I understand the first formula. I am confused about when it is appropriate to use the second formula. CFA states that this can be used to generalize a portfolio of foreign currency assets. Can someone please provide an example which would contain a “portfolio of foreign currency assets”.
After spending some time with this issue I think have solved my own question.
Essentially the user will use the first equation when evaluating the standard deviation of a single asset (or a portfolio that is designation as a single asset).
If there is combination of assets (CFA will likely only give a 2 asset portfolio) then we must use the second equation. The kicker is that StDevR1 will be the standard deviation of the investors domestic holdings and the StdDevR2 will be solution from the top equation. CFAI did not do a good job of conveying these topics and none of this information was covered as an example in the EOC questions or blue boxes, I had to go back to the the 2011 CFAI Mock PM questions 43 and 44 to piece this together.
If anyone has any additional input that would be great.
For purposes of the exam, I’m fairly sure we only need to use the first formula. It’s the same as the formula for a 2 asset portfolio that we had to learn for Level 2 (or even Level 1 I think) but the weights are assumed to be 1 for both the asset return and the currency return so the weights are left out.
The first formula is a special (and unusual) case of the second. The first gives the variance of the domestic currency returns for a portfolio denominated in a foreign currency. What makes it special (and unusual) is that the weight on RFC and the weight on RFX are both one (1): they don’t sum to 1 as is typical for that formula. The reason is that the entire (100% of the) portfolio is subject to the volatility of the foreign currency returns and the entire (100% of the) portfolio is subject to the volatility of the currency exchange rate.
The second formula gives the usual variance of returns for a portfolio comprising two assets; there is no separate foreign currency return and currency exchange rate return.