1. Hedging currencies with hindsight and regret
Kenneth L. Fisher
Chairman, CEO & Founder
Fisher Investments, Inc.
13100 Skyline Boulevard
Woodside, CA 94062-4547
650.851.3334
and
Meir Statman
Glenn Klimek Professor
Santa Clara University
Department of Finance
Leavey School of Business
Santa Clara, CA 95053-0388
408.554.4147
mstatman@scu.edu
July 2003
We thank Sridhar Chilukuri, Jennifer Chou, Ramie Fernandez, Mark Kritzman and David Tien.
Meir Statman acknowledges financial support from The Dean Witter Foundation.

2. Hedging currencies with hindsight and regret
Abstract
We find that the mean returns and standard deviations of global portfolios with hedged
currencies during the 15-year period 1988-2002 were approximately equal to those of portfolios
with unhedged currencies. Mean-variance investors who believe that the expected returns and
standard deviations of hedged portfolios are equal to those of unhedged portfolios would be
indifferent between them but behavioral investors would not be indifferent. Behavioral investors
focus on individual securities and the forces of hindsight and regret move them back and forth
between hedged portfolio and unhedged ones.

3. Hedging currencies with hindsight and regret.
It is now more than half a century since Markowitz (1952) attempted to shift the focus of
investors from individual securities to portfolios in mean-variance portfolio theory, and more
than a quarter century since ERISA enshrined that attempt into law. “Why not diversify
internationally rather than domestically?” asked Solnik’s (1974) in the year when ERISA was
signed into law. He showed that the addition of international stocks to a portfolio of domestic
stocks reduces the risk of the portfolio. Yet today’s investors remain focused on individual
securities, especially when it comes to international securities and currencies. For example, the
Investment Basics section of Fidelity (2003) says, “International investments involve greater risk
than U.S. investments, including political and economic risks, as well as the risk of currency
fluctuations.”
We find that the mean returns and standard deviations of global portfolios with hedged
currencies during the 15-year period 1988-2002 were approximately equal to those of portfolios
with unhedged currencies. Mean-variance investors who believe that the expected returns and
standard deviations of hedged portfolios are equal to those of unhedged portfolios would be
indifferent between them but behavioral investors would not. Behavioral investors focus on
individual securities and the forces of hindsight and regret move them back and forth between
hedged portfolios and unhedged ones.
Currencies in mean-variance portfolios
The down and up of the Euro is one of many demonstrations of the volatility of
currencies. The Euro was introduced in January 1999 at 1.18 to the U.S. dollar, decreased to 0.84
to the dollar by the end of May 2001 and was back to 1.18 by the end of May 2003. But,
according to mean-variance theory, the volatility of currencies does not necessarily make them
1

4. risky. Currencies can reduce the risk of portfolios if their correlations with other securities, both
international and domestic, are sufficiently low. As Solnik (1998) wrote: “Foreign currencies
provide an element of diversification against domestic budgetary, fiscal and monetary risks. For
example, domestic inflationary pressures are usually bad for domestic interest rates and often
lead to a depreciation of the currency. In this scenario, an inflationary rise in interest rates is bad
for domestic bonds and stocks but good for foreign currencies. Although the value of foreign
currencies is volatile, they bring some risk diversification to a domestic portfolio.” (p. 47)
Not all agree that currencies reduce the risk of portfolios, and those who agree that they
do often disagree on the optimal proportion of currencies in portfolios. Perold and Shulman
(1988) made the case for excluding currencies entirely from portfolios through full hedging.
“When one buys foreign currency,” they wrote “the seller is buying U.S. dollars… there is little
reason to assume that, in the long run, the rewards to bearing foreign currency risk will be one-
sided.” (p. 47) Full hedging of currencies, they argued, reduces the risk of portfolios without
reducing expected returns.
Froot (1993) made the case for fully including currencies in portfolios with no hedging.
Currencies go up and down, he noted, but they are not risky in the long run since they revert to
their fundamentals. Campbell, Viceria and White (2002) made the case for exposure to foreign
currency beyond the proportion in foreign stocks, to hedge the risk that domestic real interest
rates might decline. Investors who hold only domestic bonds should increase their currency
exposure beyond the proportion of foreign stock in the portfolio, such that the hedge ratio
exceeds one. Black (1990) offered a universal hedge ratio of 0.75 but Solnik (1998) prefers
Gastineau’s (1995) hedge ratio of 0.50. “In a sense,” wrote Solnik, “Gastineau’s ‘why bother?’
2

