Increasing Trends in the Excess Comovements in Commodity Prices Kazuhiko Ohashi and Tatsuyoshi Okimoto GS of International Corporate Strategy Hitotsubashi University November 2012
Motivations Motivations and Contributions 1. Changes in commodity price correlation have profound implications on (a) Commodity producers hedging strategies (b) Speculators investment strategies (c) Countries energy and food policies 2. Rapid growth of commodity index investment since early 2000s 3. Total value of various commodity index-related instruments purchased by institutional investors had increased from $15 billion to at least $200 billion in mid-2008 (CFTC staff report, 2008) 4. Analyze the effects of financialization process in commodity markets is one of the most important issues 1
5. Effects of financialization of commodities (a) Tang and Xiong (2010, NBER WP) i. There was a significant and increasing trend in return correlations of non-energy commodity futures prices with oil after 2004 ii. Increasing trend is significantly stronger for indexed commodities (listed in the SP-GSCI and DJ-UBS indices) than for offindexed commodities (b) Silvennoinen and Thorp (2010, WP) i. Observe a structural break in the conditional correlation processes from the late 1990s ii. Correlations between S&P500 returns and returns to the majority commodity futures have increased cases more gradual, and from much earlier in the sample iii. High expected stock market volatility (VIX) shifts correlations with S&P500 returns upwards after 2000 2
6. Weak evidence of excess comovement of commodity prices (a) Pindyck and Rotemberg (1990, EJ) i. Find the excess comovement (EC) of commodity prices ii. Commodity prices have a persist tendency to move together even if the effects of any common macroeconomic shocks are controlled iii. 5 out of 21 pairs have significant correlations iv. Highest correlation is 0.281 for copper-gold pair (b) Deb, Trivedi, and Varangis (1996, JoAE) i. Select a more homogeneous sample period of 1974-1992 ii. Use multivariate GARCH model to treat conditional heteroskedasticity and time-varying correlation in the commodity price data iii. Provide little evidence of EC (c) Few studies consider the consequence of financialization of commodities on EC 3
Contributions and Main Results 1. Examine possible regime changes in EC of commodity prices 2. Develop smooth-transition dynamic conditional correlation (STDCC) model (a) Capture time-varying conditional correlation (b) Allow a regime change in unconditional correlation 3. Regime change seems to be more important than time-varying conditional correlation for EC of commodity prices 4. Find a significant increase in EC in recent years (a) EC has been low and stable until 2000 (b) EC has increased gradually since 2000 5. Increase in EC is not a temporal phenomena due to the recent financial crisis, but a long-run trend 4
6. Increasing trend in EC is not due to changes in the effects of common macroeconomic variables 7. Correlation dynamics of off-index commodities are quite different from those of price index 8. Indexed commodities are responsible for the increase trends in excess comovement of commodity prices 5
Methodology Benchmark model 1. Pindyck and Rotemberg (1990, EJ) 2. p it = α i0 x t + α i1 x t 1 + ρ i p i,t 1 + u it (a) p it : Log of price of commodity i at time t (b) x: Vector of macroeconomic variables (c) u it : Theoretically uncorrelated error term i.e. Corr(u it, u jt ) = 0, i j 3. Test the null hypothesis of Corr(u it, u jt ) = 0 4. PR called significant positive correlations in u excess comovement 5. EC can be overestimated if we ignore the conditional heteroskedasticity and time-varying correlation (Deb, Trivedi, and Varangis, 1996) 6
