CFA Practice Question

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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.

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
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