Bias in Feeder Cattle Futures
May 13, 2004
Ryan Broxterman
Dr. John Fox
Dr. Jim Mintert
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Table of Contents
Introduction …………………………………………………...…………1
Body …………………………………………………………………….2-6
Data ……………………………………………………….………2
Model ………………………………………………….………….2
Regression Analysis ……………………………………….……...4
Forecasting ………………………………………………….…….6
Trade Simulation ………………………………………….………6
Conclusion …………………………………………………………...…..7
Bibliography …………………………………………………….……….8
Appendix
Mean Regression ………………………………………………….i
T-Stat Regression …………………………………...….…………ii
Chart of 2003-2004 Contracts ……………………………………iii
Chart of Forecast Errors …………………………………………..iv
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Bias in Feeder Cattle Futures
Introduction
Feeder cattle contracts are traded at the Chicago Mercantile Exchange. They
were first started in 1972 and now consist of 8 contract months. As long as these markets
have been around there has always been a debate about their efficiency. One sign of
market inefficiency is bias. As defined by Kastens and Schroder (1995) market bias is
“the tendency to move either up or down into expiration.”
Futures markets should be unbiased in the long run. If the market is biased you
would expect arbitrage or profit taking to occur and take the bias out of the market.
However there must be at least the perception of profit opportunity in order for traders to
trade the market. In any futures market it is important to keep this balance between
market efficiency and profit opportunity.
The objective of my research is to study past futures contracts to see if there is
indeed an upward or a downward bias in feeder cattle futures prices. Because bias is the
tendency for price of a contract to move up or down into expiration, an upward bias
would happen if the market decreased in price as the contract nears expiration. A
downward bias would occur if a market increased in price as the market neared
expiration. If there is no bias and the market is efficient you would expect the number of
contracts increasing in price to be approximately equal to the number decreasing in price.
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Data
All data for this project was obtained from the Bridge CRB program. Data was arranged
so that the last day of each contract was designated as day n, second to last day, day n-1,
the third to last day, day n-2 and so on.
A chart of each of the futures contracts was conducted from start to close to see if
there was any visible bias. This returned inconclusive results so I decided to test for
statistical significance. A small sample of the data used is attached at the end of the
report.
Model
In developing a model to determine if there is a bias in feeder cattle prices
I first needed to chose the times to analyze. I choose 2 week average intervals in order to
get around daily ups and downs in the market. I used the last two weeks (days n through
n-9 where day n is the final day) as my base and compared it to day n-80 through day n89, a two week period about 4 months before the close. I then compared these two
averages using both a simple mean change and also by running a t-test for 2 sample
means with unequal variances. The t-test provides a t-stat which indicates the statistical
significance of the mean difference.
In order for the difference in means to be
considered statistically significantly higher, the t-stat must be above 2 in absolute power.
The results of these t-tests are provided below. A significantly higher t-stat would be
upward biased while a significantly lower t-stat would be downward biased.
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January
Count
Significantly
Higher
Significantly
Lower
No Significant
Difference
March
Count
Significantly
Higher
Significantly
Lower
No Significant
Difference
April
Count
Significantly
Higher
Significantly
Lower
No Significant
Difference
May
Count
Significantly
Higher
Significantly
Lower
No Significant
Difference
26
9
17
31
14
14
3
31
13
15
3
32
15
15
2
August
count
Significantly
Higher
Significantly
Lower
No Significant
Difference
September
count
Significantly
Higher
Significantly
Lower
No Significant
Difference
October
count
Significantly
Higher
Significantly
Lower
No Significant
Difference
November
count
Significantly
Higher
Significantly
Lower
No Significant
Difference
31
10
19
2
30
8
19
3
30
10
16
4
31
14
13
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My third step was to then run a regression. I regressed both the t-stats and the
mean changes in separate regressions against a time factor which was figured starting
with 1 for 1972 contracts, 2 for 1973 contracts and so on. I also used dummy variable to
represent each of the 8 contract months using January as my default.
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Regression Analysis
The difference in means between the final 2 weeks and the earlier 2 week period
(day n-80 to n-89) was regressed on a time trend variable and a set of dummy variables
representing different contract months. The results can be found in the Appendix page 1.
