variance of foreign currancy asset return translated into variance of domestic currency returns

CFA Level III
#1

Hi all,

I thougt I was understanding something while preparing to Level III exam unless I reached volume 4 (Wiley - FI and Equity portfolio management), which describes how variance in home currency returns are calculated. Could you please clarify. Whould appriciate it a lot.

According to curriculum (page 16)

σ2 (Rdc) = σ2 (Rfc) + vσ2 (Rfx)= 2* σ (Rfc) * σ (Rfx) *p (Rfc; Rfx)

where

σ2 (Rdc) - variance of home currency returns,

σ2 (Rfc) - variance of foreign currency return,

σ2 (Rfx) - variance of foreign currency itself.

Question:

I do not understand the logic of the formula. Probably there is a typo in the book and instead of “equality” mark in the right part there should be “plus”? I mean “+ 2* σ (Rfc) * σ (Rfx) *p (Rfc; Rfx), as opposed to original of " = 2* σ (Rfc) * σ (Rfx) *p (Rfc; Rfx)”

thanks a lot

#2

This is covered in CFA Institute’s published errata: http://www.cfainstitute.org/Eratta/2015_level_III_errata.pdf

#3

Thanks a lot, that explians everything!

but then I have another question. I am not sure whether you have the latest curriculums, given that you are a chartholder already. But on page 61 of the same volume 4 there is an example, which among others clarifies how variance of risk free asset in foreign currency should be translated into variance in domestic currency.

it is given, that

Foreign currency risk-free asset’s return (Rfc) - 4%

Foreign currency return itself (Rfx) - 5%

Asset risk σ (Rfc) 0%

Currency risk σ (Rfx) 8%

So it is explained, that “the expected risk (ie standard deviation) of the domestic currency return for the foreign currency risk free asset is equal to (1.04) * 8%=8.3%”

The explanation is not quite clear to me. why it is proposed to multiply the Return figure (Rfc) by standard deviation (σ R fx) in order to get the standard deviation of the domestic currency return??

As I understand, variance (standard deviation) of risk free asset is 0, and its correlation with exchange rate fluctuation is 0 as well. therefore, given the folmula in my original post “σ2 (Rdc) = σ2 (Rfc) + vσ2 (Rfx) + 2* σ (Rfc) * σ (Rfx) *p (Rfc; Rfx)”, the variance for home currency should be equal exactly to variance of of exchange rate fluctuationsv (ie 8%). That seems logical. if i have invested in foreign currency risk free asset, and my future pay off under this asset is certain, then the only source of risk for me is the FX fluctuations. Am I wrong?

#4

You’re quite welcome.

I covered that second bit in this thread: http://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/91338972

#5

unbelievable, Magician. Cannot imagine how you do that :wink: many many thanks

#6

You’re quite welcome.