Exchange Rate Slides 2024 PDF

3. Arbitrage in the exchange market  Plan 1. (Uncovered) Interest Rate Parity (UIRP) 2. The covered Interest Rate Parity and the forward rate 3. The carry trade & risk premia in the exchange rate market 2 Im...

3. Arbitrage in the exchange market  Plan 1. (Uncovered) Interest Rate Parity (UIRP) 2. The covered Interest Rate Parity and the forward rate 3. The carry trade & risk premia in the exchange rate market 2 Implications of arbitrage in financial markets Idea: returns on same financial assets matter in determining the price of the currency and should be the same in any two countries. Relevant only if there are free capital flows, no transaction costs and no restrictions in banking Home Y Y(1+i) time t t+1 Foreign Y/St (Y(1+i*)/St)EtSt+1 So I want 𝑌 Y 1+𝑖 = 1 + 𝑖 ∗ 𝐸t𝑆𝑡+1 𝑆𝑡 ln 1 + 𝑖 = ln 𝐸t𝑆𝑡+1 − ln 𝑆𝑡 + ln 1 + 𝑖 ∗ 𝑖 ≈ Et𝑠𝑡+1 − 𝑠𝑡 + 𝑖 ∗ Where (s) S is the (log of the) spot exchange rate.  The “Uncovered” Interest Rate Parity (IRP) To make investors equally happy, the change in the exchange rate should be therefore given by ∗ 𝐸𝑡 ∆𝑠𝑡,𝑡+1 = 𝑖𝑡,𝑡+1 − 𝑖𝑡,𝑡+1 If the interest rate in one country is higher, the currency of that country should depreciate in the future! Investors want to have the same rate of return on their assets irrespective of the currency of denomination In frictionless markets, arbitrage works. If there are higher returns expected in one country, capital flows there.  “Uncovered” interest rate parity Expected rate: i = (Etst+1 - st) + i* return on Expected return on home bonds currency return foreign bonds where "E" here is the expectations operator at time t. “Uncovered” because the future exchange rate is expected. UIRP and forecasting?  Question Should I use the Interest Rate Parity (IRP) to forecast exchange rate changes? Answer: It’s not that simple!  Problems with the interest rate parity as a forecasting tool (I) Which variables are here exogenous? The relationship tells us what the change in the exchange rate should be between the spot (today) rate and some value of the exchange rate in the future. The problem is whether, if there is a change in the exchange rate required, it is the spot rate that should adjust or the expected future exchange rate! We cannot measure expectations about exchange rates!  Problems with the interest rate parity as a forecasting tool (II) Suppose that there is a shock (new information is available) so that suddenly i > i* If the expectation about the future exchange rate stays constant (for example, the interest rate differential is not due to expected inflation differentials) then the spot rate needs to appreciate! If the market expects a future depreciation of the currency that is equal to the one required by the IRP, than there is no effect on the spot exchange rate. UIRP and Fixed Exchange Rate Systems  Application: fixed exchange rates, free capital flows and interest rates With a fixed exchange rate, it has to be the case in a credible regime that Est+1 = st Therefore, the interest rate parity (free capital flows and arbitrage!) implies that i = i* The domestic interest rate has to be equal to the foreign interest rate. There is no independent monetary policy! – Note a problem: Inflation has to be exactly the same as in the foreign country if the real interest rate is the same in both countries. Otherwise, capital will flow out! Interest rates in the Eurozone and Denmark UIRP under an assumption of constant future exchange rate: “transitory” shocks channeled via monetary policy The UIRP relation in a small open economy Exchange rate (domestic/foreign currency) Expected return on Euro deposits S i Interest rate An increase in the domestic interest rate and the change in the exchange rate Exchange rate (domestic/foreign currency) S1 S2 Expected return on Euro deposits i1 i2 Interest rate  Intuition after a rate hike (I) If (a) the return i* in the foreign country stays constant (b) the expected future rate Est+1 remains constant in the minds of investors The only adjustment can come from the spot exchange rate so that the return in the foreign currency is now higher. This is only possible if the spot exchange rate appreciates today so that it depreciates by more throughout the investment horizon.  Intuition after a rate hike (II) When you say: home assets become more attractive in the eyes of investors as they offer higher yield and that is why the spot exchange rate appreciates you tacitly assume (a) & (b)!  Application: Rate hike in a country On Oct 7, 2021, the Polish central bank increased its base rate from 0.1 to 0.5% This made liquid and safest Polish assets more attractive in the eyes of investors as they offered higher yield. What do you believe should be a response of the PLN/USD exchange rate? PLN/USD rate that day USD/EUR rate on Sep 21, 2022 (Fed Funds increased by 0.75% @2pm) “Transitory” interest differentials and exchange rates The U.S. and zone interest rates 2020-2024 How can you reconcile UIRP with PPP?  How to reconcile the UIRP with the PPP? What is the nominal interest rate? Interest = real remuneration of capital + compensation for inflation Assume that the real interest rate rr is equal across countries. If i = pt+1 - pt + r and i* = p*t+1 – p*t + r then ∗ ∗ ∆𝑠𝑡,𝑡+1 = 𝑖𝑡,𝑡+1 − 𝑖𝑡,𝑡+1 = 𝜋𝑡,𝑡+1 − 𝜋𝑡,𝑡+1 So, there is (theoretically) a close relation with PPP (aka the Fisher effect).  The Fisher effect in data Source: Feenstra and Taylor, 2012