Scenario:
Suppose you are working with a financial system that processes millions of transactions every day. To detect anomalies, understand customer behavior, or ensure compliance, analysts often need to examine both the relationships between transactions (combinations) and the order in which transactions occur (permutations).
Statistical Concepts:
In probability theory, permutations and combinations are methods of counting the possible outcomes.
N = Total number of elements in the sample space (here, number of transactions).
r = Number of elements selected at a time (e.g., pairs of transactions).
r = Number of elements selected at a time (e.g., pairs of transactions).
Combinations: Choosing r elements from N, where order does not matter.
Example: Choosing r=2 transactions from N=5 results in possible pairs. In combinations, (A,B) is considered the same as (B,A), so duplicates are ignored.
Permutations: Choosing r elements from N, where order matters.
Example: Choosing r=2 transactions from N=5 results in possible sequences. In permutations, (A,B) is different from (B,A), so both orders are considered.
In this article, we will use a simple scenario with sample data to show how permutations and combinations, and running balances can be applied in SQL to uncover useful insights.
Sample Table: tbl_Sample_Transactions
CREATE TABLE tbl_Sample_Transactions (
TransactionID INT,
AccountID VARCHAR(10),
TransactionDate DATE,
Amount DECIMAL(10,2),
Type VARCHAR(20)
);
INSERT INTO tbl_Sample_Transactions VALUES
(1, 'A001', '2024-01-01', 500, 'Deposit'),
(2, 'A001', '2024-01-02', -200, 'Withdrawal'),
(3, 'A001', '2024-01-03', -100, 'Transfer'),
(4, 'A002', '2024-01-01', 1000, 'Deposit'),
(5, 'A002', '2024-01-04', -300, 'Withdrawal'),
(6, 'A002', '2024-01-05', -200, 'Transfer'),
(7, 'A003', '2024-01-02', 700, 'Deposit'),
(8, 'A003', '2024-01-03', -400, 'Withdrawal'),
(9, 'A003', '2024-01-06', -100, 'Transfer'),
(10,'A003', '2024-01-07', 300, 'Deposit');
SELECT * FROM tbl_Sample_Transactions
1) Combinations: Transaction Pairs (Order Doesn’t Matter)
Combinations are useful when we want to study pairs of transactions that occur together, regardless of order. For financial analysis, this helps detect linked activities such as deposit–withdrawal pairs or withdrawal–transfer pairs.
Here, in this query we consider combinations of r=2 transactions from N. We avoid duplicates by considering only one side (Txn1, Txn2) and ignoring the flipside.
-- Combinations (N, r=2)
SELECT
t_left.AccountID,
t_left.TransactionID AS Txn1,
t_left.Type AS Txn1Type,
t_right.TransactionID AS Txn2,
t_right.Type AS Txn2Type
FROM (
SELECT *,
ROW_NUMBER() OVER (PARTITION BY AccountID ORDER BY TransactionID) AS rn
FROM tbl_Sample_Transactions
) t_left
INNER JOIN (
SELECT *,
ROW_NUMBER() OVER (PARTITION BY AccountID ORDER BY TransactionID) AS rn
FROM tbl_Sample_Transactions
) t_right
ON t_left.AccountID = t_right.AccountID AND t_left.rn < t_right.rn
WHERE t_left.AccountID = 'A003' -- Filter the Account A003 for Analysis
ORDER BY t_left.AccountID, Txn1, Txn2;
Result:
Financial Insights from Combinations:
- A Deposit paired with a Withdrawal (Txn7 and Txn8) highlights immediate cash-out after funding. Fraud detection teams often flag this as potential cash recycling, where funds are deposited and withdrawn quickly to disguise their origin.
- A Withdrawal paired with a Transfer (Txn8 and Txn9) suggests funds are being moved across accounts after withdrawal. This is a classic layering technique in money laundering, where money is shuffled to obscure its trail.
- A Deposit paired with another Deposit (Txn7 and Txn10) indicates repeated funding activity. Analysts use this to study liquidity behavior, customer saving patterns, and potential inflows from multiple sources.
2) Permutations: Transaction Sequences (Order Matters)
Permutations are useful when we want to study the order of transactions. In financial terms, this helps us analyze transaction flows — the exact sequence in which deposits, withdrawals, and transfers occur.
Here, in this query we consider the permutations of r=2 transactions from N, considering both directions (Txn1 → Txn2 and Txn2 → Txn1).
-- Permutations (N, r=2)
SELECT
t_left.AccountID,
t_left.TransactionID AS Txn1,
t_left.Type AS Txn1Type,
t_right.TransactionID AS Txn2,
t_right.Type AS Txn2Type
FROM (
SELECT *,
ROW_NUMBER() OVER (PARTITION BY AccountID ORDER BY TransactionID) AS rn
FROM tbl_Sample_Transactions
) t_left
INNER JOIN (
SELECT *,
ROW_NUMBER() OVER (PARTITION BY AccountID ORDER BY TransactionID) AS rn
FROM tbl_Sample_Transactions
) t_right
ON t_left.AccountID = t_right.AccountID AND t_left.rn <> t_right.rn
WHERE t_left.AccountID = 'A003' -- Filter the Account A003 for Analysis
ORDER BY t_left.AccountID, Txn1, Txn2;
Result:
Financial Insights from Permutations:
- A Deposit followed by a Withdrawal (Txn7 → Txn8) shows immediate cash-out after deposit. This sequence is a strong indicator of suspicious activity, often linked to fraud or money laundering.
- A Withdrawal followed by a Deposit (Txn8 → Txn7) reflects replenishment after overdraft. This sequence provides insights into customer liquidity management and spending behavior.
- A Transfer followed by a Deposit (Txn9 → Txn10) highlights funds being moved and then topped up. Analysts interpret this as either legitimate fund management or potential layering in money laundering schemes.
Running balances are a way to track how account funds evolve over time. This is essentially a permutation analysis extended across the entire sequence of transactions.
Instead of viewing each transaction separately, we calculate the cumulative impact of all the transactions in sequence.
This approach provides a continuous picture of how deposits, withdrawals, and transfers affect the account balance at every step in time.
-- Running Balance calculation for all Accounts
SELECT
AccountID,
TransactionID,
TransactionDate,
Amount,
SUM(Amount) OVER ( PARTITION BY AccountID ORDER BY TransactionDate
ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW
) AS Running_Balance
FROM tbl_Sample_Transactions
ORDER BY AccountID, TransactionDate;
Result:
Financial Insights from Running Balance:- The account starts with a deposit of 500, then decreases to 300 after a withdrawal, and further reduces to 200 after a transfer.
- Running balances make it easy to spot accounts that are trending downward and may risk overdraft.
- Compliance teams can monitor whether balances stay above required minimums.
- Customer behavior can be analyzed more easily: steady deposits indicate saving habits, while frequent withdrawals or transfers highlight spending or fund movement patterns.
- Risk managers can use these balances to forecast liquidity needs and detect unusual depletion trends across accounts.
Examples in this article are for illustration only. Real-world financial systems involve added complexities such as multi-currency, regulatory rules, and fraud detection. Always validate queries and logic against your organization’s compliance and data governance requirements.
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Thanks, TAMATAM ; Business Intelligence & Analytics Professional
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Thanks, TAMATAM ; Business Intelligence & Analytics Professional
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