Post trade allocation how much are bunched orders costing your performance Ali Hirsaand Massoud Heidari

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Post trade allocation: how much are bunched orders

costing your performance?

Ali Hirsa?and Massoud Heidari??

Summary. Individual trade orders are often bunched into a block order for processing eﬃciency,

where in post execution, they are allocated into individual accounts. Since Regulators have not

mandated any speciﬁc post trade allocation practice or methodology, entities try to rigorously

follow internal policies and procedures to meet the minimum Regulatory ask of being procedurally

fair and equitable. However, as many have found over the years, there is no simple solution for post

trade allocation between accounts that results in a uniform distribution of returns. Furthermore,

in many instances, the divergences between returns do not dissipate with more transactions, and

tend to increase in some cases. This paper is the ﬁrst systematic treatment of trade allocation risk.

We shed light on the reasons for return divergence among accounts, and we present a solution that

supports uniform allocation of return irrespective of number of accounts and trade sizes.

Key words: trade allocation; bunched orders; block trades, separately managed accounts; un-

der/over allocation; optimal rounding; machine learning; fair and equitable; direct indexing; broker;

investment manager; advisor; CFTC;NFA.

1 Overview

Often times, investors have a choice to invest in a co-mingled vehicle (Fund), or to invest in

a separately managed account3(SMA) that mimics the performance of the underlying Fund.

All investors in the Fund, regardless of their size and the time of their investment, receive

the same future gross returns, without any tracking errors. The disadvantage is that the

investors generally have to adhere to the terms and conditions of the Fund, as a limited

partner.

To retain control of their assets, transparency, and to be able to construct personalized

portfolios4, more and more institutional clients have opted to invest in an SMA, while the

?Industrial Engineering and Operations Research, Columbia University, ali.hirsa@columbia.edu

Chief Scientiﬁc Oﬃcer, Ask2.ai, ali.hirsa@ask2.ai

?? Massoud Heidari contributed to this paper in his personal capacity. The information, views,

and opinions expressed herein are solely his own and do not necessarily represent the views of

Point72, L.P. or its aﬃliates. Point72, L.P. and its aﬃliates are not responsible for, and did not

verify for accuracy, any of the information contained herein.

3SMAs are portfolios of individual securities managed by an asset management ﬁrm (see [6], [4] for

a more detailed description of SMAs).

4SMAs can be built speciﬁcally for each investor based on their personal investment goals

and expectations, including the exclusion of any speciﬁed securities. Many asset man-

agement ﬁrms oﬀer customized portfolios through SMAs. Here is a statement on Black-

rock website, www.blackrock.com/us/ﬁnancial-professionals/investment-strategies/managed-

accounts, regarding their SMAs: “Blackrock Separately Managed Accounts (SMAs) provide enhanced

capabilities to meet your clients’ ﬁnancial goals.”

arXiv:2210.15499v1 [q-fin.TR] 13 Oct 2022

2 Ali Hirsa & Massoud Heidari

manager directs investments through a sub-management contract. In most cases, SMAs and

the Fund have the same investment objective, and the SMAs seek to replicate the returns of

the Fund.

In a Fund, all trades are tracked and accounted for at the Fund level, and gross returns

of these trades are distributed among all clients in an identical manner. In contrast, when

dealing with SMAs all trades need to be allocated between SMAs in a proportional manner

ﬁrst, and the returns are calculated for each individual SMA separately. Have in mind this is

also the case for block trades [2], as the Fund manager still needs to allocate those block

trades into all accounts (in this case to the Fund also).

In principle, this is a straightforward problem: allocate trades proportional to relative

account size, and then calculate returns. However, in practice, since trades hardly take place

at a single price, or at the same time, and because one cannot divide securities into random

fractions, allocations need to resort to rounding, which, as we will show, is the source of

divergence in returns among accounts (and between SMAs and the Fund). For block trades,

we can imagine situations where the manager pre-designs trading sizes to avoid fractional

allocation and rounding but as the number of accounts increases with diﬀerent account

sizes would make it very challenging. The rounding forces a choice between accounts to be

over-allocated and accounts to be under-allocated, which leads to uneven distribution of

returns. Furthermore, repeated application of a mechanical decision rule for the over/under

allocation of trades (bias) will often-times lead to larger and larger divergence of returns

among accounts and between the SMAs and the Fund. To prevent large tracking errors,

and to provide all accounts with equitable and even distribution of returns, the industry

has adopted various approaches for allocation of trades, generally processed, at the end

of each trading day. This is often a manual and time-consuming process - the art of trade

allocation - and does procedurally tries to ensure fair and equitable treatment of all accounts.

The general premise is that the fair and equitable rationale is met via rigorously applied

procedures that do not exhibit outward biases towards any of the accounts. However, as we

will note in the paper, using any of the prevalent methodologies results in return divergence

between accounts and the premise that the accounts balance out over time maybe ﬂawed.

Thus our objective in this paper is to shed light on the problem of trade being allocated

across multiple accounts or other vehicles. In speciﬁc, despite the mathematical rigor of the

underlying process, we will use some simple examples to show the source of the problem,

which leads to the divergence of returns, and present a solution to remedy the problem.

