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Reading 18: Currency Exchange Rate (Exchange Rate (Nominal vs. Real Rates,…
Reading 18: Currency Exchange Rate
Exchange Rate
Definition
:
The price of one unit of currency in term of another
\(\frac{PriceCurrency}{BaseCurrency}\)
Nominal vs. Real Rates
Nominal Rate
Ex USD/EUR = 1.44 --> 1 EUR (Base Currency) = 1.44 USD (Price Currency)
is the quoted rate at any point in time
Real Rate
Measure change in relative purchasing power over time
\(Rate_{real}(Price/Base)=Rate_{nominal}(p/b)\times \frac{CPI_{base}}{CPI_{price}}\)
\(\Delta Rate_{real}(Price/Base)=(1+\Delta Rate_{nominal}(p/b)) \times \frac{1+\Delta CPI_{base}}{1+\Delta CPI_{price}}\)
\(\Delta Rate_{Nominal}(Price/Base)=(1+\Delta Rate_{real}(p/b)) \times \frac{1+\Delta CPI_{price}}{1+\Delta CPI_{base}}\)
Note: always remind which one is price, which one is base currency
is the nominal rate adjusted for inflation in each country compared to a base period
Approximation:
Change in Real rate = Change in Nominal Rate + Base Country's inflation - Price Country inflation
Spot vs. Forward Rates
Spot rate
:
The rate for immediate delivery
Forward rate
:
Rate for exchange at future date.
Direct vs. Indirect
Direct
:\( \frac{Domestic}{Foreign}\)
Indirect
: \( \frac{Foreign}{Domestic}\)
Foreign Exchange Market
Largest financial market in terms of daily transaction value.
Sell vs. Buy side
Buy side
Corporations, Funds, Gov and Central banks, etc.
Sell side
Large multinational banks.
Hedger vs Speculator
Hedger
Enter transactions that decrease existing foreign exchange risk.
Speculator
Enter transactions that increase existing exchange risk (to look for profit)
Appreciation vs. Depreciation
\(\Delta = \frac{Rate_{t1}}{Rate_{t0}}-1\)
When Price/Base rate decrease, you can say that BASE CURRENCY DECREASES BY \(\Delta\)% , NOT "Price currency increase by\(\Delta\)% "
To calculate the amount of appreciation for PRICE currency, must take reciprocal and then calculate \(\Delta_{reciprocal}\)
If Price Appreciate by \(\Delta\)% against Base, then Base depreciate by \(\frac{1}{1+\Delta}-1\) against Price
If
Price Depreciates
by \(\Delta\)% against Base, then Base appreciate by \(\frac{1}{1-\Delta}-1\) against Price
Cross rate
:\(\frac{C_{a}}{C_{b}} \times \frac{C_{b}}{C_{c}}=\frac{C_{a}}{C_{c}}\)
Point Basis Conversion
Point
Unit of the last digit of quotation
Spot rate: USD/EUR=1.4158
Forward quote: +25.3
-->Forward rate: USD/EUR= 1.4158+0.0025.3=1.41833
Percentage
= \(\frac{R_{forward}}{R_{Spot}}-1\)
Spot rate: USD/EUR=1.4158
Forward quote: +1.787%
-->Forward rate: USD/EUR= 1.4158x(1+0.01787)=1.4411
Forward quote is points above (below) spot
If spot < forward We say "Currency Price is traded at a FORWARD PREMIUM relative to Currency Base"
Arbitrage relationship
When the forward rate does not correctly reflect the difference between the interest rate.
How to
S1: Borrowing in one currency
S2: Convert into another at spot rate
S3: Investing the proceeds.
S4: Convert the proceeds to original currency
S5: Payback the loan and interest
S6: The remainders are riskless profits
No-arbitrage condition for 1-year forward rate
\(\frac{R_{forward}}{R_{Spot}}= \frac{1+r_{PriceCurrency}}{1+r_{BaseCurrency}}\)
The rate is quoted in annual, but you may need to find the effective monthly, quarterly or daily rate. You must convert from annual to the desirable one (by dividing the stated annual rate)
If F > S (trade at a forward premium) then \(r_{price} > r_{base}\)
To calculate arbitrage profit
Tính riêng biệt tỷ lệ vế trái và vế phải, so sánh cái nào lớn hơn, lấy hiệu số từ 2 tỷ lệ đó. Nhân hiệu với 100(%) sẽ ra % profit
Or
Step 1: Take a loan of X (dollar) at rate A%. Calculate Payment to be made = X x (1+A%)
Step 2: Convert X (dollar) into foreign currency
Step 3: Invest in foreign land for some time, earn interest
Step 4: Convert back to domestic
Step 5: Use the converted amount to pay for payment (in step 1)
Step 6: The remaining amount is risk free
Exchange Rate regimes
Country without own currency
Formal dollarization
Use the currency of another country.
Monetary Union
Several countries use a common currency
Cons:
Cannot have monetary policy nor control of your own currency
Country with their own currency
Currency broad arrangement
Explicit commitment to exchange domestic currency for a specified foreign currency at a fixed rate.
Conventional fixed peg arrangement
A country pegs its currency within margin of \(\pm \) 1% vs. other currency. Control via
Direct intervention in the FX markets
Indirectly via monetary policy changes
Pegged exchange rate within a band
A country pegs its currency within wider margin vs. other currency
Crawling peg
Exchange rate is adjusted periodically, typically for inflation adjustment.
Active: Announced and implemented
Passive: Managed but market driven
Management of exchange rate within crawling bands.
Width of the bands that identify permissible exchange rate is increased over time.
Manage floating rates
No target exchange rate, but managed through direct intervention of the FX market or monetary policy
Independently floating
Exchange-rate is completely market-driven
Ideal currency regime
Credibly fixed exchange rate
All currencies is fully convertible
Each country can have independent monetary policies to pursuit domestic objectives
Relation between Exchange Rates, Trade and Capital
Elasticity approach
Marshall-Lerner condition
:
if \(W_{export}\times \varepsilon_{export} +W_{import}\times (\varepsilon_{import}-1)=\varepsilon_{Marshall-Lener} >0\)
W: Proportion of Import. export in total trade
\(\varepsilon\): Elasticity of import, export
Depreciation of domestic currency will decrease trade deficit
As imports become more expensive and export becomes cheaper
Response to currency depreciation must be elastic enough to improve trade deficit
If \(W_{export}=W_{import}\)
The simplified version of Marshall-Lerner condition:
\(\varepsilon_{export}+\varepsilon_{import}>1\)
Change in Trade Balance=εML × Total Trade × Depreciation
New Trade balance= Export - Import + Change in Trade Balance
J-Curve effect
In short-run, due to existing contracts, export and import are relatively
inelastic
Currency depreciation may initially lead to a larger trade deficit
In long-run, elastic increases
Currency depreciation leads to a reduction in trade deficit
(X-M) = (Private savings - investment) + (tax revenue - Government Spending)
(X-M) > 0
Trade surplus when private savings + government surplus > domestic investment
(X-M) < 0
Trade deficit when (private savings - domestic investment) < budget deficit
Absorbtion Approach
Includes the effects of currency depreciation on capital flows and trade flows
(X - M) = National income - Expenditure
For depreciation to improve trade balance
National income must increase relative to expenditure
National savings (Private + Government) must increase relative to domestic investment in physical capital
Wealth effect:
if the government of a country experiencing full employment moves to depreciate its currency --> purchasing power reduces --> Households respond by reducing expenditures and increasing savings