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International Parity Conditions. (or chapter 4). Agenda. What is PPP & law of one price? What is exchange rate pass-through? How do interest rates & exchange rates link? Interest rate parity? What is covered interest arbitrage? What is uncovered interest arbitrage?. ¥. $.

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agenda
Agenda
  • What is PPP & law of one price?
  • What is exchange rate pass-through?
  • How do interest rates & exchange rates link?
  • Interest rate parity?
  • What is covered interest arbitrage?
  • What is uncovered interest arbitrage?
prices and exchange rates

¥

$

Prices and Exchange Rates
  • Law of one price:
  • product’s price same in all markets

P$ S = P¥

  • where spot exchange rate is S, yen per dollar.
purchasing power parity law of one price
Purchasing Power Parity & Law of One Price

Absolute purchasing power parity:

  • spot exchange rate is determined by relative prices of similar basket of goods.

Relative purchasing power parity:

  • Relative change in prices b/n countries determines change in forex rate.
absolute ppp big mac index
Absolute PPP: Big Mac Index
  • Economist’s Big Mac PPP:
    • Big Mac in China costs Yuan 9.90.
    • Big Mac in US costs $2.71.
    • Implied PPP exchange rate
slide6

Economist,

4/ 2003

relative ppp

4

P

PPP line

3

2

1

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

-1

-2

-3

-4

Relative PPP

% change spot rate foreign currency

US$/ yen

InfJAPAN- InfUS

slide8
But:
  • PPP is not very accurate predictor…
    • Why?
  • PPP holds well over very long term…
  • PPP holds better for countries w/ high inflation & underdeveloped capital markets…
    • Why?
is forex under over valued
Is forex under-/over- valued?
  • Use forex indices: trade-weighted bilateral exchange rates b/n the home country & trading partners
  • Nominal exchange rate index : use actual exchange rates.
  • Real effective exchange rate index indicates how the weighted average purchasing power of the currency has changed relative to some arbitrarily selected base period.
slide10
Q:
  • Can you tell when a currency is overvalued?
  • Why the real exchange rate deviates from 100?
slide11

Real Effective Exchange Rate Indices

United States & Japan (1995 = 100)

exchange rate pass through

€/$

Exchange Rate Pass-Through
  • Pass-through: change in prices of imported/exported goods when exchange rate changes
    • BMW made in Germany cost @ spot rate US$ 35,000.
    • where P$ is the price in US$, P€ is price in euros, S is spot rate
    • Euro appreciates by 20%. But BMW is now only $40,000.
    • Pass-through:
    • Degree of pass-through: 14.29 % / 20 % = 0.71 or 71 %
interest rates exchange rates
Interest Rates & Exchange Rates?
  • What is a fair nominal interest rate?
      • Well, can ask a banker … or read Irvin Fisher…
    • Fisher Effect:nominal interest rates in each country are equal to the required real rate of return plus compensation for expected inflation.

i = r +  + r 

  • iis nominal rate, r is real rate,  is expected rate of inflation.
  • FE good for short maturity bonds, NOT long maturity ones.
    • Why?
international fisher effect

FC

International Fisher effect
  • International Fisher effect (Fisher-open):

spot exchange rate change equals opposite of interest rate differential.

where S is indirect quote.

  • Direct Quotes: US$/ Foreign Currency.
  • Indirect Quotes: Foreign Currency / US$.
  • Fisher-open not precise in short-term.
    • Why?
  • Should include forex risk premium.
forward rate
Forward Rate
  • Forward Rate
    • A forward rate: exchange rate quoted today for settlement @ future date
forward rate16
Forward Rate
  • Spot rate SF 1.48/$
  • 90-day euro Swiss franc deposit rate 4% p.a.
  • 90-day euro-dollar deposit rate 8% p.a.
premium or discount
Premium or discount?
  • Forward premium ordiscount : % difference b/n spot & forward rates in annual percentage terms.
    • For indirect quotes (FC per home currency, FC/$) then
    • Swiss franc sells forward @ premium 3.96% p. a.

(takes 3.96% more US$ to get franc at 90-day forward rate)

    • For direct quotes ($/FC), use (F-S)/S.
currency yield curve forwards

Interest

yield

Euro yield curve

6.0 %

5.0 %

Forward premium on

low interest rate currrency

4.0 %

Eurodollar

yield curve

3.0 %

2.0 %

1.0 %

1

2

3

4

5

6

Months

Currency Yield Curve & Forwards
interest rate parity irp
Interest Rate Parity (IRP)
  • Interest rate parity:difference in national interest rates for securities of similar risk & maturity should be equal to opposite of forward rate discount/ premium for foreign currency.

or

slide20

Interest Rate Parity (IRP)

i $ = 8 % per annum

(2 % 90 days)

Start

End

 1.02

$1,000,000

$1,020,000

$1,019,993

Dollar money market

S = SF 1.4800/$

F90 = SF 1.4655/$

Swiss franc money market

 1.01

SF 1,480,000

SF 1,494,800

i SF = 4 % per annum

(1 % 90 days)

90 days

covered interest arbitrage cia
Covered Interest Arbitrage (CIA)
  • Because spot & forward markets are not in equilibrium, arbitrage exists.
  • Covered interest arbitrage (CIA): invests in currency that offers higher return on covered basis.
slide22

Eurodollar rate = 8.00 % per annum

Start

End

Arbitrage

Potential

 1.04

$1,000,000

$1,040,000

$1,044,638

Dollar money market

S =¥ 106.00/$

F180 = ¥ 103.50/$

Yen money market

 1.02

¥ 106,000,000

¥ 108,120,000

Euroyen rate = 4.00 % per annum

Covered Interest Arbitrage (CIA)

180 days

uncovered interest arbitrage uia
Uncovered Interest Arbitrage (UIA)
  • Uncovered interest arbitrage (UIA): investors borrow in currencies w/ low interest rates & convert proceeds into currencies w/ high interest rates.
  • “Uncovered” because investor does not sell the currency forward.
slide24

Investors borrow yen at 0.40% per annum

Start

End

 1.004

¥ 10,000,000

¥ 10,040,000 Repay

¥ 10,500,000 Earn

¥ 460,000 Profit

Japanese yen money market

S =¥ 120.00/$

S360 = ¥ 120.00/$

US dollar money market

 1.05

$ 83,333,333

$ 87,500,000

Invest dollars at 5.00% per annum

Uncovered Interest Arbitrage (UIA): The Yen Carry Trade

Then exchanges

the yen proceeds

for US dollars,

investing in US

dollar money

markets for

one year

360 days

slide25

Interest Rate Parity (IRP) & Equilibrium

4

3

Percentage premium on

foreign currency (¥)

2

1

4.83

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

-1

-2

-3

Percent difference between

foreign (¥) and domestic ($)

interest rates

X

U

-4

Y

Z

forward rate unbiased predictor

Exchange rate

F2

S2

Error

Error

F3

F1

S3

Error

S4

Time

t 1

t 2

t 3

t 4

Forward Rate - Unbiased Predictor?

S1