## _wp10151

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---

### I. INTRODUCTION — scope, approach, and main empirical insights
- Scope:
  - Perspectives: German, Japanese, British and American investors.
  - Asset classes: bond and equity investments in France, Germany, Japan, the U.K., and the U.S.
  - Sample period: January 1975 to December 2009 (almost the entire period of free-floating exchange rates, includes the financial crisis of 2007 to 2009).
  - Investment horizons analyzed: up to five years (quarterly and annual horizons emphasized).
- Approach:
  - Compare simple hedge ratios (0, 50, 100 percent) and optimal minimum-variance hedge ratios exploiting the full covariance structure.
  - Use 3-month bank deposit rates to construct hedged return series rather than T-bill rates.
- Key empirical findings:
  - The case for hedging is generally not decreasing with increasing investment horizon over the last 35 years; some horizons up to five years show hedging less effective, while other cases show optimal over-hedging (shorting a currency).
  - Short positions in the Yen reduced portfolio risk via diversification because associated carry trade profits were largely uncorrelated with bond and equity returns.
  - Results are base-currency specific — an investor’s base currency matters significantly for hedging policy conclusions.
  - Risk perspective:
    - Bonds: full hedging is optimal in almost all cases because exchange rate volatility dominates bond return volatility.
    - Equities: currency–equity covariances are complex and country-specific; optimal currency positions vary (e.g., hedge or over-hedge Pound exposure; maintain some exposure to DM/Euro).
    - Multi-country portfolios: short positions in the British Pound and long positions in the DM/Euro would have been optimal over the sample; for Yen and U.S. Dollar full hedging would have been optimal over the full sample with over- and under-hedging optimal in sub-periods.
  - Return perspective:
    - Differences in hedged and unhedged returns generally not statistically significant for most cases.
    - Forward bias/UIP failure: investors from low interest rate currencies, especially the Japanese Yen, would have benefited from keeping currency exposure.
  - Crisis-period behavior:
    - During 2007–2009 the Euro became extremely pro-cyclical and fell along with equity markets, so historical-based Euro exposures would have produced substantial additional currency losses.

### II. LITERATURE REVIEW — theoretical anchors and empirical precedents
- Theoretical benchmarks referenced:
  - Solnik (1974); Perold and Shulman (1988); Froot (1993); Black (1989a).
- Empirical context:
  - Campbell et al. (2010): USD, EUR, CHF moved against world equity markets (1975–2005); full hedging tends to be optimal for bonds.
  - Eun and Resnick (1988): currency risk largely undiversifiable.
  - UIP/forward bias literature (Fama (1984), Engel (1996)): documents failure of uncovered interest rate parity; carry-trade profits for low-rate currencies.
- Practitioner behavior:
  - Common use of simple hedge ratios of 0, 50, 100 percent; major hedged indices fully hedge each foreign currency into the base currency using beginning-of-period investment values.
  - Practical reasons: instability of optimal hedge ratio estimation and time-varying currency–equity correlations (observed swings from plus 40 percent to minus 40 percent across decades in the dataset).

### III. DATA — sources, coverage, and construction choices
- Data coverage and frequency:
  - 1975M1 to 2009M12; monthly data; results for horizons up to five years.
- Data sources:
  - MSCI value-weighted indices adjusted for dividends for stock returns.
  - IMF IFS for government bond yields, spot exchange rates, CPI.
  - Three-month deposit rates: IFS for Japan; DataStream for Germany, France, U.K., U.S.
- Bond return construction:
  - Long-term bond portfolio returns approximated using Campbell, Lo, and MacKinlay (1997) due to limited pre-1986 data.
- EUR/EMU considerations:
  - Post-Euro: interest rate differentials between Germany and France virtually disappeared and exchange rate movements ceased; analysis presents the German perspective following Table 1.
- Descriptive statistics (Table 1 summary, annualized rolling changes/real returns, full sample 1975–2009):
  - CPI annualized averages:
    - U.K.: 5.6 percent per year.
    - France: 4.4 percent per year.
    - U.S.: 4.2 percent per year.
    - Germany: 2.5 percent per year.
    - Japan: 1.8 percent per year.
  - Real annualized three-month deposit rates (averages and standard deviations):
    - France Average 3.26 Standard Deviation 2.84.
    - Germany Average 2.49 Standard Deviation 1.57.
    - Japan Average 0.19 Standard Deviation 1.56.
    - United Kingdom Average 2.66 Standard Deviation 3.11.
    - United States Average 2.02 Standard Deviation 2.24.
  - Real equity index (MSCI) averages and standard deviations:
    - France Average 9.89 Standard Deviation 24.97.
    - Germany Average 8.46 Standard Deviation 24.43.
    - Japan Average 5.38 Standard Deviation 22.57.
    - United Kingdom Average 8.45 Standard Deviation 16.92.
    - United States Average 7.56 Standard Deviation 17.26.
  - Real bond returns (IFS) averages and standard deviations:
    - France Average 4.86 Standard Deviation 7.82.
    - Germany Average 4.90 Standard Deviation 6.11.
    - Japan Average 4.27 Standard Deviation 6.43.
    - United Kingdom Average 5.03 Standard Deviation 7.23.
    - United States Average 4.17 Standard Deviation 8.15.
  - Additional note: 3.3 percent in France. Volatility of deposit rates has been low not exceeding 3.1 percent per (statement continued in source).

