## _wp06194

## Source details

**Canonical URL:** [_wp06194](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06194.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06194.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06194.pdf.json)

---

### I. Introduction and motivation
- Examines whether foreign exchange risks are priced in stock markets and whether those risk prices vary over time.
- Key channels by which the U.S. dollar direction affects stock valuations: (i) earnings growth; (ii) interest rates; and (iii) the risk premium for unhedged participants.
- Concern: global imbalances and potential currency realignment could increase global financial market fragility.
- Innovation: tests whether factor-specific shocks cause investors to change their risk pricing, particularly whether exchange-rate-specific shocks have direct effects on equity risk-pricing.

### II. Contribution and general approach
- Contributions
  - Assesses extent to which foreign exchange risks are priced in stock markets.
  - Assesses time-varying nature of risk pricing to determine whether investors now require more return for the same amount of currency risk.
  - Tests whether factor-specific shocks (especially exchange-rate shocks) cause persistent changes in risk prices.
- Parsimonious three-factor representation used:
  - national market (wealth portfolio),
  - long-term interest rates (discount factor, opportunity cost, leveraged assets),
  - trade-weighted exchange rates.
- Assets: country sector indices from the G-7 equity markets (market-value-weighted industry portfolios).
- Risk prices calculated separately for each market; notes evidence for international APT with common global risk premia but significant home bias remains.

### III. Model specification and hypotheses
- Builds on a three-factor APT/CAPM extension with exchange rate factor (Adler and Dumas, 1983).
- Return-generating process for industry i uses factor betas β for market, long-term interest rate, and nominal exchange rate; orthogonalization applied so mean of interest rate and exchange rate factors are zero conditional on market.
- Uses expected-return-beta risk-pricing equation and a joint-estimation system leading to nonlinear restriction of the APT constant; tests of this restriction use the small sample adjusted likelihood ratio statistic.
- Conditional model extension: risk prices modeled as linear functions of lagged factor-specific information (equation (10)).
- Two null hypotheses tested:
  - exchange rate risk is not conditionally priced in each market;
  - risk prices are stable (not time-varying).

### IV. Estimation methods
- Two main approaches discussed:
  - Pricing-kernel/GMM approach with instruments H (macro and financial variables); potential issues with persistent/integrated instruments imparting persistence in risk-price shocks.
  - Iterated nonlinear seemingly-unrelated regression (NLSUR) for joint estimation of factor loadings and risk prices (asymptotically equivalent to ML and technically more efficient); adopted here using asymptotic maximum likelihood techniques.
- Also implements standard two-pass regression (time-series to estimate betas, cross-section to estimate risk prices) with both OLS and GLS.
- Adjusts standard errors for errors-in-variables using Shanken (1992b) correction (Shanken formulas retained).

### V. Data and preliminary statistics
- Sample frequency and period:
  - monthly data,
  - January 1974 to February 2005.
- Assets: Datastream value-weighted Level III industry portfolios (maximum number of industries 33; minimum number observed: 29 in Italy).
- Excess return: local currency log total return index change over monthly local risk-free rate.
- Factor definitions:
  - first factor: excess return over local three-month rate of Datastream value-weighted total market return index,
  - second factor: log change in the 10-year benchmark government bond yield,
  - third factor: log change in the IMF nominal effective exchange rate index (International Financial Statistics).
- Orthogonalization rationale: factor covariance matrices show in most markets a strong inverse relationship between equity market and bond yields; relationship between exchange rates and the other two asset classes is more ambiguous but relatively high correlations exist in most markets.
- Return distribution at industry level: skew = -0.1 and kurtosis = 2.95 (simple unweighted averages).

### VI. Main empirical results

- APT specification tests
  - Testing the APT specification (equation (6)) against the unrestricted return-generating equation (1): the null hypothesis could be accepted at the 5 percent level for all markets except Italy.
  - For Italy, the null could be accepted at the 10 percent level.

