How does desk-level capital allocation work under the FRTB, and why does it matter?

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AcadiFi · Accepted Answer

Under the FRTB, the trading desk is the fundamental unit of capital computation. This is a major departure from pre-FRTB rules where banks could compute market risk capital at a more aggregated level.

## Desk Definition

A trading desk is a group of traders or accounts that:
- Operate under a clearly defined **business strategy**
- Have a designated **head trader** with P&L responsibility
- Are subject to specific **risk limits**
- Have **defined instruments** they can trade

Examples: Rates desk, Credit trading desk, FX options desk, Equity exotics desk.

## IMA Eligibility Per Desk

Each desk must independently qualify for the Internal Models Approach (IMA) by passing:

1. **Backtesting** — VaR at 97.5% and 99% confidence levels
2. **P&L attribution** — RTPL vs HPL comparison (Spearman + KS tests)

If a desk fails either test, it falls back to the Standardized Approach (SA) for that desk. This is the "desk-level opt-in" feature of FRTB.

## Capital Components Under IMA

For each IMA-eligible desk, capital consists of:

**IMA Capital = max(ES_{t-1}, m_c x ES_avg) + DRC + SES**

Where:
- ES = expected shortfall at 97.5% with liquidity-adjusted horizons
- m_c = multiplier (floor of 1.5, increased by backtesting failures)
- DRC = default risk charge
- SES = stressed expected shortfall (calibrated to a stress period)

## Cross-Desk Aggregation

Here is the critical point about diversification:

**There is LIMITED diversification benefit across desks under FRTB.**

The aggregated ES across desks is:

**ES_aggregate = sqrt[SUM(ES_i^2) + SUM_{i != j} rho_{ij} x ES_i x ES_j]**

But FRTB imposes a **constrained correlation** structure that limits diversification benefits compared to a fully correlated or uncorrelated assumption.

Additionally, the **SA capital floor** acts as a backstop — even if IMA capital is lower, the bank must hold at least a percentage of what the SA would require.

## Numerical Example

Winthrope Bank has three trading desks:

| Desk | Approach | ES Capital | DRC | Total |
|---|---|---|---|---|
| Rates | IMA | $45M | $8M | $53M |
| Credit | SA (failed P&L test) | $62M | — | $62M |
| Equities | IMA | $38M | $12M | $50M |

IMA desks aggregate with partial diversification:
ES_IMA = sqrt(45^2 + 38^2 + 2 x 0.5 x 45 x 38) = sqrt(2025 + 1444 + 1710) = sqrt(5179) = $72M

Add DRC: $72M + $8M + $12M = $92M (IMA component)
Add SA desk: $92M + $62M = **$154M total market risk capital**

Notice that Credit desk's failure to pass P&L attribution forces it onto the SA, which is typically more conservative.

For more on FRTB capital rules, check our FRM Part II question bank.

How does desk-level capital allocation work under the FRTB, and why does it matter?

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