P&L Attribution

Before describing attribution it is necessary to define the P&L types that appear as reference values and outputs.

MTD and YTD P&L are computed as:

\[\text{MTD P\&L} = PV_\text{now} - \text{Monthly Adjustments} - \text{Brokerage Adjustments}\] \[\text{YTD P\&L} = PV_\text{now} - \text{YTD Adjustments} - \text{Brokerage Adjustments}\]

The fundamental decomposition of daily P&L is:

\[\underbrace{D_1 M_1 T_1 - D_0 M_0 T_0}_{\text{Total P\&L}} = \underbrace{(D_1 M_1 T_1 - D_0 M_1 T_1)}_{\text{Trade Activity}} + \underbrace{(D_0 M_1 T_0 - D_0 M_0 T_0)}_{\text{Market Data}} + \underbrace{(D_0 M_1 T_1 - D_0 M_1 T_0)}_{\text{Time}}\]

Where:

• \(D_0\), \(D_1\): Trade population at Day 0 and Day 1
• \(M_0\), \(M_1\): Market data (spots, vols, rates) at Day 0 and Day 1
• \(T_0\), \(T_1\): Valuation dates at Day 0 and Day 1

The three components are mutually exclusive and exhaustive:

                                  ┌─ NEW
             ┌─ TRADE ACTIVITY ──┤─ AMEND / RESTRUCTURE
             │                   │─ CANCEL
             │                   │─ EXPIRED
             │                   │─ EXERCISED
             │                   │─ FIXINGS
             │                   │─ FUNDING ROLLS
TOTAL P&L ───┤                   │─ CONTRA REVENUE (Brokerage)
             │                   └─ CVA / RESERVES
             │
             ├─ MARKET DATA ─────┬─ FX SPOT
             │                   ├─ ATM VOL
             │                   ├─ RISK REVERSAL
             │                   ├─ STRANGLE
             │                   ├─ IR PROJECTION
             │                   ├─ IR DISCOUNT
             │                   └─ CROSS EFFECTS
             │
             └─ TIME (THETA)

A fourth category, Unexplained P&L, captures any residual. A well-implemented attribution should drive this to zero. Its presence indicates missing or misclassified attribution components.

The full formula including cross effects:

\[\text{Market Movements} = (\text{ATM} + \text{RR} + \text{STR} + \text{FX Spot} + \text{IR Discount} + \text{IR Projection}) + \text{Cross Effects}\] \[\text{Cross Effects} = \text{Bump All} - (\text{ATM} + \text{RR} + \text{STR} + \text{FX Spot} + \text{IR Discount} + \text{IR Projection})\]

Bump and Reset is the standard methodology for market data attribution. Each component is computed by bumping only that component from Day 0 to Day 1 while holding all others at Day 0 levels. The baseline is always Day 0.

Bump and Reset ensures all components add to total market movements (up to cross effects). It does not capture interaction terms between components; those appear in the Cross Effects bucket.

In Bump and Run, bumps are applied cumulatively in a defined order. The \(\Delta P\&L\) at each step is measured against the previous step, not against Day 0.

Bump and Run is complementary to Bump and Reset. It is better for detecting cross-effects (a large step 2 increment implies a strong ATM×Spot interaction). Bump and Reset is better for attributing absolute magnitudes to individual components.

Trade Activity explains the P&L contribution from changes to the trade population between Day 0 and Day 1. It uses Day 1 market data for all sub-components so that trade changes and market data changes do not interact.

\[\text{Trade Activity} = D_1 M_1 T_1 - D_0 M_1 T_1\]

Sub-buckets (additive):

\[\text{Trade Activity} = \text{New} + \text{Amended} + \text{Cancelled} + \text{Expired} + \text{Exercised} + \text{Fixings} + \text{Funding Rolls} + \text{Contra Revenue} + \text{CVA} + \text{Reserves}\]

The market data component captures the P&L from changes in market rates and prices between Day 0 and Day 1, holding the trade population and date constant.

\[\text{Market Data} = D_0 M_1 T_0 - D_0 M_0 T_0\]

Sub-buckets (Bump and Reset methodology):

The time component captures the P&L resulting purely from the passage of one business day, holding market data and trade population constant.

Under Bump and Reset (Theta First): \[\Theta = NPV(D_0, M_0, T_1) - NPV(D_0, M_0, T_0)\]

Under Bump and Run (Theta Last): \[\Theta = NPV(D_0, M_1, T_1) - NPV(D_0, M_1, T_0)\]

Determining the correct deal population for an explain requires care:

• From a Market Data perspective, only Day 0 trades matter.
• From a Trade Activity perspective, all trade changes must be captured: trades that only exist on Day 0 (matured, cancelled, expired), trades that only exist on Day 1 (new), and trades that exist on both days.
• Settled positions must be included. A forward that matured on Day 1 appears as a cash Nostro position in the ledger on Day 1; if the cash position is omitted from trade activity, a spurious unexplained P&L appears.

1. Trade cut: Snapshot of the trade population.
2. Market data cut: Snapshot of market data (spots, forwards, vols, rates).
3. AM Flash / PM Flash: Preliminary P&L. Finance generates an exception report comparing traders' expected P&L against the Finance P&L. Traders sign off exceptions.
4. Rate sign-off: Finance formally approves the market data cut.
5. Full P&L execution: The official Flash is produced with all exceptions and trader comments attached and published.
6. Diff analysis: Comparison of AM Flash vs EOD Flash; exceptions reviewed. Final sign-off can only be completed once the total P&L difference is below a configured threshold.
7. EOD start: Full Actual P&L begins.

P&L is held in its denominated currency (the denomination of each cash flow). At EOD, all amounts are consolidated into the functional currency of the business unit (e.g. GBP for a London-based unit).

Any P&L from spot conversion of non-domestic P&L is recorded as a P&L Adjustment (FX Adjustment). Traders are expected to hedge this FX exposure.

The aggregation hierarchy:

Trade → Structure → Book → Sub-Portfolio → Portfolio → Branch → Firm

• Currency — hub note for natural, functional, and aggregation currency.
• Business Unit — the organisational hierarchy this aggregation rolls up through.