- Unconditional foreign exchange risk pricing (two-pass regression focus, OLS emphasized with Shanken-adjusted standard errors)
  - Across the G-7, only the United States, United Kingdom, and Germany exhibit foreign exchange risk prices that were statistically significant using adjusted standard errors.
  - United States:
    - Industry portfolios with a positive factor loading to the exchange rate receive a risk premium of 0.5 percent per unit of risk.
    - Industries benefiting from this risk premia were predominantly domestic, including financials.
    - This result contradicts Jorion (1990).
  - Germany: positive risk premium on the exchange rate.
  - United Kingdom: negative risk premium on the exchange rate.
  - Japan did not appear to price exchange rate risk in the unconditional model; large differences between OLS and GLS estimates for Japan suggest caution.

- Conditional foreign exchange pricing (joint estimation and time variation)
  - Test 1 (Null that foreign exchange risk price is zero):
    - Joint estimation rejects the null in all markets except Germany and France; Italy is borderline.
  - Test 2 (Null that the risk price is constant):
    - In all markets where risk prices were nonzero, the null was rejected at the 5 percent level.
    - Factor-specific shocks changed investor risk pricing in the United States, the United Kingdom, Italy, and Canada.
  - Representation of conditional risk price (lag order up to three):
    - Each risk price is equal to λ_FX where:
      - λ_FXt = a_FX,0 + ∑_{l=1}^{3} a_FX,l f_{t-l}
    - Note: In most cases, a lag order of four obtained the highest information criteria.

- Table 1. Estimated Foreign Exchange Risk Pricing Coefficients (presented in text as authors’ calculations)
  - U.S.
    - Coeff: 0.0063  -0.5471  0.3618  -0.2049
    - Std error: 0.0025  0.1360  0.1461  0.1423
    - t-stat: 2.52  -4.02  2.48  -1.44
  - U.K.
    - Coeff: -0.0031  -0.2103  -0.1607  -0.1569
    - Std error: 0.0019  0.1178  0.1292  0.1242
    - t-stat: -1.63  -1.79  -1.24  -1.26
  - Japan
    - Coeff: 0.0018  0.0968  0.5206  0.0023
    - Std error: 0.0033  0.1495  0.1574  0.1447
    - t-stat: 0.55  0.65  3.31  0.02
  - Canada
    - Coeff: 0.0100  0.0336  -1.4154  0.0125
    - Std error: 0.0030  0.2307  0.3403  0.2332
    - t-stat: 3.33  0.15  -4.16  0.05

- Conditional-pattern findings by country
  - United States
    - Time-variation in the U.S. foreign exchange risk price is empirically notable.
    - Market rewards positive exposure to the currency; market requires a risk premium for industries vulnerable to a depreciating U.S. dollar.
    - When the U.S. dollar experiences unanticipated declines, this risk premium tends to rise.
    - Recent negative currency-specific shocks have forced the risk price to increase to levels not seen since the aftermath of the Plaza Accord in 1984.
  - Japan
    - Expected conditional risk price is insignificant from zero, confirming unconditional results.
    - Risk prices in Japan have been marginally positive, consistent with stocks with currency exposure playing a hedging role for the consumption basket.
    - Risk prices are sensitive to factor-specific shocks, and factor shocks can cause the risk price to change sign.
    - Whenever an unanticipated appreciation of the currency occurs, this risk price rises significantly; during sharp yen depreciation risk prices can turn negative.
  - Canada
    - Exhibits the same broad pattern as the United States: risk prices for currency exposure have been positive for many years.
    - Prices react inversely to factor shocks: risk premiums increased when the currency declined.
    - Dominating factor is the Canadian dollar—U.S. dollar exchange rate; periods of relative U.S. dollar strength associated with a higher risk premium; U.S. dollar weakness has lowered the premium.

