## _wp08221 - References

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---

### Introduction
- Commodities have remerged as an attractive asset class following a strong price run; evidence suggests financial investors have raised exposure.
- Commodity futures provide exposure to macro risk factors (inflation, real interest rates, exchange rates) and may offer diversification relative to equities.
- Paper objective: assess macro risk exposure offered by commodity futures and test whether these risks are priced using Merton’s (1973) ICAPM.
- Paper structure: II outlines ICAPM; III reviews risk-pricing literature for commodities; IV describes data; V discusses estimation; VI presents results; VII concludes.

### Merton’s ICAPM: theoretical framework
- Model setup:
  - Single risky asset instantaneous return dY/Y; riskless asset return dB/B; single state variable S following stochastic Itô process.
  - Stationary processes assumed; equations (1)–(4) define dynamics and correlation ρ.
- Investor problem:
  - Maximize expected present value of utility ∫_0^∞ E[U(C,t)] dt subject to intertemporal budget constraint (equations (5)–(7)).
  - Bellman equation and Itô’s lemma lead to first-order conditions for consumption C and portfolio share α (equations (11)–(13)).
- Equilibrium risk-premium decomposition (equation (14)):
  - Two components:
    - γ0 × cov(risky asset, aggregate portfolio return) — traditional CAPM price × quantity of market risk.
    - γ1 × cov(risky asset, state variable changes) — price × quantity of state-variable risk.
  - γ0 = - J_WW / J_W is Arrow-Pratt relative risk aversion; r_Y = dY/Y.

### Identifying state variables
- Choice of state variables is subjective; ICAPM suggests variables that affect marginal utility of wealth.
- Author follows Ferson and Harvey (1991) in selecting macro state variables; APT allows inclusion of any priced factor.

### Brief review of the literature (commodities)
- Two theories for commodity futures risk premium:
  - Keynes (1930): positive risk premium if speculators provide insurance to producers; sign may be negative if consumer hedging dominates.
  - Storage, convenience yield, opportunity cost theories (Kaldor 1939; Working 1949; Brennan 1958).
- Empirical findings summarized:
  - Fama and French (1987): basis variation responds to storage costs and interest rates; agricultural commodity risk premia ranged between 1–2 percent.
  - Gorton and Rouwenhorst (2006): collateralized commodity futures risk premium similar in size to stocks over 45 years.
  - Jagannathan (1985), Bessembinder (1992): little evidence of non-zero ICAPM risk pricing for many commodities; idiosyncratic hedging pressure matters.
  - Khan, Khoker, and Simin (2008): macro factors predict commodity-specific factors (hedging pressure, scarcity proxy).

### Data
- Prices for 17 commodity futures from the Commodities Research Bureau (CRB) database; month-end data, continuously rolled into nearest-future; sample period January 1973 to February 2008.
- Returns measured on a collateralized basis (one-month Treasury bill plus long futures position); excess return is change in position value over risk-free rate.
- State variables used:
  - Global equity market total returns in U.S. dollars (proxy for market portfolio).
  - Inflation shocks: residuals of ARIMA(2,2,3) applied to U.S. CPI.
  - Real short-term interest rates: U.S. three-month Treasury bill yield minus CPI inflation over previous 12 months.
  - Change in slope of yield curve: yield gap between U.S. three-month T-bill and U.S. 10-year Treasury note.
  - U.S. dollar nominal effective exchange rate (Federal Reserve index).
- Table 1 summary statistics (Jan-1973 to Feb-2008):
  - Gold Annualized Return 7.72; Volatility 20.3; Sharpe ratio 0.38; Max return 25.5; Min. return -24.4; Skew 0.66; Kurtosis 6.8.
  - Average row in Table 2: Average 1.5 0.1 -0.002 0.003 -0.2 0.04

### Estimation methods: quantities (betas) and prices (gammas) of risk
- Macro risk exposure estimated by regressions of each commodity excess return on macro factors; betas termed “risk quantity coefficients”.
- Evidence of time-varying betas; rolling 60-month regressions used to capture dynamics (Figure 2).
- Pricing estimation:
  - Fama-MacBeth two-step approach implemented:
    - Stage 1: rolling 60-month regressions to estimate β_it from rit = α_i + Σ_j β_ij f_jt + e_it (equation (15)).
    - Stage 2: cross-sectional regressions r_t = γ_0 ι + β_t γ + υ_t (equation (16)), γ estimated as time-average of cross-sectional γ̂_t (equation (17)).
  - Shanken (1992) adjustment used for standard errors to account for estimated betas.
  - Joint pricing error test follows Cochrane (equation (19)).

