I am trying to understand how these things are the same. This is the way I think of it.
Let’s say we have USD/EUR = 1.35
USD IR for next year is 6%
EU IR for next year is 2%
Borrow in EUR and pay 2%
Invest in USD and gain 6%
According to UIP, the USD should depreciate with 4% against the EUR, we don’t believe UIP will hold so we engage in this carry trade.
Trading the Forward Rate Bias
The forward price indicates that USD should depreciate by 4% against the EUR, based on UIP. In other words the USD/EUR FORWARD (to buy USD) trades at a discount. We don’t believe the UIP will hold.
So we buy the USD today in the spot market, and agree to sell USD in 1y through a EUR/USD forward contract.