### VII. Conclusions and interpretations
- A. A role for equity assets as a currency-hedging instrument
  - Market imperfections (frictional trading costs, restrictions on tradable securities, informational asymmetries) can prevent full hedging using first-best strategies.
  - If foreign exchange risk (broad consumption-basket sense) is not fully hedged, investors will extract a risk premium from assets that underperform when the currency weakens to bridge the hedging gap.
  - For most markets in this study, it is possible to accept the null that exchange rate risk is priced, implying certain equity assets fulfill a role as a currency-hedging instrument.
  - For almost every market where risk is priced, the premium is positive.
- B. An empirical positive risk pricing puzzle?
  - Home bias implies low weights of foreign equities in countries’ wealth portfolios; developed-economy investors have other instruments to hedge currency risk, which would imply a zero risk price of currency exposure in the stock market.
  - Potential explanations for observed positive currency risk pricing:
    - Asset-liability matching by institutional investors facing home currency liabilities: (i) defined benefit pension funds; (ii) life insurance funds; (iii) property and casualty insurance funds.
    - Institutional investors face relatively lower currency risk when invested in home equity assets; beneficiaries face consumption risk through currency volatility and would optimally hedge but cannot fully implement currency overlay strategies.
    - As a partial hedge, investors either hold more foreign assets, or accept a lower equilibrium rate of return on domestic stocks that perform well when the home currency is weak; retail investor preference to remain in domestic equities (noted particularly in the United States) can make the second choice optimal, producing a positive equilibrium risk price for currency exposure in the equity market.
- C. Risk prices most significant in North America
  - United States and Canadian equity markets exhibit relatively high and positive risk-prices for currency exposure; these risk prices are sensitive to exchange-rate-specific shocks.
  - In Europe, there is less evidence of currency risk-pricing, suggesting investors feel more fully hedged or use different instruments.

### Appendix A — Summary correlation statistics (January 1974–February 2005)
- Table A1. Correlation Matrices for Factor Log Returns (authors’ calculations)
  - U.S.
    - Stock market: 1.000
    - Bond yield: -0.159
    - Exchange rate: -0.096
  - U.K.
    - Stock market: 1.000
    - Bond yield: -0.287
    - Exchange rate: 0.2571.0000.011
  - Japan
    - Stock market: 1.000
    - Bond yield: 0.056
    - Exchange rate: 0.101
  - Germany
    - Stock market: 1.000
    - Bond yield: -0.133
    - Exchange rate: -0.090
  - France
    - Stock market: 1.000
    - Bond yield: -0.215
    - Exchange rate: -0.008
  - Italy
    - Stock market: 1.000
    - Bond yield: -0.129
    - Exchange rate: -0.054
  - Canada
    - Stock market: 1.000
    - Bond yield: -0.287
    - Exchange rate: 0.170

*Source: _wp06194 - References (IMF working paper content as provided).*

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

### References

### I. Introduction and Motivation
- The study examines whether foreign exchange risks are priced in stock markets and whether those risk prices vary over time.
- Key channels by which the U.S. dollar direction affects stock valuations: (i) earnings growth; (ii) interest rates; and (iii) the risk premium for unhedged participants.
- Concern: global imbalances and potential currency realignment could increase global financial market fragility.
- Innovation: test whether factor-specific shocks cause investors to change their risk pricing, particularly whether exchange-rate-specific shocks have direct effects on equity risk-pricing.

### A. Contribution of this Paper
- Assesses extent to which foreign exchange risks are priced in stock markets.
- Assesses time-varying nature of risk pricing to determine whether investors now require more return for the same amount of currency risk.
- Tests whether factor-specific shocks (especially exchange-rate shocks) cause persistent changes in risk prices.

### B. General Approach
- Uses a parsimonious three-factor representation:
  - national market (wealth portfolio),
  - long-term interest rates (discount factor, opportunity cost, leveraged assets),
  - trade-weighted exchange rates.
- Assets: country sector indices from the G-7 equity markets (market-value-weighted industry portfolios).
- Risk prices calculated separately for each market.
- Notes evidence for international APT with common global risk premia, but significant home bias remains.

