Predictive Dynamics in Commodity Prices

Transcription

1 A. Gargano 1 A. Timmermann 2 1 Bocconi University, visting UCSD 2 UC San Diego, CREATES

2 Introduction Some evidence of modest predictability of commodity price movements by means of economic state variables Bessembinder and Chan (1992): T-bill rate, dividend yield, junk bond premium have limited predictive power over movements in agricultural, metals and currency futures prices Hong and Yogo (2011): limited in-sample predictability of commodity spot and futures returns by means of similar economic variables Acharya et al. (2011): mild empirical evidence of predictability of petroleum spot returns from fundamental hedging demand variables and the term spread 1 / 32

3 Questions asked here How strong was out-of-sample predictability of commodity spot returns over the last two decades ( )? Which (if any) predictors improve forecasts? financial or macroeconomic variables such as inflation, money supply, industrial production, unemployment rate? Does predictability vary across different horizons (monthly, quarterly, annual)? Does predictability vary over the economic cycle? Rapach, Strauss and Zhou (2010) Henkel, Martin, and Nardari (2011) Can commodity price volatility or price declines be predicted? 2 / 32

4 Findings (I) Modest evidence of out-of-sample predictability of monthly movements in commodity spot price indexes T-bill rate, default return spread and money supply growth help predict commodity prices at the monthly frequency At longer horizons, out-of-sample commodity price predictability strengthens considerably Only growth in money supply, M1, is capable of consistently predicting commodity spot price movements across horizons Return predictability is notably stronger for the raw industrials and metals indexes and weaker for foods, fats-oils, livestock, and textile indexes 3 / 32

5 Findings (II) Multivariate models tend to be dominated by estimation error and so do not produce precise out-of-sample forecasts Forecast combinations offer some improvements Ridge regresssion Subset combination Stronger evidence that some macro variables predict commodity price movements during recessions than in expansions Inflation fails to predict commodity price movements in expansions, but its predictive power is strong during recessions 4 / 32

6 Findings (III) Few, if any, state variables improve the out-of-sample predictive accuracy of an AR(1) model for realized commodity volatility During economic recessions, variables such as industrial production, money supply, and unemployment improve forecasts of monthly commodity volatility when added to the AR(1) model Variables capable of predicting increasing commodity prices are different from those predicting price declines Lagged volatility, returns, and money supply growth predict the magnitude of increases in commodity prices Decreasing inflation linked to lower future commodity prices 5 / 32

7 Data: Commodity prices Commodity spot prices measured by Reuters/Jeffries-CRB indexes compiled by Commodity Research Bureau raw industrials: burlap, copper scrap, cotton, hides, lead scrap, print cloth, rosin, rubber, steel scrap, tallow, tin, wool tops, and zinc foodstuffs: butter, cocoa beans, corn, cottonseed oil, hogs, lard, steers, sugar, and wheat metals: copper scrap, lead scrap, steel scrap, tin, and zinc Unweighted geometric mean of individual commodity prices Sample period: 1947m1-2010m12 Commodity spot returns computed as r t+1:t+h P t+h P t P t 6 / 32

8 Spot Prices and Returns (Metals) 7 / 32

9 Data Characteristics Returns on commodity indexes have lower mean than value-weighted stock returns right-skews higher kurtosis than stocks some serial correlation for three of the commodity indexes Summary Statistics Fats & Oils Foods Industrials Livestock Metals Textiles Commodity Stock Bond mean (%) std (%) skew kurt AR(1) / 32

10 Predictor variables Dividend Price Ratio (dp) Treasure Bill (tbl) Long Term Rate of Returns (ltr) Term Spread (tms) Default Return Spread (dfr) Inflation (infl) Investment to Capital Ratio (ik) Industrial Production ( IND) Unemployment ( UN) Money Stock ( M1) Commodity volatility (cvol) 9 / 32

11 In-sample predictability Univariate return regressions: r t+1:t+h = β 0h + β 1h x t + ε t+1:t+h Return predictability varies a great deal across different horizons Variables such as the inflation rate are insignificant in monthly regressions but become significant at the quarterly and annual horizons Only growth in the money supply seems capable of predicting commodity returns across all three horizons Return predictability is stronger for industrials and metals and weakest for fats-oils, foods, and textiles 10 / 32

