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Stock Market Predictability and Industrial Metal Returns Ben Jacobsen University of Edinburgh [email protected] Ben R. Marshall* Massey University [email protected] Nuttawat Visaltanachoti Massey University [email protected] First draft: June 2010 This draft: September 2014 Abstract Price movements in industrial metals such as copper and aluminum predict stock returns world wide. Increasing metal prices are good news for equity markets in recessions and bad news in expansions. Industrial metals returns forecast changes in the economy and information gradually diffuses from metals to stocks through both the discount rate and cash flow channels. Out-of-sample R2’s are as high as 9%. A horse race of asset pricing model explanations shows industrial metals are a state variable in an ICAPM framework. There is also some evidence to support both a production and consumption asset pricing explanation. Keywords: industrial metals, state-switching, return predictability, gradual information diffusion, business cycle, ICAPM, production asset pricing, consumption asset pricing JEL classification codes: G11, G14 Acknowledgements: We thank Andrea Bennett, Henk Berkman, Glenn Boyle, Jon Dark, Frans DeRoon, Spencer Martin, Kenneth Singleton, seminar participants at Victoria University Wellington, Deakin University, Otago University, the University of Newcastle, the University of Auckland, and the University of Melbourne, and conference participants at the 2010 Australian Finance and Banking Conference and 2011 New Zealand Finance Colloquium for comments. All errors are our own. *Corresponding Author: School of Economics and Finance, Massey University, Private Bag 11-222, Palmerton North, New Zealand. Email: [email protected]; Tel: +64 6 350 5799. 1 Stock Market Predictability and Industrial Metal Returns Abstract Price movements in industrial metals such as copper and aluminum predict stock returns world wide. Increasing metal prices are good news for equity markets in recessions and bad news in expansions. Industrial metals returns forecast changes in the economy and information gradually diffuses from metals to stocks through both the discount rate and cash flow channels. Out-of-sample R2’s are as high as 9%. A horse race of asset pricing model explanations shows industrial metals are a state variable in an ICAPM framework. There is also some evidence to support both a production and consumption asset pricing explanation. Keywords: industrial metals, state-switching, return predictability, gradual information diffusion, business cycle, ICAPM, production asset pricing, consumption asset pricing JEL classification codes: G11, G14 2 1. Introduction Price movements in industrial metals such as copper and aluminum predict stock returns. Metal price increases signal a stock market decrease the following month in expansions and a stock market increase in recessions. The out-of-sample R2’s, which range from 3% to 9%, compare favorably to those generated by the majority of more well established predictors.1 Our results are consistent with financial news media stories which often present industrial metal returns as being important leading indicators of the economy and equity markets. Analysts cite increasing industrial metals prices as being a positive sign when the economy is depressed.2 However, in expansions, rising industrial metals prices are frequently seen as signaling an overheating economy and inflation, which is widely viewed as bad news.3 Academic studies also suggest a possible predictive link. Garner (1989), for instance, shows that movements in commodity prices lead CPI inflation and provides two reasons for this. First, commodities are inputs in the production process. Second, because commodity prices are set in auction markets they “respond more rapidly than the prices of manufactured goods and services to demand pressures or supply shocks” (p. 508). More recently, Awokuse and Yang (2003) show the CRB commodity price index can be used to predict industrial 1 Goyal and Welch (2008) show a range of popular predictors, such as dividend yield, generate out-of-sample R2’s that are frequently not different to zero. Rapach, Strauss, and Zhou (2010) find that combination forecasts based on these variables result in out-of-sample R2’s from 1-4%. This is also the range Rapach, Strauss, and Zhou (2012) document for predictions of international equity market returns based on US stock returns. More recently, Kelly and Pruitt (2013) document particularly strong forecasting ability (out-of-sample R2 of 13%) using a factor derived from cross-section book to market ratios. 2 For instance: “…some analysts saw encouraging signs in the rise in copper since the start of the year. Its past correlation with industrial demand supported hopes that the economy had started to make small steps towards recovery and healthy inflation—rather than sliding into a protracted, severe period of falling prices and shrinking output.” (Mandaro, 2009). http://www.marketwatch.com/story/dr-coppers-forecasting-ability-tested-year 3 For example, Sandra Pianalto, President of the Federal Reserve Bank of Cleveland (2006): “Understanding why the prices of commodities, like copper, increase or decrease is one of the many pieces of the puzzle that we as policymakers try to fit together to help us figure out how the economy and inflation will perform in the future… the elevated inflation numbers concerned me, and indeed they still do.” 3 production. We investigate links between industrial metal returns and economic series and find they have strong predictive ability for both growth, inflation, and unemployment series. Increasing industrial metal prices signal increased growth and inflation and decreased unemployment in both recessions and expansions. The fact that improvements in the economy coincide with increases in the stock market in recessions and