Uebung 3 - Foreign Exchange Und International Diversification
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Transcript of Uebung 3 - Foreign Exchange Und International Diversification
Foreign Exchange
International Diversification
Dr. Lukas Hengartner
26 March 2008
Financial Analysis – Übungen8,105 MAccFin
FS08
Übung 3 �26 March, 2007
Part I – Besprechung Problem Set 2
Overview Übung 3
Part II – Foreign Exchange Fundamentals
Part III – Foreign Exchange Parity Relations
Part IV – International Diversification
Übung 3 �26 March, 2007
Part I – Besprechung Problem Set 2
Overview Übung 3
Part II – Foreign Exchange Fundamentals
Part III – Foreign Exchange Parity Relations
Part IV – International Diversification
Übung 3 �26 March, 2007
Part I – Besprechung Problem Set 2
Overview Übung 3
Part II – Foreign Exchange Fundamentals
Part III – Foreign Exchange Parity Relations
Part IV – International Diversification
Übung 3 �26 March, 2007
Exchange rate development CHF / USD
Source: NZZ (2008)
Übung 3 �26 March, 2007
Exchange rate development USD / Euro
Source: FAZ (2008)
Übung 3 �26 March, 2007
Exchange rate quotations
� Direct exchange rate:Domestic price of a foreign currency� Example: 1.57 CHF / EUR (if
Switzerland is domestic country)
� Indirect exchange rate:Amount of foreign currency equivalent to one unit of the domestic currency� Example: 0.637 EUR / CHF (if
Switzerland is domestic country)
� 1.57 CHF / EUR (if Euro zone is domestic country)
Übung 3 �26 March, 2007
Triangular arbitrage and cross-rates
� Two ways of moving from one currency to another� Go directly from one currency to another� Go through a third currency
� Alternative ways of moving from one currency to another impose restrictions on prices
� Example: S (CHF/EUR) = 1.575; S(CHF/GBP) = 2.017
� Triangular arbitrage opportunity: Quoted cross-rate between to foreign currencies that is different from the cross-rate implied by the domestic country exchange rate against the two foreign currencies
Übung 3 �26 March, 2007
Appreciation and depreciation
� Appreciation of a currency� Example: Appreciation of the
CHF against the EUR (Switzerland as the domestic country)
� Direct exchange rate CHF / EUR goes down (e.g. from 1.57 to 1.55 CHF/EUR)
� Indirect exchange rate EUR / CHF goes up (e.g. 0.637 to 0.645 EUR/CHF)
� Depreciation of a currency� Example: Depreciation of the
CHF against the EUR (Switzerland as the domestic country)
� Direct exchange rate CHF / EUR goes up (e.g. from 1.57 to 1.59 CHF/EUR)
� Indirect exchange rate EUR / CHF goes down (e.g. from 0.637 to 0.629 EUR/CHF)
Übung 3 26 March, 2007
Calculating exchange rate changes
� By definition, the % appreciation of currency A against currency B will not equal the % depreciation of currency B against currency A
� Example
� Theoretical foundation: Siegel-Paradox
Übung 3 26 March, 2007
Bid-ask spreads
� Bid price: Price at which the bank is willing to buy a currency� Ask price: Price at which the bank is willing to sell a currency� Spread: Difference between ask price and bid price� Quotation:
� S(CHF/EUR) = 1.5590 – 1.5595� The bank is willing to buy a EUR for 1.5590 CHF� The bank is willing to sell a EUR for 1.5595 CHF
� Spreads are larger when there is more exchange rate uncertainty (volatility)
� Spreads are larger for currencies that have a low trading volume
Übung 3 �26 March, 2007
Forward exchange rates
� Rates contracted today, but with delivery and settlement in the future, usually 30 or 90 days later
� Quotation� F(CHF/EUR)90 = 1.5585 – 1.5595� The bank buys EUR in 90 days for 1.5585 CHF� The bank sells EUR in 90 days for 1.5595 CHF� You can buy EUR in 90 days for 1.5595 CHF � You can sell EUR in 90 days for 1.5585 CHF
� Example� You have 10,000 CHF and will sell them forward to buy 10,000 / 1.5595
= 6,412.31 EUR in 90 days.� You have 10,000 EUR and will sell them forward to get 10,000*1.5585 =
15,585.00 CHF in 90 days.
