ST L
V A C 1’ O
Mf l CRC
T 7 A N S F ER
TEST L
vflCFD
vA C R p
TRANSFER
F F F 33 T E S T L
RF T4
MAC R O
Tf l BA
macro
TRflNSEE0
GGG 3 3 TEST I
RF T 5
MflCR U
v ACPO
Tfl B«>
HhH 3 3 TPf l NSPF0
AflflA
TRADE
RETl
TflRl
BR RA
RFTl
T AB I
CCCA
RET?
TAB?
DDDA
RFT?
T f l R?
EEEA
RE T 3
TAB7
GENFRATF
ADVANCE
"f l CRO
TEST L
MA C R O
MACRO
TP f " S t E P
TFST L
MACRO
MACRO
TRANSFER
TEST L
MflCKC
MACRO
T P A N sF E 1
TEST L
MflCRn
MflCPU
TRANSFFr
TEST L
"ER G
C Pt
TRflNSFH
’« C
* FF-H 3 2
C l , K l B H C C C 33
ASSIGN, 3« VI 2 ,
2 7 , 2 8 , 2 9 , 30, 3
, H H H 33
C I , K I 9 9 , n o n 33
A S S I G N , 4 , V l 3,
2d, 2 * , 3 0 , 31
,n H H 3j
C l , K 2 h 2 , H E 3"!
A S S I G N , A . V H , I6 i
2 E , 2 9,3 C , 3 I
, HliH 3 3
C l , K2 9 A , F F r I7
A S S I G N , S , V l c ,6 , 7
29,33,31
, h 'I.i 3 J
C I , K 325 , G G G 3 3
3 S S I G N , 6 , V l 5,
30,31
,HHH33
C I, K 3 6 7 ,Hr H 33
ASSIGN,7,Vl2
Bi
, A A A3 3
, , , 1 * 7 , ,f
3
7,l,Xb,e,2
C l , K I 7 8 , HRB4
A S S I G N , 3 , V B fA
32, 3 3 , 3 A , 3 5 , J
,H H H A
C l 1 K l 8 ° .CCC 4
A S S I G N , 3,V«,A
I6 « 7
32,33,34,35,3
,D H H A
C l , K l 99 , O b D A
ASS I G N , A , V 9 , 5
33,34,35,3o
, nH H A
C l , K 2 6 2 ,EEFA
A S S I G N , 4 , V 1C* j » 6 ,7
33,34,35,3b
, M H H4
C l , K2 94 , F F F ,
A S S I G N , 5 ,Vl I, 6 , 7
34,35,31
, H HH A
FFF4
RE T 4
T AB 4
GGG4
RETS
I AB 5
HHH 4
AAA44
TRADE
RETI
TABl
BEb4 4
RE T l
TABl
CCC 4 4
RET2
TABZ
UOU 4 4
RET2
T AB 2
EEE44
RE T 3
TAB3
FFF44
RE T4
TABA
GGG44
RE T5
T An 5
HHH 4 4
TEST L
XAC %0
* ACkU
TRANSFER
TEST L
MACau
MAC R O
TABULATE
T k ANSFEP
GENERATE
ADVANCE
y ACRG
TEST L
MACRO
MACRO
TRANSFER
TEST I
MACRO
PACPO
TRANSFER
TEST I
MAC R O
MACRO
T P AN S f E 9
TEST L
MACRO
MACRO
T R A N S F ER
TEST L
MACRO
MAC R O
TRANSFEn
TEST L
MACRO
MAC R O
TRANSFER
IFST L
MACRO
MACRO
T k ANSf E d
generate
AAA5
TRADE
Rf Tl
TAHl
BPB 8
ADVANCE
MACdO
TEST L
" ACkC
v ACkf
TRANSFER
TEST L
Cl , < 3 2 5 , 0 0 0 4
4 8 0 1 0 0 , f , V l I »7
3 5,
,HH H 4
C I«K 3 6 7,hHH 4
A S S I G N , 7 , V12
76
56
,A5A4
,,,1,7,,'
0
I 7 , , X 1,18,2
C I, < I ,8,80344
ASSI GN, 3 , V t i , 4 , 5 , 6 , 7
3 7 , 3 B, 3 9 , 4 0 , 4 1
, HHH44
C l , Kl Ei'i , C C C 4 4
A S S I G N , 3 , Vl 3 , 4 , 5 , 6 , 7
37.36.39.40.41
, H H H 44
C l , K I 9 9 , O D D 44
A S S I G N , 4 , V I3 , 5 , o,7
3b,39,40,41
, HH H4 4
C1;K262,E[[44
ASSIGN,4 , V ] 4 , 5 , 6 , 7
36.30.40.41
,H H H 4 4
C l , K2 94 I FFF44
A S S I G N , 5 , Vt 5 , 6 , 7
39.40.41
,H H M 4 4
C I,< 3 25 , 0 0 0 44
A S S I G N , 6 , V I5 , 7
40.41
,HHH4 4
C I , K 3 6 7 , H H H 44
ASSIGN,7,Vl2
4I
,A A A 4 4
, , , I , 7, ,FO
“A , I , X 3 , 1 0 , ^
C l , K l 73,09"5
A S SI G N , 3,V o , 4,5,6,7
42,43,44,45,66
, HHHc
C l , Kl H O , C C C c
•*4
NI
RFTl
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CCC5
R F T2
T AB 2
O D D 1'
R ET 2
T AB 2
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T AC 3
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TAB4
GGGS
PFTS
TAEF
HFHS
AAASS
TRADE
RFTl
TAB I
BPBSS
RF T I
TARl
CCC S 5
RE T 2
TAB?
