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FRM Part II · FRM Exam Part II · Credit Risk

A one-year zero-coupon bond from a firm trades at a yield of 6.0% (continuously compounded) while the risk-free rate is 4.0%. Assuming a constant recovery rate of 40% of face value paid at maturity and a constant hazard rate, what is the approximate risk-neutral hazard rate, using the exact relation exp(-yT)= exp(-rT)[ (1-q) + q*R ] with q the one-year default probability? (exp(-0.02)=0.9802)

The hazard rate is about 3.3% per year. The price ratio exp(-0.02)=0.9802 equals 1 minus 0.6q, so q is about 3.3%. Dividing the spread by loss given default of 60% is the key step; using the raw 2% spread ignores recovery.

  1. AAbout 3.3% per yearCorrect
  2. BAbout 2.0% per year
  3. CAbout 5.0% per year
  4. DAbout 1.2% per year

Explanation

Price ratio: exp(-0.06)/exp(-0.04)=exp(-0.02)=0.9802 = 1 - q(1-R) = 1 - 0.6q. So q = 0.0198/0.6 = 0.0330. Hazard = -ln(1-q) = about 3.36%, roughly 3.3%. The 2.0% answer ignores recovery (spread/1), and 5.0% wrongly multiplies by 0.4 instead of dividing.

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