# Hedged return computation issue

Hey guys:

Here is the problem to solve:  we hold a portfolio of European stocks, currently worth EUR 300.000. The spot exchange rate is 1.10 USD/EUR.
We hedge the currency risk with a 3-month futures contract on the EUR at 1,15 USD/EUR.
A week later the portfolio is worth EUR 320.000, the spot exchange rate is 1,20 USD/EUR and the futures exchange rate is USD 1,23 USD/EUR.

How would you compute the RFX (currency return) & RFC (asset return, this one is easy) & total return?
My reflex was to take into account only the two spots price & the initial future contract into account. However, it seems that the 1,23 USD/EUR futures one week later matters.

Many thanks,

Alex

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Current Portfolio Value in USD = 300*1.10 = 330

Future Portfolio Value in USD=320*1.20 = 384

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You Sold 1 futures contract for 300 Notional at 1.15. at the time of expiry (hedge lifting) it is worth 1.23 . I am saying fx contract should be sold to hedge the risk of the FX appreciating? (could be wrong here).

so -300 * (1.15 - 1.23) = +24

RFC=384-330/330 = 54/330

RFX= 24/300*1.15

CP

This is my thinking:

RFC = (320*1.2)/(330*1.1)-1 = 16.4%

Since we hedged the currency (by selling Euro in three months), if we need to “close” the futures contract, this would result in a loss, since I sold the Euro at 1.15 and hence exiting or buying at 1.23:

RFX = 1.15/1.23-1 = -6.5%

So total return = (1+RFC)*(1+RFX) = 8.80%

Let me know if this matches your approach.

Since we hedged RFX and have locked into FP of 1.15, RDC is only change in RFC (foreign asset return) times initially hedged USD-EUR/ spot in time T0 USD/EUR. Whereas, USD/EUR spot in T0 was referred to initial cost of purchasing foreign asset.

RDC  in T1 = ((320 KEUR/300 KEUR) X (1.15 / 1.10)) - 1 = (1.07 x 1.05) -1 = 13 %

How would we know to hedge an ending value of 320?? Good guess in advance. I’m assuming theyhedged the full 300 we started with.  Then the last 20 in gain is exposed to the spot rate

googs beat me to it: we need to know the size of the futures contract.

The reason you use the new price on the futures contract is that it (along with the new spot rate) will give you the discount rate for your existing futures contract.

To compute the total return you need the original value of the portfolio in USD (using the original spot exchange rate), the current value of the portfolio in USD (using the current spot exchange rate), and the current value of the futures contract (using the original forward rate, the current forward rate, and the current spot rate).

Simplify the complicated side; don't complify the simplicated side.

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