Übung 3 �26 March, 2007
Nominal and real exchange rates
� Nominal exchange rate = Compounding of real exchange rate and the expected rate of inflation
� Linear approximation
(1+r) = (1+�)(1+E(I))
r ~ � + E(I)
Übung 3 �26 March, 2007
Factors of currency appreciation / depreciation
� Differences in national inflation rates� The currency of a country with high inflation tends to depreciate� The currency of a country with low inflation tends to appreciate
� Changes in real interest rates� If a country’s real interest rate increases, it will lead to an appreciation of
its currency� If a country’s real interest rate decreases, it will lead to a depreciation of
its currency
� Changes in investment climate� An improvement in a country’s investment climate will lead to a currency
appreciation through increased financial inflows
� Differences in economic performance?
Übung 3 �26 March, 2007
Part I – Besprechung Problem Set 2
Overview Übung 3
Part II – Foreign Exchange Fundamentals
Part III – Foreign Exchange Parity Relations
Part IV – International Diversification
Übung 3 �26 March, 2007
International Parity Relations
Interest rate parity- covered
- uncovered
Relative purchasing power parity
International Fisher
relation
Foreign exchange
expectation
Übung 3 �26 March, 2007
Covered interest rate parity defined
� No-arbitrage-condition that links spot exchange rates, interest rates and forward rates
� How the forward rates are determined in the market
� Linear approximation
Forward discount (premium) equals the interest rate differentialbetween two currencies
F(1+rDC) = S(1+rFC) ���� F/S = (1+rFC) / (1+rDC)
f ~ (F-S)/S = (rFC – rDC)
Übung 3 �26 March, 2007
Covered interest rate parity - illustration
Time 0 Time 1
US Dollars
Euros
Spot €/$ = 0.8Forward €/$ = ?
Borrow at 10%
Lend at 14%
Übung 3 �26 March, 2007
Interest rate parity - example
� The spot exchange rate between the Euro (domestic country) and the CHF (foreign country) is S = CHF 1.575 per Euro. Suppose that the risk-free interest rate in the Euro zone is 4.5% and the risk-free interest rate in Switzerland is 3.0%.a) Calculate the approximate forward exchange rateb) Calculate the exact forward exchange rate
Übung 3 �26 March, 2007
Purchasing power parity (PPP)
� Linking spot exchange rates and inflation� States that the spot exchange rate adjusts perfectly to inflation
differentials between two countries� Absolute PPP:
� Exchange rate should be equal to the ratio of the average price levels in the two economies
� Average version of the Law of one price (based on CPI or GDP deflator)
Übung 3 �26 March, 2007
Law of one price
� Example Big Mac Index
When expressed in a common currency, the
same good should sell for the same price in different
countries
Source: The Economist (2007)
Übung 3 ��26 March, 2007
Relative Purchasing Power Parity
� Exchange rate movements should exactly offset any inflation differential between the two economies
� The currency with the higher inflation rate will depreciate� Linear approximation:
� Implication for international investments: The real return on an asset is identical for investors from any country (if PPP holds)
S1/S0= S(1+IFC)/(1+IDC)
s ~ S1/S0 – 1 = IFC - IDC
Übung 3 ��26 March, 2007
Purchasing power parity - example
� The spot exchange rate between the Euro (domestic country) and the CHF (foreign country) is S0 = CHF 1.575 per Euro. Suppose that the expected annual inflation in the Euro zone is 3.0% and the expected inflation for Switzerland is 1.5%.a) Calculate the approximate expected spot exchange rate one year aheadb) Calculate the exact expected spot exchange rate one year ahead
Übung 3 ��26 March, 2007
International Fisher relation
� Real interest rates are equal (and stable) across the world� The interest rate differential between two countries should be equal
to the expected inflation rate differential
� Linear approximation
(1+rFC)/(1+rDC) = (1+E(IFC))/(1+E(IDC))
rFC – rDC ~ E(IFC) - E(IDC)
Übung 3 ��26 March, 2007
International Fisher relation - example
� The spot exchange rate between the Euro (domestic country) and the CHF (foreign country) is S0 = CHF 1.575 per Euro. Suppose that the expected annual inflation in the Euro zone is 3.0% and the expected inflation for Switzerland is 1.5%. Interest rates are 4.5% in the Euro zone and 3.0% in Switzerland.a) Demonstrate how interest rates are related to expected inflation rates by approximation? b) Demonstrate how interest rates are related to expected inflation rates exactly? c) What is the real risk-free interest rate for the Euro zone and for Switzerland?
