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Commentary Russell Research Commentaries provide
original research or analysis of specific
topics and events.
Grant W. Gardner is an analyst in Research
in Tacoma. Statistical Estimates of the
Normal Currency Hedge
Ratio: Best Practice or Best
Guess?
Grant W. Gardner
Douglas Stone Douglas Stone is Director of Research at
Nicholas Applegate in San Diego, CA. Note: This paper is based partially on
research that will appear in a forthcoming
article in the Financial Analysts Journal. We wish to thank Amy Barton for
programming assistance. This research was
begun while Douglas Stone was an analyst
at Frank Russell Company. November 1995 Statistical Estimates of the Normal Currency Hedge Ratio: Best Practice or Best Guess? 1 Introduction
An essential element of currency risk management is determining a normal hedge
ratio. As explained in two earlier Commentaries [Gardner (1994a,b)], the normal
hedge ratio can be thought of as the fraction of a portfolio’s currency exposure
that an investor would offset with forward contracts if forced to choose a
permanent, constant policy. Because it is a permanent policy, the value of the
normal hedge ratio is based on the longrun behavior of currencies and asset
returns. If an investor uses passive currencyrisk management that ignores trends
and shortterm fluctuations in currency values, then the normal hedge ratio should
be maintained constantly. Alternatively, if the investor attempts to add value by
actively managing the portfolio’s currency exposure, then the normal hedge ratio
serves as the strategic benchmark used to judge the success of this active currency
management.
Conceptually, finding the value of the normal hedge ratio is straightforward.
As explained in the earlier Commentaries, standard meanvariance optimization
can be used to derive a hedge ratio that maximizes the total portfolio’s riskadjusted return. This technique underlies the discussions of currencyrisk control
found in Froot and Perold (1993), Glen and Jorion (1993), Jorion (1989),
Kritzman (1993), Lee (1989), and Nesbitt (1991), among others.
To calculate the normal hedge ratio, an investor needs values for expected
returns, variances, and covariances that reflect the longrun behavior of currency
and asset returns. Of course the “true” values of these parameters are unknown
and must be estimated. Even when correct statistical techniques are used and the
data sample is large, the parameter estimates contain degrees of error. When these
estimates are used to calculate the normal hedge ratio, this error is translated into
error in the estimate of the hedge ratio. The potential size of this error is a critical
issue. If the estimation error is very large, then the confidence region for the true
value of the normal hedge ratio is large and the point estimate is not very useful in
constructing a currency hedging strategy.1
Results from the earlier Commentaries suggest that the estimation error may
be significant. This Commentary provides a more detailed examination of the
estimation error for investors based in the United States, the United Kingdom, and
Japan. We find that when the estimate of the normal hedge ratio is based on
sample values of the mean returns, standard deviations of returns, and
correlations, the error of the estimate is so large as to make it essentially useless as
a guide to currency risk management for investors with moderate or high degrees
of risk tolerance. This result holds both when the hedge ratio is allowed to take on
any value and when it is constrained to be between zero and one.
The primary cause of this error is the low precision of the sample mean as an
estimate of the expected return on currency. This fact suggests that useful
estimates of the normal hedge ratio might be possible if the sample mean was
replaced by some moreprecise alternative estimate of the expected return on
currency. However, we present Monte Carlo results that suggest that any such
alternative estimate must be dramatically more precise than the sample mean in
order to provide useful estimates of the normal hedge ratio for investors with
moderate and high risk tolerance. The overall message of these results is that
statistical estimates of the normal hedge ratio probably have little value as a guide
to managing currency risk for investors with moderate or high risk tolerance.
1 Jobson and Korkie (1980) examine the distribution of estimated portfolio weights in a general
meanvariance portfolio problem. This issue is closely related to the concept of “estimation risk” as
discussed by Klein and Bawa (1976), and Jorion (1985, 1986). These authors focus on the potential
loss in utility of using portfolio weights derived from an optimization that uses sample estimates of
parameters. 2 Russell Research Commentary 2 The Normal Hedge Ratio 2 The Normal Hedge Ratio
To illustrate the framework used by most institutional investors, currency
managers, and consultants for calculating the normal hedge ratio (also called the
“strategic” or “policy” hedge ratio), consider a simplified portfolio that contains
composite domestic and foreign assets as well as a composite forward currency
contract that is used to hedge currency risk.2 The returns on the domestic and
foreign assets are represented by the returns on the indexes chosen to represent
asset classes. The foreign currency return is likewise represented by the weighted
return on the currencies included in the index of foreign assets.
