9. This number is obtained by simply multiplying the net exposure by the factor volatility. The sign of the move depends on the interpretation of the factor. In the case of the yield-curve movements, we know that R = –KRD × ΔKR, where KRD is the duration associated with the KR point. In our example – (–0.44) × 32.2 bp = +14.2 bp.

10. This reversal is clearly related to the fact that the 10-year point on the curve is usually highly correlated to the 5-, 20-, and 30-year ones. In our case, our short position on the 10-year point is more than compensated by the positive exposure to the other points in the curve. Netting out, the positive exposure effect (long duration) dominates when all changes are taken in a correlated fashion.

11. The marginal contribution is the derivative of the TEV with respect to the loading of each factor, so its interpretation holds only for small moves. Therefore, a more realistic reading may be that if we reduce the exposure to the 30-year by 0.1 years, the TEV would be reduced by around 1.3 bp.