5. approach is cleaner. He assumes that 0.50 is the best. Why 0.50? Because it is halfway between
0 and 1, neither of which is appropriate.” (p. 49).
What do the data tell us about the risk and returns of hedged and unhedged portfolios?
Consider U.S. investors with global portfolios composed of 60% in stocks and 40% in fixed
income securities. The stock portion is divided equally between U.S. stocks and international
stocks while the fixed income portion is divided equally between U.S. Treasury bills and U.S.
Treasury bonds1
. CRSP 1-10 Index represents U.S. stocks and MSCI Indexes represent
international stocks. MSCI provides currency-hedged and currency-unhedged returns of
international stocks since 1988 and our analysis is for the 15-year period from 1988 through
20022
.
Comparison of the returns of hedged and unhedged global portfolios is consistent with
the argument that the expected return of currencies is zero. Consider a global portfolio where
MSCI-Europe Index represents international stocks. The annualized return of the unhedged
global portfolio during the 1988-2002 period was 9.80%, only 0.14% higher than the 9.66%
annualized return of the hedged portfolio. The difference between the returns of the hedged and
unhedged global portfolios where the MSCI-Pacific Index represents international stocks was
also small, but in the opposite direction. The annualized return of the unhedged portfolio was
6.72%, somewhat lower than the 7.08% annualized return of the hedged portfolio. The
difference between the annualized returns of the hedged and unhedged portfolios where the
EAFE index represents international stocks tilts toward the Pacific Index more than it does
1
T-bond and U.S. T-bill data are from Ibbotson Associates.
2
MSCI provides both price appreciation and total returns for the unhedged series but only price appreciation for the
hedged series. We computed total returns for the hedged series by adding to its price appreciation the difference
between the total returns and price appreciation of the unhedged series.
3

6. toward the European Index. The annualized return of the hedged portfolio is 8.50%, somewhat
higher that the 8.21% annualized returns of the unhedged portfolio. (See Table 1)
We turn to a comparison of the risk of hedged and unhedged portfolios and begin with
correlations. Correlations among securities were generally lower in unhedged portfolios than in
hedged ones. For example, the correlation between the returns of unhedged EAFE stocks and US
stocks is 0.59, lower than the 0.68 correlation between the returns of hedged EAFE stocks and
US stocks3
. Similarly, the 0.01 correlation between unhedged EAFE stocks and US T-bills is
lower than the 0.05 correlation between hedged EAFE stocks and US T-bills. However, the 0.00
correlation between unhedged EAFE stocks and U.S. T-bonds is higher than the –0.02
correlation between hedged EAFE stocks and U.S. T-bonds. (See Table 2)
While correlations between returns were generally lower in unhedged portfolios than in
hedged ones, the risk of unhedged portfolios, measured by the standard deviation of returns, was
not much different from that of hedged portfolios. The annualized standard deviation of a global
unhedged portfolio where EAFE stocks play the role of international stocks is 8.91%, only
slightly higher than the 8.80% standard deviation of a fully hedged portfolio. Still, consistent
with Black (1990), a global portfolio that was 75% hedged is less volatile than portfolios that are
unhedged, 25% hedged, 50% hedged, fully unhedged, or 150% hedged. The standard deviation
of the portfolio that was 75% hedged is 8.76%.
The least volatile portfolio where European stocks play the role of international stocks
was the one with the 25% hedge ratio, but differences between standard deviations at different
hedge ratios remain small, ranging from 8.81% where the hedge ratio was 25% to 9.45% where
the hedge ratio was 150%. The least volatile portfolio where Pacific stocks play the role of
international stocks was the one with the 100% hedge ratio, but once again the differences
3
Correlations were calculated from monthly returns.
4