### Results — key findings
- Macro risk exposures (Table 2 highlights):
  - R-squared statistics for almost all commodities (except gold) are very low: much price variation is commodity-specific.
  - All 17 commodities show inverse relation to U.S. real interest rates; precious metals and energy show significant exposure to real interest rates and U.S. dollar index.
  - Three commodity clusters after controlling for macro factors (within-group average correlation):
    - Precious metals — gold, silver, platinum (0.66).
    - Agricultural — corn, soybeans, wheat (0.57).
    - Energy — crude oil, natural gas (0.62).
- Priced macro risk:
  - Real interest rate risk is the only macro factor priced across specifications.
  - Coefficient on real interest rates averages about 0.5 percent per month across specifications (significant and time-varying).
  - Illustrative calculation for gold:
    - Average beta of gold future on real interest rate ≈ -0.005.
    - Annual risk premium for bearing interest rate exposure = 12 x 0.6 = 7.2 percent.
    - Implied negative expected annual excess return = -0.005 x 7.2 = - 3.6 percent.
  - Table 3 Fama-MacBeth multivariate specification (Arbitrage pricing theory restriction γ_0 = 0 imposed): reported coefficients include Real term (0.0002), U.S. dollar index (0.0064), Stock market 0.6197 **.
- Time variation in risk pricing:
  - Interest rate risk premium varies over time and is inversely correlated with real interest rate levels: as real rates decline (rise), cost of insurance increases (falls).
- Commodity-specific risk premium:
  - Intercept in specifications including intercept is statistically non-zero and economically significant.
  - Commodity-class intercept contributes an annualized 5.4 percent to expected return of the asset class.
- Model fit and limitations:
  - Joint test of pricing errors failed to reject null at 1 percent level for the multivariate model, but low R-squareds for beta equations indicate many commodity-specific drivers remain unmodeled.
  - Model intended for equilibrium pricing insight rather than forecasting.

### Interpretation and implications
- Interpretation of priced real interest rate risk:
  - Commodities with negative betas to real interest rates act as insurance in “bad times” when investment opportunities are scarce and expected wealth gains are reduced.
  - Frankel (2006) mechanisms for why real commodity prices fall as real rates rise:
    - present value effect on future revenues,
    - higher opportunity cost of carry reducing inventories,
    - higher returns on competing financial instruments reducing commodity demand.
- Exchange rate risk:
  - Despite correlations, exchange rate risk is not priced in these estimations; easier currency hedging and PPP considerations may explain lack of currency premia.
- Policy / investment implications:
  - Long-term investors entering commodity asset class should continuously update and refine estimates of macro risk exposures and pricing due to time variation.
  - Open questions remain: regional macro risk exposures, role of global vs. U.S. interest rates, and whether commoditization by large financial investors will homogenize asset-class behavior.

### Conclusion (selected)
- Commodity futures offer some macro risk exposure, varying across the asset class; precious metals, copper, and energy are more sensitive to interest rate and currency movements, agricultural commodities less so.
- Interest rate risk is priced and interpretable as insurance against bad times; exchange rate risk is not priced in this analysis.
- Many unanswered questions remain regarding region-specific risk, global interest rates, and the effects of increasing financial investor participation.