The total return on the portfolio, rp , is equal to
rp = w d rd + w f r f − w f he ,
where: (1) wd is the fraction of wealth allocated to the domestic asset,
w f is the fraction of wealth allocated to the foreign asset,
h is the hedge ratio (the fraction of the value of foreign assets offset
with a short position in the forward currency market), e is the currency return (the gain on a long position in foreign
currency, normalized by the beginningofperiod spot rate),
rd is the return on the domestic asset, and
r f is the return on the foreign asset in terms of domestic currency.
The normal hedge ratio is the value of the hedge ratio that maximizes the
meanvariance utility function U = E rp −
where: 12
σp,
T (2) E rp is the expected value of the total portfolio return, σ 2 is the variance of the portfolio return, and
p
T is the investor’s level of risk tolerance.
Formally, the optimal value of h should be found simultaneously with the optimal
portfolio allocation weights wd and wf . However, in order to simplify the analysis
and focus on currency risk, we take the allocation weights as given. We then
derive the normal hedge ratio by taking the derivative of equation (2) with respect
to h, setting this derivative equal to zero, and then solving for h. Following this
*
procedure, the normal hedge ratio, h , is
h* = 1−
where: 1 T E[ e] σ z
−
ρ ez , 2
wf 2 σe
σe (3) E e is the expected value of the currency return,
σ e is the standard deviation of the currency return,
σ z is the standard deviation of the return of a zero exposure
portfolio that is completely hedged, and
ρ ez is the correlation coefficient of the return on the zero exposure
portfolio and the currency return. The normal hedge ratio given in equation (3) can be negative (indicating that
the investor should increase currency exposure beyond what is already in the
portfolio) or greater than one (indicating that the portfolio should have a net short
position in currency). However, many institutional investors constrain the range
2 This framework is discussed in more detail in Gardner (1994a,b). November 1995 3 Statistical Estimates of the Normal Currency Hedge Ratio: Best Practice or Best Guess?
of the hedge ratio to be between zero (completely unhedged) and one (completely
hedged). Because of the quadratic form of the optimization problem, it is easy to
show that the optimal value of the constrained hedge ratio is
*
hconstrained 0 = h *
1 if h * < 0
if 0 ≤ h * ≤ 1 (4) if h > 1
* 3 Estimating the Normal Hedge Ratio
To calculate either the unconstrained [equation (3)] or constrained [equation (4)]
normal hedge ratio, an investor needs longrun values for the expected currency
return, the variances of the returns on currency and the zeroexposure portfolio,
and the correlation of these returns. These parameters are unknown, and,
consequently, the “true” normal hedge ratio is unknown. However, it can be
estimated. The most common way of doing this is to calculate the sample values
of the parameters for a long sample and substitute them in equation (3). Table 1
shows the “conventional” estimates of both the unconstrained and constrained
normal hedge ratios for investors with various levels of risk tolerance based in the
United States, the United Kingdom, and Japan. The portfolios of assets being
hedged are typical of Russell clients in each of the three countries.
