53 lines
2.9 KiB
Plaintext
53 lines
2.9 KiB
Plaintext
281
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SElECTINg THE BEST FuTurES PrICE SErIES For SySTEM TESTINg
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■ Constant-Forward (“Perpetual”) Series
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The constantforward (also known as “perpetual”) price series consists of quotes for prices a constant
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amount of time forward. The interbank currency market offers actual examples of constantforward
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price series. For example, the threemonth forward price series for the euro represents the quote for
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the euro three months forward from each given day in the series. This is in contrast to the standard
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u.S. futures contract, which specifies a fixed expiration date.
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A constant forward series can be constructed from futures price data through interpola
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tion. For example, if we were calculating a 90 day constant forward (or perpetual) series and
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the 90day forward date fell exactly one third of the way between the expirations of the nearest
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two contracts, the constant forward price would be calculated as the sum of two thirds of the
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nearest contract price and one third of the subsequent contract price. As we moved forward in
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time, the nearer contract would be weighted less, and the weighting of the subsequent contract
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would increase proportionately. Eventually, the nearest contract would expire and drop out of
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the calculation, and the constant
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forward price would be based on an interpolation between the
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subsequent two contracts.
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As a more detailed example, assume you want to generate a 100day forward price series based on
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euro futures, which are traded in March, June, September, and December contracts. T o illustrate the
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method for deriving the 100
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day constantforward price, assume the current date is January 20. In
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this case, the date 100 days forward is April 30. This date falls between the March and June contracts.
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Assume the last trading dates for these two contracts are March 14 and June 13, respectively. Thus,
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April 30 is 47 days after the last trading day for the March contract and 44 days before the last trad
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ing day for the June contract. T o calculate the 100
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day forward price for January 20, an average price
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would be calculated using the quotes for March and June euro futures on January 20, weighting each
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quote in inverse proportion to its distance from the 100
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day forward date (April 30). Thus, if on Janu
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ary 20 the closing price of March futures is 130.04 and the closing price of June futures is 130.77, the
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closing price for the 100
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day forward series would be:
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44
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91 1300 4 130 77 130 42(. )( .) .+=47
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91
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Note that the general formula for the weighting factor used for each contract price is:
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W CF
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CC W FC
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CC1
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2
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21
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2
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1
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21
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= −
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− = −
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−
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where C1 = number of days until the nearby contract expiration
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C2 = number of days until the forward contract expiration
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F = number of days until forward quote date
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W1 = weighting for nearby contract price quote
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W2 = weighting for forward contract price quote |