What shift magnitude should I use for key rate and factor risk measurement?

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AcadiFi · Accepted Answer

The shift magnitude choice is a trade-off between linearity and numerical precision. Too small and floating-point noise swamps the signal. Too large and you pick up convexity effects that violate the locally-linear assumption underlying 'first-derivative' risk measures.

Standard practice by use case:

1. Daily risk reporting (PV01, KR01, DV01) → 1 bp. Standard convention. Banks and asset managers universally use 1 bp for headline risk numbers because the result is directly interpretable as 'dollars per basis point.'

2. Scenario analysis / stress testing → 50 bp, 100 bp, 200 bp. Captures non-linear behavior (convexity, option gamma) that the linear measure ignores.

3. Regulatory capital (FRTB, SA-CCR) → prescribed shifts by regulators, often 15-100 bp depending on asset class and tenor bucket.

4. Practitioner hedging → match to expected daily move. If the typical daily 10y move is 6 bp, use 5 bp shift for hedge calibration.

Precision considerations:

- At 1 bp, a $100M 10-year portfolio shows a KR01 around $80-100K. The difference between model and real price using 1 bp versus 0.5 bp shifts should be under 0.5% of KR01 (if not, there's model instability).

- Below 0.1 bp, numerical noise from the pricing model becomes a concern — finite-difference methods lose precision.

- Above 100 bp, convexity effects can change KR01 by 10-20% for long-duration portfolios. The 'shocked KR01' at +200 bp may differ substantially from the 'base KR01.'

Example — Ashwright Global Bonds runs three reports:
- Daily: 1 bp KR01 (tight control)
- Weekly: 100 bp stress (captures convexity)
- Regulatory: FRTB-prescribed shifts

A common beginner mistake is scaling up a 1 bp number to estimate a 200 bp move. For a long-duration bond with gamma, this understates the shocked value. Always recompute at the actual shock size for scenarios.

The rule of thumb: use 1 bp for daily gamma-neutral reporting, use the actual expected shock magnitude for scenarios.

What shift magnitude should I use for key rate and factor risk measurement?

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