How interest rate will affect foreign exchange rate?

High interest rate will slow the economy and make the equity asset less attractive, the currency depreciates.

However, according to carry trade, when interest rates are relatively high in a country, capital moves into that country and, as a result, the currency strengthens.

Is this a contradiction?

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High interest rates slows down businesses because they can’t borrow at cheap rates. High interest rates hurt borrowers.

High interest rates bring in investors from outside that want to earn that high interest rate. High interest rates are great if you’re an investor investing in those rates.

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Higher interest rate is attractive to bond investors, as they get to buy at a lower price (due to the higher rate). Given this, foreign investors will be encourage to take advantage of this higher rates and thus will demand for more of the domestic currency, thereby leading to appreciation of the domestic currency.

interest rates increase - currency appreciates - prices drop Why? More demand for the currency, people want to hold bonds in that denominated currency so increase demand for that currency

interest rates decrease - currency depreciates - prices increase Why? Less demand for money (nobody wants those bonds) or on a dollar per dollar basis your purchasing power goes down why because your currency has depreciated

I always think of housing market to remember this Low Interest rates everybody wants to borrow to buy a house - so what happens the price on the homes usually go up because at the same monthly payment people can afford a higher home price because interest rates are low. Also because interest rates are low and borrowing is so cheap and SO many people are buying it has a positive impact on the economy growth wise High interest rates everybody doesn’t want to borrow to buy a home because at the same price the monthly payment is too high. So what happens eventually people lower the prices of there home so people can have that monthly payment even at a higher interest rate

But, interest rates increase - economy will slowdown - it will not attract investment - currency depreciate.

Right?

No

The higher rates are attractive to investors as they buy lower priced bonds and receive higher ROIs. Because of that, when your country has higher rates, foreign demand to invest in such bonds will increase. The demand for the USD increases, etc. so that these investors can get in on the action. All helps the $ appreciate (as something increases in demand the price goes up, right? Econ 101).

Regarding prices, try not to get away from thinking of things as TVM. Discount rates on FCF of equities can be calculated through the build up method. As bond rates increase, the final built up rate increases. What happens when you divide the FCF by a larger denominator? You get a smaller PV and intrinsic value of the equity. Same with the bonds themselves, as you increase the rates, your coupon payments received and return of principal are discounted by a larger rate, i.e. larger denominator, and the PV of the bond drops. Same can go for real estate as it’s going to affect your cap rate and prices can fall.

“Note that long-term capital flows may have the effect of reversing the usual relationship between short-term interest rates and the currency. This is explained by the fact that a cut in short-term rates would be expected to boost economic growth and the stock markets, thereby making long-term investments more attractive. In this environment, central banks face a dilemma. Whereas they might want to raise interest rates to respond to a weak currency that is threatening to stimulate the economy too much and boost inflation, the effect may actually be to push the currency lower. Hence, the effectiveness of monetary policy is much reduced. "

This is from curriculum. I am confused…

" Whereas they might want to raise interest rates to respond to a weak currency that is threatening to stimulate the economy too much and boost inflation, the effect may actually be to push the currency lower"

I am equally confused, but I try to explain this by picturing the Fed.

The Fed might want to raise rates in respond to an overheating economy to tame inflation. Typically, when interest rate is high, it leads to appreciation. However, in the past 30 years or so, the Fed had OVERSHOOT the target pretty much every time which led the market into a recession. What happens to the USD during a recession? It depreciates.

So, when the Fed raise rates, it typically leads to an appreciation of USD; however, if the market perceives that the Fed is raising too fast and/or too much, the market tanks and the dollar depreciates. A very recent example, 12/21/2018.

There will be times when reality deviates from theory. Theory tends to examine one or more set of factors at a time. Reality have too many cross currents at a single time.