decreases in expansions is consistent with Boyd, Hu, and Jagannathan (2005), as we describe in more detail below. This paper contributes to the literature on several levels. First, it is a new predictability study. After concluding that none of the well-studied predictive variables have strong out-of-sample power in the post 1975 period, Goyal and Welch (2008, p. 1504) suggest researchers should “explore more variables and/or more sophisticated models (e.g., through structural shifts….)” We follow these suggestions and document how economically important industrial metal price changes have predictive ability for the stock market.4 Price changes in industrial metals also share the desirable predictor features mentioned by Henkel, Martin, and Nardari (2011, p. 564) in that they are “precisely measured, high-frequency, market traded ex ante quantities as opposed to quarterly, lagged or often-revised government statistics.” Our paper compliments other recent evidence of new return predictors of stock returns. Driesprong, Jacobsen and Maat (2008), Cooper and Priestley (2009), Jones and Tuzel (2012), and Bakshi, Panayotov, and Skoulakis (2014) show oil price changes, the output gap, new orders of durable goods, and the Baltic Dry shipping index respectively all predict stock returns. Second, we show how the same information (e.g. industrial metal price increases) can have a positive impact on stock returns in one economic state and a negative impact in another. 4 In contrast to other commodities, industrial metals seem to be relatively unaffected by confounding factors Energy prices may be influenced by political uncertainty and seasonalities in demand, agricultural commodities tend to be seasonal, and precious metals also serve as safe havens. 4 Pesaran and Timmermann (1995) show that different variables are better at predicting US stock returns at different times due to (p. 1224) “economic regime switches.” More recently, a number of studies find that many predictors tend to give stronger signals in economic recessions than in expansions (e.g., Dangl and Halling, 2012; Henkel, Martin, and Nardari, 2011; Rapach, Strauss, and Zhou, 2012). However, our finding of the same variable having a strong positive relation with stock returns in one state and a strong negative relation in another is, to our knowledge, new. Our work is related to McQueen and Roley (1993) and Boyd, Hu, and Jagannathan (2005), who show that identical macroeconomic announcements can mean different things for the stock market in different economic states.5 Third, we develop a modified version of the simple predictive regression model that can be applied in situations when predictability varies across states. This model is flexible enough to handle a range of alternative ways of specifying states and is particularly useful for conducting out-of-sample tests. Industrial metal changes forecast positive stock returns in one state and negative stock returns in another when we use four different state specifications. The first state specification relies on the usual binary variable for NBER expansions and regressions. In our second specification we replace the NBER variable with a business cycle indicator derived from the Chicago Fed National Activity Index (CFNAI) business cycle data. Recession probabilities from Chauvet and Piger (2008) are the third specification we test. They generate these from applying a regime switching model to industrial production, real manufacturing and trade sales, real personal income excluding transfer payments, and 5 For example, Boyd, Hu, and Jagannathan (2005) show that an increase in unemployment is seen as good news for the stock market in expansions, as it is interpreted as indicating a reduced chance of interest rate increases. However, increasing unemployment in contractions is seen as a negative signal indicating that future profits and dividends are likely to be lower. 5 nonfarm payroll employment. In the final approach we derive recession probabilities from a probit model based on the term spread, default spread, the short rate, and dividend yield. Fourth, we provide evidence regarding the nature of the linkage between industrial metal prices and stock returns. We show 74-86% of information in industrial metals is reflected in equity prices contemporaneously in expansions and 64-69% is reflected contemporaneously in recessions. The remainder gradually diffuses into equity returns over time. This is consistent with Hong and Stein’s (1999) observation that return predictability can result from information being reflected gradually in returns, and Hong, Torous, and Valkanov’s (2007) suggestion that slow-information diffusion can lead to cross-asset return predictability particularly when these assets are important to the economy. We show industrial metal returns predict changes in important economic series including indicators of economic activity, unemployment, and inflation. Increasing industrial metal prices indicate increasing inflation and economic activity in both recessions and expansions. Increasing industrial metal prices also predict decreases in the total return on ten-year Government bonds in both recessions and expansions, which is consistent with the indications of increases in economic series such as inflation. The information from industrial metal returns works its way into stock returns through both the discount rate and cash flow channels. Both channels are consistent with the sign-switching observation of increasing industrial metal prices being good news for equities in recessions and bad news in expansions. We also consider whether there is evidence of investors learning of the predictive ability of industrial metals and trading away some of this predictability over time. Our results do not support this theory. The predictive relation does not change in expansions over time and the evidence is indicative of it strengthening rather than weakening in recessions in more recent times. 