Gide used a six-month forward currency contract to convert yen to euro - So why is the Euro Area 6 month annualized rate the answer?
Just can’t connect the dots…
i trip on this question everytime i see it.
my problem is i always use exponential to calculate the rate.
Without the question hints you “30 day convention”, we just use exponents right?
30 / 360 day convention - is only used for LIBOR contracts.
and here it would be [1 + r * N/360].
for anything else - EAR, BEY, calculation of Forwards from Spots - which are not based on LIBOR - use the (1+r) ^(X/12) – for months of N/365 for Days.
This convention is also consistent with the “conversion of Interest Rate Puts/Calls for the EAR calculation” at that time use the 365/X in the exponent.
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he is expecting 50 Mill $ delivery in 6 months.
Current Spot = 1.1930 USD/EUR - Euro amount = 50 / 1.1930 = 41.911 Mill Eur.
Now if Euro depreciated - he will lose on the amount of USD he gets back. He buys a 50M USD Forward contract . he is thus guaranteed the forward rate of 1.2030 – which translates to the 2.13% 6 month rate.
1.1930 * (1 + .0377*.5) / (1+0.0213*0.5) = 1.2026 – 1.2030 approx.
now we start from how hedging with forward works…
You have an asset dominated in yen (receive within 6months). To hedge the position (yen depreciation), you borrow yen (and pay japan risk free rate charge), convert to eur at spot rate (you locked the position at spot rate), loan the eur received (6months) to get EU risk free rate return.
If the forward is fairly priced, the forward rate will incorporate the spot rate and difference between the 2 risk free rate as mentioned above.
ie forward (exchange) rate (sell yen) = spot rate (Y/E)* (1 + Ry)/(1+Re)
Ry - risk free of yen / Re …eur
In this case, the forward is fairly priced so you will receive the amount of eur = spot amount + risk free rate (EU) - the risk free rate is the answer.
I gave it to you above;
1.1930 * (1 + .0377*.5) / (1+0.0213*0.5) = 1.2026 – 1.2030 approx.
It was a USD/EUR - so using IRP - US rate on top, EUR rate on the denominator.
发表于 2013-4-22 06:04
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