Table 1
Conventional Estimates of the Normal Hedge Ratio
Unconstrained Normal Hedge Ratio
Investor Risk Tolerance
T=0 (minimum variance) T=25
T=50
T=100 US Portfolio 1.11
0.18
0.75
2.61 UK Portfolio 1.25
1.33
1.41
1.57 Japanese Portfolio 0.58
0.74
0.90
1.22 Constrained Normal Hedge Ratio
Investor Risk Tolerance
T=0 (minimum variance) T=25
T=50
T=100 US Portfolio 1
0.18
0
0 UK Portfolio 1
1
1
1 Japanese Portfolio 0
0
0
0 US
Portfolio: 40% S&P 500 Index
40% Lehman Brothers Aggregate Bond Index
20% Morgan Stanley Capital International Europe, Australia, Far
East Index UK
Portfolio: 45% FT  A All Share
25% FT  A UK Government All Stocks
30% CapitalWeighted 17Country Index of NonUK Equities Japanese
Portfolio: 25% TOPIX Index
60% Salomon Brothers BMI Japan Bond Index
15% CapitalWeighted 17Country Index of NonJapanese Equities
Each of the sample parameters used to calculate the conventional estimates
appearing in Table 1 is a random variable which estimates the true value of a 4 Russell Research Commentary 3 Estimating the Normal Hedge Ratio parameter with error. Consequently, the estimated normal hedge ratio is also a
random variable that estimates the true normal hedge ratio with error. It is
important for the investor to know the potential size of this error in order to know
how much confidence to place in the estimate of the hedge ratio. The natural
measure of this potential error is the standard deviation of the estimated hedge
ratio. With an estimate of this standard deviation and a reasonable idea of other
characteristics of the distribution, an investor can construct confidence intervals
for the true normal hedge ratio.
For some common estimators, such as a sample mean or the coefficients of a
leastsquares regression, there are wellknown formulas for estimating the
standard deviation of the estimator when the data satisfies certain assumptions.
Unfortunately, even if the underlying sample returns are assumed to have “nice”
propertiesindependent draws from identical joint normal distributionsthere is
no known formula for estimating the standard deviation of the estimate of either
version of the normal hedge ratio.3
In situations where there is no known formula for the standard deviation of an
estimator, a bootstrap method can be used.4 Briefly, this method consists of
randomly selecting, with replacement, N observations from a data sample of N
observations.5 The estimator of interest is then calculated using this randomly
selected set of observations. This process of drawing samples and calculating the
estimator is repeated many times, creating an empirical distribution of the
estimator. The standard deviation of this empirical distribution is then used to
estimate the standard deviation of the estimator. Also, the empirical distribution
can be used to directly calculate confidence regions.
Table 2 shows the means and standard deviations of the bootstrap empirical
distributions of the estimates of the constrained and unconstrained normal hedge
ratios. The complete distributions for a risk tolerance of 50 are shown in Figures 1
through 6. 3 The estimate of the unconstrained minimumvariance hedge ratio is a regression coefficient
whose standard error can be directly calculated. The standard error of the minimumvariance hedge
ratio calculated using regression techniques is very close to that of the estimated standard deviation
from the bootstrap technique shown in Table 2.
4 The literature on bootstrap methods is very large. Two introductions to this technique are Efron
(1982) and Mooney and Duval (1993).
5 The simple methods employed here require that the observations be independent. Conventional tests on the autocorrelations of data series showed no evidence of serial correlation. November 1995 5 Statistical Estimates of the Normal Currency Hedge Ratio: Best Practice or Best Guess?
Table 2
Bootstrap Estimates of the Normal Hedge Ratio
Unconstrained Normal Hedge Ratio
Investor
Risk Tolerance US Portfolio
Mean
Std Dv T=0 (min. variance) UK Portfolio
Mean Std Dv Japanese Portfolio
Mean
Std Dv 1.11 0.59 1.19 0.45 0.63 0.88 T=25 0.16 3.24 1.63 1.79 0.66 4.60 T=50 1.44 6.59 2.07 3.71 0.68 9.09 T=100 3.99 13.34 2.95 7.60 0.72 18.16 Constrained Normal Hedge Ratio
Investor
Risk Tolerance US Portfolio
Mean
Std Dv UK Portfolio
Mean Std Dv Japanese Portfolio
Mean
Std Dv T=0 (min. variance) 0.83 0.27 0.90 0.21 0.11 0.25 T=25 0.45 0.47 0.75 0.39 0.40 0.48 T=50 0.41 0.48 0.64 0.48 0.44 0.49 T=100 0.39 0.48 0.59 0.48 0.47 0.50 Figure 1
US Portfolio
Distribution of Unconstrained Normal Hedge Ratio Cumulative
Frequency Frequency (%) 100% 8% 90% 7% 80%
6%
70%
5% 60%
50% 4% 40% 3% 30%
2%
20%
1% 10%
0% 0%
35 30 25 20 15 10 5 0 5 10 15 Hedge Ratio 6 Russell Research Commentary 3 Estimating the Normal Hedge Ratio Figure 2
UK Portfolio
Distribution of Unconstrained Normal Hedge Ratio
Cumulative
Frequency Frequency (%)
14% 100%
90% 12%
80%
10% 70%
60% 8% 50%
6% 40%
30% 4% 20%
2%
10%
0% 0%
11 6 1 4
9
Hedge Ratio 14 19 24 Figure 3
Japanese Portfolio
Distribution of Unconstrained Normal Hedge Ratio
Cumulative
Frequency Frequency (%)
6% 100%
90% 5%
80%
70% 4% 60%
3% 50%
40% 2%
30%
20% 1% 10%
0% 0%
26 23 20 17 14 11 8 5 2 1 4 7 10 13 16 19 22 Hedge Ratio November 1995 7 Statistical Estimates of the Normal Currency Hedge Ratio: Best Practice or Best Guess?