7. between standard deviations at different hedge ratios are small, ranging from 9.02% when the
hedge ratio was 100% to 9.73% when the hedge ratio was zero. (See Table 3)
Currencies in behavioral portfolios
The word hedge brings to mind insurance, where homeowners who lost their homes to
fire receive checks from their insurance companies. But hedging currencies does not provide
insurance. Indeed, hedging currencies is a bet as much as it is a hedge. The volatility of
unhedged global portfolios during the 15 years 1988-2002 was not much different from that of
hedged portfolios and the worst annual return of unhedged portfolios was not much different
from that of hedged portfolios. The evidence might persuade mean-variance investors to pick
one portfolio, hedged or unhedged, and stick with it since neither is closer to the mean-variance
efficient frontier. But behavioral investors are not likely to stick with one portfolio.
Mean-variance portfolio theory teaches investors to focus on portfolios rather than on
individual securities and choose portfolios from the mean-variance efficient frontier. But most
investors fail to learn the lesson. Instead, most investors focus on individual securities and build
behavioral portfolios as pyramids of securities, where layers are associated with particular goals.
Securities in the bottom layers of portfolios serve the goal of downside protection, designed to
protect investors from being poor, while securities in the top layers of portfolios serve the goal of
upside potential, designed to give investors a shot at being rich. Shefrin and Statman (2000)
developed behavioral portfolio theory, and Fisher and Statman (1997) showed that the advice of
mutual fund companies conforms to behavioral portfolio theory.
The identity of securities in the upside potential layers changes over time but their goal,
making investors rich, remains the same. International stocks were in the upside potential layer
in the 1970s and 1980s, Internet stocks were there in the late 1990s, and hedge funds are there
5

8. today. Behavioral investors follow a cycle of hindsight and regret where they conclude, with
hindsight, that they could have seen with foresight the securities that would make them rich, and
suffer the pain of regret because they did not. In the late 1970s and 1980s U.S. investors nodded
their heads when advisors explained the mean-variance benefits of international stocks, but they
bought international stocks as sure winners for the upside potential layers of their behavioral
portfolios. As Middleton (2003) wrote, “Foreign investing became fashionable when U.S.
markets were relatively weak, beginning in the late 1970s. Between 1976 and 1989, the Europe,
Australian, Far East Index surged more than sixfold, while the S&P 500 didn’t even quadruple.”
International stocks that zoomed past U.S. stocks in the late 1970s and 1980s lagged behind them
in the 1990s and early 2000s and the hindsight that brought international stocks into fashion in
the 1970s and 1980s took them out of fashion in the 1990s and early 2000s. “The sagging
interest in Asian and European funds has sounded alarm bells among many financial experts
whose mantra is diversification,” wrote Tan (1998).
Some have argued that the sagging interest of U.S. investors in international stocks in the
late 1990s and early 2000s is due to the increasing correlations between the returns of U.S.
stocks and international stocks. For example, Fuerbringer (2002) wrote “Americans once
invested abroad to reduce portfolio risk – if the United States market fell, foreign ones often rose.
But this diversification has been hard to get in Europe in recent years because its markets have
become very closely correlated with the performance of Wall Street. So when stock fall here,
they fall there, or vice versa.” (BU6). But this cannot be true. The benefits of diversification
between international stocks and U.S. stocks were very high in the 1990s and early 2000s. For
example, while the correlation between (unhedged) international EAFE stocks and U.S. CRSP 1-
10 stocks during 1997-2001 was high, at 0.81, the difference between their annualized returns
6

