The allocation method defines how to assign trade prices to the various accounts when applying an allocation.
In this Article
Methods Supported by Theorem
Example of Results
Comparison Chart
FAQ
| ⚠️ | Trade Managers are solely responsible for running a fair and equitable allocation methodology. |
Software and tools are designed to meet a trade manager's needs, but the manager is at all times responsible for insuring fair and equitable allocations and meeting any compliance, regulatory or legal requirements.
Standard practices may or may not be suitable for a particular manager.
Methods Supported by Theorem
Theorem supports Low to High, High to Low, Best Fit, and Average (APS) methods when allocating trade prices to accounts or aliases.
When allocating fills that have multiple prices to two or more allocation accounts, the Price Method commands the allocation algorithm on how to assign prices to the various accounts.
High to Low (HTL) and Low To High (LTH) assign trade prices based on a sorting of all of the trade prices against the account numbers.- High to Low assigns the first account the highest price, and continues sorting through remaining accounts in alphabetical order assigning trade prices from lowest to highest price.
- Low to High performs the opposite to high to low; the first account receives the lowest trade price, continuing so that the last account receives the highest price.
All trades always follow the same sort (either high to low or low to high), including buys and sells.
Average (APS) assigns the volume weighted mathematical mean price to all accounts.
Theorem supports on exchange decimal APS. The mean is calculated to 10 decimal points.
Theorem does not support trade price rounded APS. This style of averaging determines the mean price and allocates to the nearest exchange price increment.
Best Fit (BF) determines combinations of fill prices to arrive as close as possible to the mean.
Theorem supports a linear and heuristic methodology for determining the combination of trades.
When the Use Incoming setting is turned on, the combination of fills will adjust to the mean of the ending position instead of the prices in the allocation.
Simple Example Using Two Accounts and Three Fills
Shares: Account A (60%) and Account B (40%)
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Fills: Bought 10 at aggregate average price of 94.25
| Time | Quantity | Trade Price |
| 9:00 AM | BUY 3 | 94.50 |
| 9:02 AM | BUY 6 | 94.00 |
| 9:30 AM | BUY 1 | 95.00 |
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Allocation Results
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Low to High Assign the lowest price to the first (sorted alphabetically) account, and so on. |
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| Allocated Acct | Allocated Qty | Allocated Price |
| A | 6 | 94.00 |
| B | 3 | 94.50 |
| B | 1 | 95.00 |
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High to Low Assign the highest price to the first (sorted alphabetically) account, and so on. |
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| Allocated Acct | Allocated Qty | Allocated Price |
| A | 1 | 95.00 |
| A | 3 | 94.50 |
| A | 2 | 94.00 |
| B | 4 | 94.00 |
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Best Fit Knowing that the average of all fills is 94.25, determine the combination of fills that gives each account this average. |
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| Allocated Acct | Allocated Qty | Allocated Price |
| A | 3 | 94.50 |
| A | 3 | 94.00 |
| B | 3 | 94.00 |
| B | 1 | 95.00 |
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Average Pricing Assign the weighted average of all fills to each account. |
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| Allocated Acct | Allocated Qty | Allocated Price |
| A | 3 | 94.25 |
| B | 3 | 94.25 |
- The allocated quantity is always the same: 6 to account A and 4 to account B. The quantity and price algorithms are independent of each other.
- All methods except APS use the filled trades so that the total quantities per fill price in the results are exactly the same:
- 6 @ 94.00, 3 @ 94.50, and 1 @ 95.00
- The APS price method always produces synthetic trades. Every account receives one and only one trade that does not have a fill price:
- Share X Quantity @ Volume Weighted Average Price
- All allocations must be the same side (buy vs sell). If buys and sells are allocated together, they will be allocated sequentially based on the earliest fill time; if the earliest fill time is a buy, then all buys will allocate before all sells.
Comparison Chart
Note: This comparison is based on opinion by Theorem's operational trade flow experts.
Trade managers, investors, and operators may have different requirements and parameters that dictate the suitability of various price allocation methods. This chart compares some common considerations based on the standard implementation of each price method
Frequently Asked Questions About Price Methods
What is the Best Price Method to Use?
Why Not Always Use APS?
Does Best Fit Guarantee the Best Combination?
What is the difference between Linear and Heuristic for Best Fit?
Can Multiple Trade Allocation Methods Be Used for the Same Accounts?
What Happens When Averaging Only One Price?
What is the Best Price Method to Use?
This depends on the individual needs of the trade manager and many other factors.
- Trading strategies that allocate only once per day (when allowed) generally favor APS allocations for compatible markets and brokers.
- Low to High and High to Low are generally considered "low tech" options but still may be suitable for many programs.
- Best Fit corrects deviations over time and particularly suitable for trading strategies that are increasing or decreasing positions in the same products daily.
Why Not Always Use APS?
- In exchange cleared derivatives, many markets do not allow synthetic trades to be created and thus APS is not allowed.
- Some executing and clearing brokers may not support APS allocations, or have different rules about when and how APS may be used.
- If a one time deviation occurs because of a partial fill, redemption, subscription, or other issue, APS will "bake in" the deviation and make it difficult to correct over time unless manual action is taken to correct the deviation in future allocations.
Does Best Fit Guarantee the Best Combination?
No.
Determining the perfect combination of trades is a complex combinatorial optimization problem that can not be solved by brute force or any known mathematical operation for all allocation problems. In some cases, it might be possible for simpler algorithms or even a trial and error process to produce better results for specific sets of trades, but Theorem's Best Fit algorithms have been optimized to create reproducible results in reasonable time periods that gravitate towards minimal price deviation over the long term.
What is the difference between Linear and Heuristic for Best Fit?
Linear and Heuristic are both types of solve algorithms Theorem uses to determine the best combination of trades to achieve the best outcome. The functional difference is the trade off between speed and optimal allocation results when performing allocations that have many price levels and the total fill quantities are greater than 1,000.
- Linear formulates the allocation task as a program whose objective is to minimize the maximum (or total) deviation in mean price across all accounts. It is computationally intensive but, given sufficient runtime, provides the optimal allocation.
- Heuristic delivers a near-optimal allocation in milliseconds. It uses an efficient approximation technique to balance mean prices across accounts (aliases).
Can Multiple Trade Allocation Methods Be Used for the Same Accounts?
Yes. Theorem supports using and applying different allocation instructions based on user preference or situation. It is up to the manager, not any allocation tool, to insure that compliance rules, regulations, and laws are followed to insure that all accounts receive fair allocations.
The most common reason to use multiple trade price methods is to use APS for markets where it is allowed and Best Fit on other markets.
What Happens When Averaging Only One Price?
Note: APS always creates synthetic average trades, even when there is only a single fill or multiple fills with the same price.
In many post trade workflows, the use of APS is built into the executing and clearing broker's processing systems-- the brokers may expect or require average prices in all circumstances. In order to maintain compatibility with these systems, Theorem will always create synthetic allocation trades when APS is used as the trade price method.