### References list (selected verbatim entries)
- Adler, Michael, and Bernard Dumas, 1983, “International Portfolio Choice and Corporation Finance: A Synthesis,” Journal of Finance, Vol. 38, No. 2, pp. 925–984.
- Bessembinder, H., 1992, “Systematic risk, hedging pressure, and risk premiums in futures markets”, Review of Financial Studies, Vol. 5, No. 4, pp. 637–667.
- Brennan, M. J., 1958, “The Supply of Storage,” American Economic Review, 48 (March), pp. 50–72.
- Campbell, John Y. and Luis Viciera, 2002, Strategic Asset Allocation, Oxford University Press.
- Chen, Nai-Fu, Richard Roll, and Stephen A. Ross, 1986, “Economic Forces and the Stock Market,” The Journal of Business, Vol. 59, No. 3, pp. 383–403.
- Cochrane, John H., 2001, Asset Pricing, Princeton, New Jersey.
- Fama, Eugene F. and Kenneth R. French, 1987, “Commodity Futures Prices: Some Evidence on Forecast Power, Premiums, and the Theory of Storage,” Journal of Business, Vol. 60, No. 1, pp. 55–73.
- Fama, Eugene F. and Kenneth R. French, 1992, “The Cross-Section of Expected Stock Returns,” The Journal of Finance, Vol. 47, No. 2, pp. 427–465.
- Fama, Eugene F., and James D. MacBeth, 1973, “Risk, Return, and Equilibrium: Empirical Tests,” Journal of Political Economy, Vol. 81, No. 3, pp. 607–636.
- Ferson, Wayne E. and Campbell R. Harvey, 1991, “The Variation of Economic Risk Premiums,” The Journal of Political Economy, Vol. 99, No. 2, pp. 385–415.
- Frankel, Jeffrey, 2006, “The Effect of Monetary Policy on Real Commodity Prices,” in Asset Prices and Monetary Policy, John Campbell, ed., University of Chicago Press.
- Gorton, Gary, and K. Geert Rouwenhorst, 2006, “Facts and Fantasies about Commodity Futures,” Financial Analysts Journal, Vol. 62, No. 2, pp. 47–68.
- Jagannathan, Ravi, 1985, “An Investigation of Commodity Futures Prices Using the Consumption-Based Intertemporal Capital Asset Pricing Model,” The Journal of Finance, Vol. 40, No. 1, pp. 175–191.
- Kaldor, N., 1939, “Speculation and Economic Stability,” Review of Economic Studies, 7 (October), pp. 1–27.
- Keynes, J. M., 1930, The Applied Theory of Money, A Treatise on Money, Vol. 2, Macmillan, London.
- Khan, Saqib A, Zeigham I. Khoker, and Timothy T. Simin, 2008, "Expected Commodity Futures Returns.” Available at SSRN: http://ssrn.com/abstract=1107377
- Merton, Robert C., 1973, “An Intertemporal Capital Asset Pricing Model”, Econometrica, Vol. 41, No. 5, pp. 867–887.
- Shanken, Jay, 1992, “On the Estimation of Beta-Pricing Models,” The Review of Financial Studies, Vol. 5, Number 1, pp. 1–33.
- Working, H., 1948, “Theory of the Inverse Carrying Charge in Futures Markets,” Journal of Farm Economics, 30 (February), pp. 1–28.

### Appendix — Table A1: Correlation Matrix of Excess Returns, Jan-1973 to Feb-2008
- Commodities (column order): Gold; Silver; Copper; Platinum; Crude oil; Corn; Soybeans; Wheat; Live cattle; Lean hogs; Cocoa; Sugar; Cotton; Orange juice; Heating oil; Natural gas.
- Average correlations by commodity (exact values):
  - Gold: 0.18
  - Silver: 0.20
  - Copper: 0.15
  - Platinum: 0.20
  - Crude oil: 0.08
  - Corn: 0.16
  - Soybeans: 0.17
  - Wheat: 0.15
  - Live cattle: 0.06
  - Lean hogs: 0.06
  - Cocoa: 0.08
  - Sugar: 0.06
  - Cotton: 0.08
  - Orange juice: 0.06
  - Heating oil: -0.01
  - Natural gas: 0.06
- Source note: Source: Author's estimates.
- Significance note: Figures in bold are statistically significant at the 95 percent level.

### Appendix — Table A2: Correlation Matrix of Residuals from Five-Factor Beta Models, Jan-1973 to Feb-2008
- Commodities (column order as in Table A1).
- Average residual correlations by commodity (exact values):
  - Gold: 0.16
  - Silver: 0.18
  - Copper: 0.14
  - Platinum: 0.18
  - Crude oil: 0.08
  - Corn: 0.15
  - Soybeans: 0.17
  - Wheat: 0.14
  - Live cattle: 0.05
  - Lean hogs: 0.05
  - Cocoa: 0.06
  - Sugar: 0.05
  - Cotton: 0.07
  - Orange juice: 0.06
  - Heating oil: -0.01
  - Natural gas: 0.05
- Source note: Source: Author's estimates.
- Significance note: Figures in bold are statistically significant at the 95 percent level.