### IV. METHODOLOGICAL and IMPLEMENTATION NOTES
- Hedging constructs and comparisons:
  - Simple hedge ratios evaluated: 0, 50, 100 percent.
  - Optimal hedge ratios estimated via minimum variance exploiting full covariance structure; tested for single-country and multi-country portfolios and across sub-samples.
- Hedged return construction improvement:
  - Use 3-month bank deposit rates instead of T-bill rates to mitigate comparability and liquidity issues; Table 4 quantifies impact (1990M1–2009M12 panel comparisons: deposit-rate-based vs exchange-rate-based mean absolute deviations: U.S./U.K. 0.08, U.S./Japan 0.11, U.S./France 0.04, U.S./Germany 0.04; T-Bill-based deviations higher: U.S./U.K. 0.11, U.S./Japan 0.19, U.S./France 0.10, U.S./Germany 0.11).
- Horizon analysis:
  - Distinguish short and long horizons; estimate k-period hedge ratios using log-returns.
  - Evidence indicates horizon effects are not uniformly supportive of reduced hedging at longer horizons.

### V. EMPIRICAL IMPLICATIONS and PRACTICAL TAKEAWAYS
- Currency hedging policy should be investor-specific:
  - Base currency materially affects optimal hedging strategy.
- Asset-class differences:
  - Bonds: full hedging generally warranted because exchange rate volatility is the dominant risk driver.
  - Equities: hedging depends on asset–currency covariances that are time-varying and country-specific; optimal positions may include over-hedging or maintaining exposure.
- Time-variation and crisis risk:
  - Historical correlations can reverse; reliance on historical correlations without accounting for regime shifts (e.g., 2007–2009) can produce large unexpected currency losses.
- Practical recommendation for practitioners:
  - Simplicity (0, 50, 100 percent hedges) is common and defensible given estimation instability, but practitioners should be aware of time-varying correlations and crisis-period behavior that can alter hedge effectiveness.

### SUMMARY STATISTICS AND RETURN COMPONENTS (selected precise figures)
- Data coverage: 1975M1 to 2009M12; monthly data.
- Table 1 annual arithmetic averages and standard deviations (rolling annual changes/returns, percentages):
  - CPI: France Average 4.39 Standard Deviation 3.99; Germany Average 2.51 Standard Deviation 1.67; Japan Average 1.79 Standard Deviation 2.64; United Kingdom Average 5.65 Standard Deviation 4.74; United States Average 4.19 Standard Deviation 2.91.
  - Real 3-month deposit rate: France Average 3.26 Standard Deviation 2.84; Germany Average 2.49 Standard Deviation 1.57; Japan Average 0.19 Standard Deviation 1.56; United Kingdom Average 2.66 Standard Deviation 3.11; United States Average 2.02 Standard Deviation 2.24.
  - Real equity index (MSCI): France Average 9.89 Standard Deviation 24.97; Germany Average 8.46 Standard Deviation 24.43; Japan Average 5.38 Standard Deviation 22.57; United Kingdom Average 8.45 Standard Deviation 16.92; United States Average 7.56 Standard Deviation 17.26.
  - Real bond returns (IFS): France Average 4.86 Standard Deviation 7.82; Germany Average 4.90 Standard Deviation 6.11; Japan Average 4.27 Standard Deviation 6.43; United Kingdom Average 5.03 Standard Deviation 7.23; United States Average 4.17 Standard Deviation 8.15.
- Components of international returns and variance decomposition:
  - Exchange rate volatility contributes between 16 and 40 percent to equity investment volatility.
  - For bond portfolios, exchange rate risk can contribute up to 95 percent of total unhedged return volatility.
  - Example quarterly observations (Table 2, selected entries):
    - German perspective vs Japan: Exchange rate gain/loss 0.62; Currency excess return -0.11; Equities unhedged return 2.34; Bonds unhedged return 2.10.
    - Japanese perspective vs France: Exchange rate gain/loss -0.70; Currency excess return 0.67; Equities unhedged return 2.75; Bonds unhedged return 1.51.
    - U.K. perspective vs Japan: Exchange rate gain/loss 1.44; Currency excess return -0.09; Equities unhedged return 3.21; Bonds unhedged return 2.95.
    - U.S. perspective vs Japan: Exchange rate gain/loss 1.04; Currency excess return 0.02; Equities unhedged return 2.73; Bonds unhedged return 2.52.
- Hedging implementation observations:
  - Hedge beginning-of-period balances is common; average quarterly return due to unhedged difference between beginning- and end-of-period values is below 0.07 percent for all base currency/foreign investment combinations considered.
  - Hedging via borrowing/lending and forwards are equivalent if covered interest parity holds: (1+i_dom)/(1+i_for) = 1+δ_t.

