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FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models

A bank hedges a bond portfolio using a Gauss+ model estimated from historical yield curve changes. Principal component analysis of the model's factor loadings shows that the first three factors explain nearly all curve variance. What should the risk manager conclude about hedging with key-rate exposures?

The manager should hedge exposure to several factors, typically level, slope and curvature, because a hedge on only the first factor leaves slope and curvature risk unhedged. When three factors explain nearly all curve variation, matching those exposures leaves small residual risk.

  1. AHedging only the first factor is sufficient because other factors are always negligible
  2. BHedging against several factors, such as level, slope and curvature, reduces residual risk that a one-factor hedge would leaveCorrect
  3. CHedging is impossible once more than one factor is used
  4. DOnly the factor with the fastest mean reversion needs hedging

Explanation

If three factors explain nearly all variation, a hedge neutralizing exposure to those three leaves little residual risk. A first-factor-only hedge leaves slope and curvature risk, which can be material for non-parallel moves. Multifactor hedging is feasible using several hedge instruments.

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