DDDSS
RF Tl'
TAP 2
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RE T 3
TAP 0
FFFbS
,4 A C h U
MACRO
TRANSFER
TEST L
MACRO
*7 C R D
TcANSFFr
TE ST L
'ALR n
M ACRG
TRANSFER
TEST L
MACRO
macro
T 2 ANSFfcR
TFST L
MACRC
MACRO
Th A N S F E R
TEST L
MACRO
^ AC RU
I A G U L A TE
TaANSFtD
GENERATE
ADVANCE
MACRO
TEST L
MACRO
MAC3O
TRANSFER
Tf ST L
MACRO
MACRO
TPANSFF 0
TEST L
MACRO
MACRO
TB A N S F E R
TEST L
MACRO
macro
TRANSFER
IESt L
m ACFO
VACRC
TF f JS F L R
TfSTL
ass IO',, 3,V'),4,'j,6, 7
42,43,44,45,4^
,HHh 5
C I ,K I 9 4 , O D D 5
A S S I G N , 4,74,5,6,7
4 3,44 ,45» 46
, It4HS
C I.K 2 62 ,F t U 5
4SSIGIN, 4, Vi C, 5,o, 7
43,44,45» 46
,H H H 6
C I,K 2 ^4,F FH 5
A S S I G N , f ,V ll ,6,7
4 4 , 4 4 » *6
,iiH,i5
C1.K 325 ,GCGh
A S S I GN, 6 , Vl I , 7
45,46
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C I,K367 ,HHHS
ASSIGN,,,Vl2
46
56
, AA AS ^
w
,,,I, 7»*r
n
X 3 ,2 0, 2
7 8 , P B 0 SS
N , 3» V 8 , 4 , 5 , 6 , 7
,49,5,51
7
'CUSS
,Vi 3,5,6,
, H h HS 5
Cl,K 294,FFhSS
ASSIGN, 5,V I5,o, 7
49,5 3 , 4 I
,HHHS5
C I , K 325 , " C G S F
RF TA
TPfiA
GCG5S
RF 1 5
T P3 F
Hh H5 5
»,LC*L
YACRQ
T R A M S F CR
TFST L
MPCRU
MAC R C
TRANSFER
START
RFSFT
START
RFSFT
START
RFStT
STP9 T
RF Sr T
S I ART
RFSFT
START
RFSFT
START
RFSET
START
RFStT
S T A r- U
RFStT
ST ART
RESET
START
RE S E T
START
RESET
START
RESET
start
RESET
START
RESET
START
RESET
STA9 T
RESET
START
RESET
STA9 T
RESET
start
F NE
' . SS Ib N , c , V i , ,
S O 4Si
4 F; HH 5 S
C l 4 K T o Z 4 HF i H 5 S
ASSIGN,T t V l0
5I
,AAASS
366
36 6
3 Ob
3 66
3 66
366
366
366
Too
366
366
3oo
366
3o6
3 oo
3 6o
366
06 6
366
0 66
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4N
SUF R CU T IGE
IMPLICIT
GPDF1CI.K.X)
ItiTECtR(X)
s o *3= s u M r = s u v i = S u m i c = S u m j o = E x p 5= E x p J v = U
D I M E N S I O N I ( I , 3 0 ) , Xf I , 7)
C m I C U L A T I ON ’F S I M P L E 3- )A1 MOVI NG A Vt RA Gf
C
IE
(K.Lf .2)
PO
IQ J = K - P tK
GCt H
PD
S 0 > 3 = 5 U M ? 4 l ( I ,J )
IC
C U M I NUf
Pb
30
G O T C 30
I F (K.E««. P) G O T O P '
,
S U " J = If I,29) + l ( l , 3 0 ) + I ( i,I)
G O T O 30
S U v U = I U , 3 0 ) + 1 ( 1 , I )+ r ( I ,2 >
X ( I , I ) = SUM 3/ 3
C A L C U L A T I O N OE S I vPLL r. -,XY WflVING A V E R A G E
A N D E X P O N E N T I A L r- D A Y M O V I N G A V E R A G E
Tf ( K . L f . 4 ) G O T O 4 J
U U 32 J = K - 4 , K
S U M b = S U M S + T C I , J ) ; c X P 5 = l X? 5 + ( J * I ( 1 , J) )
3?
