Methods for Post-Trade Allocation

Abstract

A computer-implemented method for providing an allocation of a filled order made at a particular time, that involves receiving at least a price of a filled order made at a later time; generating a starting allocation across multiple managed accounts based at least in part on allocation factors of each of the multiple managed accounts; generating at least one additional allocation based at least in part on the starting allocation; determining a closest-fitting allocation according to a metric from amongst the starting allocation and the at least one additional allocation, the metric being based at least in part on the price of the filled order made at the later time and on a price of the filled order made at the particular time; and outputting the closest-fitting allocation.

1 . A computer-implemented method for providing an allocation of a filled order made at a time t- 1 , comprising:
 receiving at least a price of a filled order made at a time t;   generating a starting allocation across multiple managed accounts based at least in part on allocation factors of each of the multiple managed accounts;   generating at least one additional allocation based at least in part on the starting allocation;   determining a closest-fitting allocation according to a metric from amongst the starting allocation and the at least one additional allocation, the metric being based at least in part on the price of the filled order made at the time t and on a price of the filled order made at the time t- 1 ; and   outputting the closest-fitting allocation.   
     
     
         2 . The method of  claim 1 , wherein:
 the multiple managed accounts comprise at least two accounts; and   the at least one additional allocation comprises, for each member of a set of non-zero integer pairs, a perturbation of the starting allocation for each unique pair of managed accounts amongst the multiple managed accounts that is based at least in part on adding to allocated integer values of the starting allocation associated with both members of the unique pair, an integer value associated with a corresponding non-zero integer value of the member of the set of non-zero integer pairs.   
     
     
         3 . The method of  claim 2 , wherein:
 the set of non-zero integer pairs comprises [+1 −1], [+2 −2], and [+3 −3].   
     
     
         4 . The method of  claim 2 , wherein:
 the multiple managed accounts comprise at least three accounts; and   the at least one additional allocation further comprises, for each member of a set of non-zero integer triplets, a perturbation of the starting allocation for each unique triplet of managed accounts amongst the multiple managed accounts that is based at least in part on adding to allocated integer values of the starting allocation associated with all three members of the unique triplet, an integer value associated with a corresponding non-zero integer value of the member of the set of non-zero integer triplets.   
     
     
         5 . The method of  claim 4 , wherein:
 the set of non-zero integer triplets comprises [+2 −1 −1], [−2 +1 +1], [+3 −2 −1] and [−3 +2 +1].   
     
     
         6 . The method of  claim 4 , wherein:
 the multiple managed accounts comprise at least four accounts; and   the at least one additional allocation further comprises, for each member of a set of non-zero integer quadruplets, a perturbation of the starting allocation for each unique quadruplet of managed accounts amongst the multiple managed accounts that is based at least in part on adding to allocated integer values of the starting allocation associated with all four members of the unique quadruplet, an integer value associated with a corresponding non-zero integer value of the member of the set of non-zero integer quadruplets.   
     
     
         7 . The method of  claim 6 , wherein:
 the set of non-zero integer quadruplets comprises [+1 −1 +1 −1];   
     
     
         8 . The method of  claim 7 , wherein:
 the set of non-zero integer pairs comprises [+1 −1], [+2 −2], and [+3 −3]; and   the set of non-zero integer triplets comprises [+2 −1 −1], [−2 +1 +1], [+3 −2 −1] and [−3 +2 +1].   
     
     
         9 . The method of  claim 8 , wherein:
 the set of non-zero integer pairs, the set of non-zero integer triplets and the set of non-zero integer quadruplets each comprise no further members.   
     
     
         10 . The method of  claim 2 , wherein:
 the generating of the at least one additional allocation is further based on a determination of whether the perturbation contains a negative allocation when the filled order made at the time t- 1  is to buy contracts or a positive allocation when the filled order made at the time t- 1  is to sell contracts, and, if so, an adjustment is made to the perturbation that ensures that the at least one additional allocation does not contain a negative allocation when the filled order made at the time t- 1  is to buy contracts or a positive allocation when the filled order made at the time t- 1  is to sell contracts.   
     
     
         11 . The method of  claim 10 , wherein:
 the adjustment comprises changing the negative allocation to zero and iteratively subtracting one from an allocation of an account with a highest allocation until a sum of allocations across all of the multiple managed accounts equals a quantity of the filled order made at the time t- 1 .   
     
     
         12 . The method of  claim 10 , wherein:
 the adjustment comprises changing the positive allocation to zero and iteratively adding one to an allocation of an account with a lowest allocation until a sum of allocations across all of the multiple managed accounts equals a quantity of the filled order made at the time t- 1 .   
     
     
         13 . The method of  claim 1 , wherein:
 the metric is based on closeness of the starting allocation and the at least one additional allocation to a desired division of profit and loss according to the allocation factors of each of the multiple managed accounts; and   the closest-fitting allocation is guaranteed to be preferable or equivalent to any possible allocation of the filled order made at a time t- 1  according to the metric.   
     
     
         14 . The method of  claim 13 , wherein:
 the metric is minimization of Q.   
     
     
         15 . The method of  claim 14 , wherein:
 the metric applies a preference, in the event that allocations have equal Q values, to pick an allocation that has a smallest var(NPt) amongst the allocations having equal Q values.   
     
     
         16 . The method of  claim 1 , wherein:
 The at least one additional allocation comprises Θ(N̂4) additional allocations.   
     
     
         17 . The method of  claim 1 , wherein:
 generating the starting allocation comprises the steps of:   rounding to the nearest integer, for each of the multiple managed accounts, a product of the managed account's allocation factor and a portfolio net position at time t- 1 ;   determining whether the sum of absolute values of the rounded products equals the absolute value of the portfolio net position at time t- 1 ; and   if the sum of absolute values of the rounded products does not equal the absolute value of the portfolio net position at time  1 - 1 , performing an adjustment to the rounded products such that the sum of absolute values of the rounded products equals the absolute value of the portfolio net position at time t- 1 .   
     
     
         18 . The method of  claim 17 , wherein:
 the adjustment comprises iteratively performing, until the sum of the absolute values of the rounded products equals the absolute value of the portfolio net position at time t- 1 , the steps of:   determining a particular managed account whose associated rounded product has a maximum absolute value;   determining whether the sum of the absolute values of the rounded products is greater than the absolute value of the portfolio net position at time t- 1 ;   if so, incrementing or decrementing the associated rounded product of the particular managed account such that its absolute value is decreased by one; and   otherwise, incrementing or decrementing the associated rounded product of the particular managed account such that its absolute value is increased by one.   
     
     
         19 . The method of  claim 18 , wherein:
 the starting allocation, for each of the multiple managed accounts, equals the difference between an absolute value of an associated rounded product of that account multiplied by a sign of the portfolio net position at time t- 1  and that account's net position at time t- 2 .   
     
     
         20 . A computer-implemented method for providing an allocation of a filled order made at a time t- 1 , comprising:
 receiving, in an allocation processing apparatus, at least a price of a filled order made at a time t;   generating, in the allocation processing apparatus, a starting allocation across multiple managed accounts based at least in part on allocation factors of each of the multiple managed accounts;   generating, in the allocation processing apparatus, at least one additional allocation based at least in part on the starting allocation;   determining, in the allocation processing apparatus, a closest-fitting allocation according to a metric from amongst the starting allocation and the at least one additional allocation, the metric being based at least in part on the price of the filled order made at the time t and on a price of the filled order made at the time t- 1 ; and   outputting, using an output part of the allocation processing apparatus, the closest-fitting allocation.