 # Forward Rate Bias Interpretation

I understand that Forward rate bias is the same as carry trade, but I can’t get my head around it using the logic below:
Covered IRP: F/S = (1+rx)/(1+ry); quoted as X/Y, Y is foreign currency.
If: F/S > (1+rx)/(1+ry), doesn’t it mean that Currency Y has forward premium? Forward rate bias states that we sell currencies trading at a forward premium. So in this case, why don’t we sell Y and buy X? The correct answer is to sell X and buy Y.

For example:
BRL/AUD spot rate: 2.1131
BRL/AUD forward rate: 2.1392
BRL 1-year interest rate: 4%; AUD 1-year interest rate: 3%.

F/S= 2.1392/2.1131= 1.01235
(1+Rbrl)/(1+Raud) = (1+4%)/(1+3%) = 1.00971
Thus F/S > (1+Rbrl)/(1+Raud)
I would think AUD is trading at a forward premium, thus we should sell AUD and buy BRL. But the correct answer is to short BRL. I feel that I got something fundamentally wrong. Could someone please help? Thanks!

No.

\frac{F}{S} > 1 means that Y is trading at a forward premium.

\frac{F}{S} > \frac{1 + r_X}{1 + r_Y} means that there is an arbitrage opportunity (ignoring transaction costs). The forward price is too high (i.e., too much X for one Y), so you can make money by borrowing X.

It is, because \frac{F}{S} > 1, not because \frac{F}{S} > \frac{1 + r_X}{1 + r_Y}. Whether AUD is trading at a forward premium, a forward discount, or flat is irrelevant to the question of which currency to borrow for the arbitrage transaction.

Which one you buy or sell depends on how the quoted forward price compares to the arbitrage-free forward price, not on which currency is trading at a forward premium.

Yes, because \frac{F}{S} > \frac{1 + r_X}{1 + r_Y}, you’re getting too many BRL per AUD in the forward market. You want too many, not too few. Thus, you borrow BRL at 4%, convert it to AUD at the spot rate, enter the forward contract to pay AUD and receive BRL, and invest the AUD at 3%. After one year, you convert the AUD back to BRL at the forward price, pay off the BRL loan, and you’ll still have money left over: the arbitrage profit.

You did, but I fixed it up top.

I hope that I did.

My pleasure.

1 Like

I feel that I just got enlightened! Thanks so much for your detailed explanation!

You’re quite welcome.