### II. Previous Literature (Key empirical findings summarized)
- Jorion (1990): unconditional six-factor model — annual exchange rate risk premium of 0.2 percent; insignificant in various specifications (implies U.S. investors do not require compensation for currency risk).
- Dumas and Solnik (1995): conditional pricing-kernel framework with instruments — foreign exchange risk premia are a significant component of stock market returns.
- Choi, Hiraki, and Takezawa (1998): Japan — exchange risk is priced using a conditional model with a monthly risk premium of 1 percent per unit of risk; risk-price sign shifts with secular nominal exchange rate trends; conditioning coefficients for exchange rate risk prices rejected as zero.
- Baba (2000): pricing-kernel approach for Japan — rejects no-currency-risk hypothesis but cautions that implied stochastic discount factor violates nonnegativity and volatility bound restrictions.
- Bartram and Karolyi (2002): euro introduction reduced stock market risk exposure for nonfinancial firms, largest declines for firms with highest proportion of foreign sales.
- Antoniou, Garrett, and Priestley (1998): United Kingdom — exchange rate risk priced; assets benefiting from weaker currency attracted a monthly premium per unit of risk of 1.6 percent.
- Claessens, Dasgupta, and Glen (1995): currency risk priced in many emerging markets.
- Carrieri, Errunza, and Majerbi (2004): emerging markets — using GARCH-M and real exchange rates, between 20 percent and 30 percent of emerging market risk premium is accounted for by exchange rates.

### III. Model Specification
- Builds on a three-factor APT/CAPM extension with exchange rate factor (Adler and Dumas, 1983).
- Return-generating process for industry i (equation references retained as in source): factor betas β for market, long-term interest rate, and nominal exchange rate; orthogonalization applied so mean of interest rate and exchange rate factors are zero conditional on market.
- Uses expected-return-beta risk-pricing equation (equation (3)) and joint-estimation system leading to nonlinear restriction of the APT constant (equation (8)); tests of this restriction use the small sample adjusted likelihood ratio statistic.
- Conditional model extension: risk prices modeled as linear functions of lagged factor-specific information (equation (10)); tests two null hypotheses:
  - exchange rate risk is not conditionally priced in each market;
  - risk prices are stable (not time-varying).

### IV. Estimation Methods
- Two main approaches:
  - Pricing-kernel/GMM approach (common in literature) instruments H with macro and financial variables; potential issues with persistent/integrated instruments imparting persistence in risk-price shocks.
  - Iterated nonlinear seemingly-unrelated regression (NLSUR) for joint estimation of factor loadings and risk prices (asymptotically equivalent to ML and technically more efficient); adopted here using asymptotic maximum likelihood techniques.
- Also implements standard two-pass regression (time-series to estimate betas, cross-section to estimate risk prices) with both OLS and GLS; adjusts standard errors for errors-in-variables using Shanken (1992b) correction (Shanken formulas retained in source).

### V. Data and Preliminary Statistics
- Sample frequency and period:
  - monthly data,
  - January 1974 to February 2005.
- Assets: Datastream value-weighted Level III industry portfolios (maximum number of industries 33; minimum number observed: 29 in Italy).
- Excess return: local currency log total return index change over monthly local risk-free rate.
- Factor definitions:
  - first factor: excess return over local three-month rate of Datastream value-weighted total market return index,
  - second factor: log change in the 10-year benchmark government bond yield,
  - third factor: log change in the IMF nominal effective exchange rate index (International Financial Statistics).
- Orthogonalization rationale: factor covariance matrices (Table A1) show in most markets a strong inverse relationship between equity market and bond yields; relationship between exchange rates and the other two asset classes is more ambiguous but relatively high correlations exist in most markets.
- Return distribution at industry level: skew = -0.1 and kurtosis = 2.95 (simple unweighted averages).

### VI. Main Results (Selected empirical findings)
- APT specification test:
  - Testing the APT specification (equation (6)) against the unrestricted return-generating equation (1): the null hypothesis could be accepted at the 5 percent level for all markets except Italy.
  - For Italy, the null could be accepted at the 10 percent level.
- (Notes: detailed tables, figures, appendices, and coefficient estimates referenced in the source include:
  - Table 1: Estimated Foreign Exchange Risk Pricing Coefficients,
  - Figures 1–3: U.S., Japan, Canada equity market forex risk price and exchange rate shocks (12MAV),
  - Appendices A–E: Summary Correlation Statistics; Likelihood Ratio Tests of the APT Specification; Two-Pass Regression Estimates; Likelihood Ratio Tests for Foreign Exchange Risk Pricing and Time Variation; Summary of Estimated Foreign Exchange Risk Prices.)

