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FRM Part II · FRM Exam Part II · Monetary and Fiscal Policy: Safeguarding Stability and Trust

A central bank buys 10-year bonds with a duration of 8 in a large asset purchase programme. Empirical estimates suggest the programme reduces the 10-year term premium by 40 basis points. An investor holds a 10-year bond portfolio of USD 50 million with duration 8 and no other changes in yields. Ignoring convexity, what is the approximate price gain from this term premium effect?

The approximate gain is USD 1.6 million. A 40 basis point yield fall on a portfolio with duration 8 gives 8 × 0.40% = 3.2% of value, and 3.2% of USD 50 million is USD 1.6 million? Correctly, 8 × 0.004 = 3.2%, which on 50 million is 1.6 million.

  1. AUSD 0.8 million
  2. BUSD 1.6 millionCorrect
  3. CUSD 3.2 million
  4. DUSD 16 million

Explanation

Price change ≈ duration × yield change × value = 8 × 0.004 × 50 million = 1.6 million. The 0.8 million option halves duration, and 3.2 million doubles the yield move. The 16 million option misplaces the decimal by a factor of 10 by using 4% instead of 0.40%.

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