Correlation and domestic currency return

CFA Level III Economics
#1

Formula for risk of domestic currency return is: var.(RDC) = var.(RFC) + var.(RFX) + 2 x S.D (RFC) x S.D (RFX) x correlation (RFC,RFX). When correlation increases, it increases domestic-currency risk. But why does it not impact domestic-currency return? Increasing correlation in the above formula (right-side) means the Domestic-currency return increases (left-side)

#2

Why does it mean that?

They can both go up, or both go down.

#3

So Reading 19, practice problem 11, answer says: An increase in the expected correlation between movements in the foreign-currency asset returns and movements in the spot exchange rates from 0.5 to 0.8 would increase the domestic-currency return RISK but would not change the LEVEL of expected domestic-currency return. I agree with you if correlation on the right in the above formula went up (down) then domestic-currency return, RDC, would go up (down) on the left. But the answer is saying only the risk increases, not the actual return, why is this?

#4

The domestic currency return is (approximately) the foreign currency return plus the exchange rate return. If the correlation of those two returns increases, then the volatility of the returns will increase, but there’s no reason to expect that the mean return will increase: you’ll have higher highs and lower lows, but the average could be in the same place.

#5

Oh i see now, the formula above is a variance (risk) formula. So if correlation increases, then var. of RDC increases (left-side). Thanks

#6

My pleasure.

#7

If we use the rigorious formula
E(R_dc)
= E(R_fc) + E(R_fx) + E(R_fc * R_fx)

When correlation increase,
E(R_fc) will not change
E(R_fx) will not change

BUT E(R_fc*R_fx) = Cov(R_fc, R_fx) + E(R_fc)*E(R_fx) will increase.
So I think domestic currency return should increase slightly, when correlation is higher.

In the textbook it seems to ignore the r_fc*r_fx term, and it is indeed very small.

Any thoughts on how which formula should we use in the exam?

#8

The curriculum doesn’t present this formula, so you won’t have to use it.

#9

Thank you very much!

#10

My pleasure.