Covered: A hedged position in a foreign investment will earn the same rate as the domestic. This is held by an arbitrage condition (think about the arb we did in other models, borrow 1, invest, earn interest, ,pay off. That is Future = Spot (1+Foreign Rate ^T/1+Domestic^T)
Uncovered: Not held by arbitrage. it says the Expected Spot should increase/decrease by the interest rate differential. Interest Rate Foreign - Interest Rate Domestic. Uncovered ASSUMES RISK NEUTRAL. This does not hold short/medium. If it did, the carry trade would not work.
If Covered and Uncovered HOLD, then the Forward is unbiased predictor of the expected Spot
Absolute PPP: The difference in the exchange rate is based on the price levels. Spot = CPI Foreign/CPI Domestic. Assume all goods can trade across borders, etc. This usually isn’t true.
Relative PPP: This essentially says the change in the price level is the change in the inflation rates, so the % Spot changes from Inflation Foreign - Inflation Domestic
Ex ante Relative PPP: The Expected Spot changes by Expected Inflation Foreign - Expected Inflation Domestic
Inernational fisher…okay this one is crappy.
My understanding of it
Fisher Effect: The Nominal Interest Rate = Expected Inflation + Real Rate
NOW if UNCOVERED HOLD AND EX ANTE PPP HOLDS.
Taking the Nominal Foreign - Nomical Domestic, doing all that work we get.
Interest rate Nominal Foreign - Interest rate nominal Domestic = Expected Inflation Foreign - Expected Inflation Domestic + Real Rate Foregin - Real Rate domestic.
Guess what…Expected Inflation = Ex Ante PPP and Interest rate = Uncovered
So Interest rate Nominal Foreign - Interest rate nominal Domestic - Expected Inflation Foreign - Expected Inflation Domestic = Real Rate Foregin - Real Rate domestic.
Thus Expected Spot (from Uncovered) - Exected Spot (From ex ante) = 0 meaning that the Real Rates = 0. This is the Real interest rate parity, that is that real rates will converge.
Taking that nugget above (That Real Foreign - Real Domestic = 0, we can then state the…
The international fisher effect
The Difference in Nominal Interest rates is the difference in Expected Inflation, that is Nominal Foreign - Nominal Domestic = Expected Inflation Foreign - Expected Inflation Domestic.
Whew