Chapter 13 Section II

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# Chapter 13 Section II - PowerPoint PPT Presentation

Chapter 13 Section 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\$

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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↑

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

No one is willing to

hold euro deposits

No one is willing to

hold dollar deposits

Determination of the Equilibrium e.r.
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:

A depreciation

of the euro is

an appreciation

of the dollar.

A Rise in the \$ Interest Rate
• See slide 3 for intuition
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

People now

expect the euro to appreciate

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.