Model framework 1. Extend the PR model by accommodating the conditional heteroskedasticity and time-varying correlation 2. u t = (u 1t, u 2t,..., u Mt ) = H 1/2 t v t, v t iid N(0, I M ) 3. H t : Conditional variance-covariance matrix of p t 4. H t = D t R t D t 5. D t = diag(h 11,t,..., h MM,t ) 1/2 6. h ii,t = ω i + β i h ii,t 1 + α i u 2 ii,t 1 7. R t : time varying correlation matrix 8. Consider several models for the dynamics of correlation R t (a) PR model: constant correlation (D t = D) (b) DCC model: stationary model with constant unconditional mean (c) STC model: smooth trend in unconditional mean (d) STDCC model: trend stationary model with short-run dynamics 7
Dynamic conditional correlation (DCC) model 1. Proposed by Engle (2002, JBES) 2. Allow heteroskedasticity and time-varying conditional correlation 3. Similar model as that of Deb, Trivedi, and Varangis (1996) 4. Model conditional correlation as GARCH(1,1) model (a) R t = diag(q 11,t,..., q nn,t ) 1/2 Q t diag(q 11,t,..., q nn,t ) 1/2 (b) Q t = (1 a b) Q + bq t 1 + aε t 1 ε t 1 (c) ε t = D 1 t u t : standardized disturbance (d) Q: unconditional variance-covariance (correlation) matrix of ε t 5. r ij,t = (1 a b) q ij +aq ij,t 1 +bε i,t 1 ε j,t 1 ( )( ) (1 a b) q ii +aq ii,t 1 +bε 2 i,t 1 (1 a b) q jj +aq jj,t 1 +bε 2 j,t 1 6. Null of no EC: q ij = 0, i j 7. Note that conditional correlation can be nonzero, even no EC 8
Smooth transition correlation (STC) model 1. Developed by Teräsvirta (1994, JASA) in the AR framework 2. Applied to the time-varying correlation model by Berben and Jansen (2005, JIMF) and Kumar and Okimoto (2011, JBF) 3. R t = (1 G(s t ; γ, c))r (1) + G(s t ; γ, c)r (2) 4. One of the regime switching models (a) Regime 1: G = 0 = R t = R (1) (b) Regime 2: G = 1 = R t = R (2) 5. Regime transition is modeled by a logistic transition function G(s t ; γ, c) G(s t ; c, γ) = (a) s t : Transition variable (b) c: Location parameter (c) γ: Smoothness parameter 1 1 + exp( γ(s t c)), γ > 0 9
6. Can describe a wide variety of patterns of change 7. Can select the best pattern for the EC of commodity prices 8. Typical choice of a transition variable (a) s t = p i,t 1 i. R (1) : conditional R when p i,t 1 decreases largely ii. R (2) : conditional R when p i,t 1 increases largely (b) s t = t/t i. R (1) : unconditional R around the beginning of the sample ii. R (2) : unconditional R around the end of the sample 9. Adopt s t = t/t as a transition variable to capture dominant longrun trends (Lin and Teräsvirta, 1994, JoE) 10. Assume 0.01 c 0.99 to detect the correlation transition within the sample period 11. Null of no EC: r (k) ij = 0, i j, k = 1, 2 10
G(S t ) S t =10, c=0.5 =10, c=0.8 =100, c=0.2 =5, c=0.3 =1, c=0.7 11
STDCC model 1. Combine DCC and STC models (a) R t = diag(q 11,t,..., q MM,t ) 1/2 Q t diag(q 11,t,..., q MM,t ) 1/2 (b) Q t = (1 a b) Q t + bq t 1 + aε t 1 ε t 1 (c) Q t = (1 G(s t ; γ, c)) Q (1) + G(s t ; γ, c) Q (2) 2. DCC model can capture the time-varying conditional correlation 3. STC model can allow a smooth regime change in unconditional correlation 4. Null of no EC: q (k) ij = 0, i j, k = 1, 2 12
Data (1983:1-2011:7) Empirical Results 1. Indices of Primary Commodity Prices published by the IMF (a) Agricultural raw materials: timber, cotton, wool, rubber, hides (b) Beverages: coffee, cocoa beans, tea (c) Metals: copper, aluminum, iron ore, tin, nickel, zinc, lead, uranium (d) Oil: U.K. Brent, Dubai Fateh, West Texas Intermediate 2. Macroeconomic variables obtained from FRED (a) Seasonally adjusted CPI (b) Seasonally adjusted industrial production (c) Seasonally adjusted money supply (M1) (d) 3-Month Treasury bill rate (e) Trade weighted exchange rate index (f) S&P 500 13
Benchmark model 1. Same analysis as that of Pindyck and Rotemberg (1990) 2. p it = α i0 x t + α i1 x t 1 + ρ i p i,t 1 + u it 3. 4 out of 6 pairs have significant EC at the 5% significance level (a) AGR-BEV: 0.049 (b) AGR-MET: 0.116 (c) AGR-OIL: 0.193 (d) BEV-MET: 0.132 (e) BEV-OIL: 0.011 (f) MET-OIL: 0.199 4. Find weak evidence of EC consistent with PR 5. None of residuals has significant serial correlation at the 5% level 6. Squared residuals have non-negligible serial correlations 14