### EMPIRICAL RESULTS — EFFECTS OF HEDGING ON RETURNS AND VOLATILITY
- Single-country portfolios:
  - In almost all cases, null of equal means of hedged and unhedged quarterly returns cannot be rejected due to large sample variance.
  - Example economic difference: Japanese investor in French stock market No hedge 2.75 percent quarterly vs Full hedge 2.10 percent quarterly (approximate annual differential of 2.6 percent).
  - Hedging reduces volatility in almost all cases, statistically and economically significant.
  - Example bond volatility (German perspective, Japan): No hedge SD 6.57 Half hedge 3.74 Full hedge 1.83.
- Multi-country (equal-weighted global portfolios of France, Germany, Japan, U.K., U.S.):
  - Returns differences hedged vs unhedged generally not statistically significant; economic differences notable for Japanese investors.
  - Standard deviations: hedging yields economically and statistically significant risk reduction; example German perspective Global stock portfolio No hedge 8.72 Full hedge 7.87; Global bond portfolio No hedge 3.03 Full hedge 1.52.
- Optimal minimum-variance hedge ratios (quarterly single-country, Table 9, point estimates with Newey-West SEs in parentheses):
  - Bonds: hedge ratios essentially one for investors in all base currencies.
  - Stocks (selected):
    - German perspective: Japan 1.00 (0.23), U.K. 1.39 (0.12), U.S. 1.04 (0.13).
    - Japanese perspective: France 0.95 (0.13), Germany 1.05 (0.14), U.K. 1.08 (0.09), U.S. 1.05 (0.10).
    - U.K. perspective: France 0.72 (0.18), Germany 0.55 (0.14), Japan 1.05 (0.12), U.S. 0.84 (0.15).
    - U.S. perspective: France 0.82 (0.18), Germany 0.70 (0.16), Japan 0.92 (0.14), U.K. 1.00 (0.14).
- Multi-country minimum-variance hedge ratios (full-sample, Table 10, selected estimates with SEs):
  - German perspective Global stock portfolio: Japan 0.62 (0.60), United Kingdom 2.37 (0.57), United States 1.39 (0.53).
  - Japanese perspective Global stock portfolio: Germany -0.49 (0.46), United Kingdom 2.29 (0.52), United States 1.42 (0.52).
  - U.K. perspective Global stock portfolio: Germany -0.57 (0.46), Japan 1.25 (0.29), United States 0.94 (0.61).
  - U.S. perspective Global stock portfolio: Germany -0.50 (0.50), Japan 0.71 (0.54), United Kingdom 2.34 (0.57).
  - Sub-periods show instability: first half vs second half produce markedly different estimates (e.g., German perspective U.K. 4.02 (1.06) in second half).
- Horizon results (variance ratios and hedge ratios up to 5 years):
  - Variance ratios (var(unhedged)/var(hedged), Table 13):
    - Stocks: no universal pattern of hedging becoming less effective with horizon; variance ratios often increase with horizon for some base currency–market combinations (example German perspective U.S. stocks 1 Quarter 1.59 to 5 Years 2.53).
    - Bonds: variance ratios decrease strongly from quarterly to five-year horizons but remain >1 in nearly all cases (example German perspective Japan bonds 1 Quarter 12.88, 5 Years 2.94; U.S. perspective U.K. bonds 1 Quarter 9.98, 5 Years 1.62).
  - Minimum-variance hedge ratios over horizons (selected examples):
    - German perspective Japan (stocks): 1 Quarter 1.02 (0.20), 5 Years 1.93 (0.56).
    - Japanese perspective France (stocks): 1 Quarter 0.99 (0.16), 5 Years 0.30 (0.31).
    - U.K. perspective Japan (stocks): 1 Quarter 1.06 (0.11), 5 Years 1.67 (0.66).
  - Statistical precision declines with horizon (standard errors increase).
  - Conclusion: hedging generally reduces variance up to 5-year horizons for most cases, especially bonds; no universal prescription to avoid hedging at long horizons.

### MAIN CONCLUSIONS AND INVESTOR IMPLICATIONS (1975–2009 evidence)
- Currency risk contributes materially to international investment volatility: up to 40 percent for single-country equity investments and up to 95 percent for single-country bond investments.
- Hedging replaces stochastic exchange-rate changes with the known forward premium/discount, substantially reducing volatility at short horizons.
- Practical recommendations:
  - For bond investments: hedge fully (Φ ≈ 1) to minimize variance in almost all circumstances.
  - For equity investments: default to high hedge ratios (near 100 percent) unless stable negative correlations justify partial exposure; optimal hedge ratios vary by base currency, foreign market, and sub-period.
  - Base-currency-specific effects: Japanese investors historically benefited from leaving currency exposure unhedged (carry-trade gains); hedging reduced realized returns for them over the sample.
  - Calibrate hedge ratios cautiously: currency–asset correlations are unstable (notably during 2007–2009), so historical optimal hedge ratios may not persist.
  - For long-horizon investors (up to 5 years): hedging generally remains effective, particularly for bonds.
- Risk management emphasis:
  - Hedge ratio selection should account for (a) volatility of exchange rate movements, (b) covariance of exchange rates with asset returns, (c) investor base currency, (d) investment horizon, and (e) estimation risk/instability of covariances.
  - Use deposit-rate-based forward premia for practical hedging where forward market data or T-bill comparability is problematic.

*Source: _wp10151 - References (PDF chapter/section); data coverage 1975M1 to 2009M12; author's estimates using IMF IFS, DataStream, MSCI.*

### References .............................................................................................................

### _wp10151 - References .............................................................................................................