2NFA/CFTC Compliance Rule

Although there are no general methodologies for trade allocation, the NFA Compliance Rule

2-10/CFTC Regulation 1.35, the allocation of bunched orders for multiple accounts [5], sets

out three principles that should guide the allocation procedures: (1) fairness, (2) objectivity,

and (3) timeliness. In the same document, they provide examples of procedures that satisfy

these objectives. Here is an excerpt from the NFA/CFTC Compliance Rule:

“NFA Compliance Rule 2-10 adopts by reference CFTC Regulation 1.35, Among other things, this

regulation requires that bunched orders be allocated in a fair and equitable manner so that no account

or group of accounts consistently receives favorable or unfavorable treatment over time. The rule

further provides that Eligible Account Managers bear the responsibility for the fair and equitable

allocation of bunched orders.” CFTC Regulation 1.35(b)(5)

Post trade allocation: how much are bunched orders costing your performance? 3

Core Principles and Responsibilities5(source: NFA):

•The ﬁrst, which arises in all such orders, involves the question of how the total number

of contracts should be allocated to the various accounts included in the bunched order

•The second issue involves the allocation of split or partial ﬁlls

•The same set of core principles govern the procedures to be used in handling both of

these issues. Any procedure for the general allocation of trades or the allocation of split

and partial ﬁlls must be:

– designed to meet the overriding regulatory objective that allocations are non-

preferential and are fair and equitable over time, such that no account or group

of accounts receive consistently favorable or unfavorable treatment

– suﬃciently objective and speciﬁc to permit independent veriﬁcation of the fairness of

the allocations over time and that the allocation methodology was followed for any

particular bunched order; and

– timely, in that the Eligible Account Manager must provide the allocation information

to FCMs that execute or clear the trade as soon as practicable after the order is ﬁlled

and, in any event, suﬃciently before the end of the trading day to ensure that clearing

records identify the ultimate customer for each trade

In short, NFA &CFTC expect eligible account managers as ﬁduciaries to implement fair and

equitable trade allocation methods.

2.1 NFA cited examples

Here are NFA cited examples of Allocation Methodologies (source: NFA)

•Example #1 - Rotation of Accounts, Rotation of accounts on a regular cycle, usually

daily or weekly, which receive the most favorable ﬁlls.

•Example #2 - Random Allocation, Computer generated random order of accounts and

allocate the best price to the ﬁrst account on the list and the worst to the last.

•Example #3 - Highest Prices to the Highest Account (HPHA) Numbers, Some ﬁrms rank

accounts in order of their account numbers and then allocate the highest ﬁll prices to

the accounts with the highest account numbers.

•Example #4 - Average Price (APS), Calculate the average price for each bunched order

and then assign the average price to each allocated contract. In the alternative, the

program will allocate the actual ﬁll prices among the accounts included in the order to

approximate, as closely as possible, the average ﬁll price.

•Other - As observed to be fair and equitable by the Eligible Account Manager. Example,

Rounding (simple and/or adjusted/alterative)

5https://www.nfa.futures.org/rulebook/rules.aspx?RuleID=9029&Section=9

4 Ali Hirsa & Massoud Heidari

3 Sample Portfolio for Illustrative Purposes

Throughout this paper, we are going to use the sample portfolio presented in Table 1 to

illustrate the issues of allocating trades (buy of sell) into multiple accounts that would lead

to uneven distribution of returns and address shortcomings and weaknesses of the cited

examples for trade allocation. What follows applies to bunched orders and block trades for

any traded instrument including single name equity, futures, derivatives, etc in any market.

Table 1 represents trading of a single asset over two days in a fund. At the end of 1st day,

fund is short 4 with unrealized P&L of $380, and at the end of 2nd day, fund net position is

zero (ﬂat) with realized P&L of $1000.

price qty(B/S) net position bucket P&L CumP&L

day ptqtnptp&ltcp&lt

1st day

$100 8 8 - -

$130 2 10 8×(130−100)=240 $240

$150 -4 6 10×(150−130)=200 $440

$140 -10 -4 6×(140−150)=-60 $380

2nd day

$110 -4 -8 -4×(110−140)=120 $500

$115 -4 -12 -8×(115−110)=-40 $460

$110 -4 -16 -12×(110−115)=120 $580

$80 16 0 -16×(80−110)=480 $1000

Table 1. Sample Portfolio

For the fund in the sample portfolio, for simplicity, we assume it is comprised of two

clients co-mingled in the fund as shown in Figure 1 with allocation factors6of 90% & 10%

respectively.

Fig. 1. Two accounts co-mingled in a fund

6allocation factor for account ifor i= 1,...,N is calculated by αi=aumi

i=1

aumi

where AUMiis

asset under management (AUM) for account i

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Posttradeallocation:howmucharebunchedorderscostingyourperformance?AliHirsa?andMassoudHeidari??Summary.Individualtradeordersareoftenbunchedintoablockorderforprocessingeciency,whereinpostexecution,theyareallocatedintoindividualaccounts.SinceRegulatorshavenotmandatedanyspecicposttradeallocationpracti...

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