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FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage

A U.S. Treasury bond with a 4% coupon paid semiannually has face value 100. The last coupon was paid January 15 and the next is July 15 (181 days apart in a non-leap year). The bond is quoted at a clean price of 99.50 for settlement on April 15 (90 days after the last coupon). Using Actual/Actual, what is the dirty (invoice) price?

The dirty price is about 100.49. Accrued interest is the 2.00 semiannual coupon times 90/181, or 0.9945, and this is added to the 99.50 clean price to get the price the buyer actually pays.

  1. A98.51
  2. B99.50
  3. C100.49Correct
  4. D101.49

Explanation

The semiannual coupon is 2.00. Accrued interest = 2.00 x 90/181 = 0.9945. Dirty price = clean price + accrued = 99.50 + 0.9945 = 100.4945, about 100.49. Subtracting accrued gives 98.51, and using the annual coupon of 4 for the fraction gives 101.49; both are wrong.

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