Why do higher interest rates increase the value of the currency?

I've been trying to study about interest rates and foreign exchange. First of all when people say interest rate in this context do they mean interest rate set by the central bank like federal reserve ( and by that I mean the interest rate that presidents/executive branch and central banks argue over) or some other interest rate?

Secondly why does higher interest rate increase the value of the country's currency?

On top of the answer by @phdstudent, you might also want to consider how the money supply may be affected when interest rates rise.

For example, If I'm an investor and a country has just raised their borrowing rates, this may make buying that country's bonds attractive to me. If I buy bonds from a country, I must do so in that country's base currency. If I hand the country's treasury a check and they hand me a bond, the cash that I just tendered to that country is now removed from circulation thereby decreasing the money supply. That example is the most basic one I can think of without overcomplicating the answer.

Also related to your question (though not exactly what you are asking) is the reserve requirement imposed on commercial banks by their central bank. If a central bank raised the reserve requirement that would have an instant effect on the money supply and value of that country's currency.

Smaller money supply is generally associated with higher interest rates.

• Is a DMOs issuance not typically self defined according to funding requirements rather than being dependent upon immediate investor demand? In which case whether you, or any other investor, buys those bonds doesn't materially impact the currency since this is not a response to the level of rates. Additionally those funds are typically spent by the DMO, either repaying maturing debt or funding government spending so its not clear which money supply is impacted by this action. Have I missed something? – Attack68 Aug 7 '19 at 17:07
• I was just offering a basic example. What you suggest may also be the case at times. My answer was just illustrating a potential circumstance and not meant to be thought of as comprehensive. – amdopt Aug 7 '19 at 17:17

Usually you think of it as a non-arbitrage relation.

The usual formula that should hold in equilibrium (in absence frictions) is the covered interest rate parity. However, for ease of intuition let's start with the uncovered interest rate parity:

$$(1+i_{domestic}) = \frac{E_t(S_{t+k})}{S_t} (1+i_{foreign})$$

This formula basically says that two investment strategies need to yield the same payoff:

1. Deposit your money at home
2. Or, exchange your home currency to foreign currency, invest at the foreign interest rate, exchange again to the home currency.

This is by no arbitrage. If this does not hold then you can make money. So you can see that when your home currency appreciates (i.e. the ratio above increases) then this means that your interest rate must go down.