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Rate of Return on a foreign asset
Foreign asset in home currency [ et+1 ( Pt+1* + Dt+1* ) - etPt* ] / ( etPt* ) = [ et+1 ( Pt+1* + Dt+1* ) / ( etPt* ) ] - 1 = (et+1 / et ) [ ( Pt+1* + Dt+1* ) / Pt* ] - 1
1 HD = x FD = 1/e FD, i.e., e HD = 1 FD P vs. eP*
2
Time
Return on home asset
t
For example, t=January, t+1=February
Buy Asset: pay Pt
May receive dividend Dt+1 between time t and time t+1
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Rate of return of home deposit
Et (Pt+1 + Dt+1) / Pt - 1 Pt+1 = 1 Pt = 1 Dt+1 = Rt= home interest rate Et (1 + Rt) / 1 - 1 = Rt
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Expected return and expected rate of return
t+1 Sell asset: get Pt+1
Return = Pt+1+Dt+1 -Pt Rate of Return = (Pt+1+Dt+1 - Pt)/Pt
3
Return on a home asset
Pt+1 - Pt dividends or any interest payments to the asset holder Dt+1 Pt+1 - Pt + Dt+1
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Expected return and expected rate of return
Expected return on a home asset: Et (Pt+1 + Dt+1 - Pt ) = Et (Pt+1 + Dt+1) - Pt
Expected rate of return on a home asset: Et [(Pt+1 + Dt+1) / Pt - 1 ] = Et (Pt+1 + Dt+1) / Pt - 1
Covered and Uncovered Interest Rate Parity
WONG Ka Fu 26th January 2000
1
Comparing Local and Foreign Prices
Prices within a country
Prices across countries P (in home currency) P* (in foreign currency)
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Expectations
Lottery 1 0.5 probability to win 1000 0.5 probability to win 0
Expect to win 0.5 ×1000 + 0.5 ×0 = 500
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Expectations
Lottery 2 0.2 probability to win 1000 0.3 probability to win 500 0.5 probability to win 0
Some unknown quantities become known: Pt+1 = 1 Pt = 1 Dt+1 = Rt= home interest rate Pt+1*= 1 Pt* = 1 Dt+1*= Rt*= foreign interest re t is et+1
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Time
Return on foreign asset
t
For example, t=January, t+1=February
Buy Asset: pay etPt*
May receive dividend Dt+1* between time t and time t+1
t+1
Sell asset: get et+1Pt+1*
Return = et+1(Pt+1* +Dt+1* )/ - etPt*
Rate of Return = [et+1(Pt+1* +Dt+1* )/ - etPt* ]/ etPt*
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Return on a foreign asset
A foreign investor invests in a foreign asset Pt+1* - Pt* + Dt+1* = Pt+1* + Dt+1* - Pt* A home investor invests in a foreign asset et+1 (Pt+1* + Dt+1* ) - etPt*
Lottery 4
f(y) probability to win y
Expect to win Et(y) = E(y| information available at time t)
= y f(y) y dy
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Replacing assets with deposits greatly simplifies the algebra:
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Rate of Return on a home asset
Return / cost of asset at time of purchase / year Home asset in home currency ( Pt+1 + Dt+1 - Pt )/ Pt = [ ( Pt+1 + Dt+1 ) / Pt ] - 1
Expect to win 0.2 ×1000 + 0.3 ×500 + 0.5 ×0 = 350
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Expectations
Lottery 3
Pi = f(yi) probability to win yi
Expect to win
Et(y) = i Pi yi = i f(yi) yi
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Expectations