IF Summary – Lecture 3
Learning Goals
1. Define the key concepts related to the topic of foreign exchange (FX) rates
2. Describe the basic theory to model FX returns and to evaluate FX market efficiency.
Summarize its key empirical implications
3. Define the forward discount bias anomaly. Review the empirical literature on the FX
risk premium. Compare the theoretical implications with the accumulated empirical
evidence
4. Describe the more recent models of the FX rate returns and Review the associated
empirical evidence
5. Review the empirical approaches and models used for the FX forecasting
6. Evaluate the evidence on FX forecasting
Learning Goal 1: Define key concepts related to the topic of foreign exchange (FX) rates:
Notation: Home currency mentioned first; the nominal exchange rate (ER) is denoted as E or
S (for spot rate); Home currency price of 1 unit of foreign currency
- In Europe: EUR/US$=0.8436 (the asset "1 US$" costs 0.84 Euros)
o If ER goes up, Euro depreciated against US$ and vice versa!
- In US: US$/EUR=1.18 (the asset 1 EUR costs $1.18)
FX markets:
- Largest financial market; Very efficient market with small bid/ask spread and almost
no lasting arbitrage opportunities through technological advances!
- However, risks are real due to FX anomalies!
International companies face 2 FX risk that affect firm value!
1. Transaction risk
o Gain/loss when transactions are settled in foreign currency
▪ ➔ Uncertainty about the future price of foreign currencies
o E.g. Buying/selling on credit with time gap!
2. Translation risk
o Uncertainty about future home currency value of foreign assets/liabilities
denominated in for. Currency
Investors risk
- While stock prices are log-normal (constant volatility, smooth changes in prices w/o
jumps), ER have varying volatility and high jumps, making extreme outcomes more
likely compared to other assets
o ER hard to predict!
Learning Goal 2: Describe the basic theory to model FX returns and evaluate FX market
efficiency
Basic model of FX returns:
- Assume efficient speculative FX markets: No transaction costs, political-, default-,
credit risks, liquidity premium and prices reflect all public information
- Under EMH, expected arbitrage gains from long-short arbitrage strategy (short
domestic currency deposit and invest into FX deposit) is 0, so
, - Uncovered interest rate parity: The difference between the interest rate of 2
countries is equal to the change in expected exchange rate!
o
- Covered interest rate parity: Interest rate differential is equal to the difference of
the forward rate and spot rate of those 2 currencies! ➔ Allows for riskless profits if
not true!
o Difference in nominal interest rate is due to
expected appreciation/depreciation of a
currency! ➔
▪
o Realized excess returns rtFX from covered
interest rate arbitrage is equal to difference
in spot rate and forward rate of today: st – ft
o In the right example, you bet on an appreciation of the foreign currency
higher than today’s forward rate!
Summarizing the key empirical implications:
- Deviations from uncovered interest parity are possible due to non-rationality of
market participants, risk-aversion of investors (if it and it* are not risk-free),
transaction costs, market frictions, government intervention
- Tests of EMH suffer from joint-hypothesis problem: Test 1: investors have rational
expectations; Test 2: investors are risk-neutral
Learning Goal 3: Forward discount bias anomaly
Basic CIP is tested estimating a regression
- Joint hypothesis predictions: beta 0 should be 0, beta 1 should be 1!
Empirical findings:
- Forward discount bias anomaly: Beta0 is close to 0, yet beta1 is negative and ranges
from -1.3 (Swiss) —2.6 (Yen)!
- 3 empirical findings:
o 1. Forward premium (ft – st) mis-predicts the change in future spot rate
▪ Neg. relationship between forward premia and future ER
▪ Recap: Forward premium ➔ Home currency depreciates; Forward
discount ➔ Home appreciates!
o 2. Volatility of FX returns is greater than volatility of the underlying ER!
o 3. FX risk premia change signs over time
- Theoretical implications: How to account for this in the model? SDF (think of
consumption)!
o Problem: Consumption is found to be relatively stable, being 20x lower than
the volatility found in FX risk premia!
▪ Model needs to generate high volatility in SDF!
- Practical implications: Carry-trade speculative strategy
o Carry trade: Borrow in lost interest currency and invest in high interest
currency, assuming FX stays the same!