Figure 4
US Portfolio
Distribution of Constrained Normal Hedge Ratio Cumulative
Frequency
100% Frequency (%)
60% 90%
50% 80%
70% 40% 60%
30% 50%
40% 20% 30%
20% 10% 10%
0% 0%
0 0.010.09 0.100.19 0.200.29 0.300.39 0.400.49 0.500.59 0.600.69 0.700.79 0.800.89 0.900.99 1 Hedge Ratio Figure 5
UK Portfolio
Distribution of Constrained Normal Hedge Ratio
Cumulative
Frequency Frequency (%)
60% 100%
90% 50%
80%
70%
40%
60%
30% 50%
40% 20%
30%
20%
10%
10%
0% 0%
0 0.010.09 0.100.19 0.200.29 0.30
0.39 0.400.49 0.500.59 0.600.69 0.700.79 0.80
0.89 0.900.99 1 Hedge Ratio 8 Russell Research Commentary 4 Improving the Precision of the Estimates Figure 6
Japanese Portfolio
Distribution of Constrained Normal Hedge Ratio
Cumulative
Frequency
100% Frequency (%)
60% 90%
50%
80%
70%
40%
60%
30% 50%
40% 20%
30%
20%
10%
10%
0% 0%
0 0.010.09 0.100.19 0.200.29 0.30
0.39 0.400.49 0.500.59 0.600.69 0.700.79 0.80
0.89 0.900.99 1 Hedge Ratio The information in Table 2 and Figures 1 through 3 clearly shows that the
estimation error for the unconstrained normal portfolio is very large when an
investor has a moderate or high level of risk tolerance. For example, a US investor
with risk tolerance of 50 has a 50% confidence interval (the interval from the 25th
to the 75th percentile of the distribution) of (4.95, 2.94). Because of the
magnitude of the estimation error, the conventional point estimate of the
unconstrained normal hedge ratio is essentially useless as a practical guide to
currency risk management at this level of risk tolerance. The same is true for the
constrained normal hedge ratio. Table 2 and Figure 4 show that the 50%
confidence interval for a US investor with risk tolerance of 50 spans all the
permitted values from zero to one. The results for the United Kingdom and Japan
are similar.
For investors with extremely low levels of risk tolerance, the conventional
estimate of the normal hedge ratio is more useful. By way of comparison, the 50%
confidence interval for the unconstrained and constrained minimumvariance
hedge ratios of a US investor are (0.72, 1.47) and (0.72, 1), respectively.
However, for more typical confidence levels, the confidence intervals are still
quite large. For a US investor, the 90% confidence intervals for the unconstrained
and constrained minimumvariance hedge ratios are (0.21, 2.12) and (0.21, 1). 4 Improving the Precision of the Estimates
The lack of precision of the estimated normal hedge ratio can be traced primarily
to the large standard deviation of the sample mean of currency return. The sample
standard deviation of the monthly currency return is 2.75% for a US investor. November 1995 9 Statistical Estimates of the Normal Currency Hedge Ratio: Best Practice or Best Guess?
