Hi,
there is Covered “Interest rate parity” and Uncovered “Interest Rate parity”
Covered (active market for The currency pair) states that
forward rate = spot rate (1+rp)/(1+rb)
rp = Interest rate on price currency
rb = Interest rate on base currency
if The relationship does not hold, there will be arbitrage opportunity so eventually The relationship will be bound by arbitrage.
Uncovered (no active market for currency pair)
states that “The high yield currency “should” depreciate against The low yield currency for no carry trade (arbitrage) opportunity
change % in spot (A/B)= Interest rate A - Interest rate B
so, regarding your example:
Suppose
if USD interest rate 1Y is 2% and GBP interest rate is 1Y 1.5% and the spot exchange rate is 1.286 USD/GBP
The change in spot rate should be:
2% - 1.5 = 0.5% (note that the dollar should depreciate against the GBP)
the high yield currency should depreciate 0.5% against the low yield currency
that’s a “expected spot rate one year later of”
1.286(0.005) = 0.00643 + 1.286 = 1.2924 USD/GBP
CARRY TRADE
fund (loan in low yield currency) = 100 GBP
convert into USD (high yield) = 128.6 USD
Invest (128.6 @ 2%)
in one year.
Investment return = (128.6 * 1.02) = 131.17 USD
convert to GBP = 131.17/1.2924 = 101.50GBP
pay The loan
Interest = 100 * 0.015 = 1.5
principal = 100
profit = 0
if The relation does not hold there would be a profit (it may not hold but historically the distribution has excess kurtosis and negative skewness, so probability of loose is higher than the prob of profit)
I don’t know what’s the exact mechanism in uncovered interest rate parity, could be balance of payments one of many factors