FRTB SA vs IMA: the standardised approach (SA) is a regulatory formula applied to your sensitivities. The internal models approach (IMA) uses the bank's own expected-shortfall model, but only for desks that pass strict tests. IMA is not automatically cheaper, and the tests often decide the answer.
1. The standardised approach (SA)
SA capital has three parts:
- Sensitivities-based method (SBM): delta, vega and curvature charges per risk class (general interest rate risk, FX, credit spread, equity, commodity).
- Default risk charge (DRC): jump-to-default risk on credit and equity positions.
- Residual risk add-on (RRAO): 1% of notional for exotic payoffs and 0.1% for other residual risks.
Within a bucket, weighted sensitivities are aggregated with a correlation matrix, then buckets are combined with a cross-bucket correlation:
$$K_b = \sqrt{\max\Big(0,\ \sum_k WS_k^2 + \sum_k\sum_{l\ne k}\rho_{kl}WS_kWS_l\Big)}, \quad K = \sqrt{\sum_b K_b^2 + \sum_b\sum_{c\ne b}\gamma_{bc}S_bS_c}$$
The whole SBM is run under three correlation scenarios: high (correlations multiplied by 1.25, capped at 1), medium and low (the larger of 2ρ − 1 and 0.75ρ). The bank reports the scenario that gives the highest capital. Because netting depends on correlation, SA is sensitive to how a book is split across desks: charging desk by desk loses offsets that a bank-wide view would keep.
2. The internal models approach (IMA)
- Expected shortfall: 97.5% ES with liquidity horizons of 10, 20, 40, 60 and 120 days, calibrated to the worst 12-month stress window.
- Combining: IMCC mixes the all-risk-class ES with the sum of the stand-alone ES numbers, IMCC = ρ · IMCC(C) + (1 − ρ) · Σ IMCC(Ci), with ρ = 0.5.
- Non-modellable risk factors: a stressed-scenario charge (SES), aggregated with a correlation of 0.6 between charges.
- DRC on credit exposures, modelled or standardised.
- Final charge: the larger of yesterday's IMCC + SES and the multiplier (at least 1.5) times the 60-day average IMCC, plus the 60-day average SES.
3. The gates a desk must pass
- Risk factor eligibility (RFET): a factor needs enough real price observations to be modellable, for example 24 observations in a year with at least 4 in each 90-day period, or 100 observations. Otherwise it is non-modellable and attracts the heavier SES charge.
- P&L attribution (PLA): the risk model's P&L must track front-office P&L. Green needs Spearman correlation above 0.80 and Kolmogorov-Smirnov distance below 0.09. Red is Spearman below 0.70 or KS above 0.12.
- Desk backtesting: no more than 12 exceptions at 99% or 30 at 97.5% over 250 days.
Fail any gate and the desk reverts to SA. A desk in the PLA amber zone stays on IMA with a capital surcharge.
4. A worked example on a five-desk book
The Desk2Quant lab runs a constructed five-desk book on real rates and FX history through both approaches. Rates, G10 FX, an options desk and a corporate-bond desk are modelled cleanly. The emerging-market FX desk uses a proxied risk model: the INR and CNY risk factors are proxied rather than observed, and the model is cruder than the front-office pricing.
| Scenario | Capital |
|---|---|
| All desks on SA (SBM high-correlation scenario binds) | $75.5m |
| IMA with the proxied EM FX desk | $79.3m |
| IMA after fixing the proxy | $75.6m |
The EM FX desk fails PLA (Spearman about 0.16, KS about 0.37), so it falls back to SA. Mixing IMA and SA for different desks costs capital: IMA with the bad proxy comes out 5% above all-SA. Fixing the data is worth about $3.7m. Even then, on this book, IMA only roughly breaks even with SA.
5. When does IMA win?
- Large, diversified, liquid books where ES shows real offsets that SA correlations do not capture.
- Clean, observable risk factors, so few non-modellable factors.
- Risk models close to front-office pricing, so PLA passes comfortably.
- Stable desks with few exceptions.
IMA loses when books are concentrated, illiquid, option-heavy with simplified risk models, or full of proxied factors.
6. Common mistakes
- Assuming IMA is always cheaper. The eligibility tests, SES and multiplier can erase the benefit.
- Judging SA on a single correlation scenario. Always compute all three.
- Ignoring that desk-by-desk SA loses cross-desk offsets.
- Treating PLA as a model-fit exercise. It tests whether the risk model captures what the front office actually earns and loses.
7. Interview answers
Is IMA cheaper than SA? "Not automatically. It is a privilege that desks earn by passing RFET, PLA and backtesting. Non-modellable factors, the multiplier and the SA fallback can make IMA cost the same or more, as one proxied EM desk did in my project."
What does PLA test? "Whether risk-theoretical P&L tracks hypothetical P&L, using Spearman correlation and the KS statistic. Green is above 0.80 and below 0.09; red is below 0.70 or above 0.12."
Why three correlation scenarios in SA? "Netting benefits depend on correlation, and correlations rise in stress, so the rule takes the worst of high, medium and low."