6 Fifth, we run a horse race of various asset pricing models to determine whether the linkage between industrial metal prices and stock returns is consistent with one or more of these. The consistency of the positive (negative) industrial metal – stock return relation in recessions (expansions) across ten size, book-to-market equity, momentum, and industry portfolios indicates an economic rather than stock characteristic explanation. We find evidence that the predictive power of industrial metal is consistent with the ICAPM on the basis it passes the three tests of Maio and Santa-Clara (2012). We show that an industrial factor: i) forecasts stock returns, ii) earns a positive and negative risk price in crosssectional tests in different states that are consistent with the positive and negative forecasts for expected aggregate returns, and iii) has estimated relative risk aversion coefficients that are economically plausible. We also check with the predictability of industrial metal returns is consistent with production asset pricing, given the importance of industrial metals in many production processes. We generate a trading rule based on industrial metal price signals. The returns to this rule cannot be explained by either the CAPM or the Fama and French (1993) three-factor model. Furthermore, neither the habit formation consumption CAPM of Campbell and Cochrane (2000) nor the production-based asset pricing model of Cochrane (1991) fully explains the returns to industrial metal signals. However, we cannot reject the null hypothesis that either the habit formation consumption CAPM or the production-based asset pricing model contains no information. We therefore conclude that predictability of industrial metal returns is partially but not fully consistent with both models. Our results are consistent and robust. Not only do we find similar results across estimation methods and business cycle measures but also across countries. Industrial metal returns predict international equity market returns as well, even if we rely on the US business cycle. 7 Again, there is a negative relation in expansions and a positive relation in recessions in the ten countries we consider and the average out-of-sample R2 is 4.3%. Our results are also robust if we focus on results for the two most economically important industrial metals - copper and aluminum - individually. Last but not least, our results are robust to the inclusion of variables known to predict stock markets like the dividend yield, the interest rate, the term spread and the default spread. 2. Data and Method 2.1. Data We use the S&P GSCI Industrial Metals Index and the two industrial metals (aluminum, copper) that are the most important economically. S&P GSCI determines the most important commodities in the global economy and weights them accordingly. Copper has the highest weighting of the industrial metals, followed by aluminum. These two metals dominate the other industrial metals (nickel, zinc, and lead) in terms of economic performance. For instance, in 2013, the weight of copper in the S&P GSCI index is over 5 times, 6 times, and 8 times that of nickel, zinc, and lead respectively.6 We obtain the Standard and Poor’s Goldman Sachs aluminum, copper, and industrial metals price series from Thomson Reuters Datastream. These series commence in 1991, 1977 respectively. We also test the S&P GSCI Industrial Metals Index, which begins in 1977. The endpoint for our analysis is June 30, 2013. We focus on futures data because these are more 6 http://www.reuters.com/article/2012/11/05/commodity-index-gsci-idAFL1E8M5EWD20121105 8 liquid and receive more attention in the media.78 For the US, we use the S&P 500 price index, while the international equity market series are MSCI country indices. These series are from Thomson Reuters Datastream and are in local currency. The risk-free rates from each country are also sourced from Thomson Reuters Datastream. Summary statistics are provided in Appendix 1. We also obtain data for ten size, book-to-market, momentum, and industry portfolios from Ken French’s website. We use the four macroeconomic return predictors studied by Henkel, Martin, and Nardari (2011) and many others – term spread, default spread, dividend yield, and the short rate – as control variables and also to determine the state of the business cycle. The Dividend Yield is the difference between the S&P 500 total return and price indices from CRSP. The Short Rate is the yield on 90-Day Treasury Bills. The Term Spread is the difference between the yield on 10-Year Government Bonds and the 90-Day Treasury Bills. The Default Spread is the difference between Moody’s BAA Corporate Bond yield and Moody’s AAA Corporate Bond yield. These data are all obtained from FRED. We use the Chicago Fed National Activity Index (CFNAI) as a proxy for the business cycle.9 In the state switching model we introduce, we follow the Chicago Fed and define a period as a contraction period when the CFNAI-MA3 is less than -0.7, and as an expansion period when 7 Tang and Xiong (2012) show that index investment has led to the financialization of commodity futures prices in recent years. However, any movements in industrial metal prices that are related to index trading rather than the underlying fundamentals introduces noise which makes it more difficult to arrive at the result we do. 8 Fama and French (1989) show that spot – futures relation can vary over the business cycle. 