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FRM Part I · FRM Exam Part I · Interest Rate Futures

A 90-day Treasury bill is quoted at a discount rate of 4.00% (actual/360 basis on face value). What is its annualized yield on an actual/365 basis, measured as return on the purchase price?

The yield is about 4.0965%. The bill's price is 99 per 100 of face value, so the 90-day return on price is 1/99 or 1.0101%, which scaled by 365/90 gives 4.0965%. The discount rate understates yield because it uses face value, not price, as the base.

  1. A3.9600%
  2. B4.0000%
  3. C4.0404%
  4. D4.0965%Correct

Explanation

Price = 100 − 4 × 90/360 = 99. Return over 90 days = 1/99 = 1.0101%. Annualized on actual/365: 1.0101% × 365/90 = 4.0965%. The 4.0404% option annualizes on 360 days, and 4.00% is just the discount rate, which uses face value as the base.

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