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IntercommodIty SpreadS: determInIng contract ratIoS
The fact that percentage price change is a more meaningful measure than absolute price change is 
perhaps best illustrated by considering the extreme example of the gold/silver spread. The equal-unit 
approach, which neutralizes the spread against equal-dollar price changes in both markets, would 
imply the rather ludicrous spread position of 50 gold contracts versus 1 silver contract. (The contract 
size of silver is 5,000 oz; the contract size of gold is 100 oz.) Obviously, such a position would be 
almost entirely dependent upon changes in the price of gold rather than any movement in the gold/
silver spread. The disparity is due to the fact that since gold is far higher priced than silver (by a ratio 
of 32-101:1 based on the past 30-year range), its price swings will also be far greater. For example, if 
gold is trading at $1,400/oz and silver at $20/oz, a $2 increase in silver prices is likely to be accom-
panied by far more than a $2 increase in gold prices. Clearly, the relevant criterion in the gold/silver 
spread is that the position should be indifferent to equal percentage price changes rather than equal 
absolute price changes. Although less obvious, the same principle would also appear preferable, even 
for intercommodity or intermarket spreads between more closely priced markets (e.g., New Y ork 
coffee/London coffee).
Thus we adopt the definition that a balanced spread is a spread that is indifferent to equal percentage 
price changes in both markets. It can be demonstrated this condition will be fulfilled if the spread is 
initiated so the dollar values of the long and short positions are equal.
2 An equal-dollar-value spread 
2 If the spread is implemented so that dollar values are equal, then:
NU PN UPtt11 10 22 20,,== =
where  N1 = number of contracts in market 1
 N2 = number of contracts in market 2
 U1 = number of units per contract in market 1
 U2 = number of units per contract in market 2
 P1,t=0 = price of market 1 at spread initiation
 P2,t=0 =  price of market 2 at spread initiation
An equal-percentage price change implies that both prices change by the same factor k. Thus,
Pk PP kPtt tt11 10 21 20,, ,,== ==== and
where Pl,t = 1 = price of market 1 after equal-percentage price move
 P2,t = 1 = price of market 2 after equal-percentage price move
And the equity changes (in absolute terms) are:
Equity change in market 1 positio n =− ===NU kP PN UPtt11 10 10 11 1|| ,, ,t t
tt
k
NU kP P
=
==
−
=−
0
22 20 20
1 |
| ,,
|
Equity change in market 2 positio n| || ,=− =NU Pkt22 20 1 |
Since, by definition, an equal-dollar-value spread at initiation implies that N1U1P1,t = 0 = N2U2P2,t = 0, the equity 
changes in the positions are equal.
It should be noted that the equal-dollar-value spread only assures that equal-percentage price changes will 
not affect the spread if the percentage price changes are measured relative to the initiation price levels. However, 
equal-percentage price changes from subsequent price levels will normally result in different absolute dollar 
changes in the long and short positions (since the position values are not necessarily equal at any post-initiation 
points of reference).