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时间：2024-06-14
GROUP FORMATION
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Formation Deadline: July 7th, 2024
Data Assignment
Release after Quiz
Quiz 1
Saturday, 22 June 2024
Week 4 weekend
15:00-16:00
Moodle
This accounts for 15% of
your assessment
IMPORTANT RECAP
Bid Ask
Spot rate USD0.768/AUD USD0.774/AUD
BID: when WE BUY the TERM currency
ASK: when WE SELL the TERM currency
We will always get worse deals.
IMPORTANT RECAP
Spot 30-day 90-day 180-day
£:$2.0015 –30 19 – 17 26 – 22 42 – 35
SFr:$0.6963 –68 4 – 6 9 – 14 25 – 38
• Consider the following spot exchange rates along with the 30-day, 90-day and 180-day
forward quotes:
• forward bid rate < forward ask rate, therefore BASE at forward premium -> ADD
• forward bid rate > forward ask rate, therefore BASE at forward discount -> SUBSCTRACT
Forward Bid-Ask Spread Should Be Wider!
Triangular Arbitrage – Example
Bid Ask
USD1.60/GBP USD1.61/GBP
USD0.200/MYR USD0.201/MYR
MYR8.10/GBP MYR8.20/GBP
• The following table contains the spot rates for selected currencies. Determine whether an
arbitrage opportunity exists. (using direct method)
Direction 1 around the “triangle”. (CLOCKWISE direction)
• Sell GBP and buy USD at _______
• Sell USD and buy MYR at _______
• Sell MYR and buy GBP at _______
Thus, the return obtained is:
UNSW Business School
FINS5516 International Corporate Finance
Week 3
Parity Conditions (2) Fisher Effect, Interest Rate Parity, and Forecasting
Plan
Week 1: MNCs, Exchange Rate Determination and International Monetary Systems (Ch 1,2,3)
Week 2: Foreign Exchange Markets and Parity Conditions (1) PPP (Ch 6, 4)
Week 3: Parity Conditions (2) Fisher Effect, Interest Rate Parity, and Forecasting (Ch 4)
Coverage (Textbook)
Chapter 1. Introduction: Multinational Corporations and Financial Management
Chapter 2. The Determinations of Exchange Rates
Chapter 3. The International Monetary System
Chapter 4. Parity Conditions in International Finance and Corporate Forecasting
Chapter 6. The Foreign Exchange Market
Chapter 7. Currency Futures and Options Markets
Chapter 8. Currency, Interest Rate, and Credit Derivatives and Swaps
Chapter 9. Measuring and Managing Translation and Transaction Exposure
Chapter 10. Measuring and Managing Economic Exposure
Chapter 11. International Financing and National Capital Markets
Chapter 12. The Euromarkets
Chapter 13. International Portfolio Management
Chapter 14. Country Risk Analysis
Chapter 15. The Cost of Capital For Foreign Investments
Chapter 16. Corporates Strategy and Foreign Direct Investment
Chapter 17. Capital Budgeting for the Multinational Corporation
Chapter 18. Managing the International Capital Markets of Multinational Corporations
Chapter 4
Parity Conditions in International Finance and
Corporate Forecasting (2)
Parity Conditions
Parity Conditions
• A set of theoretical relationships that, in equilibrium, explain product prices, interest rates, and
spot and forward exchange rates.
• In a perfect world, arbitrage will ensure all relationships are in equilibrium.
• In the next two weeks, we will discuss 6 theoretical economic relationships:
• Absolute Purchasing Power Parity (APPP)
• Relative Purchasing Power Parity (RPPP)
• Fisher Effect (FE)
• International Fisher Effect (IFE)
• Interest Rate Parity (IRP)
• Unbiased Forward Rates Hypothesis (UFR)
Recall: General Determinants of Exchange Rates
Exchange rates vary due to differences in :
(1) Relative inflation rates
» Higher inflation → currency depreciates
(2) Relative (real) interest rates
» Higher interest rates → currency appreciates
(3) Relative economic growth (GDP) rates
» Higher GDP growth → currency appreciates
(4) Political and economic risk
» (generally) Higher risk → currency depreciates (because investors run away)
Regarding Inflation => Purchasing Power Parity
• Inflation is the logical outcome of an expansion of the money supply in excess of real
output growth.
• As the supply of money increases, the price of money, its exchange rate, must declines.
Purchasing Power Parity （PPP）
There are 2 versions of PPP:
(1) Absolute PPP:
– Asks: “What should the current exchange rate be?” (i.e., price level, S0)
(2) Relative PPP:
– Asks: “How should the exchange rate change?” (i.e., S1 – S0 = ΔS)
Absolute Purchasing Power Parity (APPP)
() =
,
,
E(et)= expected spot exchange rate at time t (direct quote).
* direct quote in currency D, its in position of term currency (numerator)
PID = domestic country Price Index
PIF = foreign country Price Index
But the assumptions are too strong for APPP to hold
RPPP is more realistic
Relative Purchasing Power Parity (RPPP)
(1) = 0 ×
1 +
1 +
() = 0 ×
(1 + )
(1 + )
E(et)= expected spot exchange rate at some future time t (direct quote).
* direct quote in currency D, its in position of term currency (numerator)
e0 = today’s spot exchange rate (direct quote).
iD = domestic country inflation rate.
iF = foreign country inflation rate.
e.g. Next year exchange rate:
Real vs. Nominal Exchange Rates
= e ×
,
,
= e ×
(1 + ,)
(1 + ,)
et = today’s spot exchange rate (direct quote, nominal)
et
real= today’s spot exchange rate (direct quote, real)
iF = foreign country inflation rate.
iD = domestic country inflation rate.
Note:
1. Adjust back to “base period” where PI =100
2. the numerator and denominator are reciprocal compared to RPPP
In essence, RPPP is to the calculate the next year nominal exchange rate,
while real exchange rate is to “remove” the influence of inflation rate (nominal)
Real vs. Nominal Exchange Rates - Example
= e ×
Suppose the price level in Australia is AUS120, the price level in the US is USD145
and nominal exchange rate is USD0.70/AUD. What is the real exchange rate?
= 0.7/ ∗
120
145
= 0.5793/
Price Index base = 100
PI = 120 means cumulative inflation 20%
3. Fisher Effect (FE)
Parity Conditions
• A set of theoretical relationships that, in equilibrium, explain product prices, interest rates, and
spot and forward exchange rates.
• In a perfect world, arbitrage will ensure all relationships are in equilibrium.
• In the next two weeks, we will discuss 6 theoretical economic relationships:
• Absolute Purchasing Power Parity (APPP)
• Relative Purchasing Power Parity (RPPP)
• Fisher Effect (FE)
• International Fisher Effect (IFE)
• Interest Rate Parity (IRP)
• Unbiased Forward Rates Hypothesis (UFR)
The Fisher Effect (FE)
• Links interest rates with inflation rates
• Real interest rates vs. Nominal interest rates
The Fisher Effect (FE)
• The Fisher Effect describes the relationship between inflation and both real and
nominal interest rates.
• What really matters to savers and investors is the net increase in wealth, the
added future consumption in return for deferring current consumption ➔ the real
interest rate
• Nominal (observed) interest rates reflect the rate of exchange between current
and future money in the market which include expected inflation
The Fisher Effect (FE)
The FE states that the nominal interest rate r is made of two components
(1) a real required rate of return a
(2) the expected inflation i
+ = ( + )( + )
Where:
r = nominal rate of return
a = real rate of return
i = expected inflation rate
➢ often approximated by
The approximation works well when the expected rate of inflation is very low.