### I. INTRODUCTION — scope, approach, and main empirical insights
- Scope:
  - Perspectives: German, Japanese, British and American investors.
  - Asset classes: bond and equity investments in France, Germany, Japan, the U.K., and the U.S.
  - Sample period: almost the entire period of free-floating exchange rates, includes the financial crisis of 2007 to 2009.
  - Investment horizons analyzed: up to five years (quarterly and annual horizons emphasized).
- Approach:
  - Compare simple hedge ratios (no hedging, half hedging, full hedging) and optimal risk-minimizing hedge ratios that exploit the full covariance structure.
  - Use 3-month bank deposit rates to construct hedged return series rather than T-bill rates.
- Key empirical findings:
  - The case for hedging is generally not decreasing with increasing investment horizon over the last 35 years; in some cases hedging becomes less effective at horizons of up to five years, but other cases show optimal over-hedging (shorting a currency).
  - Short positions in the Yen (being short Yen) have reduced portfolio risk via diversification because associated carry trade profits were largely uncorrelated with bond and equity returns.
  - Results cannot be generalized from one base currency to another — an investor’s base currency matters significantly for hedging policy conclusions.
  - Risk perspective:
    - For bond portfolios: full hedging is the optimal strategy in almost all cases because exchange rate volatility dominates bond return volatility.
    - For equity portfolios: the role of currency-equity covariances is more complex; country-specific correlations imply different optimal currency positions (e.g., hedge or over-hedge Pound exposure; maintain some exposure to DM/Euro).
    - In multi-country portfolios: short positions in the British Pound and long positions in the DM/Euro would have been optimal over the sample; for the Yen and the U.S. Dollar full hedging would have been optimal over the entire sample, with over- and under-hedging optimal in sub-periods.
  - Return perspective:
    - Differences in hedged and unhedged returns are generally not statistically significant for the most part.
    - Consistent with the forward bias/uncovered interest rate parity failure: investors from low interest rate currencies, particularly the Japanese Yen, would have benefited from keeping currency exposure associated with foreign investments.
  - Crisis-period behavior:
    - During 2007–2009 the Euro, which had tended to move against equity markets pre-crisis, became extremely pro-cyclical and fell along with equity markets, implying historical-based Euro exposures would have led to substantial additional currency losses.

### II. LITERATURE REVIEW — theoretical anchors and empirical precedents
- Theoretical benchmarks:
  - Solnik (1974): full hedging optimal if foreign currencies uncorrelated with other assets.
  - Perold and Shulman (1988): recommend full hedging assuming long-run zero currency returns and near-zero correlations; view hedging as reducing risk without affecting returns.
  - Froot (1993): argues that mean-reversion of real exchange rates (PPP) implies long-horizon investors need not hedge; his tests focus on a U.K. investor in the U.S. with long historical data.
  - Black (1989a): hedge ratios can be unstable and a wide range of values may be optimal depending on input data.
- Empirical context:
  - Campbell et al. (2010): find the U.S. Dollar, the Euro, and the Swiss Franc moved against world equity markets (1975–2005), suggesting risk-minimizing equity investors should seek exposure to these currencies; also find full hedging tends to be optimal for bonds.
  - Eun and Resnick (1988): currency risk is largely undiversifiable and reduces gains from international diversification; highlight practical problem of estimating the right hedge amount.
  - UIP/forward bias literature (Fama (1984), Engel (1996)): documents failure of uncovered interest rate parity; currencies of low interest rate countries tend not to appreciate as parity predicts, underpinning carry trade profits.
- Practitioner behavior:
  - Many institutional practitioners use simple hedge ratios of 0, 50, and 100 percent; major hedged indices (MSCI, S&P) fully hedge each foreign currency into the base currency using beginning-of-period investment values.
  - Reasons for simple rules include instability of optimal hedge ratio estimation and time-varying currency-equity correlations (observed swings from plus 40 percent to minus 40 percent across decades in the dataset).

### III. DATA — sources, coverage, and construction choices
- Sample period and frequency:
  - January 1975 to December 2009; monthly data; results for investment horizons of up to five years.
- Data sources:
  - Country stock index returns: Morgan Stanley Capital International (MSCI), value-weighted indices adjusted for dividends.
  - Government bond yields, spot exchange rates, and Consumer Price Indices (CPI): IMF’s International Financial Statistics (IFS).
  - Three-month deposit rates: IFS for Japan; DataStream for Germany, France, U.K., and U.S.
- Bond return construction:
  - Long-term bond portfolio returns not available prior to 1986 for all countries; holding-period returns obtained using approximation from Campbell, Lo, and MacKinlay (1997).
- EUR/EMU considerations:
  - With the introduction of the Euro, interest rate differentials between Germany and France virtually disappeared and exchange rate movements between them ceased; the analysis presents the German perspective following Table 1.
- Descriptive statistics highlighted (Table 1 summary elements):
  - CPI annualized averages (rolling annual changes/real returns, full sample 1975–2009):
    - U.K.: 5.6 percent per year.
    - France: 4.4 percent per year.
    - U.S.: 4.2 percent per year.
    - Germany: 2.5 percent per year.
    - Japan: 1.8 percent per year.
  - Real annualized three-month deposit rates on wholesale deposits reported to range from 0.2 percent in Japan to (table continues in source).

### IV. METHODOLOGICAL and IMPLEMENTATION NOTES
- Hedging constructs and comparisons:
  - Simple hedge ratios evaluated: 0, 50, 100 percent.
  - Optimal hedge ratios estimated via minimum variance (exploiting full covariance structure); optimality tested for single-country and multi-country portfolios and across sub-samples (first half, second half).
- Hedged return construction improvement:
  - Use of 3-month bank deposit rates instead of T-bill rates to mitigate comparability and liquidity issues (e.g., Germany and France T-bill maturities vary; Japanese T-bills illiquid before 1999).
  - Table 4 in section V quantifies the impact of using deposit rates instead of T-Bills (details in source).
- Horizon analysis:
  - Distinction between short and long investment horizons; testing whether Froot (1993) results apply in post-Bretton Woods regime and for investors based in countries other than the U.K.
  - Evidence indicates horizon effects are not uniformly supportive of reduced hedging at longer horizons.

