# Lecture 6

International Economics Analysis
Interest rate and Exchange rate
Tran Lam Anh Duong
28 February, 2018

Foreign currency
• Interest rates on time deposits in different currency：
Currency
Japanese yen
U.S. dollar
Euro
Australasian dollars
New Zealand dollars
GBP
Singaporean dollars
Norwegian Krone
Brazilian real
CNY
Turkish lira

South African rand

Interest rates （Annual rate・Before tax）

0.01%
1%
0.001%
1.4%
1.9%
0.1%
0.1%
0.01%
0.20%
1.50%
2%
6.50%
5%

Source：Shinsei Bank、Time Deposits by Maturity（8 May, 2017）

2

Foreign currency deposit process
Nominal exchange rate between
Yen and USD

1 USD = 118.15 JPY (exchange fee = 0.15 yen)

Interest rates on time deposits in USD = 1% (after
tax = 0.7968%) (Shinsei bank, 14 Jan, 2016)

142.84
138.45
132.07
122.77

132.49134.15

125.56

123.25

117.75
106.60

111.18

100.00

1 USD = 117.85 JPY (exchange fee = 0.15 yen)

90.92 90.90
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

Source：Shinsei bank
3

Interest rate and Rate of return
• Return on deposits in home currency = Interest rate
• Return on deposits in foreign currency
= Interest rate + foreign currency’s appreciation
= Interest rate + home currency’s depreciation

4

Revisit foreign currency deposit process
1 USD = 118.15 JPY (exchange fee = 0.15 yen)

Interest rates on time deposits in USD = 1% (after
tax = 0.7968%) (Shinsei bank, 14 Jan, 2016)
１．Forward transaction
⇒ Covered Interest Rate Parity
1 USD = 117.85 JPY (exchange fee = 0.15 yen)

２．Spot transaction
⇒ Uncovered Interest Rate Parity

5

Covered interest rate parity
• Forward transaction:
Period 𝒕𝒕

Invest 1
yen

Bonds in home ・Invest in home currency
currency
・Fixed interest rate 𝑖𝑖𝑡𝑡,𝑡𝑡+1
・Exchange for

Bonds in
foreign
currency

1
𝑆𝑆𝑡𝑡

1
𝑆𝑆𝑡𝑡

USD

・Fixed interest rate for bonds in

USD 𝑖𝑖𝑡𝑡,𝑡𝑡+1
・Make a contract on fixed
forward rate 𝐹𝐹𝑡𝑡,𝑡𝑡+1

Period 𝒕𝒕 + 𝟏𝟏

Income at maturity（yen）

・At maturity, principal and
interest income = 1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1 yen
・At maturity, principal and
interest income
=

1
𝑆𝑆𝑡𝑡

1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1
USD

・Exchange the income above for
yen based on forward rate made
1
𝑆𝑆𝑡𝑡

1
𝑆𝑆𝑡𝑡

1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1

1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1
𝐹𝐹𝑡𝑡,𝑡𝑡+1

1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1
𝐹𝐹𝑡𝑡,𝑡𝑡+1 yen

• Covered interest arbitrage：the process of capitalizing on the relationship between interest rate differential of two
countries while covering for exchange rate risk, happening when 1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1 ≠

1
𝑆𝑆𝑡𝑡

1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1
𝐹𝐹𝑡𝑡,𝑡𝑡+1.

6

Condition on covered interest rate parity
1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1 = 1

+ 𝑖𝑖𝑡𝑡,𝑡𝑡+1

𝐹𝐹𝑡𝑡,𝑡𝑡+1
𝑆𝑆𝑡𝑡

ln 1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1 = ln 1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1
+ ln 𝐹𝐹𝑡𝑡,𝑡𝑡+1 − ln 𝑆𝑆𝑡𝑡

ln 1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1 ≈ 𝑖𝑖𝑡𝑡,𝑡𝑡+1

ln 1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1
≈ 𝑖𝑖𝑡𝑡,𝑡𝑡+1
𝐹𝐹𝑡𝑡,𝑡𝑡+1 − 𝑆𝑆𝑡𝑡
ln 𝐹𝐹𝑡𝑡,𝑡𝑡+1 − ln 𝑆𝑆𝑡𝑡 ≈
𝑆𝑆𝑡𝑡

※𝑖𝑖𝑡𝑡,𝑡𝑡+1, 𝑖𝑖𝑡𝑡,𝑡𝑡+1
, 𝐹𝐹𝑡𝑡,𝑡𝑡+1 − 𝑆𝑆𝑡𝑡 : small

𝑖𝑖𝑡𝑡,𝑡𝑡+1 =

𝑖𝑖𝑡𝑡,𝑡𝑡+1

𝐹𝐹𝑡𝑡,𝑡𝑡+1 − 𝑆𝑆𝑡𝑡
+
𝑆𝑆𝑡𝑡

7

Capital mobility
• Capital control：there is a restriction on transaction of foreign currency
denominated assets
⇒ Even if there is interest arbitrage, transactions are not allowed.
⇒ No condition on uncovered Interest Rate Parity
• Necessary condition：Perfect capital mobility

