EUD =? What is the pressure from this arbitrage: borrow $ → iUS↑ lend GBP → iUK↓ sell $ spot → e↑ sell GBP in future → eex ↓ Until EUD =0
4) Uncovered interest rate parity:
Question: High expectation of RMB appreciation →capital inflow
What does UIP predict about RMB interest rate? What if the Chinese interest rate goes up?
1) Covered interest arbitrage--no risk: -- Comparing the return on international investment with the return on a risk-less home investment
--Both are riskless.
Given: iUK=.04, iUS=.03, e=$2/GBP, f=$1.98/GBP,
CD=?
3) Uncovered interest arbitrage (未抵补利率套 利) a. Similarity with covered interest arbitrage: --also links four market rates to an equilibrium level b. Difference: --The return is based on speculation on expected future spot exchange rate
expected ≡ uncertain → risk
International Investment without Cover
eex
1/eex
d. The formula of the expected uncovered interest differential (EUD) EUD = (1 + if)eex/e - (1 + i) where eex is the expected future spot exchange rate e. Approximated formula:
a. General procedure to invest abroad and notations
As a Chinese, investing in USD assets, you do the following: Convert RMB at spot exchange (e=RMB/$): you get 1/e USD for each RMB yuan Invest in the USD-denominated financial asset: USD return for a yuan: [(1/e)+ (1/e)if ]=(1+ if )/e where if=the US interest rate Exchange back the USD return for RMB by forward rate f (f= RMB/$ ): (1 + if)f/e
EUD =[(eex – e)/e]+ (if - i)
[(eex – e)/e]: expected rate of appreciation (depreciation if negative) of the foreign currency
Example:
Given: iUS=.03, iUK=.04, e=$2/GBP1, eex=$2.2/GBP1,
Approximately: At parity, The forward premium on the foreign currency equals interest rate difference but with opposite sign
Example Forward discount (premium) goes with a higher (lower) interest rate:
What if capital keeps flowing in? (price level)
5) Empirical evidence on CIP and UIP: (Figure 4.2,4.3) Figure 4.2: CD = F + (iUS - iF), F=foreign/$ (U.S., Japan, Germany, France) Deviations before 1980: Actual or threatened capital control in the three countries 1980—mid-80s: -- Freer flow of money in German and Japan -- Divergences for France: Political risk Mitterrand became president in 1981: capital control 81— 86 After mid-1980s: CIP holds for all 4 currencies CIP test can indicate the level of liberalization of capital flow between countries
EUD=0 OR [(eex – e)/e]+ if = I The expected return on foreign currency investment equals the return on domestic currency investment Approximately: At parity, The expected appreciation on the foreign currency equals interest rate difference but with opposite sign
d. Illustrating CIA by Lake diagram and examples: suppose you are an American
As an American: • If CD>0, you go anticlockwise Example: Given iUK=.04, iUS=.03, e=$2/GBP1, f=$2/GBP1, CD=? • If CD<0, you go clockwise Example: Given: iUK=.04, iUS=.03, e=$2/GBP, annual forward rate=$1.96/GBP, CD = ? What is the pressure from this arbitrage: Less GBP in circulation → iUK↑ More $ in circulation → iUS↓ Buy $ spot → e ↓ sell $ forward → f ↑ Until CD = 0
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b. The formula for making arbitrage decision: the covered interest differential (CD): CD = (1 + if)f/e - (1 + i) CD= f/e+ if. f/e -1- i Add and Subtract if: CD= f/e+ if. f/e- if -1+ if – i = (f/e-1)+ if- i+ if.( f/e-1) Let F = (f-e)/e=(f/e-1): CD= F+( if- i)+ if.F Assuming both if and F are small, approximately: CD = F + (if - i)
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Figure 4.3:
EUD = Expected appre.of $ + (iUS - iF), (U.S., Japan, Germany)
Data based on a survey of market participants about their expected value of the currencies UIP does not hold, at least noes not hold: Risk premium: to compensate the uncertainty Studies show the divergence is often larger than risk premium and biased (Figure 4.3)

Keep in mind that the various international parity relations hold under some strict assumptions, such as:
Not transaction and/or transportation costs Not capital control Floating exchange regimes Not import tax and restriction, not export subsidies Investors are risk-natural
If F >0 -- Forward foreign currency premium If F<0-- Forward foreign currency discount
c. Decision rule: • If CD > 0: --Buy the foreign currency spot and sell it forward --Invest it in foreign assets → net profit from the combination of the interest rate difference and the forward premium or discount • If CD <0: Invest in opposite direction: --Buying domestic assets • If CD =0: Indifference