54 lines
3.2 KiB
Plaintext
54 lines
3.2 KiB
Plaintext
455
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IntercommodIty SpreadS: determInIng contract ratIoS
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The fact that percentage price change is a more meaningful measure than absolute price change is
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perhaps best illustrated by considering the extreme example of the gold/silver spread. The equal-unit
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approach, which neutralizes the spread against equal-dollar price changes in both markets, would
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imply the rather ludicrous spread position of 50 gold contracts versus 1 silver contract. (The contract
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size of silver is 5,000 oz; the contract size of gold is 100 oz.) Obviously, such a position would be
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almost entirely dependent upon changes in the price of gold rather than any movement in the gold/
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silver spread. The disparity is due to the fact that since gold is far higher priced than silver (by a ratio
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of 32-101:1 based on the past 30-year range), its price swings will also be far greater. For example, if
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gold is trading at $1,400/oz and silver at $20/oz, a $2 increase in silver prices is likely to be accom-
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panied by far more than a $2 increase in gold prices. Clearly, the relevant criterion in the gold/silver
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spread is that the position should be indifferent to equal percentage price changes rather than equal
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absolute price changes. Although less obvious, the same principle would also appear preferable, even
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for intercommodity or intermarket spreads between more closely priced markets (e.g., New Y ork
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coffee/London coffee).
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Thus we adopt the definition that a balanced spread is a spread that is indifferent to equal percentage
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price changes in both markets. It can be demonstrated this condition will be fulfilled if the spread is
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initiated so the dollar values of the long and short positions are equal.
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2 An equal-dollar-value spread
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2 If the spread is implemented so that dollar values are equal, then:
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NU PN UPtt11 10 22 20,,== =
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where N1 = number of contracts in market 1
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N2 = number of contracts in market 2
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U1 = number of units per contract in market 1
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U2 = number of units per contract in market 2
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P1,t=0 = price of market 1 at spread initiation
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P2,t=0 = price of market 2 at spread initiation
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An equal-percentage price change implies that both prices change by the same factor k. Thus,
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Pk PP kPtt tt11 10 21 20,, ,,== ==== and
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where Pl,t = 1 = price of market 1 after equal-percentage price move
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P2,t = 1 = price of market 2 after equal-percentage price move
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And the equity changes (in absolute terms) are:
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Equity change in market 1 positio n =− ===NU kP PN UPtt11 10 10 11 1|| ,, ,t t
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tt
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k
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NU kP P
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=
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==
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−
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=−
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0
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22 20 20
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1 |
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| ,,
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Equity change in market 2 positio n| || ,=− =NU Pkt22 20 1 |
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Since, by definition, an equal-dollar-value spread at initiation implies that N1U1P1,t = 0 = N2U2P2,t = 0, the equity
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changes in the positions are equal.
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It should be noted that the equal-dollar-value spread only assures that equal-percentage price changes will
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not affect the spread if the percentage price changes are measured relative to the initiation price levels. However,
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equal-percentage price changes from subsequent price levels will normally result in different absolute dollar
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changes in the long and short positions (since the position values are not necessarily equal at any post-initiation
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points of reference). |