DCC model 1. Similar analysis as that of Deb, Trivedi, and Varangis (1996) 2. Regression with GARCH(1,1) disturbance (a) p it = 1 k=0 α ik x t k + ρ i p i,t 1 + u it (b) u it = h 1/2 ii,t v it, v it iid N(0, 1) (c) h ii,t = ω i + β i h ii,t 1 + αu 2 ii,t 1 3. GARCH(1,1) model satisfactorily eliminates the serial correlations of squared residuals 4. DCC model (a) D t = diag(h 11,t,..., h nn,t ) 1/2 (b) H t = D t R t D t (c) R t = diag(q 11,t,..., q nn,t ) 1/2 Q t diag(q 11,t,..., q nn,t ) 1/2 (d) Q t = (1 a b) Q + bq t 1 + aε t 1 ε t 1 (e) ε t = D 1 t u t 15
5. Evidence of EC becomes slightly weaker consistent with DTV 6. 3 out of 6 pairs have significant EC at the 5% significance level (a) AGR-BEV: 0.066 (b) AGR-MET: 0.094 (c) AGR-OIL: 0.213 (d) BEV-MET: 0.134 (e) BEV-OIL: 0.005 (f) MET-OIL: 0.160 7. DCC model indicates that conditional correlation fluctuates slightly with insignificant â = 0.004 and significant ˆb = 0.844 16
STC model 1. Above two models assume unconditional correlation is time-invariant, although DCC model allows time-varying conditional correlation 2. Unconditional correlation may be increasing recently (Tang and Xiong, 2010; Silvennoinen and Thorp, 2010) 3. STC model (a) R t = (1 G(s t ; γ, c))r (1) + G(s t ; γ, c)r (2) 1 (b) G(s t ; c, γ) = 1 + exp( γ(s t c)), γ > 0 (c) s t = t/t 17
Table 4: Estimation results of excess comovement for the STC model 18
4. ˆR (1) suggests that EC is small around the beginning of the sample 5. ˆR (2) indicates that EC has become much stronger toward the end of the sample 6. H 0 : r (1) ij = r (2) ij is rejected for all pairs at the 10% significance level 7. Estimated time series of R show EC has increased gradually since 2000 with average correlation about 0.398 in July 2011 19
Figure 1: Dynamics of excess comovement of commodity prices (STC model) 20
STDCC model 1. STC model does not allow conditional correlation to be time-varying 2. Combine DCC model and STC model 3. STDCC model (a) R t = diag(q 11,t,..., q nn,t ) 1/2 Q t diag(q 11,t,..., q nn,t ) 1/2 (b) Q t = (1 a b) Q t + bq t 1 + aε t 1 ε t 1 (c) Q t = (1 G(s t ; γ, c)) Q (1) + G(s t ; γ, c) Q (2) 4. Results are essentially the same as those of STC model 5. Neither parameters of DCC are insignificant with â = 0.017 and ˆb = 0.000 21
Table 5: Estimation results of excess comovement for the STDCC model 22
Figure 2: Dynamics of excess comovement of commodity prices (STDCC model) 23
6. ˆR (1) suggests that EC is small around the beginning of the sample 7. ˆR (2) indicates that EC has become much stronger toward the end of the sample 8. H 0 : r (1) ij = r (2) ij is rejected for all pairs at the 10% significance level 9. Estimated time series of R show EC has increased gradually since 2000 with average correlation about 0.369 in July 2011 24
Three state STC model 1. Two-state STC model allows only a monotonic transition with time 2. Correlations among commodity returns might become higher around the financial crisis 3. Increasing trends could be an artifact of a temporal increase at the financial crisis 4. Three state model can allow non-monotonic changes in correlations R t = R (1) + G 1 (s t ; γ 1, c 1 )(R (2) R (1) ) + G 2 (s t ; γ 2, c 2 )(R (3) R (2) ) 5. Assume 0.01 c 1 < c 2 0.99 to detect the correlation transition within the sample period 6. R t changes smoothly from R (1) via R (2) to R (3) with time 25
Figure 3: Dynamics of excess comovement of commodity prices (3state STC model) 26
7. Estimated time series of R indicates that the increasing trends in excess comovement is not an artifact produced by the financial crisis 8. Improvement of the fit by the extra regime is marginal 9. Usual information criteria support the two state model over the three state model 27