9 http://www.chicagofed.org/webpages/publications/cfnai 9 the CFNAI-MA3 is greater than -0.7. The Chicago Fed has found that this definition best aligns with the NBER business cycle, which is identified only in retrospect.10 Chauvet and Piger (2008) generate recession probabilities using a regime switching model. We use these probabilities, which are based on industrial production, real manufacturing and trade sales, real personal income excluding transfer payments, and nonfarm payroll employment, as an alternative proxy for the state of the economy.11 We take the Official US business cycle expansions and recessions from the National Bureau of Economic Research (NBER).12 2.2. Method The state-switching return predictability regression specification is given as follows: , (1) , where is the return on the equity market in month t; metal in month t-1, and , is the return on the industrial is a vector containing the four macroeconomic variables used by Henkel, Martin, and Nardari (2011). This model provides flexibility in terms of how the and variables are defined. We test four alternatives. The first 10 http://www.chicagofed.org/digital_assets/publications/cfnai/background/cfnai_background.pdf 11 We thank Chauvet and Piger (2008) for making these data available: http://research.stlouisfed.org/fred2/data/RECPROUSM156N.txt 12 http://www.nber.org/cycles.html 10 involves setting as a dummy variable that equals 1 if the economy is expanding and zero if it is contracting; and as a dummy that equals 1 if the economy is contracting and zero if it is expanding. Each month is designated as either contractionary or expansionary based on the determination of the NBER business cycle dating committee. The second alternative is identical except that we use the CFNAI index to generate dummy variables for expansions and recessions based on the approach described in Section 2.1. The third approach uses the recession probabilities generated by Chauvet and Piger (2008) based on four economic series and a regime switching model. recession probability in a given month while is set to equal the is 1 minus the recession probability. In the final approach we generate recession probabilities based on the four macroeconomic variables of Henkel, Martin, and Nardari (2011) (term spread, default spread, dividend yield, and the short rate). Many early papers document the relationship between these variables and the real economy.13 The probabilities are then inputted into the state switching model in a similar manner as described for the Chauvet and Piger (2008) probabilities. We incorporate the four macroeconomic variables from Henkel, Martin, and Nardari (2011) as control variables in each setting. Note that econometrically, the simple state switching model nests the standard regression model used widely in the predictability literature. In Appendix 2 we discuss their relations in terms of model misspecification and hypothesis testing. The two models are nested when the slope coefficients of the predicted variables are equal, which includes the null hypothesis of 13 See, for example, Fama and French (1989b) for discussion on the term spread, default spread, dividend yield and Fama and Schwert (1977) for discussion on the short rate. 11 no predictability. If the state-switching return predictability model is correct, then the traditional return predictability model is misspecified in a way similar to an omitted variables problem. However, if the standard return predictability model is correct, the state-switching model still provides consistent but less efficient estimates.14 3. Predictability Results 3.1.State-Switching Model Table 1 contains results for the simple state-switching model based on four alternative specifications of the business cycle states. These are the NBER business cycle, the CFNAI series, macroeconomic variables from Henkel, Martin, and Nardari (2011), and recession probabilities from Chauvet and Piger (2008). The results are consistent across the four business cycle specifications. The industrial metals coefficient is consistently negative in expansions and consistently positive in recessions. These coefficients are statistically significant based on Newey West standard errors. A one standard deviation increase in the industrial metal index results in an average stock market decline of 0.50% in expansions and an average increase of 1.40% in recessions, based on NBER states. Moreover, both the recession and expansion coefficients are larger when the states are specified according to the CFNAI, macroeconomic variables, and Chauvet and Piger (2008) probabilities. The stock market decreases by 0.94% and increases by 4.40% following a one standard deviation 14 A priori, there is no reason why the constant could not vary across states as well. In that case, a better specification might be to separate out expansion effects and contraction effects for the constant as well. However, when we test this possibility, we find no significant difference for the constant in our example. If anything, allowing the constant to vary across states only seems to strengthen our findings with respect to industrial metals. 12 increase in industrial metal returns when states are determined based on macroeconomic variables. None of the four macroeconomic control variables show consistent evidence of predictive ability for stock returns in the period we consider. [Please insert Table 1 here] Appendices 3 and 4 contain state-switching model results for aluminum and copper respectively. Both aluminum and copper generate similar results to the industrial metals index. There is a negative statistically significant relation between aluminum or copper returns one month and stock returns the following month in expansions. This holds regardless of whether the business cycle is defined based on NBER, CFNAI, macroeconomic variables, or Chauvet and Piger (2008) probabilities. Moreover, there is a positive statistically significant relation between aluminum or copper returns and the following month’s stock market returns in recessions. This also holds regardless of how the business cycle is measured. The aluminum results, which relate to the shorter (1991 – 2013) period, generally have larger coefficients (in absolute terms) than their industrial metal index equivalents whereas the copper coefficients are generally smaller. 