- CFA Exams
- CFA Level I Exam
- Study Session 14. Derivatives
- Reading 37. Pricing and Valuation of Forward Commitments
- Subject 4. Interest Rate Forward and Futures Contracts

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**CFA Practice Question**

Ten days ago a portfolio manager went short an FRA which would expire in 30 days and was based on 210-day LIBOR. The no-arbitrage rate he received was 6.16%. Now the current LIBOR term structure is: 20 day - 5.45%; 170 day - 5.75%; 200 day - 5.95%. What's the market value of the FRA for a $10 million notional principal?

A. -$8352.55

B. $9278.31

C. $7894.52

**Explanation:**Here the notation would be: g = 10, h - g = 20, h + m - g = 200.

L

_{g}(h - g) = L

_{10}(20) = 5.45%, and L

_{g}(h + m - g) = L

_{10}(200) = 5.95%

V

_{g}(0, h, m) = V

_{10}(0, 30, 180) = 1/(1 + 0.0545 x 20/360) - (1 + 0.0616 x 180/360)/(1 + 0.0595 x 200/360) = -0.00084

Thus, for a notional principal of $10 million, the value would be 10,000,000 x (-0.00084) = -$8352.55.

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**User Contributed Comments**
12

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

mbuechs2 |
Does anybody understand this question? 210-day LIBOR is not correct, is it? |

danlan2 |
1/annulized 20 day rate-annulized FRA rate/annualized 200 day rate |

mghebrey |
For FRA always 1+(int*d/360) so (1 + 0.0545 x 20/360) |

rameencool |
Should be discounted to today at the 200 day rate. |

rseiser |
Isn't the manager "long" the FRA when he locks in the 6.16% rate? That's why the contract is worth less than 0. |

mazen1967 |
because it short it must be profit not loss |

rhardin |
I don't get this... I thought h+m-g = 230, with h=30, g=10, and m=210 from the question info. Where is the 200 days coming from? |

arniejunior |
actually it should be - $8350.47 (loss for the long FRA) |

mishis |
rhardin: I think it's (h+m) that is 210. look at the timeline example in notes It was 10 days ago so it should be 210 - 10. |

mohzin |
is the question supposed to be "long" instead of "short"? |

janis36 |
I thought that "based on 210-day LIBOR" means that m=210. The answer implies m=180 and h+m=201. Confused. |

taz2017 |
This question should be reworded. It should say long the FRA. And second it should say 180 day libor instead of 210. There is another question where the same terminology is used but in correct way to explain 2x8 FRA (i.e. 60 day expiry, 180 day loan ; correctly in the other question. They can't both be right!) |