9. was also high, 1.15% for EAFE and 11.07% for CRSP 1-10. Global diversification did not lose
its popularity among U.S. investors in the late 1990s and early 2000s because of high
correlations but because of high regret among U.S. investors who bought international stocks as
sure winners only to suffer the pain of regret as international stocks revealed themselves, in
hindsight, as losers.
Some investors continue to hope that foresight about currencies can turn international
stocks into sure winners, combining the riches of international stocks with the riches of
international currencies. There is basis for such hope in evidence that movements of currencies
can be seen in foresight. For example, Kritzman (1993) noted that forward rates of currencies
have systematically overestimated subsequent changes in spot rates and Mark (1995) found some
predictability in the value of currencies over long horizons. However, LeBaron (1999) found
that foresight of currencies is cloudy and Barnhardt, NcNown and Wallace (1999) found fault in
typical tests that show that forward exchanged rates are biased. They found no bias in forward
rates once they corrected for these faults.
If the movements of currencies are cloudy in foresight, they are clear in hindsight and
regret kicks with equal force those who hedge and those who do not. Consider the story of the
Alaska Permanent Fund, a currency hedger, told by Pulliam (1992):
The investment managers of the Alaska Permanent Fund, the state’s oil
fund, wanted to play it safe two years ago when they begun investing in
foreign stocks.
So they decided to buy a currency hedge to protect their profits on the
portfolio from losses if the value of the dollar rose and they sold the foreign
stocks.
But instead of protecting the fund from losses, the hedge has caused $38
million in losses of its own. Disillusioned with the strategy, the fund’s
managers decided last week to abandon currency hedging altogether. ‘I
can’t find any benefit to it.’ Said William Scott, executive director of the
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10. $14 billion Alaska fund, which each year distributes a portion of the states’
oil revenue to Alaska’s 550,000 residents in the form of a dividend. ‘I just
want to stop the bleeding,’ he said.
While the Alaska Permanent Fund hedged the currencies in its portfolios, Xerox
did not.
“We seriously considered it a while ago,” said Robert Evans, an assistant
treasurer at Xerox Corp. who oversees its pension investments “But our
treasury department thought the dollar would weaken,” he said. “Indeed, it
has, and they saved us a bundle.”
The decision to avoid hedging brought a sigh of relief to Xerox in 1992 and perhaps
some pride, but regret is never far behind. “In retrospect, one should have hedged all of the
Asian currencies,” said Anthony Cragg, international equities manager at Strong Funds to
Delaney (1997).
“That’s because, besides watching stock prices plummet, U.S. investors have seen
depreciating currencies further erode the value of their investments in Asia. The
average fund investing in the region excluding Japan lost 33.7% this year, dragged
lower in part by declines of more than 40% in a number of currencies.”
Conclusion
We examined hedged and unhedged global portfolios during the 15-years from 1988
through 2002 found that hedged global portfolios were as close to the mean-variance efficient
frontier as unhedged ones. The 1988-2002 period is as unique as any period but we are assured
that it is not unrepresentative by the fact that the returns of hedged portfolios were approximately
equal to the returns of unhedged portfolios.
Mean-variance portfolio theory teaches investors to search for portfolios on the efficient
frontier with combinations of risk and expected returns that suit them best. But investors are
8

11. forever searching for sure winners. Securities that were sure to be winners in foresight often turn
out to be losers in hindsight but the pain of regret does not stop investors for long. Investors are
soon tempted to search again for future winners. Currencies present special temptations since, as
Solnik (1998) wrote, “Everyone, even a simple tourist, has an opinion on currencies,” (p. 49)
and many are happy to magnify these temptations. “How you can play the falling dollar,” was
the heading of Opdyke and Sesit (2002) article.
Investors who have reliable insights into future movements of currencies should bet on
them but words, such as hedge, should not confuse them. Those who hedge foreign currencies in
global portfolios place bets and so do those who do not hedge. Fuerbriner (2003) wrote that
“some portfolio managers have recently dropped their hedges as the dollar’s decline stretched
into its 18th
month.” We do not know if Fuerbringer’s mangers have reliable insights into the
future movements of currencies and we do not predict if they might the win the bets on their
unhedged portfolios. But we do predict that most investors, driven by hindsight and regret, will
continue to jump from bets on hedged portfolios to bets on unhedged ones, forever searching for
sure winners.
9

