Return on FC bond in DC terms regarding, next, expected, exchange

ba736

Hey guys,

I’d like to clarify a point regarding the calculation on return on a bond in the DC. I'm looking at p. 493 of CFAI Book 6, Example 4.

RFR DC = 5%
RFR FC = 3%

This implies the forward exchange rate quotes at a premium of 2%. CFAI state that the expected exchange rate appreciation of FC is 3%. The foreign exchange risk premium is then easily computed as:

(expected FC appreciation) - (forward exchange rate premium)
= 3% - 2%
= 1%

The next part is where I'm confused, calculating the return in the DC. They simply add the 3% FC RFR with 3% expected currency appreciation and get 6%. Would you not gain 1.03*1.03 or 6.09% instead? I know this seems trivial however my fear is they would put both 6.00% and 6.09% as possible answers on the exam.

On p.493 the CFAI says clearly “the DC return on FC investment is equal to the FC RFR + the expected percentage movement in the exchange rate”. This appears to conflict with Ex. 2, question 1 on p 490-491 where they multiply the two terms.

It's the same type of question, calculate the return on the foreign bond in DC. They then provide two answers, an approximate of 5% (3%+2% = 5%) using the same intuition as Example 4, then say the return is more accurately 5.06% (computed by calculating the return geometrically which makes more sense to me) as below:

Return DC = [ (FC RFR)*(FX appreciation) ] - 1
= (1.03*1.02) - 1
= 5.06%

They add in every example (Ex 2, Ex 4, and EOC 11) except for that brief note in Ex 2 where they multiply and say “more specifically”. I think the safe bet is just to add, but I wanted to hear your thoughts. Am I missing anything?

wizofoz

You are correct, it should be multiplied. But I think they're just adding it to approximate the return. Don't sweat it too much, in the exam just add and see if you get the answer. If not, multiply.

iteracom

I'm worried both will show up, the return computed from addition as well as the geometric..

The text seems to add everywhere, so I think thats the safer bet.

onelife1

CFA seems to alwas add them...

The correct one would be to multiply, but in most cases it would not make a diff...

I would not worry about CFA trying to trick you with this. I dont think thats what they are looking for