Attributing Bank NII Changes to Shift, Twist, and Butterfly Rate Shocks
Summary
The document outlines a framework for stressing a bank’s net interest income (NII) with three yield curve factors: shift for level, twist for slope, and butterfly for curvature. It proposes estimating the factors, shocking them, constructing a stressed curve, and recalculating NII. Principal component analysis of historical rate correlations is suggested as one possible way to estimate the factors, while the answer cautions that regulatory expectations may differ by jurisdiction.
The key difficulty is attributing the total NII change to individual factors. With one up or down stress for each factor, combinations create interaction scenarios; simple marginal attribution works only if factor shocks do not interact in the portfolio response. For more complex portfolios, a clean decomposition may not be possible or meaningful. If the factors are modeled as random variables, the answer suggests carrying the attribution logic into a regression setting. The discussion offers no universal industry standard and frames attribution as dependent on model behavior and stress design.
Key ideas
- Shift, twist, and butterfly shocks represent yield curve level, slope, and curvature changes.
- PCA on historical rate correlations is one possible method for deriving the factors.
- NII attribution requires considering combined shocks as well as individual factor shocks.
- Marginal changes can be added only when the portfolio response has no interactions between stresses.
- For complex portfolios, attribution may be impossible or may lack a useful interpretation.
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Full text
# Attributing the change in NII to Shift, Twist and Butterfly # Attributing the change in NII to Shift, Twist and Butterfly The movement of the zero rate curves can be decomposed into a shift movement (the level of interest rates) and a twist movement (the slope of the curve) and butterfly (the curvature of the curve). If we want to stress the net interest income (NII) of a bank by shocking these three factors, how do we attribute the change in NII of each of these factors? So far, I have identified following steps. Please correct me if I am going wrong or missing something somewhere: - Find the Shift, Twist and Butterfly (STB) - Which one is industry practice to arrive at the shift, twist and butterfly factors from the current term structure- PCA or factor model? - Shock S,T,B - Apply the required shock to the Eigen vectors of the three factors - Find the new yield curve - Add the new Eigen vectors weighted by their Eigen values to arrive at the new yield curve. - Recalculate NII based on the new yield curve - The thing that is not clear to me is how do I attribute the change in NII to the shocks given to shift, twist and butterfly. Thanks in advance. ## Answer by g g (score 3, accepted) https://quant.stackexchange.com/a/10248 Your steps 1. to 3. sound reasonable. I am not sure about industry practice (what industry?) I always do step 1. using PCA on historical correlations. If you plan to do a regulatory exercise better check with your regulator what he prefers. Most interesting to me is step 4. which - I think - is in general impossible to do. This can be achieved only in very special cases. From what you describe, you model single discrete stress scenarios such as +/-100bps flat, which is good since it is a very special case. Assuming one stress each for S,T,B you have in total 7 = 2^3-1 different scenarios (3 single stresses of S,T,B , 3 where you have two stresses S&T, S&B and T&B and one where you stress S&T&B). If your portfolio reacts in a "simple" fashion (technically: The stresses do not interact) then Delta(S&T) = Delta(S) + Delta(T) and so on and you can decompose in the obvious way by reporting the marginal changes, i.e. the differences from each single stress. If your portfolio is more complicated, you are in big trouble and you should seriously consider whether such an attribution makes sense at all. If your stress factors are random variables you need to apply the thinking above in a regression context.
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