STR model 1. STC model assumes that the effects of common macroeconomic variables are constant 2. Ignorance of changes in the effects of common macroeconomic factors might produce the increase in excess comovement 3. To examine the possibility, consider the ST regression (STR) model: p it = (1 G(s t ; γ, c))(α (1) i x t + ρ (1) i1 p i,t 1 + σ (1) ε it ) +G(s t ; γ, c)(α (2) i x t + ρ (2) i p i,t 1 + σ (2) ε it ) 4. Estimate the two-state STC model using the standardized residuals ˆε t from the STR model 5. No significant excess comovement in regime 1, but the significant excess comovement in regime 2 with significant increases 6. Correlation dynamics become more linear but increasing trends are still quiet similar 28
Table 6: Estimation results of excess comovement for the residuals from the STR model AGR-BEVAGR-MET AGR-OIL BEV-MET BEV-OIL MET-OIL Regime 1 Estimate -0.1023-0.0279-0.0144 0.0443-0.0882-0.0771 Std. Error 0.0691 0.0723 0.0906 0.0751 0.0816 0.1103 Regime 2 Estimate 0.4706 *** 0.6930 *** 0.8156 *** 0.3212 *** 0.4041 *** 0.9819 *** Std. Error 0.1190 0.1387 0.1966 0.1025 0.1162 0.2328 Test of equality Wald stat 12.8188 16.2639 9.6229 3.1250 7.9782 11.3053 P-value 0.0003 0.0001 0.0019 0.0771 0.0047 0.0008 29
Figure 4: Dynamics of excess comovement of commodity prices (STR residuals) 30
Off-index commodities 1. IMF commodity price indexes contain several off-index commodities (a) Hides (Agricultural materials, 2.6%) (b) Timber (Agricultural materials, 3.4%) i. Hardwood (1.2%) ii. Softwood (2.2%) (c) Rubber (Agricultural materials, 0.5%) (d) Wool (Agricultural materials, 0.5%) i. Fine (0.2%) ii. Coarse (0.3%) (e) Tea (Beverages, 0.3%) (f) Iron ore (Metal, 1.3%) (g) Tin (Metal, 0.2%) (h) Uranium (Metal, 0.5%) 2. Monthly price data of iron ore is available from only 2009 31
3. Uranium price does not change often for the first several years 4. Conduct the same analysis using Hides, Softwood, Tea and Tin 5. ˆR (1) suggests that EC is small around the beginning of the sample 6. ˆR (2) indicates that EC is still small around the end of the sample 7. H 0 : r (1) ij = r (2) ij is not rejected at the 10% significance level for all pairs except hides-tin pair 8. Estimated time series of R show that EC has remained at low levels throughout the sample 9. Results are qualitatively similar if the rubber or coarse wool is used instead of softwood or hides 10. Correlation dynamics of off-index commodities are quite different 32
Table 7: Estimation results of excess comovement for off-index commodities 33
Figure 5: Dynamics of excess comovement of off-index commodity prices (STC model) 34
Conclusion 1. Examine possible regime changes in excess comovement of commodity prices 2. Develop smooth-transition dynamic conditional correlation (STDCC) model (a) Capture time-varying conditional correlation (b) Allow a regime change in unconditional correlation 3. Find little EC until 2000 4. Provide new evidence of gradual significant increase in EC since 2000 5. Increase in EC is not an artifact due to the recent financial crisis nor changes in the effects of common macroeconomic variables 6. Indexed commodities are responsible for the increase trends in excess comovement of commodity prices 35
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[9] Tang, K. and Xiong, W. (2010). Index investing and the financialization of commodities. NBER Working Paper, No. 16385. [10] Teräsvirta, T. (1994). Specification, estimation, and evaluation of smooth transition autoregressive models, Journal of the American Statistical Association 89(425), 208-218. 37
Figure : Dynamics of coefficients of STR model (Agriculture) 38
Figure : Dynamics of coefficients of STR model (Beverage) 39
Figure : Dynamics of coefficients of STR model (Metal) 40
Figure : Dynamics of coefficients of STR model (Oil) 41