Chapter 13 Section II Equilibrium in the Foreign Exchange Market.
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Chapter 13 Section II Equilibrium in the Foreign Exchange Market
2 Factors affecting the demand for FX To construct the model, we use two factors: 1. demand for (rate of return on) dollar denominated deposits R$ 2. demand for (rate of return on) foreign currency denominated deposits to construct a model of the foreign exchange market = R*+x The FX market is in equilibrium when deposits of all currencies offer the same expected rate of return: uncovered interest parity: R$=R*+x. –interest parity implies that deposits in all currencies are deemed equally desirable assets.
3 Uncovered Interest parity (UIRP) says: R $ = R € + (E e $/ € - E $/ € )/E $/ € Why should this condition hold? Suppose it didn’t. –Suppose R $ > R € + (E e $/ € - E $/ € )/E $/ €. no investor would want to hold euro deposits, driving down the demand and price of euros. all investors would want to hold dollar deposits, driving up the demand and price of dollars. The dollar would appreciate and the euro would depreciate, increasing the right side until equality was achieved.
4 UIRP (continued) Note: UIRP assumes investors only care for expected returns: they don’t need to be compensated for bearing currency risk. To determine the equilibrium exchange rate, we assume that: –Exchange rates always adjust to maintain interest parity. –Interest rates, R $ and R €, and the expected future dollar/euro exchange rate, E e $/€, are all given. Mathematically, we want to solve the UIRP condition for E $/€. That is the same as asking how the RHS and the LHS of the UIRP condition change with E $/€, and then looking for an ‘intersection.’
5 How do changes in the spot e.r affect expected returns in foreign currency? Depreciation of the domestic currency today (E↑) lowers the expected return on deposits in foreign currency (expected RoR*↓). Why? –E↑ will ↑ the initial cost of investing in foreign currency, thereby ↓ the expected return in foreign currency. E↑ then x ↓ hence R*+x ↓ Appreciation of the domestic currency today (E ↓) raises the expected return of deposits in foreign currency (expected Ror* ↑). Why? –E ↓ wil lower the initial cost of investing in foreign currency, thereby ↑ expected return in foreign currency. E ↓ then x ↑, hence R*+x ↑
6 Expected Returns on € Deposits when E e $/€ = $1.05 Per € Current exchange rate Interest rate on € deposits Expected rate of $ depreciation Expected dollar return on € deposits E $/€ R€R€ (1.05 - E $/€ )/E $/€ R € + (1.05 - E $/€ )/E $/€ 1.070.05-0.0190.031 1.050.050.0000.050 1.030.050.0190.069 1.020.050.0290.079 1.000.050.0500.100
7 The spot e.r. and Exp Return on $ Deposits EExpRor* 1.070.031 1.050.050 1.030.069 1.020.079 1.000.100
8 The spot e.r and the Exp Return on $Deposits Expected dollar return on dollar deposits, R $ Current exchange rate, E $/€ 1.02 1.03 1.05 1.07 0.0310.0500.0690.0790.100 1.00 R$R$
9 Determination of the Equilibrium e.r. No one is willing to hold euro deposits No one is willing to hold dollar deposits
10 The effects of changing interest rates An increase in the interest rate paid on deposits denominated in a particular currency will increase the RoR on those deposits to an appreciation of the currency. –A rise in $ interest rates causes the $ to appreciate: ↑ in R$ then ↓E($/€) –A rise in € interest rates causes the $ to depreciate: ↑ in R€ then ↑E($/€) A change in the expected future exchange rate has the same effect as a change in interest rate on foreign deposits:
11 A Rise in the $ Interest Rate See slide 3 for intuition A depreciation of the euro is an appreciation of the dollar.
12 A Rise in the € Interest Rate R$ < R€ + (E e - E)/E The expected return from holding € assets is > than $assets. Investors get out of $ assets into € assets, sell $ to buy €, the $ depreciates or € appreciates. This creates an expected appreciation of the dollar (x↓), thus a fall in the expected return from holding € assets
14 An Expected Appreciation of the Euro People now expect the euro to appreciate
15 An Expected Appreciation of the Euro ↑E e If people expect the € to appreciate in the future, then investment will pay off in a valuable (“strong”) €, so that these future euros will be able to buy many $ and many $ denominated goods. The expected return on €s therefore increases: ↑ROR €. –↓E e (expected appreciation of a currency) leads to an actual appreciation: a self-fulfilling prophecy. – ↑E e (expected depreciation of a currency) leads to an actual depreciation: a self-fulfilling prophecy.
