MTm M
(2) Var(Pi) =∑∑ (Pit - Pim)2 / ∑ Tm - M
mt m
m = 1,2,...M
t = l,2,...Tm
where:
Var(Pi)is within-contract pooled variance for
price in market i,
Pjm is average price in market i for cash
prices corresponding to contract m,
M is the number of contracts observed
(21), and
Tm is the number of cash prices associated
with contract m.
Pooled hedging revenue variance is defined in similar
fashion as!
MTm _ M
(3) Var(Rij) =∑∑ (Rijt-Rijm)2/ ∑ Tm - M
mt m
m = 1,2,...M
t = 1,2,...Tm
where:
Var(Rij)is within-contract pooled hedging
revenue variance in market i for
hedge length j,
Rijm ɪs the mean hedging revenue in
. market i, hedge Iengthj, in contract
m, and other variables are as
previously defined.
RESULTS
Results of the analysis are summarized in Table
1. Means and standard deviations of cash market
prices and hedging revenues for the four markets are
presented. Means are included as a matter of general
interest, but the primary focus of the analysis is on
the variances. F-ratios calculated for Bartlett’s test of
equality of variances are presented in the right-hand
column of the table. They refer to the variances
(standard deviations squared) appearing on then-
respective rows. All standard deviations in the table
were calculated from pooled within-contract
variances for the variables indicated.
At the 5 percent level of significance, no
differences were found between cash market price
variances. On the other hand, differences were found
between hedging revenue variances for all three
hedging periods at the same level of significance.
These results indicate that location basis variability
was a factor in the distant markets during the study
period. Cattle feeders in these markets apparently
could not have hedged as effectively during the study
period as feeders with access to the Omaha market .
Inspection of the standard deviations presented
in Table 1 indicate something of what occurred to
hedging revenue variances as the length of hedge was
altered. Compared to cash markets, it can be seen
that the 30-week hedge caused a general reduction in
revenue variances, though the reduction was
proportionately greatest for Omaha. As length of
hedge was reduced, to 21 weeks and then to 13, there
was a tendency for revenue variances to increase,
although, with the exception of the Georgia market,
they remained below the corresponding cash market
price variances. Revenue variances for Omaha
remained below those for other markets, with the
exception of the 21-week hedge in the Southern
Plains. This exception will be discussed in the next
section. Increasing revenue variance is accounted for
by a tendency for futures contract price variances to
increase as the contracts approached maturity. That
is, prices at which the Shorter-Iength hedges were
placed tended to be more variable than some weeks
before, when the Ionger-Iength hedges were placed,
even though the contract maturity dates were the
same.
INTERPRETATION OF HEDGING
REVENUE VARIANCES
A better understanding of how location basis
VariabiUty affects hedging revenue can be gained by
examining the components of hedging revenue
variance. These components can be derived from
equation (1) and are as follows:
(4) Var(Pijt) = Var(Pit) + Var(Sjm) + Var(Lmt) +
2 Covar(PitlSjm) - 2 Covar(Pit, Lmt)
- 2 Covar(Sjnv Lmt)
where the variables are as previously defined. Of
primary interest is the covariance term linking cash
market prices with prices at which futures contracts
are covered, Covar (Pit, Lmt). This is the term which
shows how closely local market prices are tracking
with futures market prices as the futures contract
nears maturity. Because of the delivery option, this
relationship can be expected to be fairly close in a
delivery market. It may be close in distant markets as
well, but if so, the Unkage works through the dehvery
market rather than with the futures market directly.
Covariances can be further de∞mposed to
correlation coefficients, which provide standardized
measures of the cash-futures price relationships. The
correlation coefficients for the cash market-maturing
futures contract price relationships for the four
markets were as follows:
75