*Source: _wp06194 - References (IMF working paper content as provided).*

### Appendix B shows these results in detail. This implies that the APT specification is the

### _wp06194 - Appendix B shows these results in detail. This implies that the APT specification is the

### B. Unconditional Foreign Exchange Risk Pricing
- Sample and methods
  - Maximum of 33 industry portfolios in country samples.
  - Two-pass regression model produces ambiguous results on foreign exchange risk pricing.
  - Trade-off noted between the robustness of OLS versus the efficiency of GLS; focus on OLS estimation given small sample sizes and use of Shanken-adjusted standard errors (Table A3 in Appendix C reports both OLS and GLS).
- Key empirical findings
  - Across the G-7, only the United States, United Kingdom, and Germany exhibit foreign exchange risk prices that were statistically significant using adjusted standard errors.
  - For the United States:
    - Industry portfolios with a positive factor loading to the exchange rate receive a risk premium of 0.5 percent per unit of risk.
    - Industries benefiting from this risk premia were predominantly domestic, including financials.
    - This result contradicts the earlier results of Jorion (1990).
  - Germany: positive risk premium on the exchange rate.
  - United Kingdom: negative risk premium on the exchange rate.
  - Japan did not appear to price exchange rate risk in the unconditional model; large differences between OLS and GLS estimates for Japan suggest caution.

### C. Conditional Foreign Exchange Pricing
- Two sets of tests undertaken
  - Test 1: Null that foreign exchange risk price is zero.
    - Joint estimation rejects the null in all markets except Germany and France; Italy is borderline.
    - Table A4 in Appendix D reports Wald tests on risk-pricing.
  - Test 2: Null that the risk price is constant (coefficients on all lagged changes in underlying factors equal zero).
    - In all markets where risk prices were nonzero, the null was rejected at the 5 percent level.
    - Factor-specific shocks changed investor risk pricing in the United States, the United Kingdom, Italy, and Canada.
- Representation of conditional risk price (lag order up to three):
  - Each risk price is equal to λ_FX where:
    - λ_FXt = a_FX,0 + ∑_{l=1}^{3} a_FX,l f_{t-l}
  - Note: In most cases, a lag order of four obtained the highest information criteria.
- Table 1. Estimated Foreign Exchange Risk Pricing Coefficients
  - U.S.
    - Coeff: 0.0063  -0.5471  0.3618  -0.2049
    - Std error: 0.0025  0.1360  0.1461  0.1423
    - t-stat: 2.52  -4.02  2.48  -1.44
  - U.K.
    - Coeff: -0.0031  -0.2103  -0.1607  -0.1569
    - Std error: 0.0019  0.1178  0.1292  0.1242
    - t-stat: -1.63  -1.79  -1.24  -1.26
  - Japan
    - Coeff: 0.0018  0.0968  0.5206  0.0023
    - Std error: 0.0033  0.1495  0.1574  0.1447
    - t-stat: 0.55  0.65  3.31  0.02
  - Canada
    - Coeff: 0.0100  0.0336  -1.4154  0.0125
    - Std error: 0.0030  0.2307  0.3403  0.2332
    - t-stat: 3.33  0.15  -4.16  0.05
  - Source: Authors’ calculations (table presented in text).
- Conditional-pattern findings by country
  - United States
    - Time-variation in the U.S. foreign exchange risk price is empirically notable.
    - Market rewards positive exposure to the currency; market requires a risk premium for industries vulnerable to a depreciating U.S. dollar.
    - When the U.S. dollar experiences unanticipated declines, this risk premium tends to rise.
    - Recent negative currency-specific shocks have forced the risk price to increase to levels not seen since the aftermath of the Plaza Accord in 1984 (Figure 1 documents U.S. equity market forex risk price and exchange rate shocks (12MAV)).
  - Japan
    - Expected conditional risk price is insignificant from zero, confirming unconditional results.
    - Risk prices in Japan have been marginally positive, consistent with stocks with currency exposure playing a hedging role for the consumption basket.
    - Risk prices are sensitive to factor-specific shocks, and factor shocks can cause the risk price to change sign.
    - Whenever an unanticipated appreciation of the currency occurs, this risk price rises significantly; during sharp yen depreciation risk prices can turn negative (Figure 2 documents Japan equity market forex risk price and exchange rate shocks (12MAV)).
  - Canada
    - Exhibits the same broad pattern as the United States: risk prices for currency exposure have been positive for many years.
    - Prices react inversely to factor shocks: risk premiums increased when the currency declined.
    - Dominating factor is the Canadian dollar—U.S. dollar exchange rate; periods of relative U.S. dollar strength associated with a higher risk premium; U.S. dollar weakness has lowered the premium (Figure 3 documents Canada equity market forex risk price and exchange rate shocks (12MAV)).

