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### Chapter 13Section II

Equilibrium in the Foreign Exchange Market

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.

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.

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.’

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↑

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 $DepositsThe 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:

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

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.

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.

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.

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:

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.

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

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.

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.

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.

Practical application: wwww.bloomberg.com/markets/index.html: Rates and Bonds

Forward discount of $ on £ is increasing but on € decreasing.

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