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…

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.

It is the Euro area risk free rate - if you sold a Forward contract and the hedge went as per expectations

that old

r hedged = r unhedged + (id - if)

hedged will be equal to the rate at the foreign country.

If you look at what was done in the Currency Risk Mgmt chapter - with the hedge if the original principal does not change - you end up earning the risk free rate at the location you made the hedge contract for. Here the Euro is the target…

as Gide has hedged the currency risk exposure, she will be earning Yen risk free rate + interest rate differential

Exactly, so how come the Euro IR becomes the answer?

cpk123 - mind explaining it to me like a baby, would really appreciate it.

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.

rough (quick) estimation :

Yen risk free rate + interest rate differential = 0.066 + (2.13 - 0.066) = 2.13

Isn’t this the Euro contract we are talking about?

almost there cpk, how does 1.2030 translate to 2.13% in 6 months?

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.

Thanks truongdv. now it makes since, since we are assuming that IRS holds and all that hedging is perfect and all, so if everything worked as expected we get Euro RFR.

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.