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FRM Part II · FRM Exam Part II · Regression Hedging and Principal Component Analysis

A trader hedges a bond with a swap using a regression of bond yield changes on swap rate changes. Which statement about the regression hedge's residual risk is correct?

Residual risk depends on the unexplained portion of variance, 1 minus R-squared. Even the variance-minimizing beta hedge leaves this risk, so a low R-squared means a large unhedged component, regardless of whether the slope is statistically significant.

  1. AIt is eliminated if the hedge ratio is set equal to the beta
  2. BIt depends on the fraction of variance not explained by the regression, so a low R-squared implies large residual riskCorrect
  3. CIt is zero whenever the regression slope is statistically significant
  4. DIt increases as the R-squared of the regression rises

Explanation

Residual (basis) variance equals (1 − R²) times the variance of the hedged position's yield-driven P&L, so low R-squared leaves large unhedged risk. Beta minimizes variance but does not eliminate it. Significance of the slope does not imply a tight fit.

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