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FRM Part I · FRM Exam Part I · Measuring Credit Risk

A five-year zero-coupon corporate bond yields 5.80% (continuous) versus a 4.30% risk-free rate. An analyst estimates a recovery rate of 40%. Another analyst argues the recovery rate is actually 20%, with the same spreads. Holding the spread constant, how does the revised recovery assumption change the implied hazard rate, using spread = hazard x (1 - R)?

The implied hazard rate falls from 2.50% to about 1.88%. With a 1.50% spread, hazard equals spread divided by loss given default: 1.50%/0.60 versus 1.50%/0.80. A lower recovery means a larger loss per default, so a smaller default intensity explains the same spread.

  1. AHazard rises from 2.50% to 1.88%
  2. BHazard falls from 2.50% to 1.88%Correct
  3. CHazard falls from 2.50% to 1.50%
  4. DHazard rises from 2.50% to 1.88% because loss given default is larger

Explanation

Spread = 1.50%. With R=40%: hazard = 1.50/0.60 = 2.50%. With R=20%: hazard = 1.50/0.80 = 1.875%, about 1.88%. Lower recovery means larger loss per default, so fewer defaults are needed to explain the same spread; hazard falls. The 'rises' options misstate the direction.

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