- CFA Exams
- CFA Exam: Level I 2021
- Study Session 16. Derivatives
- Reading 49. Basics of Derivative Pricing and Valuation
- Subject 4. Forward Rate Agreements

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**CFA Practice Question**

A firm sells a 5 x 8 FRA, with a NP of $300MM, and a contract rate of 5.8%. On the contract expiry date, the 3 month spot LIBOR is 5.1%. The firm will receive ______.

Correct Answer: $518,390

It is calculated as: [(300,000,000 x (0.058 - 0.051) x (90/360)] / [1 + 0.051 / (360/90)]

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**User Contributed Comments**
20

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

george2006 |
the numerator= 300M * (0.007)* 90/360 = 0.525 M discounted to time t1 = 5months, it should be somewhat smaller than 0.525 M. The answer is wrong here. Or the diff might be attributed to rounding errors? |

katybo |
The firm is a seller! |

ganone |
the answer is correct. you discount at 5.1% the underlying rate. The number of day is 90 days as it is on 360 day basis. |

Bibhu |
The general formula for this Notional Principal x [(Floating - Spot) Days/360]/ [1+ Floating x days/360] Floating : 5.8% Spot 5.1% |

omer123 |
The firm takes the short position so it can borrow at the low underlying interest rate 5.1% and receive the contract rate 5.8%, it would have been reversed if the firm was the buyer. |

aakash1108 |
...i.e. it can borrow at 5.1% and lend at 5.8% and earn the spread in between i.e. 0.7%. However, the firm will earn this spread at the end of 3 months. Thus, it discounts that spread i.e. [$300MM X 0.7% X (90/360)] = $525,000 to todays value. Therefore, with discounting: PV=525,000/(1.051)^(90/360) = $518,511 (*) (*) Rounding error minimized. |

asthildur |
If you look in the notes the denominator should be 1+ (0.051*90/360) and you will get the right result of $518,390. It's because you are discounting for the time period of 90 days with the annual interest rate of 5.1% which is changed to a 90 days rate. |

viannie |
The firm sells. Using the standard formula gives negative but because the firm is the seller, the one in short position in a decreasing interest rate situation gains. Therefore the firm gets paid $518,390 (round off) |

TheHTrader |
What does 5 x 8 FRA mean in this case? |

TheHTrader |
Never mind. 5=effective 5 months from now, 8=terminated 8 months from now, based on 3-month LIBOR |

tschorsch |
The discounting in the denominator is simple multiplication, i.e. 1+rate*(n/360) because the quoted rates are the appropriate period (i.e. 3 month LIBOR in this case) and do not need to be compounded. I.e. the rate quoted was correct for the period. If you compound, you will discount by the annual yield. |

jpducros |
Rates decrease from 5.8 to 5.1 => the seller/short wins. |

ZoltanPongracz |
the formula says underlying-FRA rate and .058 was used for underlying and then the underlying figure in the denominator is .051? why is that?? |

rocyang |
[(300,000,000 x (0.058 - 0.051) x (90/360)] / [1 + 0.051x (90/360)]. |

johntan1979 |
Good luck, you all. It's not as hard as it seems. More practice will do the trick. |

jimmyvo |
You are wrong, Bibhu and rocyang. Your equations. The denominator equation should be "360/days" NOT "days/360" |

jimmyvo |
tschorsch is also wrong. equation in denominator. |

mtsimone |
The short is Float – FIxed, the Long FRA is Fixed – Float. The short made out since: Notional(Fixed – Float)(days/360/[1+(Float*days/360)] = 5118,390. The convention in IR FRAs is simple interest, noty compounded interest. |

mtsimone |
Boneheaded error: I meant the Short is Fixed – Float in the first sentence, but the calculation has it right. Rocyang has it right. |

ashish100 |
Jimmy vo multiplied by 90/360 same as divide by 360/90 |