12. Reference:
Barnhardt, Scott, Robert McNown and Myles Wallace (1999). “Non-informative tests of the
unbiased forward exchange rate,” Journal of Financial and Quantitative Analysis, v. 34, no. 2,
June: 265-291.
Black, Fischer (1990). "Equilibrium exchange rate hedging," Journal of Finance, v45(3), 899-
908.
Campbell, John, Luis Viceira and Joshua White (2002). “Foreign currency for long-term
investors,” NBER, working paper.
Delaney, Kevin (97). “Funds generally don’t hedge Asian bets,” Wall Street Journal, December
22: C27.
Fidelity (2003). “Investment Basics,” at http://personal.fidelity.com/toolbox/ric/basics2a1.html
Froot, Kenneth (1993). “Currency hedging over long horizons,” National Bureau of Economic
Research, working paper 4355.
Fuerbringer, Jonathan (200). “Currency hedges: Think with obscurity,” Wall Street Journal, July
6: BU12.
Fuerbringer, Jonathan (2002). “Weaker dollar adds to potential of foreign stocks,” Wall Street
Journal, May 26: BU6.
Kritzman, Mark (1993). “The optimal currency hedging policy with biased forward rates,”
Journal of Portfolio Management, Summer: 94-100.
LeBaron, Blake (1999). “Technical trading rule profitability and foreign exchange intervention.”
Journal of International Economics, v.49: 125-143.
Marke, Nelson (1995). “Exchange rates and fundamentals: evidence on long horizon
predictability and overshooting.” American Economic Review, 85: 201-218.
Markowitz, Harry (1952). “Portfolio selection,” Journal of Finance, 6: 77-91.
Middleton, Timothy (2003). “Why you don’t need foreign stocks,” http://moneycentral.msn.com
Posted on May 6: 1-4.
Opdyke, Jeff and Michael Sesit (2002). “How you can play the falling dollar,” Wall Street
Journal, June 11: D1.
Perold, Andre and Evan Schulman (1988). "The free lunch in currency hedging: Implications for
investment policy and peformance standards," Financial Analyst Journal, v44(3), 45-52.
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13. 11
Pulliam, Susan (1992). “Pension fund managers find currency hedge is risky business,” Wall
Street Journal, August 18: C1.
Solnik, Bruno (1974). “Why not diversify internationally rather than domestically?” Financial
Analysts Journal, Vol. 30, no. 4 (July-August): 48-54.
Solnik, Bruno (1998). “Global asset management,” Journal of Portfolio Management,
(Summer): 43-51.
Tam, Pui-Wing (1998). “Sagging interest in international mutual funds alarms advisers,” Wall
Street Journal, May 27: C25.

