Does quantitative easing appreciate or depreciate the domestic currency?

Question

410 gone says the domestic currency depreciates.

You've identified the first-order effect: the supply of local currency has increased, so its price (and from the perspective of other currencies, that's its exchange rate) decreases. That's assuming that the move wasn't already (fully) priced-in by the market.

Jess Mehta says depreciates too, but she looks like a mooch for "Crypto Coin Market Expert".

An increase in the money supply could lead to a depreciation in the exchange rate. This is for two main reasons:

Inflation: The domestic inflation will make your goods relatively less competitive and export demand will fall. Therefore, there will be less demand for the currency and its value will tend to fall on the exchange rate markets.

Lower Interest Rates: If you increased the money supply, then this reduces interest rates. Lower interest rates will also tend to reduce the value of the currency.

But Adriaan Slabbert on Quora says it appreciates.

If there is less demand for something, the price of that thing tends to fall. Since the exchange rate is the price of currency, this means that Country A’s currency should fall, i.e. it will depreciate against other currencies, leading to a higher exchange rate of Currency A/US Dollar.

Answer 1

The exchange rate can be expressed in a simple classroom monetary model as:

$$S = \tilde{m} - \psi \tilde {y} + \lambda (\tilde i)$$

Where $S$ is the exchange rate $m$ is log of money supply, $y$ log of real output $i$, interest rate, $\tilde{}$ denotes differences between variable at home and abroad (i.e. $\tilde{x} = x_{home}-x_{foreign}$), and $\psi$ & $\lambda$ are just model parameters.

So the exchange rate depends both on log of money supply and on interest rate. Furthermore the interest rate itself depends on money supply.

The answer of @410gone focuses on the first order effect of monetary expansion through changes in $m$ whereas the answer on Quora mentions only the effect monetary expansion has on exchange rate through $i$.

However, the Quora answer omits any discussion of other effects, whereas @410gone mentions there are other effects so I would say the @410gone answer is more correct in a sense it mentions that also other effects exist whereas the Quora answer pretends that increase in money supply only affects exchange rate through the interest rate.