Cul1 T IN U E
no
PO
40
G O T U 45
TE ( " . E U . I)
Th ( K . t O . 2 )
IF ( K . K . . 3 )
IF ( K . E U . h )
GOTO
GOTO
GOTO
GOTO
41
42
43
44
41
42
f XP S = I ^ I » 2 P )♦ C P *T ( l , 2 9 ) ) + ( 3 * I ( i t 3 0 ^ ) + ( 4 * r ( l ,) ) ) + ( b * U l # 2 ) )
43
GGTG
44
45
IF
47
bC
5I
4c
SUNb = I U , 3 0 ) + I(l,l) + I(l,P) + I U , 3 ) + T (l,4)
E X P 5 = 1 ( 1 , 3 0 ) + ( ? *I ( 1 , 1 ) ) + ( 3 * I ( l , 2 ) ) + ( 4 * T a , 3 ) ) t ( 5 * I ( l ,4 ))
X ( I f P ) = S U M ^ z s ; XC I, 6) = ' X P b / l b
CA L CUL AT I ON OF STMPf U PAY y OVI NG A V E R A G E
(K.LE.9)
GOTO
U
U O 47 J = K - U 1 X
S U v I n = S U M l O + I ( I 1J )
C O M INUE
GOfP 60
CO S 1 L=I ,K
S U M l O = S U v 10 + 1 C! ,1 )
CONTINUE
DO 52 L = P I+ K , )
yXl
Ui
S U M O = S L " i C t I CI , L )
52
60
61
66
67
CONTINUE
70
15 O A Y M O V I N G
AVERAGE
GOTC 70
D U 06 J = I 1K
S U M S = S U M 1 5 + 1(1 f J )
CONTINUE
65
C
C G M INUE
CALCULATION
IF ( K . L E . 1 4 ) G O T O o 5
DO 61 J = K--I^1K
SUH5=SU"15+T(1,J)
CONTINUE
DO 6 7 J = 1 6 + K , 3 ‘
StJk1I b = S U y I r + T ( I f J )
CALCULATION^cr
SI
Lfc 3G D A Y
MOVING
AVERAGE
DO 80 J = I » 3 0
S U M 3 0 = S U V 3 0 + I ( I ,J )
80
C
I 4O
CONTI NUE
C a l c i 5Il s t i o n 0 H f 'e x p o n e n t a i l 30 d a y
D O 82 J = I t K
_ _
E X P S O = EX P 3 0 * ( C 1 f . - ( K - J ) ) * i ( l t J ) )
CONTINUE
Ic C K . F u . 3 0 ) GOT') O O
D O 84 J = K + 1 , 3 0
E X P S O = F XP S C - K ( J - K ) M ( I f J ) )
C O M INUE
X(IfT)=IXP30/465
RETURN
[ NP
noving
average
REFERENCES
78
REFERENCES
Alexander, Sidney S . "Price Movements in Speculative Markets: Trends
or Random Walks," Industrial'Management Review, 2:7-26, May, 1961.
Arthur, Henry B. Commodity Futures as a Business Management Tool.
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Box, George E. P., and Gwilym M . Jenkins. Time Series Analysis:
Forecasting and Control. Revised Edition. San Francisco:
Holden - Day Inc., 1976.
