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?