Lecture10EXCHANGE RATES AND INTEREST RATES(国际经济学)
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Paradox
(CIP) (UIP) 1. 2. i$ - i£ = (F-S)/S = F/S - 1 i$ - i£ = (Se-S)/S = Se/S – 1
A higher domestic interest rate means that domestic currency is expected to depreciate over time. (Se > S or F > S) Holding F (or Se) and i£ fixed, an increase in the domestic interest rate appreciates the domestic currency, making S lower.
10
More Exercises
Q: Use the CIP or UIP to find how the exchange rate (S) will change if a. the domestic interest rate rises. b. the foreign interest rate rises. c. the domestic currency is expected to be weaker in the future.
7
Deviations from CIP
• Transactions costs • Differential taxation • Government controls (Political risk) In the presence of taxation, CIP is modified: (1-t$) i$ = (1-t£)i£ + (F-S)/S
Lecture 10
EXCHANGE RATES AND INTEREST RATES
1
Example
Suppose that 1-year interest rates on similar assets are 4% in the US and 5 % in the UK. Where will you put your money? Do you have sufficient information to make an informed decision?
11
Exchange Rates, Interest Rates and Inflation
1. The currency of a high inflation country tends to depreciate. (Relative PPP) 2. The nominal interest rate is high in a high inflation country. (Fischer effect) 3. The nominal interest rate is high if the currency is expected to depreciate. (Interest parity) In Symbol 1. $ - £ = (F-S)/S 2. i$ = r$ + $ ; i£ = r£ + £ 3. i$ - i£ = (F-S)/S
8
Uncovered Interest Parity
Uncovered interest parity holds if i$ - i£ = (Se-S)/S.
Se is the expected future exchange rate. i£ +(Se-S)/S is the expected return from uncovered investment in foreign assets. The (Se-S)/S is called the expected rate of depreciation of the domestic currency. (same as %E in expectation form)
2
The Rate of Return on Foreign Investment
The return on domestic investment = i$ $1 => $(1 + i$) The return on covered foreign investment $1 => £(1/S) sell $ for £ => £(1/S)(1+i£) earning i£ => $ F(1/S)(1+i£) selling £ forward The rate of return on foreign investment F(1/S)(1+i£) – 1 i£ + (F-S)/S
3
Example
1-year interest rates on similar assets: 4% in the US and 5 % in the UK the spot $/£ rate = 1.500 the 1-year $/£ forward rate = 1.470 The effective return on £ assets is (1.470/1.500)(1+0.05) = 1.029 or 2.9% per annum. In approximation, it is 5% + (-2%) = 3%
6
Exercises
Q: What would happen in the above case when CIP does not hold? Assume the domestic return is lower. Q: The euro is traded at a forward premium against the dollar. Between i$ and ieuro, which is higher?
A higher interest rate may mean a weaker currency (in 1) or a stronger currency (in 2). How do we explain the paradox?
13
Answer: The nominal interest rate increases for two different reasons. (a) An increase in expected inflation (b) An increase in the real interest rate In (a), money is loose and the domestic currency depreciates. In (b), money is tight and the domestic currency appreciates.Leabharlann 9Exercises
1. The 1-year $ interest rate is 6%. The 1-year ¥interest rate is 4%. The ¥/$ spot exchange rate is 100. Find the 1-year forward rate to satisfy CIP. 2. The 1-year euro interest rate is 3 %. The 1-year yen interest rate is 4 %. Is the euro expected to depreciate or appreciate against the yen? At what rate?
14
4
Investment Decision
If 1 + i$ > (F/S)(1+i£), invest in $ assets. If 1 + i$ < (F/S)(1+i£), invest in £ assets Subtract 1 from each side. Using approximation on RHS: If i$ > i£ + (F-S)/S, invest in $ assets. If i$ < i£ + (F-S)/S, invest in £ assets
5
Covered Interest Parity (CIP)
Covered interest arbitrage leads to CIP: 1 + i$ = (F/S)(1+i£). Using approximation, i$ = i£ + (F-S)/S or i$ - i£ = (F-S)/S The RHS is the forward premium on £.