Übung 3 ��26 March, 2007
Uncovered interest rate parity
� The expected currency depreciation should offset the interest rate differential between the two countries
� Linear approximation
� Based on economic theory
E(S1)/S0 = (1+rFC)/(1+rDC)
E(s) ~ rFC - rDC
Übung 3 ��26 March, 2007
Uncovered interest rate parity - example
� The spot exchange rate between the Euro (domestic country) and the CHF (foreign country) is S0 = CHF 1.575 per Euro. Suppose that interest rates are 4.5% in the Euro zone and 3.0% in Switzerland.a) Calculate the approximate expected spot exchange rate one year aheadb) Calculate the exact expected spot exchange rate one year ahead
Übung 3 ��26 March, 2007
Foreign exchange expectation relation
� The forward exchange rate, quoted at time 0 for delivery at time 1, is equal to the expected value of the spot exchange rate at time 1
� Stated relative to the current spot exchange rate
� Implications� The forward exchange rate is the best guess of the future spot rate� The forward premium (discount) is also the expected appreciation
(deprecation) of the domestic currency
F = E(S1)
f = (F-S0)/S0 = E(S1-S0)/S0= E(s)
Übung 3 ��26 March, 2007
Recapping international parity relations
� What relations are represented by the following descriptions?a) The forward discount (premium) equals the interest rate differentialb) The expected inflation rate differential should be matched by the interest rate differential, assuming real interest rates are equal c) The exchange rate movement should exactly offset any inflation differentiald) The interest rate differential is expected to be offset by the currency depreciatione) The forward discount (premium) is equal to the expected exchange rate movement
Übung 3 �26 March, 2007
Implications for international investments
� Interest rate differentials reflect expectations about currency movements
� Investing in a country with a high interest rate is not a particularly attractive option. The high interest rate is expected to be offset by a matching currency depreciation
� Investors from different countries expect the same real return on a given asset, once currency is taken into account
� Exchange risk reduces to inflation uncertainty if all these relationships hold perfectly
� Currency hedging allows investors to eliminate currency risk without sacrificing expected return, because the forward exchange rate is equal to the expected spot exchange rate
Currency risk is of little importance in this simplified world
Übung 3 �26 March, 2007
Empirical evidence - PPP
Source: Bonaduner (2007)
Übung 3 ��26 March, 2007
Empirical evidence – Real interest rates
Source: Solnik and McLeavey (2003)
Übung 3 ��26 March, 2007
Implications for international investments - revisited
� Currency fluctuations can have real effects, as the exchange rate deviates from its PPP value – real returns of one asset as measured by investors from different countries are different
� Real interest rates may differ between two countries that are atdifferent stages of the business cycle – this uncertainty adds uncertainty to a foreign investment
� Investors are not risk-neutral and may append a risk premium to the foreign exchange expectations relation
Currency risk is important in most international investment scenarios
Übung 3 ��26 March, 2007
Part I – Besprechung Problem Set 2
Overview Übung 3
Part II – Foreign Exchange Fundamentals
Part III – Foreign Exchange Parity Relations
Part IV – International Diversification
Übung 3 ��26 March, 2007
Market capitalization in developed countries
Source: Bodie / Kane / Marcus (2008)
Übung 3 ��26 March, 2007
Issues in foreign investments
� What are the risks involved in investment in foreign securities?� Are there benefits to diversification in foreign securities?
Übung 3 ��26 March, 2007
Foreign exchange risk
� Variation in return related to changes in the relative value of the domestic and foreign currency
� Total return = investment return & return on foreign exchange� Return in local currency is a function of two factors:
1. Return in the foreign market2. Return on the foreign exchange
Übung 3 ��26 March, 2007
Stock Market returns in USD and local currencies
Source: Bodie / Kane / Marcus (2008)
Übung 3 ��26 March, 2007
Country specific risk
Source: Bodie / Kane / Marcus (2008)
Übung 3 �26 March, 2007
The benefits of international diversification
Source: Solnik (1976) in Bodie / Kane / Marcus (2008)
Übung 3 �26 March, 2007
Efficient diversification by various methods
Source: Bodie / Kane / Marcus (2008)
Übung 3 ��26 March, 2007
Diversification by market capitalization: National markets versus regional funds
Source: Bodie / Kane / Marcus (2008)
Übung 3 ��26 March, 2007
Diversification benefits and bear markets
Source: Bodie / Kane / Marcus (2008)
Regional Indexes around the Crash, October 14 – October 26, 1987
Übung 3 ��26 March, 2007
Diversification Benefits over Time
Übung 3 ��26 March, 2007
Correlation of international equity returns
Source: Bodie / Kane / Marcus (2008)
Übung 3 ��26 March, 2007
Conclusion of international diversification
� Potential benefits from international diversification for investors, but probably decreasing diversification benefits over time
� However: International investing offers greater opportunities for active managers and diversification is only a small part of the gain from international investing