### VII. CONCLUSIONS
A. A Role for Equity Assets as a Currency-Hedging Instrument
- Market imperfections (frictional trading costs, restrictions on tradable securities, informational asymmetries) can prevent full hedging using first-best strategies.
- Investors will seek hedging proxies in securities that provide cover against the risk they wish to hedge.
- If foreign exchange risk (broad consumption-basket sense) is not fully hedged, investors will extract a risk premium from assets that underperform when the currency weakens to bridge the hedging gap.
- For most markets in this study, it is possible to accept the null that exchange rate risk is priced, implying certain equity assets fulfill a role as a currency-hedging instrument.
- For almost every market where risk is priced, the premium is positive (Appendix E summarizes estimates using all methods).

B. An Empirical Positive Risk Pricing Puzzle?
- Home bias in global equity markets implies low weights of foreign equities in countries’ wealth portfolios.
- Developed-economy investors have other instruments to hedge currency risk; optimal use would imply a zero risk price of currency exposure in the stock market.
- Potential explanations for observed positive currency risk pricing:
  - Asset-liability matching by institutional investors facing home currency liabilities:
    - (i) defined benefit pension funds;
    - (ii) life insurance funds;
    - (iii) property and casualty insurance funds.
  - Institutional investors face relatively lower currency risk when invested in home equity assets; beneficiaries face consumption risk through currency volatility and would optimally hedge but cannot fully implement currency overlay strategies.
  - As a partial hedge, investors either:
    - hold more foreign assets, or
    - accept a lower equilibrium rate of return on domestic stocks that perform well when the home currency is weak.
  - Given retail investor preference to remain in domestic equities (noted particularly in the United States), the second choice can be optimal, producing a positive equilibrium risk price for currency exposure in the equity market.

C. Risk Prices Most Significant in North America
- United States and Canadian equity markets exhibit relatively high and positive risk-prices for currency exposure; these risk prices are sensitive to exchange-rate-specific shocks.
- Even if other asset classes hedge U.S. dollar depreciations, investors will demand a high risk premium for currency exposure through equities.
- In Europe, there is less evidence of currency risk-pricing, suggesting investors feel more fully hedged or use different instruments; less advanced equity culture in much of Europe may contribute to this result.

*Source: Authors’ calculations and text from the IMF working paper content unit provided.*

### APPENDIX A

### APPENDIX A

### Summary Correlation Statistics
- Table A1. Correlation Matrices for Factor Log Returns, January 1974–February 2005
- Source: Authors’ calculations.

- U.S.
  - Stock market: 1.000
  - Bond yield: -0.159
  - Exchange rate: -0.096

- U.K.
  - Stock market: 1.000
  - Bond yield: -0.287
  - Exchange rate: 0.2571.0000.011

- Japan
  - Stock market: 1.000
  - Bond yield: 0.056
  - Exchange rate: 0.101

- Germany
  - Stock market: 1.000
  - Bond yield: -0.133
  - Exchange rate: -0.090

- France
  - Stock market: 1.000
  - Bond yield: -0.215
  - Exchange rate: -0.008

- Italy
  - Stock market: 1.000
  - Bond yield: -0.129
  - Exchange rate: -0.054

- Canada
  - Stock market: 1.000
  - Bond yield: -0.287
  - Exchange rate: 0.170

*Source: Authors’ calculations.*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06194.pdf_