### V. EMPIRICAL IMPLICATIONS and PRACTICAL TAKEAWAYS
- Currency hedging policy should be investor-specific:
  - Base currency materially affects optimal hedging strategy; policymakers and institutional investors should tailor hedging decisions to the investor’s home currency.
- Asset-class differences:
  - Bonds: full hedging is generally warranted because exchange rate volatility is the dominant risk driver.
  - Equities: hedging decisions depend on asset-currency covariances that can be time-varying and country-specific; optimal positions may include over-hedging or maintaining exposure.
- Time-variation and crisis risk:
  - Historical correlations can reverse; reliance on historical correlation patterns without accounting for structural or regime shifts (e.g., 2007–2009) can produce large unexpected currency losses.
- Practical recommendation for practitioners:
  - Simplicity (0, 50, 100 percent hedges) is common and defensible given estimation instability, but practitioners should be aware of time-varying correlations and crisis-period behavior that can alter hedge effectiveness.

*Source: content unit _wp10151 - References (PDF chapter/section, sample period and tables described in text).*

### 3.3 percent in France. Volatility of deposit rates has been low not exceeding 3.1 percent per

### _wp10151 - 3.3 percent in France. Volatility of deposit rates has been low not exceeding 3.1 percent per

### Summary statistics and asset returns
- Data coverage extends from 1975M1 to 2009M12; data are monthly.  
- Table 1 (annual arithmetic averages and standard deviations of rolling annual changes/returns, in percentages) highlights:
  - Consumer Price Index (CPI) averages and standard deviations: France Average 4.39 Standard Deviation 3.99; Germany Average 2.51 Standard Deviation 1.67; Japan Average 1.79 Standard Deviation 2.64; United Kingdom Average 5.65 Standard Deviation 4.74; United States Average 4.19 Standard Deviation 2.91.
  - Real 3-month deposit rate averages and standard deviations: France Average 3.26 Standard Deviation 2.84; Germany Average 2.49 Standard Deviation 1.57; Japan Average 0.19 Standard Deviation 1.56; United Kingdom Average 2.66 Standard Deviation 3.11; United States Average 2.02 Standard Deviation 2.24.
  - Real equity index (MSCI) averages and standard deviations: France Average 9.89 Standard Deviation 24.97; Germany Average 8.46 Standard Deviation 24.43; Japan Average 5.38 Standard Deviation 22.57; United Kingdom Average 8.45 Standard Deviation 16.92; United States Average 7.56 Standard Deviation 17.26.
  - Real bond returns (IFS) averages and standard deviations: France Average 4.86 Standard Deviation 7.82; Germany Average 4.90 Standard Deviation 6.11; Japan Average 4.27 Standard Deviation 6.43; United Kingdom Average 5.03 Standard Deviation 7.23; United States Average 4.17 Standard Deviation 8.15.
- Real equity market returns to local investors vary: Japan about 5.4 percent per year; France 9.9 percent over the sample period.
- Volatility observations: equity volatilities are substantial across countries (e.g., France Standard Deviation 24.97); real returns on long-term government bonds are between 4 and 5 percent for all countries and volatilities between 6 and 8 percent.

### Components of international investment returns — currency effects
- Unhedged nominal return decomposition (approximation): ̃r_b,t ≈ x̃_t + ẽ_t where x̃_t is foreign-currency return and ẽ_t is percentage change in base currency per unit of foreign currency. Cross-product x̃_t ẽ_t is small for quarterly returns.
- Variance decomposition: exchange rate fluctuations contribute to variance through var(ẽ_t) and covariances with foreign asset returns.
- Table 2 (quarterly returns, in percentages) key observations (selected entries):
  - German perspective: Exchange rate gain/loss vs Japan 0.62; Currency excess return vs Japan -0.11; Equities: unhedged return Japan 2.34; Bonds: unhedged return Japan 2.10.
  - Japanese perspective: Exchange rate gain/loss vs France -0.70; Currency excess return vs France 0.67; Equities unhedged return France 2.75; Bonds unhedged return France 1.51.
  - U.K. perspective: Exchange rate gain/loss vs Japan 1.44; Currency excess return vs Japan -0.09; Equities unhedged return Japan 3.21; Bonds unhedged return Japan 2.95.
  - U.S. perspective: Exchange rate gain/loss vs Japan 1.04; Currency excess return vs Japan 0.02; Equities unhedged return Japan 2.73; Bonds unhedged return Japan 2.52.
- Interpretation highlights:
  - Japanese investors experienced exchange rate losses on investments in all countries due to Yen appreciation, yet currency excess returns for Japanese investors were substantial (0.35 percent for the U.S. to 0.67 percent for France quarterly), consistent with the Yen as a funding currency in the carry trade.
  - Siegel’s paradox: excess currency return pairs generally above zero because percentage gains/losses are quoted in different numeraire currencies.
- Variance decomposition (Tables 3a/3b):
  - Exchange rate volatility contributes between 16 and 40 percent to equity investment volatility.
  - For bond portfolios, exchange rate risk can contribute up to 95 percent of total unhedged return volatility.
  - Covariance of currency returns with asset returns generally matters less than currency variance itself, but covariance structures are unstable over time.

