# Double hedging strategy

Hi!

Can someone walk me through how the foreign i/r is converted to domestic i/r through the fx hedging?

Thank you!

Qn:

Before entering into currency futures and options contracts, Wulf and Bauer discuss the possibility of also hedging market risk due to changes in the value of the assets. Bauer suggests that in order to hedge against a possible loss in the value of an asset Wulf should short a given foreign market index. Wulf is interested in executing index hedging strategies that are perfectly

correlated with foreign investments. Bauer, however, cautions Wulf regarding the increase in trading costs that would result from these additional hedging activities.

Assuming Wulf and Bauer are successful in hedging both the foreign currency exposure and market risk exposure from the appreciation and depreciation of the asset, the expected return would be closest to:

Ans: B) the domestic risk-free rate.

Explanation

If Bauer shorts the appropriate amount of the index and the short position is perfectly correlated with the investment, the return must be the foreign risk-free rate. If Bauer then chooses to hedge the currency risk, he knows the exact value of the foreign currency to hedge and that the return to the (double) hedging strategy must be the domestic risk-free rate.

I tried to mathematical-ize it so can become clear:

DC=FC+FX (domestic currency return = foreign asset return [long] + foreign exchange return[long] )

return on hedged FC= foreign rf return (hedging foreign asset [short]=foreign rf => you effectively just removed the risk using foreign risk free instrument)

return on hedged FX= domestic rf return [long] -foreign rf return [-long=short] => domestic rf return