subtracting/adding std. dev (R 45, Problem 1)

The solution to P1 shows that we are subtracting one std dev. from another to find the contribution of the currency risk. I was under the impression that you only added or subtracted variances, not std dev.

Yep - you can’t add std. devs.

your are technically not subtracting it (even though you do in this problem) first you calculate std of foreign asset in base currency (say $), then you compare it to std of foreign asset in local currency (say euro) and the difference is contribution of currency risk For example lets say dollar is your base currency, you have a German asset with std of 15%, std of exchange rate is 10%, and correlation between exchange rate and German asset return in euros is 0 (for simplicity) First you calculate asset std in dollars (.15^2 + .1^2)^.5 = .18 (approximatelly) from this you can say that contribution of currency risk is 18% - 15% = 3%, even though the standalone exchange risk is 10% if correlation between local market and exchange risk is negative, the contribution of currency risk can get negative, in such situation exchange rate will reduce the risk of an asset in base currency compared to foreign currency