Interest Rates vs. Currency Depreciation

Well, this is my first shot at the CFA Level I and first post in the forum. It seems like there are a lot of people on here smarter than I am, so hopefully someon can help clear this up for me.

Expansionary monetary policy states that as the money supply is increased, the interest rate decreases and the domestic currency depreciates. However, the equation for the arbitrage-free forward exchange rate contradicts those effects and essentially shows that, as the interest rate decreases in one (domestic) country, the value of that currency actually appreciates against any other (foreign) currency, assuming that the interest rates for the other (foreign) currency either remain the same or decrease less than the interest rate decrease in the domestic country.

So, correct me if I’m wrong, but monetary policy states that a currency depreciates with an interest rate decrease but the calculation for the forward-rate actually shows that currencies appreciate with decreased interest rates…

Am I just trying to make a connection where there isn’t one? Is it just a matter of timing and explained by the J-curve - that the stated monetary policy effects are long-term and the exchange rates simply react faster so that a currency first appreciates (increasing the trade deficit) then depreciates (reducing the trade deficit)?

Thanks in advance.

I think this may help. If interest rates are low, the domestic currency is depreciated vs foreign (less foreign currency chasing more domestic) E.g. weak dollar and recently weakening euro. Evidence seen by China’s (viewed as unfair) low rates which depreciated their currency (therein, stimulating exports); caveat being high inflation given healthy consumer spending. This is why US has had such low rates, fighting deflation due to low consumer spending/confidence.

Perhaps I’m completely off, someone feel free to correct me. Been a while since my international finance class.