3.2. Out-of-Sample Results The importance of out-of-sample tests for return predictability studies is well accepted. Goyal and Welch (2008, 1456) note “the OOS performance is not only a useful model diagnostic for the IS regressions but also interesting in itself for an investor who had sought to use these models for market-timing.” We compute the out-of-sample R2 used by Campbell and Thompson (2008) and Goyal and Welch (2008) among others. This is specified as: 13 ∑ 1 ∑ (2) or 1 where , and (3) are the fitted values from the state-switching predictive regression and the average historical return (both estimated for period t-1), respectively. denotes the reduction (in percentage terms) in the forecasting error of the state-switching return prediction model relative to the historical mean model. and are the mean square predicted errors of the state-switching and historical mean models. Furthermore, we follow Rapach Strauss, and Zhou (2012) and Clark and West (2007) and calculate changes in mean squared predicted error ( - ). As per Clark and McCracken (2001), we use an encompassing test to examine whether the historical mean forecast has predictive power or encompasses the state-switching model forecast. The encompassing statistic is computed as follows: where ∑ (4) ( ) is the forecast error from historical mean (state-switching) model. We measure the economic significance of state-switching model by investing in the market (risk free asset) if the predicted stock return is greater (less) than the risk free return. We then calculate the certainty equivalent return or the performance fee ( as per Fleming, Kirby and 14 Ostdiek (2001) by equating average utilities from the model strategy and those from the buy and hold return. (5) where and respectively; average utility: are the return from the state-switching and buy and hold models is the estimated performance fee of the state-switching model; is the . We use a coefficient absolute risk aversion, , of 3. If out-of-sample results are based on information that an investor did not have available to them at the time then the findings can be subject to hindsight bias. As noted in Section 2, a CFNAI-MA3 reading above (below) -0.7 indicates an expansionary (recessionary) period. This threshold was determined by back-testing, and the CFNAI data series was back filled in historical periods, so, to ensure hindsight bias is not driving the results, the CFNAI out-ofsample tests in this section use only data that have been available to investors in real-time and that investors knew of the -0.7 threshold at this time. The first release of the CFNAI was in March 2001; this release makes mention of the -0.7 recession threshold. The March 2001 announcement related to the state of the economy in January 2001. Our out-of-sample tests therefore start with a prediction of the April 2001 equity market return. For each month, we regress the S&P 500 return for month t-1 on the industrial metals return for month t-2 to generate a beta coefficient. This coefficient, together with the state of the economy at t-1 and the industrial metals return at t-1 are then used to make a forecast for the S&P 500 return in month t. If this forecast is greater than the risk-free 15 rate in month t-1, a long S&P 500 position is established. If the forecast is lower, we assume the investment is in the risk-free asset. In the example above where the April 2001 S&P return is predicted, we need to use the known state of the economy at the end of March 2001. The real-time information available at this point is the January CFNAI (released on March 5). Some other 2001 and 2002 monthly results were released with a two-month lag, but from June 2002 onward, all monthly results were released at the end of the following month.15 This means that to predict, for instance, the July 2002 S&P return as at the end of June, the May CFNAI result and the June industrial metals return are used. We also generate results using the CFNAI series that is revised through time. This allows a comparison to be made with the real time results and for analysis to be completed over a longer period including when the CFNAI real time series was not available. Neither NBER nor Chauvet and Piger (2008) data are available in real time so these cannot be used in this section to define recessions and expansions. However, investors can observe financial variables that indicate the state of economy on a real-time basis. These variables are the term spread, the default spread, the dividend yield and the short-term interest rate. We lag by two years each of these four variables as explanatory variables in the probit model with the NBER recession dummy as dependent variable to estimate the probability of recessions.16 We apply these to the same 2001 – 2013 time period as for the CFNAI and also to the 1994 – 2013 period, which is simply half our total sample period. 15 All announcements and release dates are available at: http://www.chicagofed.org/webpages/publications/publications_listing.cfm 16 NBER announces the state of economy with delay. The longest delay is 21 months for the November 2001 trough, announced on July 17, 2003. Using two-year lag in the probit model conservatively ensures no lookahead bias. 16 The Table 2 results indicate strong out-of-sample predictive power. When the real-time CFNAI (macroeconomic variables) are used as a proxy for the business cycle the is 7.11% (2.64%) for the 2001 – 2013 period, while the non-real-time CFNAI generates an even larger of 8.83%. The remains at a similar level when the longer period of 1994 – 2013 is used. It is 2.96% based on the macroeconomic variables and 6.94% when the CFNAI is used to define the business cycle. These are highly statistically significant. We first determine statistical significance based on bootstrapped critical values of the following the approach adopted by Goyal and Welch (2008). As they note, this is based