# Bonds hedged return with forward discount ( Interest Rate Parity)

Hi guys, I have a question on the unhedged return with forward discount. Kaplan book 3, p79, Example 6
US- based portfolio manager
USD 6 mo LIBOR = 1.2%
GBP 6 mo LIBOR=1.4%
annualized yield

The unhedged return is =2.34%(rolling yield) + 1% (ccy appreciation)

The solution says that since the GBP has a higher interest rate 1.4% vs USD 1.2%
GBP is going to be traded at a forward discount, which leads to (1.4-1.2)/2=0.1%
Hedged return is therefore 2.34-0.1=2.24%
I don’t understand why they are subtracting the forward discount
This is my thought process. Since it’s US based manager, you will eventually turn GBP into USD, so the worry is GBP will depreciate. Thus, to hedge, you short GBP ( say the forward price is 1.3 USD/GBP). Now with the forward discount (1.2 USD/GBP). When you short and the price of GBP drops, you gain. So I think it should 2.34+0.1=2.44% for the hedged return.

What’s wrong in my thought process?Many thanks in advance!!

Let’s assume that the spot USD/GBP (i.e. DC/FC) is 1.40 (arbitrary). Based on the LIBOR rates above, the 6-month forward rate for USD/GBP is:

F_{USD/GBP} = S_{USD/GBP} \times \frac{1 + LIBOR_{USD} \times \frac{6}{12}}{1 + LIBOR_{GBP} \times \frac{6}{12}}

F_{USD/GBP} = 1.40 \times \frac{1 + 0.012 \times \frac{6}{12}}{1 + 0.014 \times \frac{6}{12}} = 1.3986 ~~(F < S)

To hedge, you will sell GBP forward 6 months (i.e. sell base currency) at USD/GBP 1.3986, so the gain from the hedge is:

\frac{F_{USD/GBP} - S_{USD/GBP}}{S_{USD/GBP}} = \frac{1.3986 - 1.4}{1.4} = -0.1\%

Hence, your hedged return = 2.34\% + (-0.1\%)

An alternative qualitative description:

To hedge, you’re selling the GBP forward. Given the interest rate differential (GBP rate is higher), the quote in the forward market will be for the GBP to depreciate (i.e. it is selling at a forward discount). So by hedging, you are guaranteeing that you will lose than 0.1% on the hedge.

By contrast, if you think the GBP is going to appreciate i.e. you disagree with the market, then you don’t want to lock in the depreciation by selling it forward at the ‘lower’ price.

Thank you! I was confused with forward discount, comparing two forward rate.

Should be compare forward rate with spot rate

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Thanks!