Thus the sample estimate of the standard deviation of the sample mean with 60
observations is
σ (e ) = 2.75 60 = 0.36 .
To see the importance of this standard deviation for the precision of the estimated
normal hedge ratio, suppose that all of the parameters needed to calculate the
normal hedge ratio are known except for the expected value of the currency
return. If the expected value of the currency return is estimated by the sample
mean, then the standard deviation of the estimated normal hedge ratio for a US
investor with risk tolerance of 50 is
Tσ ( e )
σ (h * ) =
= 5.87 ,
(5)
2w f σ 2
e which is only slightly lower that the bootstrap standard deviation of 6.59 given in
Table 2.6 The standard deviations of the sample mean monthly currency returns
for the United Kingdom and Japan are 0.41 and 0.34, respectively. Thus imprecise
estimates of this parameter are a major factor in the imprecise estimates of the
normal hedge ratios for these countries as well.
Since the primary cause of low precision in the estimate of the normal hedge
ratio is the low precision of the sample mean currency return, it follows that if the
sample mean could be replaced by an alternative, moreprecise estimate of the
currency return, then a useful estimate of the normal hedge ratio would be
possible. The critical question is whether such an alternative estimate of the
expected currency return exists.
We address this question in the following way. We first examine how much
more precise some alternative estimate must be in order to provide useful
confidence intervals for the normal hedge ratio. We then briefly discuss the
empirical literature on exchange rate behavior and forecasting in order to evaluate
how likely it is that an alternative estimate with this degree of precision exists.
To evaluate how precise an estimate of expected currency return must be, we
performed a Monte Carlo experiment. We generated 1000 simulated 60month
samples of returns on currency and a zeroexposure US portfolio. These simulated
samples were independent draws from a joint normal distribution with parameters
equal to the US historical sample described in Table 1. For each of the 1000
simulated samples, the constrained and unconstrained normal hedge ratios were
calculated, assuming a risk tolerance of 50. These normal hedge ratios used
variances and correlations calculated from the simulated samples. However, rather
than using the sample mean of the currency return as the estimate of the expected
currency return, we used the sample mean of a “forecast variable” that was
constructed to have the same expected value as the currency return but a smaller
standard deviation. The normal hedge ratios constructed in this manner represent
estimated normal hedge ratios one would obtain if there existed an estimate of the
expected currency return that had greater precision than the sample mean.
Table 3 shows the results of this Monte Carlo experiment for several versions
of the forecast variable that give varying degrees of improvement in precision.
For example, the row labeled “50%” gives the mean and standard deviation of the
1000 simulated hedge ratios when the forecast variable used to estimate the
expected currency return has a standard deviation that is 50% of the sample mean
currency return. Note that the row labeled “0%” are the results when the sample
6 The precision problem caused by using the sample mean currency return as an estimate of
expected currency return is an example of a more general problem encountered in using meanvariance optimization in portfolio construction. Sample mean returns of financial assets typically
have large standard deviations, and this error causes low precision in the estimates of optimal
portfolio weights. This same problem has been discussed in the context of estimation risk. See the
references in footnote 1 for alternative estimates to the sample mean that reduce estimation risk. 10 Russell Research Commentary 4 Improving the Precision of the Estimates mean currency return is used as the estimate of the expected currency return.
Consequently, these results are very similar to those from the bootstrap estimates
for a US investor with T=50 shown in Table 2. Similarly, the row labeled “100%”
contains the results for the case where the expected currency return is known.
Also shown are the “true” values of the unconstrained and constrained normal
hedge ratios that were calculated using the parameter values employed to generate
the simulated samples.
Table 3
Effects of Improved Estimates of E[e]
Reduction in estimate
error of E[e]
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100% Unconstrained Normal Hedge Ratio
(True value = 0.75)
Mean
Std. Dev.
0.69
6.29
0.68
5.33
0.86
5.09
0.65
4.34
0.81
3.72
0.94
3.17
0.75
2.62
0.86
1.96
0.89
1.46
0.83
0.95
0.81
0.68 Constrained Normal Hedge Ratio
(True value = 0.00)
Mean
Std. Dev.