on the work of Mark (1995) and Kilian (1999). The are statistically significant at the 1% level. The MSPE Difference is negative in each instance, indicating a lower prediction error when industrial metals are used for forecasts rather than the historical mean. The MSPE-adjusted test, which was developed by Clark and West (2007), is based on the null hypothesis that the forecast based on industrial metal returns is the same as that generated by the historical mean. This null hypothesis can be rejected in all of the three scenarios. The historical mean forecast is a nested model within the state-switching model. Clark and McCracken (2001) develop an encompassing test for one-step ahead forecasts from nested linear models. The encompassing test determines whether a historical mean contains all useful forecast information including the forecast information from the state-switching model. Our results reject all encompassing hypotheses so the state-switching model contains incremental useful forecast information. We compute an annualized certainty equivalent return, which measures economic importance of forecasting stock returns based on industrial returns in the state-switching model. Based on a simple strategy that invests in a stock market (risk free asset) if the forecasted stock return is above (below) the risk free rate, we find a state- 17 switching model commands a performance fee from 1.78% to 4.09% per annum relative to a naïve buy and hold strategy. [Please insert Table 2 here] The Appendix 5 results show there is strong out-of-sample performance and economic significance when either aluminum or copper returns are used as the predicative variable. The for the 2001 – 2010 period based on the CFNAI business cycle is 5.27% for aluminum and 7.96% for copper. As with the industrial metal index results, all MSPE differences are negative for the aluminum and copper specifications and the MSPE adjusted p-value is statistically significant. This indicates that the null hypothesis that the forecast returns based on aluminum and copper are the same as those using the historical mean model can be rejected. 4. Explanations for Predictability The results we present in Section 3 indicate that increases in industrial metal prices forecast increases in stock prices in contractions and decreases in stock prices in expansions. This result holds both in and out of sample. In this section, we investigate the mechanism(s) in which information from industrial metal returns works its way into stock returns and whether the predictive relation we document is consistent with any existing asset pricing models. In terms of the mechanisms, we ask: 1) whether industrial metal returns contain information about the economy, 2) if industrial metal information gradually diffuses into stock returns, 3) 18 whether industrial metal returns predict variations in cash flows or discount rates or both, and 4) whether the predictability declines over time on account of investors becoming aware of it. We then check whether industrial metal predictability is consistent with prominent asset pricing models. We ask whether: 1) an industrial metals factor model is consistent with the Intertemporal CAPM (ICAPM) with industrial metals being a state variable, 2) given the importance of industrial metals to the production process, if the predictability of industrial metal returns is consistent with production asset pricing, and 3) whether the Consumption CAPM can explain the predictability. 4.1. Predictability Mechanisms 4.1.1. Economic Linkages We now turn our attention to the question of whether price changes in industrial metals predict economic variables. The idea that industrial metals price changes may provide important information about the economy is widely documented in the financial press. For instance: … copper has a PhD in economics. Because copper is used in everything from electrical wiring to water pipes, it is seen as a good measure of the economy. If demand for copper falls, then it’s believed the economy is slowing.17 Empirical studies, such as Garner (1989) show that movements in commodity prices lead CPI inflation, while Awokuse and Yang (2003) find the CRB commodity price index can be used to predict industrial production. We add to this literature by investigating whether movements 17 http://www.whocrashedtheeconomy.com/?p=34 19 in the industrial metals index predict a range of growth and inflation series using the regression: where is the change in the economic series in month t. The growth and employment economic series include the: Industrial Production Index, Capacity Utilization (Total Industry), Manufacturers’ New Orders of Durable Goods, ISM Manufacturing (PMI Composite Index), and the inverse of the Civilian Unemployment Rate. The inflation series include the: Consumer Price Index, Personal Consumption Expenditures, and the Producer Price Index. All series are sourced from the Federal Reserve Bank of St. Louis, with the exception of Producer Price Index (PPI), which we obtain from the Bureau of Labor Statistics. The overall growth / employment and inflation economic series are an equal-weighted average of their components. The Table 3 results indicate that increases in industrial metal prices in a given month are followed by, on average, increases in growth and employment and inflation in the following month. This relation is evident in both expansions and recessions but is more pronounced in recessions. The coefficients are 4-5 times larger and the statistical significance is stronger. Taken together, the Table 3 results indicate that an answer to Chairman Bernanke’s (2008) question: “….what signal should we take from recent changes in commodity prices about the strength of global demand or about expectations of future growth and inflation?” is that industrial metal returns contain important information for growth and inflation. [Please insert Table 3 here] The Table 1 and Table 3 results are consistent with the results of economic announcements and stock returns literature. McQueen and Roley (1993) show economic announcement signaling higher economic activity have a negative effect on the stock market when the 20 economy is strong but not when it is weak, while Boyd, Hu, and Jagannathan (2005) show the stock markets rises when there are announcements of an increase in unemployment in expansions but the same announcements result in stock market declines in contractions. In expansions, increased unemployment or decreases in employment appear to suggest there is less chance of interest rate increases while increased employment in contractions indicate that growth is picking up and both of these are positive for the stock market. 