- CFA Exams
- CFA Level I Exam
- Study Session 14. Derivatives
- Reading 37. Pricing and Valuation of Forward Commitments
- Subject 5. Fixed-Income Forward and Futures Contracts

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**CFA Practice Question**

An investor bought a bond (par value: $1,000) when it was originally issued with a maturity of 30 years. The bond pays semi-annual coupons of $60. The first coupon occurs 181 days after issue, the second 365 days, the third 547 days, the fourth 730 days, and so. 120 days later he entered into a forward contract that would allow him to sell the bond in 612 days (from the contract initiation date) at a then no-arbitrage price of $875.44. Now, 365 days since he entered into the forward contract, the risk-free rate is 7% and the new price of the bond is $1,034.75. What's the value of the forward contract for the investor?

A. $81.84

B. $74.26

C. $93.79

**Explanation:**Now it is the 485th day of the bond's life (120 + 365). There are two coupons to go, one occurring in 547 - 485 = 62 days, and the other in 730 - 485 = 245 days. The present value of the coupons is now: $60/1.07

^{62/365}+ $60/1.07

^{245/365}= $116.65.

There are 612 - 365 = 247 days now remaining until the contract's expiration. The value of the forward contract is then: $1,034.75 - $116.65 - $875.44/1.07

^{247/365}= $81.84.

This positive value represents a loss to the investor, as his position is "short."

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**User Contributed Comments**
4

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

danlan2 |
Use stat with following data: X1=1034.75, Y1=1 X2=-60, Y2=1.07^(-62/365) X3=-60, Y3=1.07^(-245/365) X4=-875.44, Y4=1.07^(-247/365) We will get sigma(XY)=81.84 |

wollogo |
Danlan - its 120 days since purchasing the bond that he enters into the futures contract. Ree2 - The coupon on day 730 is before he sells the bond which is on day 732 (120 days after purchasing the bond + 612 days after purchasing the forward) |

Rotigga |
Orig Length of contract = 612 days Now at t=365 or 120+356=485 days since investor bought the bond Remaining days in contract = 612-365 = 247 days Contract ends from POV of orig = 120+612 = Day 732 PV(Coupons) = 60/(1.07)^[(547-485)/365] + 60/(1.07)^[(730-485)/365] = 116.65 Value = 1,034.75 - 116.65 - 875.44/(1.07)^[(612-365)/365] = 81.84 |

janis36 |
managed to calculate this in 89 seconds. |