# Confusion with Currency Hedging Techniques

It’s been a long study day for me and maybe I’m just mentally tired, but I’m having trouble with this seemingly easy question.

The expected (local currency) return on the bonds is 8.50%, and the 1-year risk-free yields are 1.3% in the United States and 4.6% in Australia. The spot exchange rate is USD0.6900/AUD1 and the one-year forward rate is USD0.6682/AUD1

If the Australian currency risk is fully hedged, the bond’s expected return will be closest to:

5.20%.

5.34%.

3.90%.

Because IRP holds in this case, I used the formula “ Domestic interest rate + (Local Market return – Foreign Interest Rate) “

1.3 + (8.5 – 4.6) = 5.2%

The answer takes the LMR and adds the forward discount. (.6682-.69 / .69 = - 3.16%)

8.5 + ( - 3.16) = 5.34%

Am I right to assume that the first formula (“ Domestic interest rate + (Local Market return – Foreign Interest Rate) “ ) is just an approximation and that we should always calculate the actual forward premium / discount. If so, should we only be using this formula when trying to find the highest hedged currency returns across different markets (because all returns would be approximated)?

The IRP doesn’t hold, you use the forward return instead.

Unhedged currency Risk

Rdc = Rfc + Rfx —> (1+Rdc) = (1+Rfc) x (1+Rfx)

Hedged currency Risk

Rdc = Rfc + (Fwd-Spot) / Spot

Hedged currency risk and asset return

Rdc = RFR (domestic)