### Appendix — Figure A1: Estimated Risk Prices, 1979–2008
- Figure title: Estimated Risk Prices, 1979–2008
- Panels and axis tick values (verbatim):
  - Commodity-specific (intercept): -0.020, -0.015, -0.010, -0.005, 0.000, 0.005, 0.010, 0.015, 0.020, 0.025, 0.030; x-axis years: 1980 1984 1987 1990 1993 1997 2000 2003 2006.
  - Global stock market: -0.04, -0.03, -0.02, -0.01, 0.00, 0.01, 0.02, 0.03, 0.04; x-axis years: 1980 1984 1987 1990 1993 1997 2000 2003 2006.
  - Yield curve: -0.80, -0.60, -0.40, -0.20, 0.00, 0.20, 0.40, 0.60, 0.80; x-axis years: 1980 1984 1987 1990 1993 1996 1999 2003 2006.
  - U.S. dollar index: -0.03, -0.02, -0.01, 0.00, 0.01, 0.02, 0.03; x-axis years: 1980 1984 1987 1990 1993 1997 2000 2003 2006.
- Model series shown: Model with intercept; Model without intercept.
- Source note on figure: Source: Author's estimates.

*Source: _wp08221 - REFERENCES (source PDF content provided).*

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

### _wp08221 - References..............................................................................................................

### Introduction
- Commodities have remerged as an attractive asset class following a strong price run; evidence suggests financial investors have raised exposure.
- Commodity futures provide exposure to macro risk factors (inflation, real interest rates, exchange rates) and may offer diversification relative to equities.
- Paper objective: assess macro risk exposure offered by commodity futures and test whether these risks are priced using Merton’s (1973) ICAPM.
- Paper structure: II outlines ICAPM; III reviews risk-pricing literature for commodities; IV describes data; V discusses estimation; VI presents results; VII concludes.

### Merton’s ICAPM: theoretical framework
- Model setup:
  - Single risky asset instantaneous return dY/Y; riskless asset return dB/B; single state variable S following stochastic Itô process.
  - Stationary processes assumed; equations (1)–(4) define dynamics and correlation ρ.
- Investor problem:
  - Maximize expected present value of utility ∫_0^∞ E[U(C,t)] dt subject to intertemporal budget constraint (equations (5)–(7)).
  - Bellman equation and Itô’s lemma lead to first-order conditions for consumption C and portfolio share α (equations (11)–(13)).
- Equilibrium risk-premium decomposition (equation (14)):
  - Two components:
    - γ0 × cov(risky asset, aggregate portfolio return) — traditional CAPM price × quantity of market risk.
    - γ1 × cov(risky asset, state variable changes) — price × quantity of state-variable risk.
  - γ0 = - J_WW / J_W is Arrow-Pratt relative risk aversion; r_Y = dY/Y.

### Identifying state variables
- Choice of state variables is subjective; ICAPM suggests variables that affect marginal utility of wealth.
- Author follows Ferson and Harvey (1991) in selecting macro state variables; APT allows inclusion of any priced factor.

### Brief review of the literature (commodities)
- Two theories for commodity futures risk premium:
  - Keynes (1930): positive risk premium if speculators provide insurance to producers; sign may be negative if consumer hedging dominates.
  - Storage, convenience yield, opportunity cost theories (Kaldor 1939; Working 1949; Brennan 1958).
- Empirical findings summarized:
  - Fama and French (1987): basis variation responds to storage costs and interest rates; agricultural commodity risk premia ranged between 1–2 percent.
  - Gorton and Rouwenhorst (2006): collateralized commodity futures risk premium similar in size to stocks over 45 years.
  - Jagannathan (1985), Bessembinder (1992): little evidence of non-zero ICAPM risk pricing for many commodities; idiosyncratic hedging pressure matters.
  - Khan, Khoker, and Simin (2008): macro factors predict commodity-specific factors (hedging pressure, scarcity proxy).

### Data
- Prices for 17 commodity futures from the Commodities Research Bureau (CRB) database; month-end data, continuously rolled into nearest-future; sample period January 1973 to February 2008.
- Returns measured on a collateralized basis (one-month Treasury bill plus long futures position); excess return is change in position value over risk-free rate.
- State variables used:
  - Global equity market total returns in U.S. dollars (proxy for market portfolio).
  - Inflation shocks: residuals of ARIMA(2,2,3) applied to U.S. CPI.
  - Real short-term interest rates: U.S. three-month Treasury bill yield minus CPI inflation over previous 12 months.
  - Change in slope of yield curve: yield gap between U.S. three-month T-bill and U.S. 10-year Treasury note.
  - U.S. dollar nominal effective exchange rate (Federal Reserve index).
- Table 1 summary statistics (Jan-1973 to Feb-2008):
  - Example entries (percent unless otherwise specified): Gold Annualized Return 7.72; Volatility 20.3; Sharpe ratio 0.38; Max return 25.5; Min. return -24.4; Skew 0.66; Kurtosis 6.8.
  - Average row in Table 2: Average 1.5 0.1 -0.002 0.003 -0.2 0.04 (preserves exact formatting from source).

