when we say interest rate parity, we mean “covered interest rate parity” , is it? what is the difference between covered and uncovered, only looks like assume expected S1 = forward rate in covered. any idea? Thanks.

uncovered interest rate parity has to do with exchange rate expectations = interest rate differentials. covered interest rate parity has to do with forward rates = interest rate differentials. Covered expresses the ability to make a hedged investment and arbitrage. uncovered is a relationship, and that’s it. Page 99 of Schweser, for reading 19 of economics, book 2, graphs this nicely.

in covered you can assume that you can use a forward contract, or that f/s=1+id/1+if where f is the forward rate and s is the spot. in uncovered, no deriv instruments exist, so instead of the forward, you use the expected future spot rate es1/s=1+id/1+if where es1 is the expected future spot