Currency Hedging
-
Upload
as111320034667 -
Category
Documents
-
view
55 -
download
0
description
Transcript of Currency Hedging
Currency hedging: Perceptions and misperceptions
April 2003
Prof. Dr. Heinz ZimmermannUniversität Basel - Wirtschaftswissenschaftliches Zentrum (WWZ)
Seite 2Heinz Zimmermann
Contents.
• The free lunch (zero cost) currency hedging argument. • Empirical papers on the return effects of currency hedging.• The story about the Siegel paradox.• Explaining the paradox: PPP deviations.
Seite 3Heinz Zimmermann
The finance perspective on currency risk.
Theory of International Finance
Portfolio Theory:
• Currencies as separate asset class
• Portfolio efficiency anddiversification of currency risks
• Individual hedging of currency exposures
Asset Pricing:
• Impose conditions of market clearing and equilibrium
• Determine market price(s) of risk(s)
Equilibrium Hedging:
• Implications of market equilibrium for individual portfolios
• Equilibrium risk premia and hedge ratios for every asset, including currencies
If currency risk is rewarded, full hedging
cannot be optimal!
Source: Zimmermann and Mertens
Seite 4Heinz Zimmermann
The academic discussion.
• Models: Solnik (1974), Sercu (1980), Adler and Dumas (1983)• Provocation: Pérold and Schulman (1988) vs. Black (1989/90), • The debate: Adler and Prasad (1990), Adler and Jorion (1992),
Solnik (1993a)• Evidence: Dumas and Solnik (1995), De Santis and Gérard (1997)
Seite 5Heinz Zimmermann
The pricing of currency risk: Two counterpositions.
There are two fundamentally different positions:
• e.g. Perold/ Schulman (1988): Free lunch of currency hedging. Foreign exchange market as a zero sum game - gains and losses between party and counterparty compensate.
• So, the expected return on currencies is zero. • Therefore, systematic currency hedging does not affect average
returns. Full hedging is optimal.
Seite 6Heinz Zimmermann
Cont.
The counterposition is as follows:
• e.g. Black (1989/90): there is a positive expected return on currencies for all currencies alltogether: the so-called Siegel paradox; Siegel (1972).
• So: there is no free lunch of currency hedging. Investors optimally hedge only part of their forex exposure.
• But: can a simple mathematical result imply real arbitrage opportunities?
• What are the implications for the definition of exchange risk?
Seite 7Heinz Zimmermann
Implications from the Siegel paradox?
...or: the real meaning of forex risk.
Seite 8Heinz Zimmermann
Exchange rate risk and expected returns
Exchange rate CHF/USD1.0
Exchange rate CHF/USD2.0
Exchange rate CHF/USD0.5
50%
50%
Expected rate CHF/USD....1.25
USD appreciates/CHF depreciates
USD depreciates/CHF appreciates
Seite 9Heinz Zimmermann
Exchange rate risk and expected returns
Exchange rate USD/CHF....1.0
Exchange rate USD/CHF....0.5
Exchange rate USD/CHF....2.0
50%
50%
Expected rate USD/CHF....1.25
Seite 10Heinz Zimmermann
Exchange rate risk and expected returns
Expected exchange rate return of the Swiss investor
25%
25%Expected exchange rate return of the US investor
So, the foreign exchange risk implies a positive expected returnfor BOTH investors, the Swiss and the US. Is this an arbitrage opportunity?
Seite 11Heinz Zimmermann
The mathematical point
Mathematically, the explanation of the „puzzle“ is due to the following fact:
This is known as Jensen’s inequality.
However, this result does not help us explaining whether the puzzle creates an arbitrage opportunity.
[ ]SESE
11>
Seite 12Heinz Zimmermann
The economic relevance
Why is the question economically relevant at all?
Is forex risk a zero sum game?
The US and Swiss investor could pool their positions and share the gains from the positive expected return.
If forex risk is rewarded with a positive risk premium for the US andthe Swiss investor, then full currency hedging is not optimal for allinvestors irrespective of their home currency.
Seite 13Heinz Zimmermann
Analyzing the puzzle with real goods
We assume that the Swiss investor has an income of 1000 CHF.There is only one good - call it „wine“. The price per bottle is 10 CHF.
We assume that the US investor has an income of 1000 USD.Given the initial exchange rate of 1.00 the price per bottle is 10 USD.
• What is the quantity of wine which could be purchased by the twoinvestors, initially and after the exchange rate change?