12 In-sample Predictability Fats & Oils Foods Industrials Livestock Metals Textiles Commodity Stock Bond Monthly dfr ** 0.435** 0.559** infl IND *** *** 0.340** 0.421*** M *** ** 0.091** 0.067** AR(1) 0.088* 0.099** 0.363*** 0.097** 0.299*** 0.129* 0.278*** * Quarterly dfr * * ** infl *** ** ** * ** IND * * M *** 0.284** 0.417** 0.256*** 0.246*** AR(1) *** *** 0.157** 0.252*** Annual dfr * infl * * * ** ** * IND ** * ** ** * M ** 1.211** 1.055** 1.682** 0.867* 1.091** AR(1) / 32

13 Out-of-sample predictability Simulated recursive forecasts: ˆr t+1 t = ˆβ tz t, ˆβ t = t t ( z τ 1 z τ 1 ) 1 ( z τ 1 r τ ) τ=1 z t = (1x t ) τ=1 Performance measured by the relative out-of-sample R 2 -value: T 1 R 2 t=r = 1 (r t+1 ˆr t+1 t ) 2 T 1 t=r (r t+1 ˆr t+1 t bmk )2 Clark-West test for statistical significance: T 1 MSE adj = P 1 t=r T 1 T 1 ēt+1 t 2 P 1 êt+1 t 2 +P 1 t=r ( r t+1 t ˆr t+1 t ) 2 t=r 12 / 32

14 Empirical Out-of-sample findings Predictability is strongest for industrials, metals, and the broad commodity price index, weaker for fats-oils, foods, and livestock Many negative R 2 values due to parameter estimation error Monthly results: the highest R 2 values are obtained for industrial raw materials and metals when the default return spread is used as the predictor Quarterly results: models based on T-bill rate, inflation, or money supply growth generate positive and statistically significant R 2 Annual results: R 2 around 10-20% found for the T-bill rate, term spread, and some macroeconomic predictors (industrial production, money supply, unemployment rate) 13 / 32

15 Out-of-sample R 2 Fats-Oils Foods Industrials Livestock Metals Textiles Commodity Stock Bond Monthly dfr * 2.094* 4.500* infl IND M ** * AR(1) *** *** ** Quarterly dfr infl 5.137** 1.464** 7.673* 5.328** 3.821* ** IND M ** ** 5.378** 3.255** AR(1) *** * 4.549** 6.026** Annual dfr * infl 6.227* * 8.099* 8.704* * IND ** ** ** 8.286** * ** M * *** * 7.347** *** *** AR(1) / 32

16 Evolution in OoS return predictability Cumulated sum of squared error differential between the benchmark model and a candidate prediction model proposed by Goyal and Welch (2008): SSE t = t eτ 2 (Bmk) τ=1 t eτ 2 (Model) τ=1 SSE t > 0 : benchmark beaten by forecast model SSE t < 0 : benchmark better than forecast model 15 / 32

17 CumSum for Money supply growth 16 / 32

18 Predictability in recessions and expansions Evaluate differences in predictability in recessions vs. expansions: (r t+1:t+h r t+1:t+h t ) 2 (r t+1:t+h ˆr t+1:t+h t ) 2 = α+βnber t+1 +ε t+1:t+h Little evidence of commodity price predictability during expansions Significantly stronger predictability during recessions Industrial production growth, growth in money supply have significantly stronger predictive power during recessions Predictability of commodity prices is highly state dependent 17 / 32

19 Predictability and Business cycle: Recession out-of-sample R 2 Fats-Oils Foods Industrials Livestock Metals Textiles Commodity Stock Bond Monthly dfr ** 4.128* *** infl *** 3.175*** 0.813* 1.547*** *** IN * 7.771** ** ** M * ** AR(1) 3.577** *** 5.073*** *** * 1.598*** Quarterly dfr infl *** 3.686*** *** *** *** *** *** 1.614** 9.597*** IN *** M *** *** ** AR(1) ** / 32