0.42
0.48
0.43
0.48
0.39
0.47
0.40
0.47
0.36
0.47
0.33
0.45
0.32
0.44
0.24
0.39
0.17
0.33
0.08
0.21
0.04
0.12 Table 4 shows the results for an alternative Monte Carlo experiment. These
results were generated in the same manner as those shown in Table 3 except that
the values of the variances and covariances were set equal to their true values
rather than their sample values. These results represent an extreme case where the
investor has complete knowledge of the variances and correlation. Note that for
cases where the error reduction is less that 80%, the results of Tables 3 and 4 are
quite similar. This fact is indicative of the point made earlier that most of the error
in the estimate of the normal hedge ratio is due to the lack of precision in
estimating the expected value of the currency return.
Table 4
Effects of Improved Estimates of E[e]
(All parameters except E[e] known)
Reduction in estimate
error of E[e]
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100% Unconstrained Normal Hedge Ratio
(True value = 0.75)
Mean
Std. Dev.
0.78
5.81
0.63
5.10
0.59
4.92
0.89
4.20
0.75
3.50
0.74
2.99
0.72
2.40
0.80
1.75
0.81
1.18
0.76
0.59
0.75
0.00 Constrained Normal Hedge Ratio
(True value = 0.00)
Mean
Std. Dev.
0.41
0.48
0.41
0.48
0.42
0.48
0.36
0.46
0.37
0.46
0.33
0.45
0.31
0.43
0.23
0.39
0.14
0.29
0.03
0.11
0.00
0.00 The results of Tables 3 and 4 show that in order for estimates of the normal
hedge ratio to have standard errors that are small enough to make them useful as November 1995 11 Statistical Estimates of the Normal Currency Hedge Ratio: Best Practice or Best Guess?
practical guides to currency risk management, an investor with moderate or high
risk tolerance needs some method of estimating the expected return on currency
that is dramatically more precise than the sample mean. For example, even if there
existed some alternative estimate that eliminated 80% of the estimation error
contained in the sample mean, the standard deviation of the estimate of the
unconstrained normal hedge ratio exceeds one. The standard deviation of the
constrained normal hedge ratio is such that confidence regions for typical
confidence levels include most of the interval from zero to one.
Empirical research on the behavior of exchange rates offers little
encouragement of finding dramatically better estimates of expected currency
return. Structural models of currency behavior that condition the expected
currency return on “fundamental” financial and macroeconomic variables offer no
significant improvement over naive forecasts of no change in the exchange rate.
Another strand of exchange rate research examines the time series properties of
currencies. An important finding of this research is that the return on currency
exhibits serial dependence over certain time intervals. One implication is that
technical trading rules for currency may be profitable. However, there is no
evidence that this information can be used to construct precise point estimates of
the expected value of the return on currency. 7
In sum, useful estimates of the confidence interval of the normal hedge ratio
require estimates of the expected return on currency that are much more precise
than are currently available. 5 Summary and Final Comments
The results of this Commentary strongly suggest that the usual paradigm for
estimating a portfolio’s normal hedge ratio is of little practical use to investors
with moderate to high risk tolerance. For such investors, the normal hedge ratio
cannot be estimated with reasonable precision. The primary cause of this problem
is the lack of precise estimates of the return on currency.
For investors in the United States and the United Kingdom, these results
reinforce the conclusion reached in two earlier Commentaries [Gardner
(1994a,b)]. For typical Japanese portfolios, this earlier work concluded that there
was support for an unhedged normal hedge ratio. However, the results presented
in this Commentary indicate that no such definite conclusion can be justified. The
reason for the difference in results is that the earlier research did not fully account
for the imprecision involve in estimating the expected return on currency.
The obvious implication of these results is that an investor should be very
skeptical of normal hedge ratios derived by purely statistical techniques. In terms
of being able to estimate the “true” normal hedge ratio that an investor would use
if he or she had full knowledge of the probability distribution that generated
currency and asset returns, even “best practice” statistical estimates are essentially
no better than randomly choosing a number between zero and one.
