Data:

Foreign-currency AUD asset return RFC = 4.0%

Foreign-currency NZD asset return RFC = 6.0%

Foreign-currency RFX= 5% for both

Asset risk σ(RFC) = 0% for both

Currency risk σ(RFX) AUD = 8%

Currency risk σ(RFX) NZD = 10%

Correlation (USD/AUD; USD/NZD) +0.85

Then is says: Although RFX is a random variable—it is not known in advance—the RFC term

is in fact known in advance because the asset return is risk-free. Because of this Nguyen can make use of the statistical rules that, first, σ(kX) = kσ(X), where X is a random variable and k is a constant; and second, that the correlation between a random variable and a constant is zero. These results greatly simplify the calculations because, in this case, she does not need to consider the correlation

between exchange rate movements and foreign-currency asset returns. Instead, Nguyen needs to calculate the risk only on the currency side. Applying these statistical rules to the above formula leads to the following results:

A The expected risk (i.e., standard deviation) of the domestic-currency

return for the Australian asset is equal to (1.04) × 8% = 8.3%.

B The expected risk (i.e., standard deviation) of the domestic-currency

return for the New Zealand asset is equal to (1.06) × 10% = 10.6%.

*Can someone explain why are we multiplying the return by std. dev. to get the currency risk (std. dev.) if it is already provided to us at the first place?* I do recognize that under A and B they label it as expected risk of the domestic-currency r; however, it is not part of the formula for risk of the domestic currency:

σ2(RDC) ≈ σ2(RFC) + σ2(RFX) + 2σ(RFC)σ(RFX)ρ(RFC,RFX)

In example 1 in the beginning of this reading it is a simple plug and chug into the formula based on the data provided.

What follows is: σ2(RDC) = (0.5)2(8.3%)2 + (0.5)2(10.6%)2 + [(2)0.5(8.3%)0.5(10.6%)0.85]

= 0.8%

My take was that we would simply be inputting 8% and 10% instead of 8.3 and 10.6 computed in A and B. Thoughts?