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