≈+
The Fisher Effect (FE) - Example
• If an investor requires a real return of 3.5%, and the expected inflation rate is
2.5%, then the expected rate of return is:
1+=(1+)(1+)
=1+0.0351+0.025−1
=0.060875 6.0875%
Note: Expected rate of return = Nominal interest rate
• Using the approximation of the Fisher Effect, we arrive at:
≈ +
≈ 3.5%+2.5%=6%
FE – Real Interest Rates across Countries
The FE also asserts that real returns are equal across countries: aD = aF
• Why? If expected real returns were higher in one currency than another, capital would
flow to the country.
• This process of arbitrage would, in the absence of government intervention, continue
until expected real returns were equalized.
Formally
1 + = 1 + →
+
+
=
+
+
→
+
+
=
+
+
Fisher Effect: 1 + r = (1 + a)(1 + i)
FE – Real Interest Rates across Countries
− ≈ −
Difference in nominal
interest rate
Difference in inflation
rates
Assuming rD and rF are relatively small, the approximated form is
The nominal interest rate differential must equal the anticipated inflation differential.
FE – Real Interest Rates across Countries
The nominal interest rate differential must equal the anticipated inflation
differential.
• Currencies with higher rates of inflation should have higher nominal
interest rates than currencies with lower rates of inflation.
• e.g., if Australia has a 3% higher inflation rate than the US, nominal
interest rates should be approx. 3% higher in Australia.
Short-term nominal interest rates vs. Inflation
rate (2017)
– Countries with higher
inflation have higher
nominal rates.
– General consensus is that
real rates of return
differentials between
countries are small.
4. International Fisher Effect (IFE)
The International Fisher Effect (IFE)
• Links spot exchange rates with interest rates
• A combination of the PPP and the FE
The International Fisher Effect (IFE)
• PPP: exchange rate changes changes in inflation rate differentials
• A rise in Australian inflation rate relative to the other country will
decrease the value of AUD
• FE: expected inflation rate differentials nominal interest rate
differentials
• A rise in Australian inflation rate will increase Australian nominal
interest rates
• IFE= PPP + FE : exchange rate changes nominal interest rate
differentials
• A rise in Australian interest rate relative to the other country will
decrease the value of AUD
The International Fisher Effect (IFE)
• PPP: 1 = 0 ×
1 +
1 +
• IFE= PPP + FE
• FE:
1 +
1 +
=
1 +
1 +
1 = 0 ×
1 +
1 +
Understanding IFE
The IFE:
( + )
( + )
=
ഥ
0
→ ( + )
=
ഥ
0
( + )
where ഥ is the expected exchange rate (DC/FC) at time t
The one-period model:
+ =
1
0
( + ) → approxinated by − =
1 − 0
0
– Assuming is relatively small
Expected Return from
Investing at home
Expected Return from
Investing at abroad
Understanding IFE
Assuming rD and rF are relatively small, the approximated form is
1 − 0
0
≈ −
Percentage change
in exchange rate
Difference in nominal
interest rates
Generalized IFE (very similar to RPPP)
• There is no reason to assume that expectations of inflation rates are constant
per period. In practice, expectations change.
• Thus, the T-period formulation of IFE is:
• The expression of IFE is general and allows for both constant and non-constant
expectations of the rate of inflation in a country.
= 0 ×
ς=1
(1 + ,)
ς=1
(1 + ,)
IFE - Example
The one-year nominal interest rates year nominal interest rate in Australia is 4.5% and the one-
year interest rate in the US is 2%. If the current spot exchange rate is USD0.77/AUD, what is
the expected exchange rate in one year under IFE?
( + )
( + )
=
ഥ
0
→ 1,$/$ = 0,$/$ ×
+
+
The expected exchange rate in one year is USD0.77/AUD ×(1.02/1.045) = USD0.7516/AUD.
– As AUD has depreciated , this implies that the expected rate of inflation in AUS is higher
than the expected rate of inflation in the US.
5. Interest Rate Parity (IRP)
Parity Conditions
• A set of theoretical relationships that, in equilibrium, explain product prices, interest rates, and
spot and forward exchange rates.
• In a perfect world, arbitrage will ensure all relationships are in equilibrium.
• In the next two weeks, we will discuss 6 theoretical economic relationships:
• Absolute Purchasing Power Parity (APPP)
• Relative Purchasing Power Parity (RPPP)
• Fisher Effect (FE)
• International Fisher Effect (IFE)
• Interest Rate Parity (IRP)
• Unbiased Forward Rates Hypothesis (UFR)
The Interest Rate Parity (IRP)
• Links spot exchange rates, forward exchange rate, and interest rates
• The nominal interest rate differential should determine the spread
between forward and spot exchange rates
Interest Rate Parity (IRP)
(1) IFE says that the nominal interest rate differential should equal the expected change in
exchange rate
& (2) Forward rates are the market’s estimate of the spot rate at a specific date in the future
=> IRP states that interest rate differential should equal to the spread between spot and
forward exchange rates
• The currency of the country with a lower interest rate should be at a forward premium
in terms of the currency of the country with a higher rate.
• This ensures that the return on a domestic investment = the return on a hedged (or
‘‘covered’’) foreign investment of identical risk
• Notion of Covered Interest Rate Parity (CIRP)
Covered Interest Rate Parity (CIRP)
Covered IRP: Return on a domestic investment = Return on a hedged foreign
investment
( + )
=
0
( + )
where is the forward rate for settlement at time t
The one period model:
+ =
1
0
( + ) → approxinated by − =
1 − 0
0
• By approximation, interest differential = forward differential in an efficient market
with no transaction costs
One-period CIRP
= 0 ×
1 +
1 +
ft = forward exchange rate at time t (direct quote, nominal)
e0 = today’s spot exchange rate (direct quote, nominal)
rD = Nominal interest rate in domestic country
rF = Nominal interest rate in foreign country
Generalized CIRP
• There is no reason to assume that nominal interest rates are constant per
period.
• Thus, the T-period formulation of CIRP is:
• The expression of CIRP is general and allows for both constant and non-
constant expectations of the rate of inflation in a country.
= 0 ×
ς=1
(1 + ,)
ς=1
(1 + ,)
Understanding CIRP
1 − 0
0
≈ −
Forward premium
or discount
Difference in
nominal interest
rates
Understanding one-period CIRP
• If the hedged foreign return does not equal the domestic return:
• If + <
1
0
( + ) →funds will flow from domestic market to foreign market
• If + >
1
0
( + ) → funds will flow from foreign market to domestic market
• … until return rates are equalized
• CIRP implies there are no covered interest arbitrage opportunities, such that
1
0
=
+
+
• High interest rates on a currency are offset by forward discounts, low interest rates
are offset by forward premiums
Understanding one-period CIRP
• Covered IRP implies that a domestic investment (loan) can be replicated by combining a
foreign investment (loan) with a forward contract.
• Domestic Return: You invest 1 AUD today in the AU market, you will receive ( + ) AUD
next year.
• Hedged Foreign Return (6 steps):
1. You borrow 1 AUD today for a period 1 year at
2. You sell 1 AUD in the spot market and receive =
1
USD [Note that is the AUD/USD
rate]
3. You invest
1
USD in the US market, so you will receive
1
( + ) USD in one year
4. You add a forward contract to sell
1
( + ) USD next year in exchange for AUD at
the forward rate +1
5. At t+1, you sell
1
( + ) USD in exchange for
+1
( + ) AUD
6. At t+1, you need to repay ( + ) AUD
In equilibrium, there is no arbitrage <=> Under CIRP: + =
+
( + )
CIRP – Example 1
• You decide to borrow AUD10,000 and obtain the following from an analyst.
