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CFA Level I · CFA Level I Exam · Yield and Yield Spread Measures for Floating-Rate Instruments

A two-year FRN pays quarterly at 3-month reference rate + 0.60% (quoted margin). The required margin is 0.85%. Par value is 100. On a reset date, the price is closest to (assume a flat discount rate equal to the reference rate + required margin and that the reference rate is 4.00% annualized, with the coupon set at the start of each period, simplified to a level 4.60% coupon):

The price is about 99.5. The coupon of 4.60% is below the required 4.85% rate, so the FRN trades slightly below par. Discounting eight quarterly coupons of 1.15 and the par value at 1.2125% per quarter gives roughly 99.52.

  1. A98.2Correct
  2. B99.5
  3. C100.0

Explanation

Quarterly coupon = 4.60%/4 = 1.15 per 100. Discount rate per quarter = 4.85%/4 = 1.2125%. PV of an 8-period annuity: 1.15 x [1-(1.012125)^-8]/0.012125. (1.012125)^8 = 1.10125, so its inverse is 0.90806, giving an annuity factor of 7.5800 and PV coupons 8.717. PV of par = 90.806. Total = 99.52, which is closest to 99.5, so the key must be 99.5.

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