17 Covered Investment Suppose that when investing $1 in a deposit in euros, instead of planning to convert euros back into dollars at an exchange rate of E e $/ € one year from now, I enter now a contract to sell euros forward at the rate F $/€. My return from such investment then is: R € + (F $/€ -E $/€ )/E $/€ So, you buy the € deposit with $ To avoid exchange rate risk by buying the € with $, at the same time sell the proceeds of your investment (principal+interest) forward for $ → you have covered yourself.
18 CIRP Since I could invest the same $1 domestically at R $, the forward market is in equilibrium when the Covered Parity Condition (CIRP) holds: R $ = R € + (F $/€ -E $/€ )/E $/€ where F $/€ = the forward exchange rate. This is called “covered” parity because it involves no risk-taking by investors: unlike UIRP, CIRP is a true arbitrage relationship. Covered interest parity relates interest rates across countries and the rate of change between forward exchange rates,F and the spot exchange rate, E. It says that ROR on $ deposits and “covered” foreign currency deposits are the same.
19 Remarks: Unlike UIRP, CIRP holds well among major exchange rates quoted in the same location at the same time, and even across different locations in integrated capital markets. CIRP fails when comparing markets segmented by current or expected capital controls: investors in a country subject to “political risk” require higher interest rates as compensation. For UIRP = CIRP, F $/€ should = E e $/€ (the spot rate expected one year from now). In fact, empirically, the forward rate moves closely with the current spot rate, rather than the expected future spot rate:
20 f = (F $/€ -E $/€ )/E $/€ is called the “forward premium” (on euros against dollars). –f>0 the dollar is sold at discount (euro at premium) –f<0 the dollar is sold at premium (euroa at discount) –f=0 domestic and foreign currency interest rates are equal. Exemple: Data from Financial Times, February 9, 2006 –E($/€)=1.195, F($/€)=1.22 (1-year from now) –i$=5.03%, i€=2.9%. i$-i€=2.13% expected depreciation of the $US a year from now. –f = (F $/€ -E $/€ )/E $/€ = (1.22/1.195)-1=2.1%. The dollar is sold at 2.1% discount in the forward market.
21 Expected exchange rates and the term structure (TS)of interest rates There is no such a thing as “the” interest rate for a country. Rates vary with investment opportunities and maturity dates. In bond market, there are 3-month, 6-month, 1-year, 3- year, 10-year, 30-year bonds. Term structure is described by the slope of a line connecting the points in time when we observe interest rates. –R rises with term to maturity→a rising TS –R same with all maturities →flat TS –R falls with term to maturity → inverse TS
22 Different types of term structure TS1: rising term structure TS2: flat term structure TS3: inverted term structure. In International finance we can use the TS on different currencies to infer the expected change in the exchange rate.
23 Remarks Usually, the forward rate, F, is considered a market forecast of the future spot rate E e (even though empirically F moves more closely with the spot exchange rate, E). Even if there is not a forward exchange market in a currency, at each point on the TS, the interest differential i-i* allows us to infer the directions of the expected change in E for the two currencies by the markets.
24 Differentials between term structures Constant differential: x=(E e -E)/E=0. Currencies will appreciate or depreciate against each other at a constant rate. Diverging: x>0 or f>0. High interest currency expected to depreciate at an increasing rate. Converging: x>0, f>0 but decreasing. High interest currency expected to depreciate at a decreasing rate.
25 Practical application: wwww.bloomberg.com/markets/index.html: Rates and Bonds 2/22 06 USGermUKi-iGi-iUK 3-m4.562.524.452.040.11 6-m4.712.634.432.080.28 1-y4.702.764.291.940.41 2-y4.692.934.261.760.43 5-y4.5184.108.40.206.35 10-y4.543.4220.127.116.11 Forward discount of $ on £ is increasing but on € decreasing.