4.1.2. Gradual Information Diffusion Hong, Torous, and Valkanov (2007) suggest that slow-information diffusion can lead to cross-asset return predictability particularly when these assets are important to the economy. Consistent with this, Driesprong, Jacobsen and Maat (2008) show how oil price changes predict future stock market returns world-wide and their evidence supports gradual information diffusion as the underlying cause. Just like oil, industrial metals are important inputs in the economy even though, as US Federal Reserve Chairman Bernanke (2008) observed18, it is not always clear what pointer should be taken from price movements in important commodities such as these. We investigate if there is evidence of information from industrial metal returns diffusing into the stock market using the specification of Rapach, Strauss, and Zhou (2013) as follows: & & , & , & , (6a) & , & , & , & , (6b) 18 Chairman Bernanke (2008) asked: “….what signal should we take from recent changes in commodity prices about the strength of global demand or about expectations of future growth and inflation?” 21 , , , (7a) , , (7b) , Equations 9 and 10 are the expected return components for the S&P 500 and industrial metals respectively. As per Rapach, Strauss, and Zhou (2013), the expected return on the S&P 500 is generated, based on the T-bill and dividend yield on the S&P 500. We assume industrial metal returns are related to the return on the T-bill and the return on mining sector stocks.19 & & , , 1 , & , (8) Where: & , is the S&P return shock at time t+1 is a diffusion parameter measuring the proportion of the impact of industrial metal return shock contemporaneously incorporated into S&P return. is total impact of industrial metal return shock on S&P. The coefficient of IM in Equation 8 shows the larger the industrial metal return impact on the S&P 500, represented by , the stronger the predictability relation. Further, greater information frictions, represented by a smaller , results in stronger predictive power for industrial metal returns. 19 These data are sourced from Ken French’s website. 22 The null hypotheses of no information diffusion therefore are: : 0, (9a) 1 (9b) We reject the first null hypothesis if industrial metal return shocks affect S&P returns ( 0 . As Rapach, Strauss, and Zhou (2013) note, if the predictor variable (in our case industrial metal) returns are irrelevant for stock returns then lagged industrial metal returns will not predict stock returns. Rejecting the second null hypothesis ( 1 ) indicates that not all information from industrial metal returns is reflected in stock returns contemporaneously. We estimate the model in equation 10 as follows: Let Ω be a vector of 8 parameters: Ω , , & , , & , , , & , , , , , (10) , We use a two-step GMM process to estimate Ω using 9 moment conditions as follows. , 0, & , , , & , 0, , (11) 0, 0, & , 0, , (12) 0, & , 0, , & , & , 0 & , 0, (13) (14) 23 We investigate whether there is evidence of gradual information diffusion in expansions and contractions separately. The estimate in expansions is 0.74 and 0.86 for the NBER and CFNAI business cycle respectively. The equivalent estimates in recessions are 0.64 (NBER) and 0.69 (CFNAI). These suggest 74-86% of information in industrial metal prices is reflected in equity prices contemporaneously in expansions and 64-69% is reflected contemporaneously in recessions. By way of comparison, Rapach, Strauss, and Zhou (2013) find an average of 0.86 in their analysis. This suggests information from industrial metal returns diffuses into stock returns more slowly than information from U.S. stock returns diffuses into international stock returns. The gradual information diffusion model findings, that equity prices appear to be more predictable with the previous month’s industrial metal price movements is recessions is consistent with Table 1. The estimates, which quantify the economic impact for stock returns of industrial metal returns, are also consistent with the Table 1 results. The relation between industrial metal returns and stock returns in negative in expansions and positive in contractions and the relation is stronger in recessions. In Panels C and D, we test the null hypotheses in equations 9a and 9b. The result indicate that these can be rejected, both individually and jointly, in expansions and recessions based on NBER business cycles. Five of the six CFNAI business cycle results are equivalent. The exception is the null hypothesis that information is not incorporated contemporaneously in expansions, which cannot be rejected. [Please insert Table 4 here] 24 4.1.3. Bond Returns Predictability, and Cash Flows Versus Discount Rates We test the ability of the state-switching industrial metal predictability model to predict tenyear Government bond total returns and present the results in Table 5. These indicate increases (decreases) in industrial metal returns signal decreases (increases) in industrial metal returns in both recessions and expansions. This is consistent with the Table 3 economic series predictability. Increasing industrial metal prices indicate increasing inflation in both