Learning Goals
1. Define the key concepts related to the topic of foreign exchange (FX) rates
2. Describe the basic theory to model FX returns and to evaluate FX market efficiency.
Summarize its key empirical implications
3. Define the forward discount bias anomaly. Review the empirical literature on the FX
risk premium. Compare the theoretical implications with the accumulated empirical
evidence
4. Describe the more recent models of the FX rate returns and Review the associated
empirical evidence
5. Review the empirical approaches and models used for the FX forecasting
6. Evaluate the evidence on FX forecasting
Learning Goal 1: Define key concepts related to the topic of foreign exchange (FX) rates:
Notation: Home currency mentioned first; the nominal exchange rate (ER) is denoted as E or
S (for spot rate); Home currency price of 1 unit of foreign currency
- In Europe: EUR/US$=0.8436 (the asset "1 US$" costs 0.84 Euros)
o If ER goes up, Euro depreciated against US$ and vice versa!
- In US: US$/EUR=1.18 (the asset 1 EUR costs $1.18)
FX markets:
- Largest financial market; Very efficient market with small bid/ask spread and almost
no lasting arbitrage opportunities through technological advances!
- However, risks are real due to FX anomalies!
International companies face 2 FX risk that affect firm value!
1. Transaction risk
o Gain/loss when transactions are settled in foreign currency
▪ ➔ Uncertainty about the future price of foreign currencies
o E.g. Buying/selling on credit with time gap!
2. Translation risk
o Uncertainty about future home currency value of foreign assets/liabilities
denominated in for. Currency
Investors risk
- While stock prices are log-normal (constant volatility, smooth changes in prices w/o
jumps), ER have varying volatility and high jumps, making extreme outcomes more
likely compared to other assets
o ER hard to predict!
Learning Goal 2: Describe the basic theory to model FX returns and evaluate FX market
efficiency
Basic model of FX returns:
- Assume efficient speculative FX markets: No transaction costs, political-, default-,
credit risks, liquidity premium and prices reflect all public information
- Under EMH, expected arbitrage gains from long-short arbitrage strategy (short
domestic currency deposit and invest into FX deposit) is 0, so
, - Uncovered interest rate parity: The difference between the interest rate of 2
countries is equal to the change in expected exchange rate!
o
- Covered interest rate parity: Interest rate differential is equal to the difference of
the forward rate and spot rate of those 2 currencies! ➔ Allows for riskless profits if
not true!
o Difference in nominal interest rate is due to
expected appreciation/depreciation of a
currency! ➔
▪
o Realized excess returns rtFX from covered
interest rate arbitrage is equal to difference
in spot rate and forward rate of today: st – ft
o In the right example, you bet on an appreciation of the foreign currency
higher than today’s forward rate!
Summarizing the key empirical implications:
- Deviations from uncovered interest parity are possible due to non-rationality of
market participants, risk-aversion of investors (if it and it* are not risk-free),
transaction costs, market frictions, government intervention
- Tests of EMH suffer from joint-hypothesis problem: Test 1: investors have rational
expectations; Test 2: investors are risk-neutral
Learning Goal 3: Forward discount bias anomaly
Basic CIP is tested estimating a regression
- Joint hypothesis predictions: beta 0 should be 0, beta 1 should be 1!
Empirical findings:
- Forward discount bias anomaly: Beta0 is close to 0, yet beta1 is negative and ranges
from -1.3 (Swiss) —2.6 (Yen)!
- 3 empirical findings:
o 1. Forward premium (ft – st) mis-predicts the change in future spot rate
▪ Neg. relationship between forward premia and future ER
▪ Recap: Forward premium ➔ Home currency depreciates; Forward
discount ➔ Home appreciates!
o 2. Volatility of FX returns is greater than volatility of the underlying ER!
o 3. FX risk premia change signs over time
- Theoretical implications: How to account for this in the model? SDF (think of
consumption)!
o Problem: Consumption is found to be relatively stable, being 20x lower than
the volatility found in FX risk premia!
▪ Model needs to generate high volatility in SDF!
- Practical implications: Carry-trade speculative strategy
o Carry trade: Borrow in lost interest currency and invest in high interest
currency, assuming FX stays the same!
