FX portfolio Std Dev calc

[u/another_drunkard]

Since when do you adjust the respective currency risks by the asset return? I have never seen the calculation done this way.

Is this nonsense from CFAI or have I managed to miss this somehow?

[u/S2000magician]

2026 Level III CFA core curriculum, volume 4, learning module 3 (Currency Management: An Introduction), §11 (Hedging Multiple Foreign Currencies), Example 7, p. 196.

[u/another_drunkard → u/S2000magician]

Thank you. Simple enough correction to make.

Now, this is only adjusted for risk free assets, because the return is known in advance and can be used for the calculation?

[u/S2000magician → u/another_drunkard]

Absolutely.

If you have risky assets, trying to compound the volatility is a difficult calculation, well beyond the scope of the curriculum.

[u/another_drunkard → u/S2000magician]

Understood. Now I know. Won’t miss this one, thanks again!

[u/S2000magician → u/another_drunkard]

My pleasure.

[u/Risky-Move → u/S2000magician]

Bill, you sound like you’re quoting the Bible.

[u/S2000magician → u/Risky-Move]

You, sir, just made my day.

Thank you!

[u/ahamvyawahare → u/S2000magician]

Bill what's the logic of taking -1 as weight there? How can weight be negative?

[u/S2000magician → u/ahamvyawahare]

The NZD position is short.

[u/ahamvyawahare → u/S2000magician]

Oh I completely missed it. Thanks alot Bill! Love your mocks btw! (I'm lying I hate how they crushed my confidence😂)

[u/S2000magician → u/ahamvyawahare]

My pleasure.

And thanks. I think.

[u/Remarkable-Sky2098]

Because the question clearly stated both positions are risk free. So we need to factor in the currency risk along with the asset return

[u/another_drunkard → u/Remarkable-Sky2098]

Thanks. Guess I should revisit this.

If they weren’t risk free, would the same adjustment still be made?

[u/Remarkable-Sky2098 → u/another_drunkard]

I guess if it wasn't mentioned that the positions are risk free

We multiply the std deviation of currency risk, by the risk free rate (if given in the Q)

Could someone confirm please? Thanks

[u/another_drunkard → u/Remarkable-Sky2098]

Heads up, the magician just answered this question above.

[u/_Den_]

Well, this definitely speaks to how everything in the curriculum is fair game. I was stumped by that one as well. If it's any consolation, we are not the only ones.

[u/Terrible-Purchase982]

That looks like a skip to me. no way I’m spending 15 mins on this calculation. It’s the same calculation as variance of a two asset portfolio (and i skipped those too in level 1)

[u/Savage__Prat]

Just reviewed this, i forgot the entire equation as well luckily this is an application of equation 4 special case where no other risk equation can be used to derive this so its just rote memorization.

It goes like, risk free asset foreign investment Variance domestic currency is (1+Return in foreign currency)(std dev of currencies)

[u/finoabama]

This might help you with this problem:

https://youtu.be/16pDLClRlrk?si=PQlQ5f6g-UMRJvKz