### Estimation methods: quantities (betas) and prices (gammas) of risk
- Macro risk exposure estimated by regressions of each commodity excess return on macro factors; betas termed “risk quantity coefficients”.
- Evidence of time-varying betas; rolling 60-month regressions used to capture dynamics (Figure 2).
- Pricing estimation:
  - Fama-MacBeth two-step approach implemented:
    - Stage 1: rolling 60-month regressions to estimate β_it from rit = α_i + Σ_j β_ij f_jt + e_it (equation (15)).
    - Stage 2: cross-sectional regressions r_t = γ_0 ι + β_t γ + υ_t (equation (16)), γ estimated as time-average of cross-sectional γ̂_t (equation (17)).
  - Shanken (1992) adjustment used for standard errors to account for estimated betas.
  - Joint pricing error test follows Cochrane (equation (19)).

### Results — key findings
- Macro risk exposures (Table 2 highlights):
  - R-squared statistics for almost all commodities (except gold) are very low: much price variation is commodity-specific.
  - All 17 commodities show inverse relation to U.S. real interest rates; precious metals and energy show significant exposure to real interest rates and U.S. dollar index.
  - Three commodity clusters after controlling for macro factors (within-group average correlation):
    - Precious metals — gold, silver, platinum (0.66).
    - Agricultural — corn, soybeans, wheat (0.57).
    - Energy — crude oil, natural gas (0.62).
- Priced macro risk:
  - Real interest rate risk is the only macro factor priced across specifications.
  - Coefficient on real interest rates averages about 0.5 percent per month across specifications (significant and time-varying).
  - Illustrative calculation for gold:
    - Average beta of gold future on real interest rate ≈ -0.005.
    - Annual risk premium for bearing interest rate exposure = 12 x 0.6 = 7.2 percent.
    - Implied negative expected annual excess return = -0.005 x 7.2 = - 3.6 percent.
  - Table 3 Fama-MacBeth multivariate specification (Arbitrage pricing theory restriction γ_0 = 0 imposed): reported coefficients include Real term (0.0002), U.S. dollar index (0.0064), Stock market 0.6197 ** (t-statistics shown in source).
- Time variation in risk pricing:
  - Interest rate risk premium varies over time and is inversely correlated with real interest rate levels: as real rates decline (rise), cost of insurance increases (falls) (Figure 3).
- Commodity-specific risk premium:
  - Intercept in specifications including intercept is statistically non-zero and economically significant.
  - Commodity-class intercept contributes an annualized 5.4 percent to expected return of the asset class (consistent with Keynes’ backwardation/insurance view).
- Model fit and limitations:
  - Joint test of pricing errors failed to reject null at 1 percent level for the multivariate model, but low R-squareds for beta equations indicate many commodity-specific drivers remain unmodeled.
  - Author notes model is for equilibrium pricing insight rather than forecasting.

### Interpretation and implications
- Interpretation of priced real interest rate risk:
  - Commodities with negative betas to real interest rates act as insurance in “bad times” when investment opportunities are scarce and expected wealth gains are reduced.
  - Frankel (2006) offers three mechanisms for why real commodity prices fall as real rates rise: present value effect on future revenues, higher opportunity cost of carry reducing inventories, and higher returns on competing financial instruments reducing commodity demand.
- Exchange rate risk:
  - Despite correlations, exchange rate risk is not priced in these estimations; easier currency hedging and PPP considerations may explain lack of currency premia.
- Policy / investment implications:
  - Long-term investors entering commodity asset class should continuously update and refine estimates of macro risk exposures and pricing due to time variation.
  - Open questions remain: regional macro risk exposures, role of global vs. U.S. interest rates, and whether commoditization by large financial investors will homogenize asset-class behavior.

### Conclusion (selected)
- Commodity futures offer some macro risk exposure, varying across the asset class; precious metals, copper, and energy are more sensitive to interest rate and currency movements, agricultural commodities less so.
- Interest rate risk is priced and interpretable as insurance against bad times; exchange rate risk is not priced in this analysis.
- Many unanswered questions remain regarding region-specific risk, global interest rates, and the effects of increasing financial investor participation.