20 Multivariate Regressions Variable selection based on AIC or BIC across 2 K models Ridge regression shrinks OLS estimates towards zero. Single parameter λ regulates the amount of shrinkage: t K ˆβ λt = arg min (r τ z τ hβ λt ) 2 + λ βλtj 2 λ τ=1 j=1 ˆr RIDGE t+h t = z t ˆβ λt Subset regressions - averaging over k variate models ˆr t+1 t = 1 K K x ti ˆβ it i=1 Rapach, Strauss and Zhou (2010) obtained as special case 19 / 32

21 ICs suggest the best model varies over time 20 / 32

22 Out-of-sample R 2 (Model selection) AIC works reasonably well at all horizons for industrials, metals and total index BIC produces less reliable performance Fats-Oils Foods Industrials Livestock Metals Textiles Commodity Stock Bond Monthly AIC BIC Quarterly AIC BIC Annual AIC BIC / 32

23 Multivariate results: Ridge and subset Monthly: positive R 2 values around 10% (industrials), 8% (metals) and 4-5% (broad index) Quarterly: R 2 values are somewhat higher for industrials, metals and the broad commodity index Annual: R 2 values in the range 20-35% for the broad commodity index and some of the disaggregate indexes 22 / 32

24 Out-of-sample R 2 for Ridge Regression λ Fats-Oils Foods Industrials Livestock Metals Textiles Commodity Stock Bond Monthly *** *** *** *** *** *** *** *** ** Quarterly *** *** ** *** *** ** *** *** 3.711* ** Annual * ** ** ** 9.492** *** *** * ** ** ** ** *** *** * ** ** * * ** / 32

25 Complete Subset Selection 24 / 32

26 OoS R 2 for complete subset regression Including 5-8 predictor variables doubles or triples the value of the out-of-sample R 2 compared with the equal-weighted combination of univariate forecasts k Fats-Oils Foods Industrials Livestock Metals Textiles Commodity Stock Bond Monthly *** *** ** *** *** ** Quarterly *** ** 1.351* 2.846** *** *** ** Annual * ** 7.775** 6.159** 6.535* 9.271** * ** ** * ** *** ** 25 / 32

27 Forecasting commodity price volatility log(cvol 2 t+1 ) = β 0 + β 1 log(cvol 2 t ) + β 2 x t + u t+1 Estimate of β 1 is close to 0.8 and highly significant No evidence that time-varying predictors (other than the lagged volatility) help predict realized variance During recessions several macroeconomic variables (growth in industrial production, money supply growth, and changes in the unemployment rate) improve the OoS forecasts of monthly commodity volatility when added to the AR(1) model 26 / 32

28 Realized Volatility, Dow Jones-AIG Commodity Index 27 / 32

29 Commodity Variance Predictability Monthly β OoSR 2 OoSRExpan 2 OoSRRecess 2 dp *** * tbl ltr tms 4.403*** 1.332** ** dfr infl * IN *** M ** ** UN *** AR(1) 0.811*** *** 28 / 32

30 Predictability of price increases/decreases max(0, r t+1:t+h ) = β 0h +β 1h r t h+1:t +β 2h σ t h+1:t +β 3h x t +ε t+1:t+h Monthly: Lagged volatility and lagged returns are significant Quarterly: Money supply growth and inflation are significant for raw industrials and metals Annual: Broad range of predictor variables are significant (inflation, investment-capital ratio and unemployment) Different predictors work for max(0, r t+1 ) and min(0, r t+1 ) Money supply growth, lagged volatility, and the lagged return predict increases in commodity prices inflation and industrial production are better predictors of decreases in commodity prices 29 / 32

31 Predictability of price increases based on money supply growth 30 / 32

32 Predictability of price increases Monthly Fats-Oils Foods Industrials Livestock Metals Textiles Commodity Stock Bond infl ** IN * M ** ** 3.911** cvol 3.113*** 0.608** 4.054*** 3.245*** 5.904*** 4.491** 2.484*** AR(1) *** *** ** / 32

33 Conclusion Movements in commodity prices or functions of these are partially predictable Predictability varies with the economic state No single best model across all horizons Best model varies over time Evidence that multivariate approaches and forecast combinations produce better forecasts Commodity price predictability is relevant for risk management (volatility, downside risk) 32 / 32