But if this statistical technique does not give a good answer, how should an
investor choose the normal hedge ratio? Keep in mind that the procedure
described in Section 2 gives a normal hedge ratio that is optimal in the sense that
it maximizes the meanvariance utility of an investor. In principle, this is a sound
criteria for selecting the hedge ratio. But when it is impossible to know the value
of the normal hedge ratio based on this criteria, an investor should feel free to
base the choice of the normal hedge ratio on other factors.
Sometimes the reasonable choice for the normal hedge ratio is obvious. If an
investor has an allocation to foreign assets of less than 10%, currency fluctuations
7 Ramaswami (1993) provides an excellent review of recent empirical evidence on currency behavior and an extensive list of references. 12 Russell Research Commentary 6 References will have only a limited effect on total portfolio return. Unless the return on the
foreign segment of the portfolio is important to the investor for reasons other than
its contribution to the total portfolio, it seems reasonable to adopt an unhedged
normal position. A passive currency policy with an unhedged normal hedge ratio
amounts to doing nothing about currency risk. Such a policy avoids any costs
involved with monitoring and maintaining a currency position.
When a investor has a more substantial commitment to foreign assets, another
potential guide to determining the normal hedge ratio is regret.8 Regret occurs
when an obvious and very different alternative hedging strategy outperforms the
normal strategy over a given time horizon. Regret is always possible because
currency returns and asset returns are random, so that an alternative hedging
strategy can outperform the optimal normal strategy over a finite horizon. If an
investor is sensitive to regret, he or she may want to set the normal hedge ratio in
a way that minimizes potential regret. For example, if an investor feels that he or
she could be judged against both a fully hedged and a fully unhedged alternative,
a 50% hedge ratio minimizes regret.
In sum, determining the best choice for a normal hedge ratio requires a
thoughtful examination of an investor’s overall goals and constraints. Because of
their lack of precision, statistical estimates of the normal hedge ratio provide little
guidance in making this choice. 6 References
Efron, Bradley. 1982. The Jackknife, the Bootstrap and Other Resampling Plans.
Philadelphia: Society for Industrial and Applied Mathematics.
Froot, Kenneth A., and André F. Perold. 1993. “The Determinants of Optimal
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Gardner, Grant W. 1994a. “Managing Currency Risk in US Pension Plans.”
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__________ 1994b. “CurrencyRisk Management for NonUS Investors.” Russell
Research Commentary (April).
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Glen, Jack and Philippe Jorion. 1993. “Currency Hedging for International
Portfolios.” Journal of Finance 48 (December): 1865–1886.
Jobson, J. D., and B. Korkie. 1980. “Estimation for Markowitz Efficient
Portfolios.” Journal of the American Statistical Association 75 (September):
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Jorion, Philippe. 1985. “International Portfolio Diversification with Estimation
Risk.” Journal of Business 58 (July): 259–278.
__________ 1986. “BayesStein Estimation for Portfolio Analysis.” Journal of
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__________ 1989. “Asset Allocation with Hedged and Unhedged Foreign Stocks
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Klein, Roger W., and Vijay S. Bawa. 1976. “The Effect of Estimation Risk on
Optimal Portfolio Choice.” Journal of Financial Economics 3 (June): 215–
231. 8 The concept of regret in the context of currency risk management is discussed in detail in Gardner (1994a,b) and Gardner and Wuilloud (1994). November 1995 13 Statistical Estimates of the Normal Currency Hedge Ratio: Best Practice or Best Guess?
Kritzman, Mark. 1993. “The Optimal Currency Hedging Policy with Biased
Forward Rates.” The Journal of Portfolio Management (Summer): 94–100.
Lee, Adrian F. 1989. “Hedging Decisions Within the Overall Asset Allocation
Strategy.” In Managing Currency Risk, edited by Mark Kritzman and Katrina
F. Sherrerd. Charlottesville, Virginia: Institute of Chartered Financial
Analysts.
Mooney, Christopher Z., and Robert D. Duval. 1993. Bootstrapping: A
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