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Define key rate 01 (KR01) and outline what key rate shift analysis involves.

FRM® Part I · Valuation and Risk Models · Modeling Non-Parallel Term Structure Shifts and Hedging · FRM1.VR.13.b

The idea

A key rate 01 (KR01) measures the change in a portfolio's value when one chosen key rate falls by one basis point and the other key rates stay put. Rates between key rates move by interpolation, so a shift at the 5-year point fades linearly to zero at the neighbouring key maturities, giving a tent shaped shift. Key rate shift analysis means picking a set of key maturities, shifting each one in turn, repricing the portfolio and recording the value change at each. With the usual convention a long bond has positive KR01s, because it gains when rates fall, and a negative KR01 marks a net short exposure at that maturity. The shifts are built to add up to a parallel shift, so the KR01s sum to the ordinary DV01. Individual KR01s depend on the key rates and interpolation chosen, but their sum does not.

Formulas

Value change from key rate moves

ΔV = Σ KR01ₖ × fₖ

KR01ₖ
the gain from a one basis point fall in key rate k
fₖ
the fall in key rate k in basis points, negative for a rise

Each key rate's own move is applied to its own KR01. Treating a rise as a fall flips that term's sign.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which definition of a key rate 01 (KR01) is correct?

  1. The change in portfolio value for a one basis point decrease in all rates at once, a parallel shift.Why not: This is the ordinary DV01 for a parallel shift; a KR01 shifts only one key rate.
  2. The change in value for a one basis point decrease in one key rate, with other key rates held constant. - correct
  3. The change in portfolio value for a one percentage point decrease in one key rate.Why not: Uses a 100 basis point shift instead of one basis point.
  4. The change in portfolio value for a one basis point rise in the volatility of one key rate.Why not: Confuses rate sensitivity with a volatility sensitivity (vega).

KR01 isolates the exposure to one point on the curve: one key rate falls by 1bp (with interpolation to neighbouring key rates) and the others do not move. The KR01s together add up to the DV01.

A harder one

A risk system uses key rates at 2, 5, 10 and 30 years. Each key rate shift is a tent: one basis point at its own maturity, falling linearly to zero at the adjacent key maturities. Which key rates give a non-zero KR01 for a position consisting only of a 7-year zero coupon bond?

  1. Only the 5-year and 10-year key rates, between which the 7-year maturity falls. - correct
  2. Only the 5-year key rate, the nearest one to the 7-year maturity.Why not: Assigns all the risk to the nearest key rate; the shift at the 10-year key rate also moves the 7-year rate.
  3. All four key rates, since a bond is exposed to the whole curve.Why not: Ignores the tent shaped shifts: the 2-year and 30-year shifts are zero at 7 years.
  4. Only the 10-year key rate, the first key maturity at or beyond the bond's maturity.Why not: Ignores that the 5-year key rate shift also reaches the 7-year point.

A 7-year rate is moved only by the tents of the 5-year and 10-year key rates, because the 2-year tent ends at 5 years and the 30-year tent starts at 10 years. The risk is split between them by distance.

The hardest tier

Two desks hold the same portfolio. Desk X measures KR01s with key rates at 2, 5 and 10 years; Desk Y uses key rates at 1, 3, 7 and 15 years, both with linear interpolation and with shifts that together form a parallel shift. Which statement is correct?

  1. The KR01s are identical, because they are model free sensitivities of the same portfolio.Why not: KR01s depend on the choice of key rates and the interpolation rule, so the profiles differ.
  2. The sums differ by the portfolio's convexity, which depends on the number of key rates used.Why not: The sum equals the DV01 for any such set of key rates, since the shifts add up to a parallel shift.
  3. Individual KR01s differ between the desks, but each desk's KR01s sum to the portfolio DV01. - correct
  4. Desk X's KR01s sum to zero for a hedged portfolio while Desk Y's do not.Why not: Confuses a zero sum with a hedge; the sum is DV01 regardless of desk, and both change only if the portfolio changes.

The two key rate sets spread the same exposure differently along the curve, so individual KR01s differ. Because each set of tent shifts adds up to a parallel one basis point shift, each desk's KR01s still sum to the DV01.

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