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

A risk manager compares hedging a bond portfolio using a one-factor Vasicek model versus a Gauss+ style multi-factor model. The portfolio is long 10-year bonds and short 2-year bonds, so it is exposed to curve steepening. Which conclusion is most appropriate?

The multi-factor model is more appropriate because it captures non-parallel moves like slope changes. A one-factor model makes all yields perfectly correlated and so understates the residual risk of a long 10-year, short 2-year position that is exposed to curve steepening.

  1. AA one-factor Vasicek hedge is adequate because all rates move perfectly in parallel in proportion to the short rate, so the portfolio has no model-implied exposure to curve steepening
  2. BThe multi-factor model captures non-parallel moves such as slope changes, so it can show residual risk that the one-factor model, which makes all yields perfectly correlated, would missCorrect
  3. CThe multi-factor model eliminates all interest rate risk by construction because it is calibrated to the current curve
  4. DThe one-factor model is superior because additional factors only add noise and never affect hedge effectiveness

Explanation

In a one-factor model all yields are driven by one shock and are perfectly correlated, so slope risk is understated. A multi-factor model includes a slope-like factor and reveals residual exposure of a long-short maturity position. Option A overlooks that Vasicek still yields differing sensitivities by maturity but not independent slope moves; C and D are false.

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