Seite 14Heinz Zimmermann
Exchange rate risk: in real terms
Number of bottles: 1000:10=100
Number of bottles: 500:10=50
Number of bottles: 2000:10=200
Interpretation: If the exchange rate is 0.5 CHF/USD, the Swiss investor transforms his income of 1000 CHF to 2000 USD and purchases the wine at 10 USD per bottle, which gives 200 bottles.
USD appreciates/CHF depreciates
USD depreciates/CHF appreciates
Seite 15Heinz Zimmermann
Exchange rate risk: in real terms
Number of bottles: 1000:10=100
Number of bottles: 2000:10=200
Number of bottles: 500:10=50
Interpretation: If the exchange rate is 0.5 USD/CHF, the US investors transforms his income of 1000 USD to 2000 CHF and purchases the wine at 10 CHF per bottle, which gives 200 bottles.
Seite 16Heinz Zimmermann
The real effect to currency switching
Number of bottles: Swiss 100
Number of bottles: US 100
Total: 200
Number of bottles: Swiss 50
Number of bottles: US 200
Total: 250
Number of bottles: Swiss 200
Number of bottles: US 50
Total: 250
Thus, by switching currencies, forex risk makes the „society“ better off in terms of real income, in both exchange rate states. Surprising?
USD appreciates/CHF depreciates
USD depreciates/CHF appreciates
Seite 17Heinz Zimmermann
The price of wine adjusts I
Exchange rate CHF/USD1.0
Wine price per bottle 10 CHF
10 USD
Exchange rate CHF/USD2.0
Wine price per bottle 10 CHF
5 USD
Exchange rate CHF/USD0.5
Wine price per bottle: 10 CHF
20 USD
i.e. the wine prize remains constant in Switzerland, while it adjusts in the US - reciprocally to the exchange rate change.
Seite 18Heinz Zimmermann
Implications for the real income
Number of bottles: 1000:10=100
Number of bottles: 500:5=100
Number of bottles: 1000:10=100
Number of bottles: 2000:20=100
Number of bottles: 1000:10=100
Conclusion: Switching currencies does not affect real income, asmeasured by the number of bottles of wine.
USD appreciates/CHF depreciates
USD depreciates/CHF appreciates
With currency switch
Without currency switch
Seite 19Heinz Zimmermann
Implications for the real income
Number of bottles: 1000:10=100
Number of bottles: 2000:10=200
Number of bottles: 1000:5=200
Number of bottles: 500:10=50
Number of bottles: 1000:20=50
Conclusion: Switching currencies does not affect the real incomecompared to the non-switching alternative.
USD appreciates/CHF depreciates
USD depreciates/CHF appreciates
With currency switch
Without currency switch
Seite 20Heinz Zimmermann
The real effect of currency switching
Number of bottles: Swiss 100
Number of bottles: US 100
Total: 200
Number of bottles: Swiss 100
Number of bottles: US 200
Total: 300
Number of bottles: Swiss 100
Number of bottles: US 50
Total: 150
USD appreciates/CHF depreciates
USD depreciates/CHF appreciates
Seite 21Heinz Zimmermann
... and the non-switching alternative
Number of bottles: Swiss 100
Number of bottles: US 100
Total: 200
Number of bottles: Swiss 100
Number of bottles: US 200
Total: 300
Number of bottles: Swiss 100
Number of bottles: US 50
Total: 150
The quantities of wine are identical in the „switching“ and „non-switching“ case. Thus, currency switching has no real effect under this scenario (adjusted wine price).
USD appreciates/CHF depreciates
USD depreciates/CHF appreciates
Seite 22Heinz Zimmermann
Is the result suprising?
Summing up: Forex risk and that switching currencies only increases global real income (the Siegel paradox) if relative good prices remain constant.
If relative prices adjust in exactly the same way as the exchange rate, then the effect disappears. Is this surprising?
No, because the Purchasing Power Parity (or in the case of one single good, the law of one price) would hold in this case.
See next page
Seite 23Heinz Zimmermann
The exchange rate in terms of the price of wine
Exchange rate CHF/USD1.0
Wine price per bottle 10 CHF
10 USD
Exchange rate CHF/USD2.0
Wine price per bottle 10 CHF
5 USD
Exchange rate CHF/USD0.5
Wine price per bottle: 10 CHF
20 USD
i.e. the wine prize remains constant in Switzerland, while it adjusts in the US - reciprocally to the exchange rate change.