### Hedging methodology and practical considerations
- Hedging approaches:
  - Borrowing/lending hedge: short-term borrowing in foreign currency and lending in base currency to lock in known forward premium/discount.
  - Forward-market hedge: sell expected foreign currency proceeds forward; forward premium δ_t = F_{t-1}/S_{t-1} - 1.
  - Equivalence: hedging via borrowing/lending and forwards yield equivalent results if covered interest rate parity (CIP) holds: (1+i_dom)/(1+i_for) = 1+δ_t.
- Implementation choices and data:
  - Use 3-month deposit rates and 3-month T-bill rates as candidate rates; deposit rates found more comparable across France, Germany, Japan, the U.S., and the U.K.
  - Table 4 (1990M1-2009M12) comparison of forward premia: Panel A (deposit-rate-based vs exchange-rate-based) Mean absolute deviation U.S./U.K. 0.08 U.S./Japan 0.11 U.S./France 0.04 U.S./Germany 0.04; Panel B (T-Bill-based vs exchange-rate-based) Mean absolute deviation U.S./U.K. 0.11 U.S./Japan 0.19 U.S./France 0.10 U.S./Germany 0.11.
- Hedging caveats:
  - Hedging beginning-of-period balances (Φ such that expected beginning-of-period investment is hedged) is common practice; average quarterly return due to unhedged difference between beginning- and end-of-period values is below 0.07 percent for all base currency/foreign investment combinations considered.
  - Estimation risk: impossible to obtain exact ex ante desired hedge ratio; estimation risk can have very large impact over long periods.

### Impact of hedging on returns and volatility — empirical evidence (1975–2009)
- Single-country portfolios (Tables 5a/5b):
  - In almost all cases, null of equal means of hedged and unhedged quarterly returns cannot be rejected at conventional levels due to large sample variance.
  - Economic differences can be substantial: e.g., Japanese investor in French stock market No hedge 2.75 percent quarterly vs Full hedge 2.10 percent quarterly (approximate annual differential of 2.6 percent).
  - German investors: generally higher returns unhedged except investments in Japan.
  - Japanese and American investors: generally lower returns if hedged.
- Risk (Tables 6a/6b):
  - Hedging reduces volatility in almost all cases, statistically and economically significant.
  - Bond portfolios: hedging 100 percent is dominant risk-reduction strategy; e.g., German perspective bond market Japan No hedge SD 6.57 Half hedge 3.74 Full hedge 1.83.
  - Equity portfolios: hedging generally reduces volatility but optimal hedge ratios other than 100 percent arise where currency–equity correlations provide natural offsets (examples: French and German stock markets from a U.K. investor perspective; German stock market from a U.S. perspective).
- Multi-country portfolios (Tables 7/8):
  - Equal-weighted global portfolios (France, Germany, Japan, U.K., U.S.) — returns: differences between hedged and unhedged generally not statistically significant; economic differences notable for Japanese investors.
  - Standard deviations: hedging yields economically and statistically significant risk reduction for diversified portfolios; currency risk found to be largely undiversifiable (e.g., German perspective Global stock portfolio No hedge 8.72 Full hedge 7.87; Global bond portfolio No hedge 3.03 Full hedge 1.52).

### Optimal hedge ratios — single- and multi-country results
- Methodology:
  - Minimum-variance hedge ratio estimated via OLS regression of unhedged return on (ẽ_t - δ_t) (equations 14, 16), Newey-West standard errors to correct for autocorrelation from overlapping returns.
- Single-country minimum-variance hedge ratios (Table 9, quarterly results):
  - Bonds: hedge ratios essentially one for investors in all base currencies.
  - Stocks:
    - German perspective: Japan 1.00 (0.23), U.K. 1.39 (0.12), U.S. 1.04 (0.13).
    - Japanese perspective: France 0.95 (0.13), Germany 1.05 (0.14), U.K. 1.08 (0.09), U.S. 1.05 (0.10).
    - U.K. perspective: France 0.72 (0.18), Germany 0.55 (0.14), Japan 1.05 (0.12), U.S. 0.84 (0.15).
    - U.S. perspective: France 0.82 (0.18), Germany 0.70 (0.16), Japan 0.92 (0.14), U.K. 1.00 (0.14).
  - Interpretation:
    - German investors: risk-minimizing hedge ≈100% except over-hedge (1.39) for U.K. equities.
    - Japanese investors: hedge ratios statistically indistinguishable from one.
    - U.K. and U.S.: slight under-hedging optimal for some European exposures.
- Multi-country minimum-variance hedge ratios (Tables 10–12):
  - Full-sample (1975M1–2009M12, Table 10) — selected estimates (point estimates with standard errors in parentheses):
    - German perspective Global stock portfolio: Japan 0.62 (0.60), United Kingdom 2.37 (0.57), United States 1.39 (0.53).
    - Japanese perspective Global stock portfolio: Germany -0.49 (0.46), United Kingdom 2.29 (0.52), United States 1.42 (0.52).
    - U.K. perspective Global stock portfolio: Germany -0.57 (0.46), Japan 1.25 (0.29), United States 0.94 (0.61).
    - U.S. perspective Global stock portfolio: Germany -0.50 (0.50), Japan 0.71 (0.54), United Kingdom 2.34 (0.57).
  - Sub-periods show instability:
    - First half (1975M1–1992M7, Table 11): generally higher hedge ratios for some currencies (e.g., German perspective Japan 1.55).
    - Second half (1992M8–2009M12, Table 12): marked changes (e.g., German perspective U.K. 4.02 (1.06) for global stock portfolio) demonstrating time-variation and instability of optimal hedge ratios.
  - Bond portfolios: estimates more precise; full hedging remains generally optimal except slight exposure retained to British Pound in some cases.
- Key takeaways on optimal hedging:
  - Bonds: hedge ratio ≈1 is robust across investors.
  - Equities: hedge ratios vary by base currency and period; DM/Euro exposure often beneficial (negative coefficients imply seeking additional DM/Euro exposure), British Pound often pro-cyclical (over-hedge recommended in full sample), Yen and USD hedge ratios close to one but time-varying.
  - Hedge ratios are unstable over time; sub-periods can yield substantially different optimal strategies.