*Source: _wp08221 - References............................................................................................................................... 18*

### REFERENCES

### _wp08221 - REFERENCES

### References list
- Full bibliography of works cited, including journal articles, books, working papers, and web sources. Examples (verbatim entries preserved):
  - Adler, Michael, and Bernard Dumas, 1983, “International Portfolio Choice and Corporation Finance: A Synthesis,” Journal of Finance, Vol. 38, No. 2, pp. 925–984.
  - Bessembinder, H., 1992, “Systematic risk, hedging pressure, and risk premiums in futures markets”, Review of Financial Studies, Vol. 5, No. 4, pp. 637–667.
  - Brennan, M. J., 1958, “The Supply of Storage,” American Economic Review, 48 (March), pp. 50–72.
  - Campbell, John Y. and Luis Viciera, 2002, Strategic Asset Allocation, Oxford University Press.
  - Chen, Nai-Fu, Richard Roll, and Stephen A. Ross, 1986, “Economic Forces and the Stock Market,” The Journal of Business, Vol. 59, No. 3, pp. 383–403.
  - Cochrane, John H., 2001, Asset Pricing, Princeton, New Jersey.
  - Fama, Eugene F. and Kenneth R. French, 1987, “Commodity Futures Prices: Some Evidence on Forecast Power, Premiums, and the Theory of Storage,” Journal of Business, Vol. 60, No. 1, pp. 55–73.
  - Fama, Eugene F. and Kenneth R. French, 1992, “The Cross-Section of Expected Stock Returns,” The Journal of Finance, Vol. 47, No. 2, pp. 427–465.
  - Fama, Eugene F., and James D. MacBeth, 1973, “Risk, Return, and Equilibrium: Empirical Tests,” Journal of Political Economy, Vol. 81, No. 3, pp. 607–636.
  - Ferson, Wayne E. and Campbell R. Harvey, 1991, “The Variation of Economic Risk Premiums,” The Journal of Political Economy, Vol. 99, No. 2, pp. 385–415.
  - Frankel, Jeffrey, 2006, “The Effect of Monetary Policy on Real Commodity Prices,” in Asset Prices and Monetary Policy, John Campbell, ed., University of Chicago Press.
  - Gorton, Gary, and K. Geert Rouwenhorst, 2006, “Facts and Fantasies about Commodity Futures,” Financial Analysts Journal, Vol. 62, No. 2, pp. 47–68.
  - Greenwich Associates, 2008, “Financial Investors Fueling Commodities Boom”, http://www.greenwich.com.
  - Jagannathan, Ravi, 1985, “An Investigation of Commodity Futures Prices Using the Consumption-Based Intertemporal Capital Asset Pricing Model,” The Journal of Finance, Vol. 40, No. 1, pp. 175–191.
  - Kaldor, N., 1939, “Speculation and Economic Stability,” Review of Economic Studies, 7 (October), pp. 1–27.
  - Kaminsky, Graciela, and Manmohan S. Kumar, 1990, “Efficiency in Commodity Futures Markets,” IMF Staff Papers, Vol. 37, No. 3, pp. 670–699.
  - Keynes, J. M., 1930, The Applied Theory of Money, A Treatise on Money, Vol. 2, Macmillan, London.
  - Khan, Saqib A, Zeigham I. Khoker, and Timothy T. Simin, 2008, "Expected Commodity Futures Returns.” Available at SSRN: http://ssrn.com/abstract=1107377
  - Kolos, Sergey P. and Ehud I. Ronn, (2008), “Estimating the Commodity Market Price of Risk for Energy Prices,” Energy Economics, Volume 30, Issue 2, March 2008, pp. 621–641.
  - Longstaff, Francis, and Ashley W. Wang, (2004), “Electricity Forward Prices: A High-Frequency Empirical Analysis,” The Journal of Finance 59 (4), pp. 1877–1900.
  - Merton, Robert C., 1973, “An Intertemporal Capital Asset Pricing Model”, Econometrica, Vol. 41, No. 5, pp. 867–887.
  - Pensions and Investments, 2007, “European funds dig into agricultural commodities”, August, http://www.pionline.com.
  - Pensions and Investments, 2008, “UK funds shift to fixed income, alternatives,” January, http://www.pionline.com.
  - Roache, Shaun K., 2006, “Currency Risk Premia in Global Stock Markets,” IMF Working Paper, WP/06/194.
  - Ross, S., 1976, “The Arbitrage Theory of Capital Asset Pricing,” Journal of Economic Theory, 13, pp. 341–360.
  - Santis, Giorgio de, and Bruno Gerard, 1997, “International Asset Pricing and Portfolio Diversification with Time-Varying Risk,” The Journal of Finance, Vol. 52, No. 5, pp. 1881–1912.
  - Shanken, Jay, 1992, “On the Estimation of Beta-Pricing Models,” The Review of Financial Studies, Vol. 5, Number 1, pp. 1–33.
  - Shanken, Jay, and Guofu Zhou, 2007, “Estimating and Testing Beta Pricing Models: Alternative Methods and Their Performance in Simulations,” Journal of Financial Economics, 84, pp. 40–86.
  - Sharpe, William F., 1964, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk,” Journal of Finance, 19 (3), pp. 425–442.
  - Working, H., 1948, “Theory of the Inverse Carrying Charge in Futures Markets,” Journal of Farm Economics, 30 (February), pp. 1–28.

