Unhedged return of a currency

There is a question in a Schweser past paper that has: A U.S based pension plan has gathered info to assess the performance of its international equity portfolio managers: beginning currency value ending currency value euros per dollar 0.75 0.7 The unhedged return of the EUR is given in the answer as: (EUR0.75/USD) / (EUR 0.7/USD) - 1 Why is unhedged return, beginning / end. Not end / beginning?

The EUR un-hedged return is indeed calculated as (exch. rate t1) / (exch. rate t0) - 1 i.e. end / beginning - 1.

The complication here is that the quote is given as EUR/USD and to calculate the return in EUR as end / beginning we need the EUR to be the BASE in our P/B quote.

In other words we need the reciprocals of the ending exch. rate over beginning exch rate:

(1/0.07) / (1/0.075) - 1

which can be rearranged as

(0.075 / 0.07) - 1

Good luck, Carlo

It is the End/beginning (Future/Spot). It asked about the unhedged return of the Euro. Which is the reciprocal of the unhedged returns of the USD. The rates in the questions are on USD. Convert them to euro (reciprocal) then divide Future/Spot. You’ll get the same results as in the answer. Basic algebra

yep, i got tricked by this question too, but it’s obvious when you see it. You need to make sure you are quoting the correct currency, which in this case is the EUR.

So if we are looking at the returns on a currency, we need that currency to be the base currency (denominator), is that correct? Hence why for EUR return it is is USD/EUR.

Make sure the currency we are looking at in terms of returns is the base currency. This is why we had to take the recipricol of the given exchange rates in the quesiton

Ask yourself this: if you wanted to know the price appreciation of, say, oil, would you compare quotes of USD/bbl, or bbl/USD?

I, for one, have never seen a McDonald’s menu that lists hamburgers/USD.

To complicate things, you would need to have the euro has the priced currency if the question asked something about domestic currency return, right?

not if you ask a French person.

So essentially, the question is asking for the unhedge EUR portion:

Make EUR the base and find USD per EUR : 1.42 ending EUR value divided by 1.33 minus 1 = 7.1%

Which is also equivalent to the EUR per USD: 0.75 Beginning divided by 0.70 minus 1 = 7.1%

The lesson here seems to be that no matter what, the currency we are hedging, regardless of long or short is always the base?

Valuable CFA lesson that will imprint this concept in your head: