- CFA Exams
- CFA Level I Exam
- Study Session 14. Derivatives
- Reading 37. Pricing and Valuation of Forward Commitments
- Subject 8. Interest Rate Swap Contracts

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**CFA Practice Question**

Consider a one-year interest rate swap with semi-annual payments. The annualized fixed rate is 7.84%. The term structure of LIBOR spot rates is given as follows:

On day 0: L

_{0}(180) = 7.2%, and L_{0}(360) = 8.0%.On day 90: L

_{90}(90) = 7.1%, and L_{90}(270) = 7.4%.Assume a notional principal of $1 million. What is the market value of the swap from the perspective of the party paying the floating rate on day 90?

A. $5,100

B. $4,200

C. -$4,200

**Explanation:**Calculate the new present value factors for 90 and 270 days:

PV

_{90}(180) = 1 / (1 + 0.071 x 90/360) = 0.9826.

PV

_{90}(360) = 1 / (1 + 0.074 x 270/360) = 0.9474.

The present value of the remaining fixed payments of 0.0392 (0.0784/2), including the hypothetical notional principal, is 0.0392 x (0.9826 + 0.9474) + 1 x 0.9474 = 1.0231.

As the market value of the remaining payments on day 90, including the hypothetical final notional principal, is 1.0, we discount 1.00 + 0.036 (which is 0.072/2) = 1.036 back 90 days to obtain 1.036 x 0.9826 = 1.0180.

Therefore, the value of the swap is (1.0231 - 1.018) x 1,000,000 = $5,100.

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**User Contributed Comments**
6

User |
Comment |
---|---|

danlan2 |
(1+0.072/2)/(1+0.071/4)=1.018 is the 90 day forward rate. Note 7.2% and 7.1% are the spot rates. |

tim2 |
Have to say I still don't get this stuff. I wonder why the 7.2% is in the calculation but the 8% is not..? |

NIKKIZ |
Tim2 - I don't get it either. But the easiest way to calculate the second part is to get the first original rate and divide it by it's corresponding latest rate as follows: [1+ 0.072(180/360)]/[1+ 0.071(90/360)] = 1.01793. I find this easier to understand... |

dakota6789 |
Tim2, the 7.2 is in the calculation because that is the 6 month rate |

somk |
I believe if i go to sleep, wake up, drink coffee or whatever brain toxic substance, i will understand this stuff. and i believe i can fly |

wuyiheng |
pig can fly |