# Cross Hedges

I’m looking for help in understanding Example 7 in the Currency Management chapter, page 361 in the CFAI books. Why is the expected risk calculated by multiplying currency risk of RFx by the known return on the t-bills? Why isn’t expected risk just sigmaRFx (since sigmaRFc is 0)?

They explain it in the example: the paragraph starting with, “Although RFX is a random variable . . . .”

Magician I was hoping you would respond!

I still don’t get it Why is RFx not known in advance? I don’t understand why we are using the statistical rule sigma(kX) = k*sigma(X)

How much will the GBP/USD exchange rate change between now and 5/14/2018?

ok, I get your point. but why do we have to multiply by the return on T-bills?

I would have thought that using the formula below to determine std dev would be sufficient:

sigma(Rdc)^2 = sigma(Rfc)^2 + sigma(Rfx)^2 +2*sigma(RFc)*sigma(Rfx)*Corr(Rfc,Rfx)

since Sigma(Rfc) = 0, the whole thing boils down to sigma(Rfx) and that’s it.

I know I am missing something simple but can’t figure it out.

Your formula applies when you’re adding returns (e.g., when you have two securities in a portfolio), not when you’re multiplying (i.e., compounding) returns. The formula for the variance of returns when they’re compounded – as they are when you have a local currency return and a currency exchange rate return – is more complicated, and is beyond the scope of the curriculum. The one special case that is in the curriculum involves one of those returns having a standard deviation of zero; that’s the case we’re discussing here. When that happens, the overall standard deviation of returns is the standard deviation of the other return multiplied by (1 + r), where r is the return that has a standard deviation of zero.

Try this: you have a fixed local return of 1% per month, and for 6 months you have exchange rate returns of 1%, 2%, 3%, -1%, -3%, and 0%. Calculate:

1. The standard deviation of the 6 exchange rate returns
2. The 6 monthly domestic currency returns (compounding the local return and the exchange rate return)
3. The standard deviation of the 6 domestic currency returns