Quick clarification question.
So the optimal hedge ratio for the currency hedge on a foreign asset (or minimum variance hedge) equals 1 + the beta of the asset to the LC.
So is the optimal hedge ratio, once you add 1 + the beta of the asset to the LC = the beta of the foreign asset to the DC?
To estimate optimal hedge ratio: regress the domestic return on the currency future return.
To estimate the economic risk: regress the local return on currency spot return.
optimal hedge ratio = 1 + economic risk. Both are betas as op said.
this reading has been deprecated 
Phew! Moral - read until the thread until the end before panic sets in.
The Curriculum talks about optimal cross-hedging ratio/ minimum-variance hedge ratio as equal to = correlation(y,x)×[std.dev.(y)std.dev.(x)] which is obtained by regressing the domestic return on the currency future return. To complicate matters this is also linked to basis risk in section 6.4.3. Im into sure about the economic risk and transaction risk part but the principle is still the same I guess?