• Can you obtain an arbitrage?
Profit = Investment Value –Borrowing Cost
Rate Bid Ask
SUSD/AUD USD0.76/AUD USD0.77/AUD
FUSD/AUD USD0.50/AUD USD0.57/AUD
rAUD 5.53% 6.28%
rUSD 3.85% 4.13%
• You will buy (base) currency at the ask exchange (higher) rate
• You will sell (base) currency at the bid exchange (lower) rate
• You will borrow currency at the ask exchange (higher) rate
• You will lend currency at the bid exchange (lower) rate
CIRP – Example 1
• Step 1: You borrow AUD10,000 today @6.28%. [Repay t=1, 10,000×(1 + 0.0628) = AUD10,628)
• Step 2: You sell AUD10,000 today at USD0.76/AUD.[AUD10,000 × USD0.76/AUD = USD7,600]
• Step 3: You invest USD7,600 today @3.85%. [USD7,600 × (1 + 0.038) = USD7,892.6]
• Step 4: You add a forward contract today to sell USD7,892.6 at forward bid rate.
• Step 5: At the end of year 1, convert USD investment into AUD [7,892.6/0.57 = AUD13,846.67]
• Step 6: Profit at the end of year 1 = AUD13,846.67 – AUD10,628 = AUD3,218.67
• Therefore, Covered Interest Rate Parity does not hold.
(reciprocal of AUD ask rate = USD bid rate i.e., 1/(USD0.57/AUD)
CIRP – Example 2
• In practice, you will need to work out what currency to borrow in to obtain a riskless profit.
• As a trader for Goldman Sachs in Kuala Lumpur, you see the following prices. Is there a
possibility for arbitrage?
• We can test whether the two no-arbitrage conditions hold directly.
Rate Bid Ask
EUR Interest Rate 6.000% 6.125%
MYR Interest Rate 10.500% 10.625%
Spot Rate MYR4.6602/EUR MYR4.6622/EUR
1-year Forward Rate MYR4.9500/EUR MYR4.9650/EUR
CIRP – Example 2
• Condition 1: No Inward Arbitrage
• There exists no inward arbitrage if and only if the quoted forward ask rate satisfies:
Rate Bid Ask
EUR Interest Rate 6.000% 6.125%
MYR Interest Rate 10.500% 10.625%
Spot Rate MYR4.6602/EUR MYR4.6622/EUR
1-year Forward Rate MYR4.9500/EUR MYR4.9650/EUR
>
1 + ,
1 + ,
Synthetic Forward Rate or Equilibrium Forward Rate
CIRP – Example 2
• Condition 1: No Inward Arbitrage
• There exists no inward arbitrage if and only if the quoted forward ask rate satisfies:
>
1 + ,
1 + ,
4.9650/ >
1 + 0.10500
1 + 0.06125
4.6602/ = 4.8523/
• The right-hand side of the inequality specifies the minimum forward ask rate. Above
that, no arbitrage can be made by borrowing EUR to invest in MYR.
CIRP – Example 2
• Condition 2: No Outward Arbitrage
• There exists no outward arbitrage if and only if the quoted forward bid rate satisfies:
Rate Bid Ask
EUR Interest Rate 6.000% 6.125%
MYR Interest Rate 10.500% 10.625%
Spot Rate MYR4.6602/EUR MYR4.6622/EUR
1-year Forward Rate MYR4.9500/EUR MYR4.9650/EUR
<
1 + ,
1 + ,
Synthetic Forward Rate or Equilibrium Forward Rate
CIRP – Example 2
• Condition 1: No Outward Arbitrage
• There exists no outward arbitrage if and only if the quoted forward bid rate satisfies:
4.9500/ <
1 + 0.10625
1 + 0.06000
4.6622/ = 4.8656/
• The right-hand side of the inequality specifies the maximum forward bid rate. Below
that, no arbitrage can be made by borrowing MYR to invest in EUR.
<
1 + ,
1 + ,
Therefore, we will borrow MYR!
CIRP – Example 2
• Step 1: You borrow 1 MYR today @10.625%. [Repay t=1, MYR1×(1 + 0.10625) = MYR1.10625)
• Step 2: You sell 1 MYR today at 1/ (MYR4.6622/EUR). [MYR1/(MYR4.6622/EUR) = EUR0.21449]
• Step 3: You invest EUR0.21449 today @6.000%. [EUR0.21449 × (1 + 0.06) = EUR0.22736]
• Step 4: You add a forward contract today to sell EUR0.22736 at forward bid rate.
• Step 5: At the end of year 1, convert EUR investment into MYR → EUR0.22736 ×
MYR4.9500/EUR = MYR1.12543
• Step 6: Profit at the end of year 1 = MYR1.12543 – MYR1.10625 = MYR0.01918
CIRP – Example 2 (optional)
Proof of Synthetic Forward Rate Condition:
You made a profit!
CIRP – Conclusion and implication
In summary, CIRP provides two implications (can be understood in two ways):
1. A domestic investment can be replicated with a foreign investment + a forward
contract.
+ =
+1
( + )
– If = 3%, = AU$1.2/US$, +1 = AU$1.25/US$, then = ?.
1 + = 1.25/1.2 x (1+3%) = 1.07 → = 7%
2. A forward contract can be replicated with money market transactions.
+1 =
+
+
+1 = 1.2 x (1+7%)/(1+3%) = AU$1.25/US$ → Forward Premium
Real word
• Deviations from covered interest
rate parity are very small prior to
the great financial crisis (2008-
2010).
• During the crisis there are large
deviations as arbitrageurs face a
lack of funding.
• But why do large deviations exist
after the crisis? Research points to
new regulation preventing arbitrage
from taking place especially at the
end of the quarter when banks
need to disclose their capital
requirements.
Interest Parity Deviations During the Financial
Crisis
Real word
• Interest rate parity holds within a certain range, due to transaction costs, spot
and forward spreads, and brokerage fees.
• Further deviations can occur due to default risk, political risk, capital controls, or
taxes.
• Governments may restrict exchange of currencies and capital inflows or
outflows
• Arbitrage will not always occur if the covered interest differential < transaction costs.
• Empirically, deviations from IRP tend to be small and short-lived
• Although they increase with market volatility
Uncovered Interest Rate Parity (UIRP)
• Covered Interest Rate Parity (CIRP) implies that a forward contract can be replicated by
combining market transactions. 1 = 0
+
+
• Combining with IFE : 1 = 0
+
+
, we will have the unbiased forward rate condition:
1 = 1
• => Uncovered Interest Rate Parity (UIRP) assumes traders remain exposed to exchange
rate risk and make, on average, zero profits from trading. the forward rate should reflect
the expected future spot rate on the date of settlement of the forward contract.
1 = 1 = 0 ×
1 +
1 +
Generalized UIRP
• There is no reason to assume that nominal interest rates are constant per
period.
• Thus, the T-period formulation of UIRP is:
• The expression of UIRP is general and allows for both constant and non-
constant expectations of the rate of inflation in a country.