14. 1a: Global portfolios where the MSCI-EAFE Index represents international stocks.
Year
1988 17.31% 19.27% -1.96%
1989 17.41% 21.34% -3.93%
1990 -5.84% -8.63% 2.79%
1991 19.12% 16.90% 2.21%
1992 1.82% 2.57% -0.75%
1993 17.35% 15.72% 1.63%
1994 3.08% -2.07% 5.15%
1995 21.58% 21.56% 0.01%
1996 9.04% 11.31% -2.27%
1997 14.05% 18.41% -4.36%
1998 17.68% 15.90% 1.79%
1999 14.30% 16.81% -2.51%
2000 -2.65% 0.51% -3.15%
2001 -8.19% -6.30% -1.90%
2002 -4.22% -8.23% 4.01%
Annualized returns during
1988-2002 8.21% 8.50% -0.29%
1b: Global portfolios where the MSCI-Europe Index represents European stocks.
Year
1988 13.76% 16.21% -2.45%
1989 22.95% 23.04% -0.09%
1990 0.38% -4.96% 5.33%
1991 19.46% 18.54% 0.92%
1992 4.31% 6.17% -1.85%
1993 16.29% 16.66% -0.36%
1994 0.21% -5.96% 6.17%
1995 24.80% 22.71% 2.09%
1996 13.50% 14.11% -0.61%
1997 20.91% 24.91% -4.01%
1998 20.18% 18.63% 1.54%
1999 11.21% 15.50% -4.30%
2000 -0.68% 1.78% -2.45%
2001 -7.62% -6.60% -1.02%
2002 -4.95% -9.61% 4.66%
Annualized returns during
1988-2002 9.80% 9.66% 0.14%
1c: Global portfolios where the MSCI-Pacific Index represents international stocks.
Year
1988 19.20% 20.90% -1.70%
1989 14.84% 20.64% -5.79%
1990 -9.41% -10.71% 1.29%
1991 18.94% 15.72% 3.22%
1992 -0.13% -0.17% 0.04%
1993 18.59% 15.21% 3.38%
1994 5.52% 0.95% 4.57%
1995 18.91% 20.90% -1.99%
1996 4.39% 8.33% -3.94%
1997 4.25% 9.32% -5.07%
1998 12.45% 9.85% 2.59%
1999 22.24% 20.70% 1.54%
2000 -6.63% -2.01% -4.62%
2001 -9.59% -5.57% -4.02%
2002 -2.02% -4.43% 2.41%
Annualized returns during
1988-2002 6.72% 7.42% -0.70%
Differences between the
return of the unhedged
Global portfolios are composed of 60% in equities and 40% in fixed income. Equities are composed of 30% in U.S. stocks
(CRSP 1-10) and 30% in international stocks. Fixed income securities are composed of 20% in U.S. Treasury bills and 20% in
U.S. Treasury bonds.
Table 1: A comparison of returns and standard deviations of global portfolios where currencies are fully hedged to those
where currencies are unhedged. 1988-2002.
Return on a global portfolio
where currency is unhedged
Return on a global portfolio
where currency is hedged
Differences between the
two
Return on a global portfolio
where currency is unhedged
Return on a global portfolio
where currency is hedged
Differences between the
return of the unhedged
Return on a global portfolio
where currency is unhedged
Return on a global portfolio
where currency is hedged

15. Table 2: Correlations between securities in hedged and unhedged global portfolios, 1988-2002
2a: Correlations where the MSCI-EAFE Index represents international stocks.
Unhedged International
Stocks
Hedged International
Stocks U.S. Stocks U.S. T-Bills U.S. T-Bonds
Unhedged Int'l Stocks 1.00 0.87 0.59 0.01 0.00
Fully Hedged Int'l Stocks 1.00 0.68 0.05 -0.02
U.S. Stocks 1.00 0.06 0.13
U.S. T-Bills 1.00 0.06
U.S. T-Bonds 1.00
2b: Correlations where the MSCI-Europe Index represents European stocks.
Unhedged International
Stocks
Hedged International
Stocks U.S. Stocks U.S. T-Bills U.S. T-Bonds
Unhedged Int'l Stocks 1.00 0.82 0.68 0.10 0.02
Fully Hedged Int'l Stocks 1.00 0.74 0.09 -0.02
U.S. Stocks 1.00 0.06 0.13
U.S. T-Bills 1.00 0.06
U.S. T-Bonds 1.00
2b: Correlations where the MSCI-Pacific Index represents Pacific stocks.
Unhedged International
Stocks
Hedged International
Stocks U.S. Stocks U.S. T-Bills U.S. T-Bonds
Unhedged Int'l Stocks 1.00 0.88 0.42 -0.05 0.01
Fully Hedged Int'l Stocks 1.00 0.47 0.00 0.03
U.S. Stocks 1.00 0.06 0.13
U.S. T-Bills 1.00 0.06
U.S. T-Bonds 1.00

16. Table 3: Volatility of hedged and unhedged global portfolios during 1988-2002
Global Portfolio where: 0% 25% 50% 75% 100% 150%
MSCI-EAFE plays the role of
international stocks
8.91% 8.81% 8.76% 8.76% 8.80% 9.03%
MSCI-Europe plays the role of
international stocks
8.56% 8.81% 8.82% 8.89% 9.02% 9.45%
MSCI-Pacific plays the role
international stocks
9.73% 9.46% 9.25% 9.10% 9.02% 9.06%
Annualized standard deviations were calculated from monthly standard deviations.
Annualized standard deviation of global portfolios where the
hedge ratio is: