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FRM Part I · FRM Exam Part I · Bond Yields and Return Calculations

A bond with face value 100 pays a 5% annual coupon semiannually. Its dirty (full) price is 102.40. The last coupon was paid 110 days ago, and the coupon period has 182 days (actual/actual). What is the clean (quoted) price, to two decimals?

The clean price is 100.89. Accrued interest is the semiannual coupon of 2.5 times 110/182, about 1.51. The clean price equals the dirty price less accrued interest, so 102.40 minus 1.51. Adding the accrual or using the annual coupon is wrong.

  1. A100.89Correct
  2. B103.91
  3. C99.38
  4. D101.65

Explanation

The semiannual coupon is 2.5. Accrued interest = 2.5 × 110/182 = 1.51. Clean price = dirty price − accrued interest = 102.40 − 1.51 = 100.89. Adding accrued interest gives 103.91. Using the full annual coupon of 5 gives accrued interest of 3.02 and a clean price of 99.38. Dividing by 365 days instead of 182 gives 101.65.

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