= 0 ×
ς=1
(1 + ,)
ς=1
(1 + ,)
6. Unbiased Forward Rate (UFR)
Unbiased Forward Rate (UFR)
• Links forward rates with future spot exchange rates
• Forward differential should equal the expected change in exchange rates
Unbiased Forward Rate (UFR)
Covered IRP: 1 = 0
+
+
Uncovered IRP or the IFE: 1 = 0
+
+
Combine the two parity conditions, we have the unbiased forward rate condition:
1 = 1
where 1 is the expected future spot rate
• The forward rate should reflect the expected future spot rate on the date of
settlement of the forward contract
Understanding UFR
The UFR can also be expressed as
1 − 0
0
=
1 − 0
0
• % forward premium = % expected exchange rate change
Forward rates will be an unbiased predictor of future spot rate when the market form
unbiased expectations of future spot rate and speculators trade forward contracts at
prices equal to market expectations.
• Investments involve risk, speculators often demand premium for holding a forward
contract
• This is sufficient to have market efficiency (i.e. no arbitrage)
– The forward rate will then not exactly equal the expected future spot rate
– Rather, the forward premium/discount will equal the expected spot rate change
UFR in Reality
• Unbiased predictors imply expected forecast error = 0
– Large errors can exist, but they should cancel out on average
• Empirically, UFR does not hold up very well
– Profitable carry trade by hedge funds: go long in foreign currencies that trade
at discount and go short in currencies that trade at a premium
– Sometimes anticipated events do not materialize (e.g. Peso problem),
invalidating statistical evidence
• Can still be consistent with market efficiency in the presence of time-varying risk
premiums
UFR in Reality: Carry Trade Example
Suppose the JPY/USD spot exchange rate is ¥100/$, the 3-month forward rate is
¥99.17/$.
1. What is the annualized forward discount?
Forward premium or discount (annual) = (99.17-100)/100 x (360/90) = -3.32%
The annualized forward discount is -3.32%.
2. In which case can a gain be made from buying USD?
• Buying USD is cheaper in the forward market. You can therefore gain by buying USD
forward and selling them at the spot rate in 3 months.
• As long as the spot JPY/USD exchange rate in 3 months does not depreciate by more
than (3.32%/4) = 0.83%, you can gain from this transaction.
• UFR would imply the USD will depreciate by exactly 0.83%!
Parity Conditions - Summary
4 definitions:
1. The spot exchange rate,
2. The forward exchange rate,
3. The interest rate,
4. The inflation,
4 Derived Key Terms:
1. The interest rate differentials, −
2. The inflation differentials, −
3. The forward differentials (forward
discount or premium),
−0
0
4. The exchange rate changes,
−
Currency Forecasting
Currency Forecasting
• Forecasting exchange rates can be crucial for a firm’s or an
investor’s future operations and profit.
• Market-based Forecasts
• Model-based Forecasts
Successful Currency Forecasting
Currency forecasting is successful only if at least one of the following criteria is met:
– Uses superior and exclusive forecasting model
– Uses information not yet incorporated in the market
– Exploits small, temporary deviations from equilibrium
– Predicts government intervention in foreign markets
Unfortunately, it is not easy or straightforward to do …
Self-correcting
Unlikely to be sustainable
Small and temporary
Feasible in fixed-rate systems
What about floating rate systems?
Market-based Forecasts
• If market efficiency holds, markets have incorporated expected currency changes in
interest and forward rates. Currency forecasts can be obtained by extracting the
predictions embodied in interest and forward rates.
Market-based Forecasts
➢ Forward rate
• Following UFR, forward rate is an unbiased estimate of the future expected spot rate:
1 = 1
• Simple and easy to use
• … but longer-term forward contracts (> 1 year) are limited
➢ Interest rate
• Following IFE: interest rate differential predicts future expected spot rates:
1 = 0
+
+
• Good for predicting longer term rates
• … but investors may require different returns on domestic vs foreign investments
Market-based Forecasts
There are two principal model-based approaches:
1. Fundamental analysis
– Most common approach
2. Technical analysis
1. Fundamental analysis
Fundamental analysis relies on the examination of macroeconomic variables that may
influence future exchange rates
• e.g. relative inflation rates, interest rates, national income growth, money supply etc.
Difficulties:
1. Need to select the right fundamentals
2. Need to be able to forecast these fundamentals
• Difficult task, how to forecast interest rates?
3. Forecasts of fundamentals needs to be different from those of the market
• Otherwise exchange rate will have already incorporated the anticipated changes in
fundamentals
1. Fundamental analysis - Example
Forecast Procedures:
Step 1: Estimate relation between historical macroeconomic variables and historical
exchange rates
Step 2: Estimate future exchange rates using the estimated relations
Suppose we use the following fundamental model to estimate the AUD/USD exchange rate in a
quarter:
+1−
= 0 + 1 + 2 + 3 ℎ
+ 4 ℎ +
• β0 = constant, expected value of the dependent variable if all X=0
• βn = coefficient(s), sensitivity of the dependent variable to changes in
independent variables
1. Fundamental analysis - Example
Using quarterly data from 2004 March - 2018 December:
A 1% increase in inflation differential is related to 1.5% increase in quarterly AUD/USD
exchange rate. – Does this relation make sense?
Estimated Coefficients:
• By how much does the exchange
rate change if the interest differential,
inflation differential, or GDP growth
changes by one unit
• Do the signs make sense based on
parity conditions?
• PPP: Higher expected inflation
→ Currency should depreciate
• IFE: Higher nominal interest rate
→ Currency should depreciate
1. Fundamental analysis - Example
Using quarterly data from 2004 March - 2018 December:
Interest rate differential and US GDP growth is not
significantly related to quarterly changes in AUS/USD rates
Testing significance
■ A coefficient’s p-value shows the
probability of observing this value of β if
the true value of β = 0
■ If β = 0, the independent variables
(interest rate differential, inflation rate
differential, GDP growth) does not have
an effect on the dependent variable
(exchange rate changes)
■ If the likelihood of β = 0 is < 0.1, 0.05, or
0.01, β is statistically significantly
related to Y at the 10%, 5%, or 1% level
1. Fundamental analysis - Example
Using quarterly data from 2004 March - 2018 December:
Prediction: Suppose economic figures in 2020 June are
What is the forecasted change in AUD/USD exchange
rate over the next quarter?
• Substitute 2020 June value into the estimated
model:
ℎ− = 0 + 1 +
2 + 3 ℎ +
4 ℎ
= -0.0210+(-0.7397)x(-0.0029815)+… = -0.035
USD is predicted to depreciate by 3.5% over the
quarter.
Interest Rate Difference -0.0029815
Inflation Rate Difference -0.0074781
AU GDP Growth 0.00253007
US GDP Growth 0.0082853
2. Technical analysis
Discover price patterns in past price and volume fluctuations that repeat themselves
• Ignore economic and political factors
• Via charting or trend analysis
Evaluating Models
• Can profits be made in the forward or money markets by using forecast
models?
• Good or bad is relative
– “Good” models are able to make better predictions than “bad” models
– … many models do not seem to outperform random walk models
• Market efficiency:
– All publicly available information is incorporated in the market price
– Future exchange rate changes should be unpredictable
Currency Forecasting
• The previous parity conditions have implications on currency forecasting
• If exchange rates can be forecasted perfectly, then exchange rate risk is
eliminated.
• Unfortunately, it is not easy or straightforward to do. The Data Practice worksheet
and assignment will give you a sense of the work involved in forecasting
exchange rates.
• Research studies have identified that random walk models are superior than most
structural models.
• Market efficiency:
• All publicly available information is incorporated in the market price.