Boyle, J. E. Speculation and the Chicago Board of Trade. New York:
Macmillan Publishing Co., 1920.
Brogan, Al S. "Crdsshedging Barley: A Montana Example."
State University, 1973.
(Mimeographed).
Montana
Cootner, Paul H.
(ed.)
The Random Character of Stock Market Prices.
Cambridge, Massachusetts: M.I.T. Press, 1964.
Graf, T.F.
"Hedging - How Effective Is It?", Journal of Farm Economcs,
35:398-413, August, 1953.
Gray, Roger W. "The Imprtance of Hedging in Futures Trading; and the
Effectiveness of Futures Trading for Hedging", in Futures Trading
Seminar, Volume I. Madison: Mirmir Publishers Inc., 1960.
Gruen, F. H. "The Pros and Cons of Futures Trading for Woolgrowers,"
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1960.
Hardy, C. 0. and L. S. Lyon. "The Theory of Hedging,"
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Journal of
Howell, L. D. Analysis of Hedging and Other Operations in Grain Futures
Washig-ton, D.C.: USDA Technical Bulletin Number 971, August, 1948
__________ . Analysis of Hedging and Other Operations in Wool and Wool
Top Futures. Washington, D.C.:USDA Technical Bulletin Number
1260, January, 1962.
79
_____________ and L. J. Watson. Relation of Spot Cotton Prices to
Futures Contracts and Protection Afforded by Trading in Futures.
Washington, D.C.:USDA Technical Bulletin Number 602, January,
1938.
Johnson, L. L.
Futures,"
"The Theory.of Hedging and Speculation iii Commodity
Review of Economic Studies, 27:139-151, June, 1970.
Kendall, M. G. "The Analysis of Economic Time Series - Part I:
Prices," Journal of the Royal Statistical Society, 96:11-25,
1953.
Larson, Arnold B. "Measurement of a Random Process in Futures Prices,"
Food Research Institute Studies, 1:313-324, November, 1960.
Mandelbrot, Benoit. "The Variation of. Certain Speculative Prices,"
Journal of Business, 36:394-419, March, 1963.
______________ . "Forecasts of Future Prices, Unbiased Markets, and
'Martingale* Models," Journal of Business, 39:242-255, January,
1966.
Mann, Jitendar S . and Richard G. Heifner. The Distribution of Shortrun Commodity Price Movements. Washington, D.C.:USDA Technical
Bulletin Number 1536, March 1976.
Markowitz, Harry.
March, 1952.
Nelson, Charles R.
casting. San
"Portfolio Selection,"
Journal of Finance, 7:77-91,
Applied Time Series Analysis for Managerial Fore­
Francisco: Holden-Day, Inc., 1973.
Ochsner, Gary L. "An Economic Analysis of Montana Wheat Exports in
the Asian Market." Unpublished M.S. thesis, Montana State
University, 1974.
Purcell, Wayne D. "More Effective Approaches to Hedging?"
. State University, 1976. (Mimeographed)
Oklahoma
Smidt, Seymour. "A Test for Serial Independence of Price Changes in
Soybean Futures", Food Research Institute Studies, 4:117-136,
1965.
80
Sanpe, R. H. and B. S. Yamey. "Test of the Effectiveness of Hedging,"
Journal of Political Economy, 73:540-544, October, 1965.
Stein, J. L. "The Simultaneous Determination of Spot and Futures
Prices", American Economic Review 51:1012-1025, December, 1961.
Stevenson, R. A. and R. M. Bear. "Commodity Futures: Trends or Random
Walks?" Journal of Finance, 25:65-81, March, 1970.
Taylor, F. M. Principles of Economics. Second Edition.
University of Michigan Press, 1913.
Ann Arbor:
Telser, L. G. "Safety First and Hedging", Review of Economic Studies,
23:1-16, 1955.
Working, Holbrook. "Hedging Reconsidered,"
35:544-561, November, 1952a.
Journal of Farm Economics,
_______________ . "Futures Trading and Hedging,"
Review, 43:544-561, June, 1953b.
American Economic
_______________ . "A Theory of Anticipatory Prices", American Economic
Review, 48:188-199, May, 1958.
MONTAkll ---- .
3 1762 10013109 I
N378
B786
cop. 2
Brogran, Al S
Simulation of moving
average hedging
strategies for winter
wheat
3 WKS USE feIWTEPUSBARY LOW*
3-