Reading 28, page 271 example 8 -cross hedge

While calculating the standard deviation of the domestic currency, i used the formula

sigma (dc)^2= sigma(fc)^2+sigma(fx)^2+2*sigma(fc)*sigma(fx)*corr

Since here the sigma(fc) is 0 , the std dev of domestic curr should have been equal to std dev of currency risk which is 8%… however it is calculated to be 8.3

could someone explain this?

Magnitude of Standard deviation. Let’s say you have 3 numbers 1,2,3. The standard deviation is sqrt(2)/3. If you mutliply these numbers by two. 2,4,6. The standard deviaton would be doubled. sqrt(8)/3 = 2*sqrt(2)/3. If you mutli a population by something the standard deviation will increase by the multiple. Your return goes is (1+ FC + (1+FX). Since all FC is multiplied by a constant FC (no deviation since risk free), the standard deviation would increase by the multiple of FX.