• Future exchange rate changes should be unpredictable.
https://docs.google.com/spreadsheets/d/1uDWGAqFXrot7WrVReMy9QyEOhaSAjCSrsKE1
kz1Go7c/edit?usp=sharing
Formation Deadline: July 7th, 2024
Data Assignment
Release after Quiz
Quiz 1
Saturday, 22 June 2024
Week 4 weekend
15:00-16:00
Moodle
This accounts for 15% of
your assessment
IMPORTANT RECAP
Bid Ask
Spot rate USD0.768/AUD USD0.774/AUD
BID: when WE BUY the TERM currency
ASK: when WE SELL the TERM currency
We will always get worse deals.
IMPORTANT RECAP
Spot 30-day 90-day 180-day
£:$2.0015 –30 19 – 17 26 – 22 42 – 35
SFr:$0.6963 –68 4 – 6 9 – 14 25 – 38
• Consider the following spot exchange rates along with the 30-day, 90-day and 180-day
forward quotes:
• forward bid rate < forward ask rate, therefore BASE at forward premium -> ADD
• forward bid rate > forward ask rate, therefore BASE at forward discount -> SUBSCTRACT
Forward Bid-Ask Spread Should Be Wider!
Triangular Arbitrage – Example
Bid Ask
USD1.60/GBP USD1.61/GBP
USD0.200/MYR USD0.201/MYR
MYR8.10/GBP MYR8.20/GBP
• The following table contains the spot rates for selected currencies. Determine whether an
arbitrage opportunity exists. (using direct method)
Direction 1 around the “triangle”. (CLOCKWISE direction)
• Sell GBP and buy USD at _______
• Sell USD and buy MYR at _______
• Sell MYR and buy GBP at _______
Thus, the return obtained is:
UNSW Business School
FINS5516 International Corporate Finance
Week 3
Parity Conditions (2) Fisher Effect, Interest Rate Parity, and Forecasting
Plan
Week 1: MNCs, Exchange Rate Determination and International Monetary Systems (Ch 1,2,3)
Week 2: Foreign Exchange Markets and Parity Conditions (1) PPP (Ch 6, 4)
Week 3: Parity Conditions (2) Fisher Effect, Interest Rate Parity, and Forecasting (Ch 4)
Coverage (Textbook)
Chapter 1. Introduction: Multinational Corporations and Financial Management
Chapter 2. The Determinations of Exchange Rates
Chapter 3. The International Monetary System
Chapter 4. Parity Conditions in International Finance and Corporate Forecasting
Chapter 6. The Foreign Exchange Market
Chapter 7. Currency Futures and Options Markets
Chapter 8. Currency, Interest Rate, and Credit Derivatives and Swaps
Chapter 9. Measuring and Managing Translation and Transaction Exposure
Chapter 10. Measuring and Managing Economic Exposure
Chapter 11. International Financing and National Capital Markets
Chapter 12. The Euromarkets
Chapter 13. International Portfolio Management
Chapter 14. Country Risk Analysis
Chapter 15. The Cost of Capital For Foreign Investments
Chapter 16. Corporates Strategy and Foreign Direct Investment
Chapter 17. Capital Budgeting for the Multinational Corporation
Chapter 18. Managing the International Capital Markets of Multinational Corporations
Chapter 4
Parity Conditions in International Finance and
Corporate Forecasting (2)
Parity Conditions
Parity Conditions
• A set of theoretical relationships that, in equilibrium, explain product prices, interest rates, and
spot and forward exchange rates.
• In a perfect world, arbitrage will ensure all relationships are in equilibrium.
• In the next two weeks, we will discuss 6 theoretical economic relationships:
• Absolute Purchasing Power Parity (APPP)
• Relative Purchasing Power Parity (RPPP)
• Fisher Effect (FE)
• International Fisher Effect (IFE)
• Interest Rate Parity (IRP)
• Unbiased Forward Rates Hypothesis (UFR)
Recall: General Determinants of Exchange Rates
Exchange rates vary due to differences in :
(1) Relative inflation rates
» Higher inflation → currency depreciates
(2) Relative (real) interest rates
» Higher interest rates → currency appreciates
(3) Relative economic growth (GDP) rates
» Higher GDP growth → currency appreciates
(4) Political and economic risk
» (generally) Higher risk → currency depreciates (because investors run away)
Regarding Inflation => Purchasing Power Parity
• Inflation is the logical outcome of an expansion of the money supply in excess of real
output growth.
• As the supply of money increases, the price of money, its exchange rate, must declines.
Purchasing Power Parity （PPP）
There are 2 versions of PPP:
(1) Absolute PPP:
– Asks: “What should the current exchange rate be?” (i.e., price level, S0)
(2) Relative PPP:
– Asks: “How should the exchange rate change?” (i.e., S1 – S0 = ΔS)
Absolute Purchasing Power Parity (APPP)
() =
,
,
E(et)= expected spot exchange rate at time t (direct quote).
* direct quote in currency D, its in position of term currency (numerator)
PID = domestic country Price Index
PIF = foreign country Price Index
But the assumptions are too strong for APPP to hold
RPPP is more realistic
Relative Purchasing Power Parity (RPPP)
(1) = 0 ×
1 +
1 +
() = 0 ×
(1 + )
(1 + )
E(et)= expected spot exchange rate at some future time t (direct quote).
* direct quote in currency D, its in position of term currency (numerator)
e0 = today’s spot exchange rate (direct quote).
iD = domestic country inflation rate.
iF = foreign country inflation rate.
e.g. Next year exchange rate:
Real vs. Nominal Exchange Rates
= e ×
,
,
= e ×
(1 + ,)
(1 + ,)
et = today’s spot exchange rate (direct quote, nominal)
et
real= today’s spot exchange rate (direct quote, real)
iF = foreign country inflation rate.
iD = domestic country inflation rate.
Note:
1. Adjust back to “base period” where PI =100
2. the numerator and denominator are reciprocal compared to RPPP
In essence, RPPP is to the calculate the next year nominal exchange rate,
while real exchange rate is to “remove” the influence of inflation rate (nominal)
Real vs. Nominal Exchange Rates - Example
= e ×
Suppose the price level in Australia is AUS120, the price level in the US is USD145
and nominal exchange rate is USD0.70/AUD. What is the real exchange rate?
= 0.7/ ∗
120
145
= 0.5793/
Price Index base = 100
PI = 120 means cumulative inflation 20%
3. Fisher Effect (FE)
Parity Conditions
• A set of theoretical relationships that, in equilibrium, explain product prices, interest rates, and
spot and forward exchange rates.
• In a perfect world, arbitrage will ensure all relationships are in equilibrium.
• In the next two weeks, we will discuss 6 theoretical economic relationships:
• Absolute Purchasing Power Parity (APPP)
• Relative Purchasing Power Parity (RPPP)
• Fisher Effect (FE)
• International Fisher Effect (IFE)
• Interest Rate Parity (IRP)
• Unbiased Forward Rates Hypothesis (UFR)
The Fisher Effect (FE)
• Links interest rates with inflation rates
• Real interest rates vs. Nominal interest rates
The Fisher Effect (FE)
• The Fisher Effect describes the relationship between inflation and both real and
nominal interest rates.
• What really matters to savers and investors is the net increase in wealth, the
added future consumption in return for deferring current consumption ➔ the real
interest rate
• Nominal (observed) interest rates reflect the rate of exchange between current
and future money in the market which include expected inflation
The Fisher Effect (FE)
The FE states that the nominal interest rate r is made of two components
(1) a real required rate of return a
(2) the expected inflation i
+ = ( + )( + )
Where:
r = nominal rate of return
a = real rate of return
i = expected inflation rate
➢ often approximated by
The approximation works well when the expected rate of inflation is very low.
