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

A 90-day Treasury bill is quoted with a discount rate of 4.00% on an Actual/360 basis. What is its bond-equivalent yield on an Actual/365 basis, approximately?

The bond-equivalent yield is about 4.10%. The bill's price is 99.00, so the 90-day return is 1/99, or 1.0101%. Annualizing with 365/90 gives roughly 4.10%, which is higher than the 4.00% discount rate because it is based on price, not face value.

  1. A4.00%
  2. B4.04%
  3. C4.06%
  4. D4.10%Correct

Explanation

Price = 100 x (1 - 0.04 x 90/360) = 99.00. The holding period return is 1/99 = 1.0101%. Annualizing on 365 days: 1.0101% x 365/90 = 4.096%, about 4.10%. The 4.04% figure is the 360-day money market yield, and 4.06% merely rescales the discount rate to 365 days without using the price.

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