### Hedging and investment horizon (up to 5 years)
- Approach:
  - Continue quarterly hedging; compute k-period hedged returns as product of quarterly hedged returns. Also estimate minimum-variance hedge ratios for k-period horizons using log-returns (equations 15–16).
- Variance ratio results (Table 13: ratio var(unhedged)/var(hedged)):
  - Stocks: no general pattern that hedging becomes less effective with longer horizons; variance ratios often increase with horizon for some base currency–market combinations (e.g., German perspective U.S. stock market variance ratios rise from 1.59 at 1 Quarter to 2.53 at 5 Years).
  - Bonds: variance ratios decrease strongly from quarterly to five-year horizons but remain >1 in nearly all cases (hedging remains beneficial). Examples (German perspective bond market Japan: 12.88 at 1 Quarter, 2.94 at 5 Years; U.S. perspective bond market U.K.: 9.98 at 1 Quarter, 1.62 at 5 Years).
- Minimum-variance hedge ratios over horizons (Tables 14a/14b):
  - No uniform decline in hedge ratios with investment horizon.
  - Examples:
    - German perspective Japan (stocks) hedge ratios: 1 Quarter 1.02 (0.20), 5 Years 1.93 (0.56) — an increase.
    - Japanese perspective France (stocks) hedge ratios: 1 Quarter 0.99 (0.16), 5 Years 0.30 (0.31) — a decline.
    - U.K. perspective Japan (stocks) hedge ratios: 1 Quarter 1.06 (0.11), 5 Years 1.67 (0.66) — increase.
    - Bond hedge ratios often remain near or exceed 1 across horizons for several base currencies.
  - Statistical precision declines with horizon (standard errors increase).
- Conclusion on horizon:
  - Currency hedging generally reduces variance up to 5-year horizons for most cases, especially for bonds.
  - In some cases less than full hedging becomes optimal at longer horizons; in other cases over-hedging becomes optimal (notably in some exposures to Japan where carry-trade profits make short-Yen positions attractive).
  - Results contrast with Froot (1993): no universal evidence that long-horizon investors should cease hedging.

### Main conclusions and implications for investors
- Currency risk materially contributes to international investment volatility: up to 40 percent for single-country equity investments and up to 95 percent for single-country bond investments.
- Hedging replaces stochastic exchange-rate changes with the known forward premium/discount, substantially reducing volatility at short horizons.
- Practical recommendations based on empirical findings (1975–2009):
  - For bond investments: hedge fully (Φ ≈ 1) to minimize variance in almost all circumstances.
  - For equity investments: default to high hedge ratios (near 100 percent) unless specific, stable negative correlations exist between currency movements and local equity returns that justify partial exposure; optimal hedge ratios vary by base currency, foreign market, and sub-period.
  - Consider base-currency-specific effects: Japanese investors historically benefited from leaving currency exposure unhedged (carry-trade gains), hence hedging reduced realized returns for them over the sample.
  - Be cautious calibrating hedge ratios solely on historical data: currency–asset correlations are unstable (notably during the financial crisis of 2007 to 2009 when correlations reversed), so historical optimal hedge ratios may not persist.
  - For long-horizon investors (up to 5 years): hedging generally remains effective, particularly for bonds; there is no universal prescription to avoid hedging at long horizons.
- Risk management emphasis:
  - Hedge ratio selection should account for (a) volatility of exchange rate movements, (b) covariance of exchange rates with asset returns, (c) investor base currency, (d) investment horizon, and (e) estimation risk/instability of covariances.
  - Use deposit-rate-based forward premia for practical hedging calculations where forward market data or T-bill comparability is problematic.

*Source: Author’s estimates, IMF IFS, DataStream; data coverage 1975M1 to 2009M12; content extracted from the provided IMF chapter/section.*