≈+
The Fisher Effect (FE) - Example
• If an investor requires a real return of 3.5%, and the expected inflation rate is
2.5%, then the expected rate of return is:
1+=(1+)(1+)
=1+0.0351+0.025−1
=0.060875 6.0875%
Note: Expected rate of return = Nominal interest rate
• Using the approximation of the Fisher Effect, we arrive at:
≈ +
≈ 3.5%+2.5%=6%
FE – Real Interest Rates across Countries
The FE also asserts that real returns are equal across countries: aD = aF
• Why? If expected real returns were higher in one currency than another, capital would
flow to the country.
• This process of arbitrage would, in the absence of government intervention, continue
until expected real returns were equalized.
Formally
1 + = 1 + →
+
+
=
+
+
→
+
+
=
+
+
Fisher Effect: 1 + r = (1 + a)(1 + i)
FE – Real Interest Rates across Countries
− ≈ −
Difference in nominal
interest rate
Difference in inflation
rates
Assuming rD and rF are relatively small, the approximated form is
The nominal interest rate differential must equal the anticipated inflation differential.
FE – Real Interest Rates across Countries
The nominal interest rate differential must equal the anticipated inflation
differential.
• Currencies with higher rates of inflation should have higher nominal
interest rates than currencies with lower rates of inflation.
• e.g., if Australia has a 3% higher inflation rate than the US, nominal
interest rates should be approx. 3% higher in Australia.
Short-term nominal interest rates vs. Inflation
rate (2017)
– Countries with higher
inflation have higher
nominal rates.
– General consensus is that
real rates of return
differentials between
countries are small.
4. International Fisher Effect (IFE)
The International Fisher Effect (IFE)
• Links spot exchange rates with interest rates
• A combination of the PPP and the FE
The International Fisher Effect (IFE)
• PPP: exchange rate changes changes in inflation rate differentials
• A rise in Australian inflation rate relative to the other country will
decrease the value of AUD
• FE: expected inflation rate differentials nominal interest rate
differentials
• A rise in Australian inflation rate will increase Australian nominal
interest rates
• IFE= PPP + FE : exchange rate changes nominal interest rate
differentials
• A rise in Australian interest rate relative to the other country will
decrease the value of AUD
The International Fisher Effect (IFE)
• PPP: 1 = 0 ×
1 +
1 +
• IFE= PPP + FE
• FE:
1 +
1 +
=
1 +
1 +
1 = 0 ×
1 +
1 +
Understanding IFE
The IFE:
( + )
( + )
=
ഥ
0
→ ( + )
=
ഥ
0
( + )
where ഥ is the expected exchange rate (DC/FC) at time t
The one-period model:
+ =
1
0
( + ) → approxinated by − =
1 − 0
0
– Assuming is relatively small
Expected Return from
Investing at home
Expected Return from
Investing at abroad
Understanding IFE
Assuming rD and rF are relatively small, the approximated form is
1 − 0
0
≈ −
Percentage change
in exchange rate
Difference in nominal
interest rates
Generalized IFE (very similar to RPPP)
• There is no reason to assume that expectations of inflation rates are constant
per period. In practice, expectations change.
• Thus, the T-period formulation of IFE is:
• The expression of IFE is general and allows for both constant and non-constant
expectations of the rate of inflation in a country.
= 0 ×
ς=1
(1 + ,)
ς=1
(1 + ,)
IFE - Example
The one-year nominal interest rates year nominal interest rate in Australia is 4.5% and the one-
year interest rate in the US is 2%. If the current spot exchange rate is USD0.77/AUD, what is
the expected exchange rate in one year under IFE?
( + )
( + )
=
ഥ
0
→ 1,$/$ = 0,$/$ ×
+
+
The expected exchange rate in one year is USD0.77/AUD ×(1.02/1.045) = USD0.7516/AUD.
– As AUD has depreciated , this implies that the expected rate of inflation in AUS is higher
than the expected rate of inflation in the US.
5. Interest Rate Parity (IRP)
Parity Conditions
• A set of theoretical relationships that, in equilibrium, explain product prices, interest rates, and
spot and forward exchange rates.
• In a perfect world, arbitrage will ensure all relationships are in equilibrium.
• In the next two weeks, we will discuss 6 theoretical economic relationships:
• Absolute Purchasing Power Parity (APPP)
• Relative Purchasing Power Parity (RPPP)
• Fisher Effect (FE)
• International Fisher Effect (IFE)
• Interest Rate Parity (IRP)
• Unbiased Forward Rates Hypothesis (UFR)
The Interest Rate Parity (IRP)
• Links spot exchange rates, forward exchange rate, and interest rates
• The nominal interest rate differential should determine the spread
between forward and spot exchange rates
Interest Rate Parity (IRP)
(1) IFE says that the nominal interest rate differential should equal the expected change in
exchange rate
& (2) Forward rates are the market’s estimate of the spot rate at a specific date in the future
=> IRP states that interest rate differential should equal to the spread between spot and
forward exchange rates
• The currency of the country with a lower interest rate should be at a forward premium
in terms of the currency of the country with a higher rate.
• This ensures that the return on a domestic investment = the return on a hedged (or
‘‘covered’’) foreign investment of identical risk
• Notion of Covered Interest Rate Parity (CIRP)
Covered Interest Rate Parity (CIRP)
Covered IRP: Return on a domestic investment = Return on a hedged foreign
investment
( + )
=
0
( + )
where is the forward rate for settlement at time t
The one period model:
+ =
1
0
( + ) → approxinated by − =
1 − 0
0
• By approximation, interest differential = forward differential in an efficient market
with no transaction costs
One-period CIRP
= 0 ×
1 +
1 +
ft = forward exchange rate at time t (direct quote, nominal)
e0 = today’s spot exchange rate (direct quote, nominal)
rD = Nominal interest rate in domestic country
rF = Nominal interest rate in foreign country
Generalized CIRP
• There is no reason to assume that nominal interest rates are constant per
period.
• Thus, the T-period formulation of CIRP is:
• The expression of CIRP is general and allows for both constant and non-
constant expectations of the rate of inflation in a country.
= 0 ×
ς=1
(1 + ,)
ς=1
(1 + ,)
Understanding CIRP
1 − 0
0
≈ −
Forward premium
or discount
Difference in
nominal interest
rates
Understanding one-period CIRP
• If the hedged foreign return does not equal the domestic return:
• If + <
1
0
( + ) →funds will flow from domestic market to foreign market
• If + >
1
0
( + ) → funds will flow from foreign market to domestic market
• … until return rates are equalized
• CIRP implies there are no covered interest arbitrage opportunities, such that
1
0
=
+
+
• High interest rates on a currency are offset by forward discounts, low interest rates
are offset by forward premiums
Understanding one-period CIRP
• Covered IRP implies that a domestic investment (loan) can be replicated by combining a
foreign investment (loan) with a forward contract.
• Domestic Return: You invest 1 AUD today in the AU market, you will receive ( + ) AUD
next year.
• Hedged Foreign Return (6 steps):
1. You borrow 1 AUD today for a period 1 year at
2. You sell 1 AUD in the spot market and receive =
1
USD [Note that is the AUD/USD
rate]
3. You invest
1
USD in the US market, so you will receive
1
( + ) USD in one year
4. You add a forward contract to sell
1
( + ) USD next year in exchange for AUD at
the forward rate +1
5. At t+1, you sell
1
( + ) USD in exchange for
+1
( + ) AUD
6. At t+1, you need to repay ( + ) AUD
In equilibrium, there is no arbitrage <=> Under CIRP: + =
+
( + )
CIRP – Example 1
• You decide to borrow AUD10,000 and obtain the following from an analyst.
