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.


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


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)


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.


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?


Implications from the Siegel paradox?

...or: the real meaning of forex risk.


Exchange rate risk and expected returns

Exchange rate CHF/USD1.0



50%

50%

Expected rate CHF/USD....1.25

USD appreciates/CHF depreciates

USD depreciates/CHF appreciates



Exchange rate USD/CHF....1.0



50%

50%

Expected rate USD/CHF....1.25



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?


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

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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.


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?


Exchange rate risk: in real terms

Number of bottles: 1000:10=100



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.




Exchange rate risk: in real terms




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.


The real effect to currency switching

Number of bottles: Swiss 100

Number of bottles: US 100

Total: 200



Total: 250



Total: 250

Thus, by switching currencies, forex risk makes the „society“ better off in terms of real income, in both exchange rate states. Surprising?




The price of wine adjusts I


Wine price per bottle 10 CHF

10 USD



5 USD


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.


Implications for the real income






Conclusion: Switching currencies does not affect real income, asmeasured by the number of bottles of wine.



With currency switch

Without currency switch


Implications for the real income






Conclusion: Switching currencies does not affect the real incomecompared to the non-switching alternative.



With currency switch

Without currency switch


The real effect of currency switching



Total: 200



Total: 300



Total: 150




... and the non-switching alternative



Total: 200



Total: 300



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).




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


The exchange rate in terms of the price of wine



10 USD



5 USD


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


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...


... 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)


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?


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.


Bonds.

Häfliger/ Wälchli/ Wydler (2000)


Stocks.



Summary.



Summary.



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.


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.

Documents

Currency Hedging