### Appendix — Table A1: Correlation Matrix of Excess Returns, Jan-1973 to Feb-2008
- Table title: Correlation Matrix of Excess Returns, Jan-1973 to Feb-2008
- Commodities (column order): Gold; Silver; Copper; Platinum; Crude oil; Corn; Soybeans; Wheat; Live cattle; Lean hogs; Cocoa; Sugar; Cotton; Orange juice; Heating oil; Natural gas.
- Average correlations by commodity (exact values from table):
  - Gold: 0.18
  - Silver: 0.20
  - Copper: 0.15
  - Platinum: 0.20
  - Crude oil: 0.08
  - Corn: 0.16
  - Soybeans: 0.17
  - Wheat: 0.15
  - Live cattle: 0.06
  - Lean hogs: 0.06
  - Cocoa: 0.08
  - Sugar: 0.06
  - Cotton: 0.08
  - Orange juice: 0.06
  - Heating oil: -0.01
  - Natural gas: 0.06
- Source note: Source: Author's estimates.
- Significance note: Figures in bold are statistically significant at the 95 percent level.

### Appendix — Table A2: Correlation Matrix of Residuals from Five-Factor Beta Models, Jan-1973 to Feb-2008
- Table title: Correlation Matrix of Residuals from Five-Factor Beta Models, Jan-1973 to Feb-2008
- Commodities (column order as in Table A1).
- Average residual correlations by commodity (exact values from table):
  - Gold: 0.16
  - Silver: 0.18
  - Copper: 0.14
  - Platinum: 0.18
  - Crude oil: 0.08
  - Corn: 0.15
  - Soybeans: 0.17
  - Wheat: 0.14
  - Live cattle: 0.05
  - Lean hogs: 0.05
  - Cocoa: 0.06
  - Sugar: 0.05
  - Cotton: 0.07
  - Orange juice: 0.06
  - Heating oil: -0.01
  - Natural gas: 0.05
- Source note: Source: Author's estimates.
- Significance note: Figures in bold are statistically significant at the 95 percent level.

### Appendix — Figure A1: Estimated Risk Prices, 1979–2008
- Figure title: Estimated Risk Prices, 1979–2008
- Panels and axis tick values (verbatim):
  - Commodity-specific (intercept): -0.020, -0.015, -0.010, -0.005, 0.000, 0.005, 0.010, 0.015, 0.020, 0.025, 0.030; x-axis years: 1980 1984 1987 1990 1993 1997 2000 2003 2006.
  - Global stock market: -0.04, -0.03, -0.02, -0.01, 0.00, 0.01, 0.02, 0.03, 0.04; x-axis years: 1980 1984 1987 1990 1993 1997 2000 2003 2006.
  - Yield curve: -0.80, -0.60, -0.40, -0.20, 0.00, 0.20, 0.40, 0.60, 0.80; x-axis years: 1980 1984 1987 1990 1993 1996 1999 2003 2006.
  - U.S. dollar index: -0.03, -0.02, -0.01, 0.00, 0.01, 0.02, 0.03; x-axis years: 1980 1984 1987 1990 1993 1997 2000 2003 2006.
- Model series shown: Model with intercept; Model without intercept.
- Source note on figure: Source: Author's estimates.

*Source: _wp08221 - REFERENCES (source PDF content provided).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08221.pdf_