These results can be interpreted by saying the in year 0 or 1971 the price 4 months before
the close will be $2.04 less than the price at the close. It can be further interpreted by
saying that in each subsequent year this price difference will drop by $.053. This
indicates that over time feeder cattle futures seem to be getting more and more efficient
or at least showing less bias. The estimated coefficients on the dummy variables show
that in months March, April, May, and November the difference in means seems to be
smaller than in January. Because the values of each of these coefficients are negative it
means that the price difference is less for these contract months than it is for January, or
that they are more efficient than January. In August, September, and October this price
difference seems to be larger, evident by the positive coefficient. This suggests that these
contract months were more inefficient.
The statistical significance of this regression does not seem to be real good. It has
an R-squared term on .0249 which is pretty small. Also the P-values of the coefficients
are fairly low. The intercept and the time factor are not too bad being .14 and .209
however the high p-values on the dummy variables tell me that there probably isn’t a lot
of difference between the different contract months.
Figure 2 shows the residuals of the regression. As you can see bias seems to
follow time periods. It seems that several contracts will be over predicted by the model
then several will be under predicted. The pattern doesn’t appear to be completely
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random. If this study would have been done 15 years ago it may have been possible to
gain profit from trading this bias however it looks like the market is becoming more
efficient which is what the regression is telling us. The results of this regression tell me
that in the January contract of 2002 the bias would be $.42/cwt. (2.04 + (20021972)*.054). This is obviously considerably lower than the $2.04/cwt. bias predicted for
1971.
A 2nd regression model was ran using the t-statistics for the test of difference in
mean between the two price periods. The results of the t-stat regression can be found on
page 2 of the appendix. The t-stat regression tells us the statistical significance of the
findings.
An intercept of 9.008 means that in year 0 or 1971 the predicted difference in
means is statistically significant because it is greater than 2. The idea that feeder cattle
futures markets are becoming more and more efficient is backed up by this regression. A
coefficient of -.231 for time means that as time goes on the statistical significance of this
mean difference gets less and less and therefore indicates the markets are becoming more
efficient. The dummy variables in this regression tell us how much the statistical
significance changes as we change contract months. Because January is the default
month, if the month we are observing is March we would subtract 1.11 from the intercept
meaning that March seems to be less statistically significant than January. March, April,
May, October, and November all are less significantly significant than January.
However, August and September seem to be more statistically significant than January,
evident by the fact that the coefficients of these terms are positive. The R-squared value
of this regression also seems to be very low. It is only .0378 while the standard error is
high at 21.63. The P-values of the intercept and time in this regression also seem to be
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good while all of the dummy variables are very poor, thus suggesting that there isn’t a lot
of change of the different contracts.
Forecasting
Results from the regression model were used to forecast the eight 2003 contracts
along with the January and March contracts of 2004. I used 2 methods to forecast the
price at expiration. For my first forecast I simply used the average futures price of day n80 threw day n-89 to predict the price at expiration. For my second forecast I used the
mean regression model that I developed. I then used the root-mean-squared forecast error
to compare these two models for performance. In this analysis the lower that the error is
the better your model is. I received a forecast error of 12.36 for the first model and an
error of error of 12.14 for the second model. This means that neither of these forecasts is
working very well at predicting the price at the close in these 10 contract months. It
further tells me that my model is only performing slightly better than the average price 4
months before the close.
Trade Simulation
For the last part of my analysis I ran a trade simulation of the 8 contracts of 2003
and the January and March contracts of 2004. I simulated trading the bias that I found by
going long one contract 90 trading days before the close and selling that contract back on
the close. I returned a net profit of $28,675 from this trading simulation. This is an
impressively high number considering the discovery mad cow disease in the U.S. on
December 23, 2003, and the sharp downtrend that it caused. This large profit didn’t
come as a surprise however due to current market conditions. During these months
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feeder cattle were in short supply and caused an inverted market. This inverted market in
turn lead to the sharp increase in price as these contracts neared expiration.
Conclusion
I have concluded that the feeder cattle futures market may have a slight
downward bias. The market seems to increase in price a little as the contract nears a
close. The overall average of each contracts difference from 4 months before the close of
the contract to the close is 88 cents/cwt. This bias however does not seem to be of great
statistical significance. This is evident by the low R-squared values in the regression and
also the high standard errors. I am not overly confident in saying that this finding was
important simply because of the fact that it is of little statistical significance. Or I at least
am confident in saying that I would not trade the bias.
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References
Bridge CRB,
Terry L. Kastens and Ted C. Schroeder, “Efficiency Tests of Kansas City Wheat
Futures,” December 1996
Terry L. Kastens and Ted C. Schroeder (1995), “A Trading Simulation Test For WeakForm Efficiency In Live Cattle Futures,” The Journal of Futures Markets, 6:649675
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