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Explain the limitations of a hedging strategy based on duration.

FRM® Part I · Financial Markets and Products · Interest Rate Futures · FRM1.FM.19.i

The idea

A duration-based hedge works well only under restrictive assumptions. It assumes small, parallel shifts in yields. If short and long yields move by different amounts, the portfolio and the futures respond differently and a residual loss remains. Duration is a linear approximation, so for large moves differences in convexity leave a gap. The futures' duration is that of the cheapest-to-deliver bond, so when the cheapest bond changes the hedge ratio becomes stale. Further, the portfolio's yield may not move one-for-one with the futures' yield. A corporate bond portfolio hedged with Treasury futures, for instance, carries credit spread risk. Durations also drift over time, so the hedge must be rebalanced. The exam answer is that the hedge protects against small parallel moves in the relevant yield curve, and is weaker otherwise.

A practice question

From the question bank, with the reason each wrong option is wrong.

A duration-based hedge with Treasury bond futures is most reliable when yield curve movements are:

  1. large and parallelWhy not: Large moves expose the hedge to convexity, which duration ignores.
  2. small and parallel - correct
  3. small and steepeningWhy not: Non-parallel moves leave the portfolio and futures exposed to different parts of the curve.
  4. large and non-parallelWhy not: Both conditions of the duration approximation fail: size and shape.

Duration measures sensitivity to small, parallel shifts. Large or non-parallel moves produce hedging errors.

A harder one

A manager holds a portfolio of 5-year notes hedged with short T-bond futures, sized on duration. Short-term yields rise by 30 bp while long-term yields rise by only 10 bp. What is the likely outcome?

  1. The portfolio loses more than the futures gain, leaving a net loss. - correct
  2. The hedge works perfectly because both yields rose.Why not: A perfect hedge needs parallel shifts; the portfolio and futures are sensitive to different parts of the curve.
  3. The futures lose more than the portfolio, leaving a net gain.Why not: The portfolio is more exposed to the larger, short-end move.
  4. The portfolio gains because the curve flattened.Why not: A rise in short yields reduces the value of the notes.

The hedge assumes parallel shifts. The notes feel the larger 30 bp move, the futures the smaller 10 bp move, so the futures gain is too small to offset the loss.

The hardest tier

A USD 100 million portfolio with duration 5.0 is hedged with futures sized to offset a parallel yield shift. In practice the portfolio's yields rise by 40 bp while the yield on the futures' underlying bond rises by 25 bp. Using duration approximations, the net result is closest to:

  1. zero, as the durations are matchedWhy not: Assumes the hedge works whatever the yield changes; matching durations only works if yield changes are equal.
  2. a gain of USD 750,000Why not: Wrong sign: the portfolio's loss exceeds the futures' gain.
  3. a loss of USD 750,000 - correct
  4. a loss of USD 2,000,000Why not: Ignores the gain on the futures altogether; the hedge still offsets the 25 bp part.

Portfolio loss = 100m x 5.0 x 0.0040 = 2,000,000. Futures gain = 100m x 5.0 x 0.0025 = 1,250,000. Net = 750,000 loss, because the yield changes were not equal.

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