• Can you obtain an arbitrage?
Profit = Investment Value –Borrowing Cost
Rate Bid Ask
SUSD/AUD USD0.76/AUD USD0.77/AUD
FUSD/AUD USD0.50/AUD USD0.57/AUD
rAUD 5.53% 6.28%
rUSD 3.85% 4.13%
• You will buy (base) currency at the ask exchange (higher) rate
• You will sell (base) currency at the bid exchange (lower) rate
• You will borrow currency at the ask exchange (higher) rate
• You will lend currency at the bid exchange (lower) rate
CIRP – Example 1
• Step 1: You borrow AUD10,000 today @6.28%. [Repay t=1, 10,000×(1 + 0.0628) = AUD10,628)
• Step 2: You sell AUD10,000 today at USD0.76/AUD.[AUD10,000 × USD0.76/AUD = USD7,600]
• Step 3: You invest USD7,600 today @3.85%. [USD7,600 × (1 + 0.038) = USD7,892.6]
• Step 4: You add a forward contract today to sell USD7,892.6 at forward bid rate.
• Step 5: At the end of year 1, convert USD investment into AUD [7,892.6/0.57 = AUD13,846.67]
• Step 6: Profit at the end of year 1 = AUD13,846.67 – AUD10,628 = AUD3,218.67
• Therefore, Covered Interest Rate Parity does not hold.
(reciprocal of AUD ask rate = USD bid rate i.e., 1/(USD0.57/AUD)
CIRP – Example 2
• In practice, you will need to work out what currency to borrow in to obtain a riskless profit.
• As a trader for Goldman Sachs in Kuala Lumpur, you see the following prices. Is there a
possibility for arbitrage?
• We can test whether the two no-arbitrage conditions hold directly.
Rate Bid Ask
EUR Interest Rate 6.000% 6.125%
MYR Interest Rate 10.500% 10.625%
Spot Rate MYR4.6602/EUR MYR4.6622/EUR
1-year Forward Rate MYR4.9500/EUR MYR4.9650/EUR
CIRP – Example 2
• Condition 1: No Inward Arbitrage
• There exists no inward arbitrage if and only if the quoted forward ask rate satisfies:
Rate Bid Ask
EUR Interest Rate 6.000% 6.125%
MYR Interest Rate 10.500% 10.625%
Spot Rate MYR4.6602/EUR MYR4.6622/EUR
1-year Forward Rate MYR4.9500/EUR MYR4.9650/EUR
>
1 + ,
1 + ,
Synthetic Forward Rate or Equilibrium Forward Rate
CIRP – Example 2
• Condition 1: No Inward Arbitrage
• There exists no inward arbitrage if and only if the quoted forward ask rate satisfies:
>
1 + ,
1 + ,
4.9650/ >
1 + 0.10500
1 + 0.06125
4.6602/ = 4.8523/
• The right-hand side of the inequality specifies the minimum forward ask rate. Above
that, no arbitrage can be made by borrowing EUR to invest in MYR.
CIRP – Example 2
• Condition 2: No Outward Arbitrage
• There exists no outward arbitrage if and only if the quoted forward bid rate satisfies:
Rate Bid Ask
EUR Interest Rate 6.000% 6.125%
MYR Interest Rate 10.500% 10.625%
Spot Rate MYR4.6602/EUR MYR4.6622/EUR
1-year Forward Rate MYR4.9500/EUR MYR4.9650/EUR
<
1 + ,
1 + ,
Synthetic Forward Rate or Equilibrium Forward Rate
CIRP – Example 2
• Condition 1: No Outward Arbitrage
• There exists no outward arbitrage if and only if the quoted forward bid rate satisfies:
4.9500/ <
1 + 0.10625
1 + 0.06000
4.6622/ = 4.8656/
• The right-hand side of the inequality specifies the maximum forward bid rate. Below
that, no arbitrage can be made by borrowing MYR to invest in EUR.
<
1 + ,
1 + ,
Therefore, we will borrow MYR!
CIRP – Example 2
• Step 1: You borrow 1 MYR today @10.625%. [Repay t=1, MYR1×(1 + 0.10625) = MYR1.10625)
• Step 2: You sell 1 MYR today at 1/ (MYR4.6622/EUR). [MYR1/(MYR4.6622/EUR) = EUR0.21449]
• Step 3: You invest EUR0.21449 today @6.000%. [EUR0.21449 × (1 + 0.06) = EUR0.22736]
• Step 4: You add a forward contract today to sell EUR0.22736 at forward bid rate.
• Step 5: At the end of year 1, convert EUR investment into MYR → EUR0.22736 ×
MYR4.9500/EUR = MYR1.12543
• Step 6: Profit at the end of year 1 = MYR1.12543 – MYR1.10625 = MYR0.01918
CIRP – Example 2 (optional)
Proof of Synthetic Forward Rate Condition:
You made a profit!
CIRP – Conclusion and implication
In summary, CIRP provides two implications (can be understood in two ways):
1. A domestic investment can be replicated with a foreign investment + a forward
contract.
+ =
+1
( + )
– If = 3%, = AU$1.2/US$, +1 = AU$1.25/US$, then = ?.
1 + = 1.25/1.2 x (1+3%) = 1.07 → = 7%
2. A forward contract can be replicated with money market transactions.
+1 =
+
+
+1 = 1.2 x (1+7%)/(1+3%) = AU$1.25/US$ → Forward Premium
Real word
• Deviations from covered interest
rate parity are very small prior to
the great financial crisis (2008-
2010).
• During the crisis there are large
deviations as arbitrageurs face a
lack of funding.
• But why do large deviations exist
after the crisis? Research points to
new regulation preventing arbitrage
from taking place especially at the
end of the quarter when banks
need to disclose their capital
requirements.
Interest Parity Deviations During the Financial
Crisis
Real word
• Interest rate parity holds within a certain range, due to transaction costs, spot
and forward spreads, and brokerage fees.
• Further deviations can occur due to default risk, political risk, capital controls, or
taxes.
• Governments may restrict exchange of currencies and capital inflows or
outflows
• Arbitrage will not always occur if the covered interest differential < transaction costs.
• Empirically, deviations from IRP tend to be small and short-lived
• Although they increase with market volatility
Uncovered Interest Rate Parity (UIRP)
• Covered Interest Rate Parity (CIRP) implies that a forward contract can be replicated by
combining market transactions. 1 = 0
+
+
• Combining with IFE : 1 = 0
+
+
, we will have the unbiased forward rate condition:
1 = 1
• => Uncovered Interest Rate Parity (UIRP) assumes traders remain exposed to exchange
rate risk and make, on average, zero profits from trading. the forward rate should reflect
the expected future spot rate on the date of settlement of the forward contract.
1 = 1 = 0 ×
1 +
1 +
Generalized UIRP
• There is no reason to assume that nominal interest rates are constant per
period.
• Thus, the T-period formulation of UIRP is:
• The expression of UIRP is general and allows for both constant and non-
constant expectations of the rate of inflation in a country.
