# Topics in Exchange Rates Interest Rates

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```					Topics in Exchange Rates & Interest Rates

Saving
It is January 1st, and you have RMB1 to save for 1 year. You can put it into: 1. Put it into a domestic currency bank account at an interest rate i. 2. a foreign currency bank account at interest rate iF.

Payoff to strategy #2
• Strategy two has three parts. 1. Buy foreign exchange at spot rate St to get {1/ St} US dollars. 2. Put {1/St } into bank account. After 1 year get US\$(1+iF)×{1/St } 3. Convert these funds into RMB at exchange rate prevailing in 1 year.
(1  i F )  St 1 St  HK \$1000

Uncovered Interest Parity
• If

(1  i F )  St 1 St

> 1+i, deposit funds

then deposit in US\$ account. • If (1  i F )  St 1 < 1+i, deposit funds
St

then deposit in HK\$ account.

• Then in equilibrium

(1  i

F

St 1 1  i )
St

Interest Rate Parity
• The only reason people would be willing to hold a US\$ account when US interest rates were lower than domestic interest rate would be if they can achieve an expected gain from an increase in the value of US\$ during the time that they were holding the account. St 1  St F • Approximately

ii 

St

10

12

14

0

2

4

6

8

Apr-92 Apr-93 Apr-94 Apr-95 Apr-96 Apr-97 Apr-98 Apr-99 Apr-00 Apr-01 Apr-02 Apr-03 Apr-04

International Interest Rates

India

Hong Kong

0

1

2

3

4

5

6

7

Ap r- 9 2 Ap r- 9 3 Ap r- 9 4 Ap r- 9 5 Ap r- 9 6 Ap r- 9 7 Ap r- 9 8 Ap r- 9 9 Ap r- 0 0 Ap r- 0 1 Ap r- 0 2 Ap r- 0 3 Ap r- 0 4

Exchange Rate Appreciation
Rupees per HK\$

Thai Interest Rates and the Dollar/Baht Rate
.32 .28 .24 16 12 8 4 0 1990 1992 1994 1996 1998 2000 .20 .16 .12

HK\$: Baht Thai Baht Time Deposit Rate - 1Year HK\$ Time Deposits - 1 year

Covered Interest Parity
• An investor has \$1 for saving. Consider two investment strategies:
1. Invest RMB1 in a domestic bond with interest rate 1+i. 2. Use RMB1 to buy 1/St foreign dollars in spot markets. Invest 1/St in foreign bonds at interest rate 1+i*. Agree on a forward contract to sell (1+i*)/St foreign currency for Ft (1  i* ) domestic dollars.
St
t

Arbitrage implies that the two strategies will have the same pay-off. 1  i  Ft (1  i* )
t

St

t

•

This implies a forward price.

Ft  St 

1  it

1  it*

Fixed Exchange Rate
• If the central bank undertakes to keep the exchange rate fixed and that is a credible undertaking, then   0. t 1 • If the relative values of currency are fixed, then funds will flow out of the domestic currency if domestic interest rates are too low and flow into domestic currency if interest rates are too high. i = iF

%
10 12 14 16 18 20 0 2 4 6 8

Jun-86 Jun-87 Jun-88 Jun-89 Jun-90 Jun-91 Jun-92 Jun-93 Jun-94 Jun-95 Jun-96
HIBOR

Interbank Rates

HIBOR vs. Fed Funds Rate

Fed Funds

Jun-97 Jun-98 Jun-99 Jun-00 Jun-01 Jun-02 Jun-03 Jun-04

Costs & Benefits of Fixed Exchange Rates
• Benefits
– Stable currency for international trade & finance

• Costs

Managed Floating
• Most developed/OECD central banks set domestic interest rates in response to domestic price levels. • Many emerging markets or developing economies either set a fixed exchange rate or simply use the currency of another country – “Dollarization” • Many other emerging markets also practice “managed floating” which sometimes adjusts the interest rate in response to domestic conditions and sometimes intervenes in foreign currency markets to stabilize the price level.

IMF Exchange Rate Classification
60 50 40

30 20 10 0 No Currency Currency Board Fixed Exchange Rate Band Crawling Peg Managed Float Free Float

Source http://www.imf.org/external/np/mfd/er/2005/eng/1205.htm

Devaluation/Revaluation
• Even economies with fixed exchange rates adjust these levels overtime. • An increase in the price of US\$ by a fixed exchange rate regime is a devaluation. • A decrease in the price of US\$ is a revaluation

Real Exchange Rate
• A country’s real exchange rate is the relative cost of that country’s good when compared to foreign goods when measured in domestic currency

PtUS St REX t  St  HOME  Pt PPPt
• Numerator: # of domestic currency units needed to by the # of foreign currency units needed to buy 1 foreign good. • Denominator: # of domestic currency units needed to buy

• An currency achieves a PPP exchange rate when the cost of purchasing foreign goods equals domestic goods S = PPP, REX = 1.

Does PPP Hold?
• Does Absolute or Relative PPP hold? • In short run, NO. Exchange rates are much more volatile than inflation rates. • In long run for countries with similar levels of development, PPP holds.
– Example. Twenty year averages for OECD countries.

Over-valued/Under-valued
• When the cost of purchasing foreign goods is
– relatively high, S > PPP and a currency is said to be undervalued. – relatively low, S < PPP and a currency is said to be overvalued.

Calculate Real Exchange Rate
• Calculate PPPt
– Get PPPReference from World Bank, U Penn etc. – Convert CPI to World Bank Reference Year Dollars for Domestic and Foreign Economy CPI
CPI t Gross Inflation Since Reference Year  CPI Reference

Gross Inflation Since Reference Year HOME PPPt  PPPReference  Gross Inflation Since Reference Year Foreign

Example
• Germany: PPP in 2002 was .9 meaning goods that cost \$1 in the US cost €.90 in Germany. • But prices (and exchange rates) have changed since then. 2002 2006

CPIUSA
CPIGermany S2006

104.5
103.3 .8

117.1
110.2

Problem
• What is the exchange rate at which Euro is neither under nor overvalued in 2006? • What is gross inflation in Germany? • What is gross inflation in USA? • What is PPP in 2006?

Relative PPP
• In the long-run, we expect prices to converge through arbitrage trade (i.e. exporters should ship goods from a cheap market to an expensive one, until prices equalize across markets). • The average growth rate of the exchange rate should be equal to the inflation differentials. S HOME US \$

gt   t

 t

Long Run: Developed Economies
Source: IFS 1975-1995
PORTUGAL ITALY SPAIN SWEDEN UNITED KINGDOM AUSTRALIA FRANCE CANADA BELGIUM GERMANY NETHERLANDS JAPAN -4.00% -2.00% 0.00% Inflation Differential 2.00% 4.00% 6.00% 8.00%

Exchange Rate Depreciation

Learning Outcome
• Use the theory of Uncovered interest parity to predict exchange rate movements with domestic and foreign interest rates. • Use the theory of covered interest parity to estimate the future price of currency. • Use the theory of purchasing power parity to suggest whether a currency is undervalued or over-valued.

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