Paradox
(CIP) (UIP) 1. 2. i$ - i£ = (F-S)/S = F/S - 1 i$ - i£ = (Se-S)/S = Se/S – 1
A higher domestic interest rate means that domestic currency is expected to depreciate over time. (Se > S or F > S) Holding F (or Se) and i£ fixed, an increase in the domestic interest rate appreciates the domestic currency, making S lower.
10
More Exercises
Q: Use the CIP or UIP to find how the exchange rate (S) will change if a. the domestic interest rate rises. b. the foreign interest rate rises. c. the domestic currency is expected to be weaker in the future.
7
Deviations from CIP
• Transactions costs • Differential taxation • Government controls (Political risk) In the presence of taxation, CIP is modified: (1-t$) i$ = (1-t£)i£ + (F-S)/S
Lecture 10
EXCHANGE RATES AND INTEREST RATES
1
Example
Suppose that 1-year interest rates on similar assets are 4% in the US and 5 % in the UK. Where will you put your money? Do you have sufficient information to make an informed decision?
11
Exchange Rates, Interest Rates and Inflation
1. The currency of a high inflation country tends to depreciate. (Relative PPP) 2. The nominal interest rate is high in a high inflation country. (Fischer effect) 3. The nominal interest rate is high if the currency is expected to depreciate. (Interest parity) In Symbol 1. $ - £ = (F-S)/S 2. i$ = r$ + $ ; i£ = r£ + £ 3. i$ - i£ = (F-S)/S
8
Uncovered Interest Parity
Uncovered interest parity holds if i$ - i£ = (Se-S)/S.
Se is the expected future exchange rate. i£ +(Se-S)/S is the expected return from uncovered investment in foreign assets. The (Se-S)/S is called the expected rate of depreciation of the domestic currency. (same as %E in expectation form)
2
The Rate of Return on Foreign Investment
The return on domestic investment = i$ $1 => $(1 + i$) The return on covered foreign investment $1 => £(1/S) sell $ for £ => £(1/S)(1+i£) earning i£ => $ F(1/S)(1+i£) selling £ forward The rate of return on foreign investment F(1/S)(1+i£) – 1 i£ + (F-S)/S
3
Example
1-year interest rates on similar assets: 4% in the US and 5 % in the UK the spot $/£ rate = 1.500 the 1-year $/£ forward rate = 1.470 The effective return on £ assets is (1.470/1.500)(1+0.05) = 1.029 or 2.9% per annum. In approximation, it is 5% + (-2%) = 3%
6
Exercises
Q: What would happen in the above case when CIP does not hold? Assume the domestic return is lower. Q: The euro is traded at a forward premium against the dollar. Between i$ and ieuro, which is higher?
A higher interest rate may mean a weaker currency (in 1) or a stronger currency (in 2). How do we explain the paradox?
13
Answer: The nominal interest rate increases for two different reasons. (a) An increase in expected inflation (b) An increase in the real interest rate In (a), money is loose and the domestic currency depreciates. In (b), money is tight and the domestic currency appreciates.Leabharlann 9Exercises
1. The 1-year $ interest rate is 6%. The 1-year ¥interest rate is 4%. The ¥/$ spot exchange rate is 100. Find the 1-year forward rate to satisfy CIP. 2. The 1-year euro interest rate is 3 %. The 1-year yen interest rate is 4 %. Is the euro expected to depreciate or appreciate against the yen? At what rate?
14
4
Investment Decision
If 1 + i$ > (F/S)(1+i£), invest in $ assets. If 1 + i$ < (F/S)(1+i£), invest in £ assets Subtract 1 from each side. Using approximation on RHS: If i$ > i£ + (F-S)/S, invest in $ assets. If i$ < i£ + (F-S)/S, invest in £ assets
5
Covered Interest Parity (CIP)
Covered interest arbitrage leads to CIP: 1 + i$ = (F/S)(1+i£). Using approximation, i$ = i£ + (F-S)/S or i$ - i£ = (F-S)/S The RHS is the forward premium on £.