= 0 ×
ς=1
(1 + ,)
ς=1
(1 + ,)
6. Unbiased Forward Rate (UFR)
Unbiased Forward Rate (UFR)
• Links forward rates with future spot exchange rates
• Forward differential should equal the expected change in exchange rates
Unbiased Forward Rate (UFR)
Covered IRP: 1 = 0
+
+
Uncovered IRP or the IFE: 1 = 0
+
+
Combine the two parity conditions, we have the unbiased forward rate condition:
1 = 1
where 1 is the expected future spot rate
• The forward rate should reflect the expected future spot rate on the date of
settlement of the forward contract
Understanding UFR
The UFR can also be expressed as
1 − 0
0
=
1 − 0
0
• % forward premium = % expected exchange rate change
Forward rates will be an unbiased predictor of future spot rate when the market form
unbiased expectations of future spot rate and speculators trade forward contracts at
prices equal to market expectations.
• Investments involve risk, speculators often demand premium for holding a forward
contract
• This is sufficient to have market efficiency (i.e. no arbitrage)
– The forward rate will then not exactly equal the expected future spot rate
– Rather, the forward premium/discount will equal the expected spot rate change
UFR in Reality
• Unbiased predictors imply expected forecast error = 0
– Large errors can exist, but they should cancel out on average
• Empirically, UFR does not hold up very well
– Profitable carry trade by hedge funds: go long in foreign currencies that trade
at discount and go short in currencies that trade at a premium
– Sometimes anticipated events do not materialize (e.g. Peso problem),
invalidating statistical evidence
• Can still be consistent with market efficiency in the presence of time-varying risk
premiums
UFR in Reality: Carry Trade Example
Suppose the JPY/USD spot exchange rate is ¥100/$, the 3-month forward rate is
¥99.17/$.
1. What is the annualized forward discount?
Forward premium or discount (annual) = (99.17-100)/100 x (360/90) = -3.32%
The annualized forward discount is -3.32%.
2. In which case can a gain be made from buying USD?
• Buying USD is cheaper in the forward market. You can therefore gain by buying USD
forward and selling them at the spot rate in 3 months.
• As long as the spot JPY/USD exchange rate in 3 months does not depreciate by more
than (3.32%/4) = 0.83%, you can gain from this transaction.
• UFR would imply the USD will depreciate by exactly 0.83%!
Parity Conditions - Summary
4 definitions:
1. The spot exchange rate,
2. The forward exchange rate,
3. The interest rate,
4. The inflation,
4 Derived Key Terms:
1. The interest rate differentials, −
2. The inflation differentials, −
3. The forward differentials (forward
discount or premium),
−0
0
4. The exchange rate changes,
−
Currency Forecasting
Currency Forecasting
• Forecasting exchange rates can be crucial for a firm’s or an
investor’s future operations and profit.
• Market-based Forecasts
• Model-based Forecasts
Successful Currency Forecasting
Currency forecasting is successful only if at least one of the following criteria is met:
– Uses superior and exclusive forecasting model
– Uses information not yet incorporated in the market
– Exploits small, temporary deviations from equilibrium
– Predicts government intervention in foreign markets
Unfortunately, it is not easy or straightforward to do …
Self-correcting
Unlikely to be sustainable
Small and temporary
Feasible in fixed-rate systems
What about floating rate systems?
Market-based Forecasts
• If market efficiency holds, markets have incorporated expected currency changes in
interest and forward rates. Currency forecasts can be obtained by extracting the
predictions embodied in interest and forward rates.
Market-based Forecasts
➢ Forward rate
• Following UFR, forward rate is an unbiased estimate of the future expected spot rate:
1 = 1
• Simple and easy to use
• … but longer-term forward contracts (> 1 year) are limited
➢ Interest rate
• Following IFE: interest rate differential predicts future expected spot rates:
1 = 0
+
+
• Good for predicting longer term rates
• … but investors may require different returns on domestic vs foreign investments
Market-based Forecasts
There are two principal model-based approaches:
1. Fundamental analysis
– Most common approach
2. Technical analysis
1. Fundamental analysis
Fundamental analysis relies on the examination of macroeconomic variables that may
influence future exchange rates
• e.g. relative inflation rates, interest rates, national income growth, money supply etc.
Difficulties:
1. Need to select the right fundamentals
2. Need to be able to forecast these fundamentals
• Difficult task, how to forecast interest rates?
3. Forecasts of fundamentals needs to be different from those of the market
• Otherwise exchange rate will have already incorporated the anticipated changes in
fundamentals
1. Fundamental analysis - Example
Forecast Procedures:
Step 1: Estimate relation between historical macroeconomic variables and historical
exchange rates
Step 2: Estimate future exchange rates using the estimated relations
Suppose we use the following fundamental model to estimate the AUD/USD exchange rate in a
quarter:
+1−
= 0 + 1 + 2 + 3 ℎ
+ 4 ℎ +
• β0 = constant, expected value of the dependent variable if all X=0
• βn = coefficient(s), sensitivity of the dependent variable to changes in
independent variables
1. Fundamental analysis - Example
Using quarterly data from 2004 March - 2018 December:
A 1% increase in inflation differential is related to 1.5% increase in quarterly AUD/USD
exchange rate. – Does this relation make sense?
Estimated Coefficients:
• By how much does the exchange
rate change if the interest differential,
inflation differential, or GDP growth
changes by one unit
• Do the signs make sense based on
parity conditions?
• PPP: Higher expected inflation
→ Currency should depreciate
• IFE: Higher nominal interest rate
→ Currency should depreciate
1. Fundamental analysis - Example
Using quarterly data from 2004 March - 2018 December:
Interest rate differential and US GDP growth is not
significantly related to quarterly changes in AUS/USD rates
Testing significance
■ A coefficient’s p-value shows the
probability of observing this value of β if
the true value of β = 0
■ If β = 0, the independent variables
(interest rate differential, inflation rate
differential, GDP growth) does not have
an effect on the dependent variable
(exchange rate changes)
■ If the likelihood of β = 0 is < 0.1, 0.05, or
0.01, β is statistically significantly
related to Y at the 10%, 5%, or 1% level
1. Fundamental analysis - Example
Using quarterly data from 2004 March - 2018 December:
Prediction: Suppose economic figures in 2020 June are
What is the forecasted change in AUD/USD exchange
rate over the next quarter?
• Substitute 2020 June value into the estimated
model:
ℎ− = 0 + 1 +
2 + 3 ℎ +
4 ℎ
= -0.0210+(-0.7397)x(-0.0029815)+… = -0.035
USD is predicted to depreciate by 3.5% over the
quarter.
Interest Rate Difference -0.0029815
Inflation Rate Difference -0.0074781
AU GDP Growth 0.00253007
US GDP Growth 0.0082853
2. Technical analysis
Discover price patterns in past price and volume fluctuations that repeat themselves
• Ignore economic and political factors
• Via charting or trend analysis
Evaluating Models
• Can profits be made in the forward or money markets by using forecast
models?
• Good or bad is relative
– “Good” models are able to make better predictions than “bad” models
– … many models do not seem to outperform random walk models
• Market efficiency:
– All publicly available information is incorporated in the market price
– Future exchange rate changes should be unpredictable
Currency Forecasting
• The previous parity conditions have implications on currency forecasting
• If exchange rates can be forecasted perfectly, then exchange rate risk is
eliminated.
• Unfortunately, it is not easy or straightforward to do. The Data Practice worksheet
and assignment will give you a sense of the work involved in forecasting
exchange rates.
• Research studies have identified that random walk models are superior than most
structural models.
• Market efficiency:
• All publicly available information is incorporated in the market price.
• Future exchange rate changes should be unpredictable.