8

Uncovered interest rate parity
• Spot transaction:
Period 𝒕𝒕

Invest 1
yen

Bonds in home ・Invest in home currency
currency
・Fixed interest rate 𝑖𝑖𝑡𝑡,𝑡𝑡+1
・Exchange for

Bonds in
foreign
currency

・Use

1
USD
𝑆𝑆𝑡𝑡

1
𝑆𝑆𝑡𝑡

USD

・Fixed interest rate for

bonds in USD 𝑖𝑖𝑡𝑡,𝑡𝑡+1
・Expected spot rate after
𝑒𝑒
one period 𝑆𝑆𝑡𝑡,𝑡𝑡+1

Expected income at maturity (after Actual income at maturity
1 period)
（yen）
・At maturity, principal and interest
income = 1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1 yen
・At period 𝑡𝑡 + 1, earn
1
𝑆𝑆𝑡𝑡

1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1
USD

・Exchange for yen with spot rate,
earning

1
𝑆𝑆𝑡𝑡

1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1
1
𝑆𝑆𝑡𝑡

1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1
S𝑡𝑡,𝑡𝑡+1

𝑒𝑒

1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1
𝑆𝑆𝑡𝑡,𝑡𝑡+1
yen

9

Equilibrium exchange rate based on uncovered
interest rate parity
Norminal exchange
• Condition on covered interest
rate parity:
𝑒𝑒
𝑆𝑆
𝑡𝑡,𝑡𝑡+1

1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1 = 1 + 𝑖𝑖𝑡𝑡,𝑡𝑡+1
𝑆𝑆𝑡𝑡

𝑖𝑖𝑡𝑡,𝑡𝑡+1 =

∗ ￥
𝑖𝑖𝑡𝑡,𝑡𝑡+1
+

𝑒𝑒
𝑆𝑆𝑡𝑡,𝑡𝑡+1

− 𝑆𝑆𝑡𝑡

𝑆𝑆𝑡𝑡

rate(𝑆𝑆𝑡𝑡 )

Income from
bonds in home
currency: 𝑖𝑖𝑡𝑡,𝑡𝑡+1
Income from bonds in foreign
currency:

𝑆𝑆 ∗
𝑖𝑖 ∗

𝑖𝑖𝑡𝑡,𝑡𝑡+1

+

𝑒𝑒
𝑆𝑆𝑡𝑡,𝑡𝑡+1
−𝑆𝑆𝑡𝑡

𝑆𝑆𝑡𝑡

Interest rate (𝑖𝑖𝑡𝑡,𝑡𝑡+1 )
10

Money market and foreign exchange market
• Analyze the following cases:

Exchange rate(𝑆𝑆𝑡𝑡 )
Income from bonds in
home currency: 𝑖𝑖𝑡𝑡,𝑡𝑡+1

Increase in money supply of Home country
Increase in money supply of Foreign country
Expanse of production in Home country
𝑆𝑆 ∗
Expectation of inflation in the future

𝑀𝑀
𝑃𝑃

Income from bonds in foreign
currency:

𝑖𝑖𝑡𝑡,𝑡𝑡+1

𝑖𝑖 ∗

Real money stock

+

𝑒𝑒
𝑆𝑆𝑡𝑡,𝑡𝑡+1
−𝑆𝑆𝑡𝑡

𝑆𝑆𝑡𝑡

Interest rate (𝑖𝑖𝑡𝑡,𝑡𝑡+1 )

Real money supply

Real money demand 𝐿𝐿(𝑌𝑌, 𝑖𝑖)
𝑀𝑀
𝑃𝑃

𝑀𝑀𝑆𝑆

11

𝑃𝑃

Time change and change in equilibrium
𝑆𝑆
𝑆𝑆
𝑆𝑆
• Permanent increase in money supply：𝑀𝑀𝑡𝑡−1
< 𝑀𝑀𝑡𝑡𝑆𝑆 = 𝑀𝑀𝑡𝑡+1
= 𝑀𝑀𝑡𝑡+2
=
𝑆𝑆
⋯ = 𝑀𝑀𝑡𝑡+𝑗𝑗

• Adjustment of price index：𝑃𝑃𝑡𝑡−1 = 𝑃𝑃𝑡𝑡 < 𝑃𝑃𝑡𝑡+1 < 𝑃𝑃𝑡𝑡+2 < ⋯ < 𝑃𝑃𝑡𝑡+𝑗𝑗
• Change in equilibrium interest rate in money market：
𝑖𝑖𝑡𝑡 < 𝑖𝑖𝑡𝑡+1 < 𝑖𝑖𝑡𝑡+2 < ⋯ < 𝑖𝑖𝑡𝑡+𝑗𝑗 = 𝑖𝑖𝑡𝑡−1
Q: What happen to exchange rate？

12

### Tài liệu bạn tìm kiếm đã sẵn sàng tải về

Tải bản đầy đủ ngay

×