### REFERENCES

### _wp10151 - REFERENCES

### Key cited works on currency hedging and international portfolio allocation
- Adler, Michael, and Bernard Dumas, 1983, “International Portfolio Choice and Corporation Finance: A Synthesis”, Journal of Finance, Vol. 38, pp. 925-984.
- Black, Fisher, 1989, “Equilibrium Exchange Rate Hedging”, Journal of Finance, Vol. 45, pp. 899-906.
- Black, Fisher, 1989a, “Universal Hedging: Optimizing Currency Risk and Reward in International Equity Portfolios”, Financial Analysts Journal, Vol. 45, No. 4, pp. 16-22.
- Campbell, John Y., Karine Serfaty-De Medeiros, and Luis M. Viceira, 2010, “Global Currency Hedging”, Journal of Finance, Vol. 65, pp. 87-121.
- Campbell, John Y., Luis M. Viceira, and Joshua S. White, 2003, “Foreign Currency for Long-Term Investors”, The Economic Journal, Vol. 113, No. 486, pp. C1-C25.
- Cantara, Michael, Ben Kottler, and Joseph Flaherty, 2007, “Managing Currency Risk in Global Equity Portfolios: Key Considerations for Institutional Investors”, MFS White Paper Series, No. 10/07.
- Chincarini, Ludwig B., 2007, “The Effectiveness of Global Currency Hedging After the Asian Crisis”, Journal of Asset Management, Vol. 8, No. 1, pp. 34-51.
- Dales, Andrew, and Richard Meese, 2001, “Strategic Currency Hedging”, Journal of Asset Management, Vol. 2, No.1, pp. 9-21.
- Gagnon, Louis, Gregory J. Lypny, and Thomas H. McCurdy, 1998, “Hedging Foreign Currency Portfolios”, Journal of Empirical Finance, Vol. 5, pp. 197-220.
- Glen, Jack, and Phillipe Jorion, 1993, “Currency Hedging for International Portfolios”, Journal of Finance, Vol. 48, No. 5, pp. 1865-1886.
- Jorion, Phillipe, 1989, “Asset Allocation with Hedged and Unhedged Foreign Stocks and Bonds”, Journal of Portfolio Management, Vol. 15, No. 4, pp. 49-54.
- Lindenhovius, Bernard, and Gerlof de Vrij, 2001, “The Search for a Balanced Hedge Ratio Policy”, Journal of Asset Management, Vol. 2, No. 1, pp. 35-46.
- Michenaud, Sebastien, and Bruno Solnik, 2008, “Applying Regret Theory to Investment Choices: Currency Hedging Decisions”, Journal of International Money and Finance, Vol. 27, pp. 677-694.
- Perold, Andre F. and Evan C. Shulman, 1988, “The Free Lunch in Currency Hedging: Implications for Investment Policy and Performance Standards”, Financial Analysts Journal, Vol. 44, No. 3, pp. 45-50.
- Solnik, Bruno, 1993, “Currency Hedging and Siegel’s Paradox: On Black’s Universal Hedging Rule”, Review of International Economics 1, pp/ 180-187.
- Srinivasan, Sayee, and Steven Youngren, 2003, “Using Currency Futures to Hedge Currency Risk”, Product Research and Development, Chicago Mercantile Exchange Inc.
- Walker, Eduardo, 2008, “Strategic Currency Hedging and Global Portfolio Investments Upside Down”, Journal of Business Research, Vol. 61, pp. 657–668.
- Chang, Kelly H., 2009, “Currency Hedging: A Free Lunch?”, MSCI Barra Research Insights. Available at SSRN: http://ssrn.com/abstract=1384584
- Cantara, Michael, Ben Kottler, and Joseph Flaherty, 2007, “Managing Currency Risk in Global Equity Portfolios: Key Considerations for Institutional Investors”, MFS White Paper Series, No. 10/07.

### Exchange rate behavior, purchasing power parity, and empirical regularities
- Akram, Farooq, Dagfinn Rime, and Lucio Sarno, 2008, “Arbitrage in the Foreign Exchange Market: Turning on the Microscope”, Journal of International Economics, Vol. 76, pp. 237-253.
- Bekaert, Geert, and Robert Hodrick, 1992, “Characterizing Predictable Components in Excess Returns on Equity and Foreign Exchange Markets”, Journal of Finance, Vol. 47, pp. 467-509.
- Engel, Charles, 1996, “The Forward Discount Anomaly and the Risk Premium: A Survey of Recent Evidence”, Journal of Empirical Finance, Vol. 3, pp. 123-192.
- Fama, Eugene F., 1984, “Forward and Spot Exchange Rates”, Journal of Monetary Economics, Vol. 4, pp. 119-138.
- Frankel, Jeffrey A., and Andrew K. Rose, 1996, “A Panel Project on Purchasing Power Parity: Mean Reversion Within and Between Countries”, Journal of International Economics, Vol. 40, pp. 209-224.
- Froot, Kenneth A., 1993, “Currency Hedging Over Long Horizons”, NBER Working Paper, No. 4355.
- Froot, Kenneth A., and Kenneth Rogoff, 1995, “Perspectives on PPP and Long-Run Real Exchange Rates”, Handbook of International Economics, III, North-Holland, Amsterdam, pp. 1647-1688.
- Froot, Kenneth A., and Richard H. Thaler, 1990, ”Anomalies: Foreign Exchange”, Journal of Economic Perspectives, Vol. 4, No. 3, pp. 179-192.
- Lothian, J.R., and Taylor, M.P., 1996, “Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries”, Journal of Political Economy, Vol. 104, pp. 488–509.
- Sarno, Lucio, and Mark P. Taylor, 1998, “Real Exchange Rates under the Recent Float: Unequivocal Evidence of Mean Reversion”, Economics Letters, Vol. 60, pp. 131-137.
- Taylor, Alan M., and Mark P. Taylor, 2004, “The Purchasing Power Parity Debate”, Journal of Economic Perspectives, Vol. 18, pp. 135-158.
- Taylor, Mark P., 1987, “Covered Interest Parity: A High-Frequency, High-Quality Data Study”, Economica, Vol. 54, pp. 429-438.

### Foundational models, econometrics, and theoretical frameworks
- Ang, Andrew, and Bekaert, Geert, 2002, “International Asset Allocation with Regime Shifts”, Review of Financial Studies, Vol. 15, pp. 1137-1187.
- Campbell, John Y., Andrew W. Lo, and A. Craig Mackinlay, 1997, “The Econometrics of Financial Markets”, Princeton University Press, Princeton, NJ.
- Levy, Haim, and Sarnat, Marshall, 1970, “International Diversification of Investment Portfolios”, American Economic Review, Vol. 60, pp. 668-675.
- Solnik, Bruno, 1974, “An Equilibrium Model of the International Capital Market”, Journal of Economic Theory, Vol. 8, pp. 500-524.

### Methodologies, data sources, and institutional references
- MSCI Barra, 2009, “MSCI Index Calculation Methodology”, available at www.mscibarra.com
- International Monetary Fund, 2000, “Review of the Method of Valuation of the SDR”, SM/00/180, July 24, 2000.
- International Monetary Fund, 2010, “International Financial Statistics: World & Country Notes”, January 2010.

*Source: _wp10151 - REFERENCES*

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