1.0
2.0
0.5
Seite 24Heinz Zimmermann
Siegel’s paradox of „positive-expected-returns-on-currencies“ is a purely nominal puzzle. Irrelevant for investors concerned about real returns, i.e. measured in foreign consumption units
Under PPP, there are no real wealtheffects from exchange rate changes.They can only be accomplished by deviations from PPP
INSIGHT 1
INSIGHT 2
• There are no implications from Siegel’s paradox for currency hedging
• It is the real exchange rate risk –i.e. inflation risk not reflected by currency rates – which affects currency hedging
IMPLICATIONS
Siegel’s Paradox comes from a misleading
change of numeraire!
Implications of the previous analysis...
Seite 25Heinz Zimmermann
... and summary.
holds holds not
• No real exchange rate risks, no premia
• No need for hedging, PPP provides the hedge!
• In real terms, the exchange rate is not stochastic, hence no inequality, no paradox (E(r)=1/E(r)=1)
• Real exchange rate risks exist, risk premia can be earned
• Full hedging foregoes rewards for bearing currency risk, not optimal
• Investors with different objective functions gain from trading with each other
PPP ...
Source: Zimmermann and Mertens, Obstfeld and Rogoff (1996, p. 586ff), Kritzman (2000)
Seite 26Heinz Zimmermann
Currency risk hedging for risky assets: empirical.
• How is the ex-post performance of portfolio returns affected if the position is „fully hedged“ against exchange rates?
• What does „fully hedged“ mean?
• What is the appropriate performance measure?
Seite 27Heinz Zimmermann
Empirical evidence on currency hedging.
The Häfliger/ Wälchli/ Wydler study addresses the following strategies:
1. Domestic Investments: investments in domestic government bonds or domestic equities.
2. Single Foreign Currency Investments: investments in bonds or equities denominated in a single foreign currency or from a single country.
3. Multi Foreign Currency Investments: investment in a global portfolio of foreign currency bonds or equities. The starting point is an original equal weighting of the four foreign markets as of December 1984, but without any rebalancing (i.e. a buy-and-hold strategy)
4. Hedged Single Foreign Currency Investments: Same as strategy 2, but with currency hedging with respect to the respective reference currency.
5. Hedged Multi Foreign Currency Investments: Same as strategy 3, but with currency hedging with respect to the respective reference currency.
Seite 28Heinz Zimmermann
Bonds.
Häfliger/ Wälchli/ Wydler (2000)
Seite 29Heinz Zimmermann
Stocks.
Häfliger/ Wälchli/ Wydler (2000)
Seite 30Heinz Zimmermann
Summary.
Häfliger/ Wälchli/ Wydler (2000)
Seite 31Heinz Zimmermann
Summary.
Häfliger/ Wälchli/ Wydler (2000)
Seite 32Heinz Zimmermann
References.
• Black, Fischer. 1989. Universal Hedging: Optimizing Currency Risk and Reward in International Equity Portfolios.. Financial Analysts Journal, vol. 45, no. 4 (July/August), 16-22.
• Black, Fischer. 1990. Equilibrium Exchange Rate Hedging Journal of Finance vol. 45, no. 3, 899-907.
• Gastineau, Gary L. 1995. The Currency Hedging Decision: A Search for Synthesis in Asset Allocation.. Financial Analysts Journal, vol. 51, no. 3 (May/June), 8-17.
• Glen, Jack, and Philippe Jorion. 1993. Currency Hedging for International Portfolios.. Journal of Finance, vol 48, no. 5, 1865-1886.
• Häfliger, Thomas, Urs Wälchli and Daniel Wydler. 2002. Hedging Currency Risk: Does It Have to Be So Complicated? Working Paper.
• Jorion, Philippe. 1989. Asset allocation with hedged and unhedged foreign stocks and bonds.. Journal of Portfolio Management, vol. 15, no. 4, 49-54.
Seite 33Heinz Zimmermann
Cont.
• Solnik, B., 1998. Global Asset Management: To hedge or not to hedge – a question that cannot be ignored, Journal of Portfolio Management 25, 43-51
• Perold, Andre F., and Evan C. Schulman. 1988. The Free Lunch in Currency Hedging, Implications for Investment Policy and Performance Standards.. Financial Analysts Journal, vol. 44, no. 3 (May/June), 45-50.
• Solnik, B., 1993. Currency Hedging and Siegel’s Paradox: On Black’s Universal Hedging Rule, Review of International Economics, 180-187
Other references see the presentation of International Asset Pricing.