- CFA Exams
- CFA Level I Exam
- Topic 7. Derivatives
- Learning Module 33. Pricing and Valuation of Forward Commitments
- Subject 6. Currency Forward and Futures Contracts

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**CFA Practice Question**

Suppose the domestic currency is the Japanese yen and the foreign currency is the U.S. dollar. Thirty days ago, Takashi, an investor in Tokyo, entered into a forward contract to buy US$ in 180 days. The forward contract price was Y107.42 with a notional principal of $3million. Today's exchange rate is Y102.13 per dollar. The annualized U.S. interest rate is 3.25%, and the annualized Japanese interest rate is 0.75%. With continuous compounding, what is the value of this contract (ignore sign)?

A. 5.42 million yen

B. 3.79 million yen

C. 18.88 million yen

**Explanation:**With continuously compounding:

*r*= ln(1.0075) = 0.7472%, and

*r(f)*= ln(1.0325) = 3.1983%

V30(0, 180) = (102.13 e

^{-0.031983 (150/365)}) - 107.42 e

^{-0.007472 (150/365)}= -6.29424

The value is -6.29424 x 3,000,000 = -18,882,707.

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**User Contributed Comments**
5

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

Adkins08 |
Am I missing something? Question says T=180/365 but the answer gives 150/365 |

dhingy |
He entered into the contract 30 days ago. Now there's only 150 days left on the contract. |

za20884 |
i did not understand why they are discounting 150 day price at US rate and then discounting forward price at yen rate...any one can explain.. |

broadex |
Easy peas: Forget continuous compounding for now(if continous compounding is treaky-this is the tip: continuos compounding approximate simple interest) Calculate future rate for exchange rate= (1.0075)^150/365 divided by (1.0325)^150/365 Multiply by current rate you get -6.313 and multiply by 3nm. Your answer is pretty close to compounded figure of 18.88 Apply the same concept to compounding you realise the the above formular is correct. |

hks101 |
just to elaborate on broadex's comment; this is what I did. Step 1: calculate Forward rate at day 30 using IRP Spot on day 30 = 102.13 F/102.13 = (1.0075^150/365) / (1.0325^150/365) F(day 30) = 101.106 Step 2: compare original forward's value vs current forward's value. 101.106 - 107.42 = -6.31 then it's just -6.31 * 3M |