Chapter 13 Section II

1. Chapter 13Section 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: uncoveredinterest 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€ + (Ee$/€ - E$/€)/E$/€ • Why should this condition hold? Suppose it didn’t. • Suppose R$ > R€ + (Ee$/€ - E$/€)/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, Ee$/€, are all given. Mathematically, we want to solve the UIRP condition for E$/€ . 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 Ee$/€ = $1.05 Per €

7. The spot e.r. and Exp Return on $ Deposits

8. Current exchange rate, E$/€ 1.07 1.05 1.03 1.02 1.00 0.031 0.050 0.069 0.079 0.100 Expected dollar return on dollar deposits, R$ R$ The spot e.r and the Exp Return on $Deposits

9. No one is willing to hold euro deposits No one is willing to hold dollar deposits Determination of the Equilibrium e.r.

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 depreciation of the euro is an appreciation of the dollar. A Rise in the $ Interest Rate • See slide 3 for intuition

12. A Rise in the € Interest Rate • R$ < R€ + (Ee - 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 ↑Ee • 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€. • ↓Ee (expected appreciation of a currency) leads to an actual appreciation: a self-fulfilling prophecy. • ↑Ee (expected depreciation of a currency) leads to an actual depreciation: a self-fulfilling prophecy.

16. Covered Interest Parity and Forward Rates

17. Covered Investment Suppose that when investing $1 in a deposit in euros, instead of planning to convert euros back into dollars at an exchange rate of Ee$/€ 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$/€should = Ee$/€ (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 Ee (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=(Ee-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 Forward discount of $ on £ is increasing but on € decreasing.