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FRM Part I · FRM Exam Part I · Swaps

A fund receives fixed 3% annually on a $200 million swap with two years remaining, and the floating rate has just reset. Since inception, rates have risen. The current annually compounded zero rates are 4.0% for 1 year and 4.5% for 2 years. What is the swap's value to the fund, rounded to the nearest $0.01 million?

The swap is worth about -$5.59 million to the receive-fixed fund. Discounting the 3% coupons and principal at 4.0% and 4.5% zero rates gives a fixed bond of 97.20 per 100. The floating leg is par, so the value is -2.795 per 100, or -$5.59 million on $200 million.

  1. A-$5.59 millionCorrect
  2. B+$5.59 million
  3. C-$2.80 million
  4. D-$6.00 million

Explanation

DF1=1/1.04=0.961538 and DF2=1/1.045^2=0.915730. Fixed bond per 100 = 3(0.961538)+103(0.915730)=2.8846+94.3202=97.2048. The floating leg is worth par, so the receive-fixed value is 97.2048-100=-2.7952 per 100, or -5.59 million on $200 million. -$6.00 million comes from summing the undiscounted shortfall 200(0.015)(2) and ignoring discounting. -$2.80 million fails to scale to the notional.

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