states and this is associated with decreasing bond returns. In Table 5 Panel B, we consider whether the equity predictability flows through a discount rate or cash flow channel or both. Following Campbell (1991), we relate the period t+1 unexpected stock return ( growth ( to changes in expectations of future stock returns and dividend . ∑ ∆ ∑ (15) As Campbell (1991) notes, a negative unexpected stock return suggests either expected future dividend growth must be lower or expected future stock returns must be higher, or both. The discounting at rate, , accounts for the fact that near-term expected stock return increases result in larger declines in today’s stock price than expected stock return increases in the more distant future. We can re-write this equation as: , , , (16) 25 Where is the unexpected component of stock return , about cash flows, and , , and , represents news represents news about future returns. Following Campbell (1991), we define a k element vector . One element is the stock return and the other elements are known by the end of period t+1. We also assume the vector follows a first-order VAR as below: (17) The VAR generates forecasts of expected returns: (18) Now the discounted sum of revisions in forecast returns can be written: , ∑ ≡ ∑ (19a) ∑ (19b) (19c) This is the discount rate channel. Where is defined to equal (p. 164). Now , , = , “a nonlinear function of the VAR coefficients” and , , , , therefore: (20) 26 This is the cash flow channel. As Campbell (1991, p. 164) points out, “these expressions can be used to decompose the variance of unexpected stock return, return, , , , into the variance of news of the unexpected stock , the variance of news about expected returns, , , and a covariance term.” According to the discounted cash flow model, increases in cash flow have a positive impact on stock prices, whereas increases in the discount rate have a negative impact on stock prices. The results in Table 5 show industrial metal returns predict equity returns through both cash flow and discount rate channels. Moreover, both channels show a sign switching relation where increasing industrial metal prices is good news for equities in recessions and bad news for equities in expansions. A negative impact on stock returns in expansions via the discount rate channel implies industrial metal price increases cause the discount rate to increase in expansions. We know from the Table 3 and 5 Panel A results, that increases in industrial metal returns forecast increases in inflation and ten-year Government bond yields (i.e. decreases in bond returns) in both expansions and recessions. The discount rate increase in expansions is therefore consistent with these driving up the nominal risk-free rate and the return investors require. A positive relation between industrial metal and stock returns in recessions via the discount rate channel implies the discount rate declines following industrial metal price increases in recessions. We know from Table 5 Panel A, that the risk-free rate increases, on average, following industrial metal price increases (i.e. bond returns decline), so a discount rate decline would require a reduction in investors’ perception of risk and the additional return (over and 27 above the risk-free rate) they require upon observing increasing industrial metal prices in recessions. This is consistent with the following observation by Mandaro (2009): “…some analysts saw encouraging signs in the rise in copper since the start of the year. Its past correlation with industrial demand supported hopes that the economy had started to make small steps towards recovery and healthy inflation—rather than sliding into a protracted, severe period of falling prices and shrinking output.” A positive impact on stock returns in recessions via the cash flow channel implies that industrial metal price increases cause cash flows to increase in recessions. The recession cash flow increase is consistent with the equity market reacting positively to the indication from industrial metals of an end to shrinking output as indicated by Mandaro (2009). A negative relation between stock and industrial metal returns through the cash flow channel in expansions suggests increasing industrial metal prices lead to cash flow declines. This is consistent with increasing commodity prices putting pressure on corporate profit margins in expansions. One example of this is provided in commentary by Kelleher and Zieminski (2011) that followed the quarterly earnings release of a number of U.S. manufacturers. They state: “Copper, which is used in cables, wires and all kinds of electrical products as well as in plumbing and heating applications, has risen the most, jumping more than 15 percent over the past three months. Those increases are putting pressure on the margins of many manufacturers, who cannot always simply raise the price of their finished goods.”20 20 Another example is Forsyth (2011) “rising commodity prices….are also beginning to be felt…as shrinking profit margins…” 28 [Please insert Table 5 here] 4.1.4. Learning We now examine whether there is evidence of investors gradually learning of the predictive ability of industrial metal returns for stock returns over time. Goyal and Welch (2008) document a decline in the performance of the dividend price ratio predictor through time, while McLean and Pontiff (2014) document the decline in predictive ability of a number of variables, which they relate to academic publication of return predictors. While we are not aware of any academic studies pre-dating this one that document the relation between industrial metals and stock returns, the influence of commodity prices on economy has been known for some time as a result of Garner (1989) and others, and the phrase “copper has a PhD in economics” has become increasingly prominent in recent times. Following Bakshi, Panayotov, and Skoulakis (2014), we investigate whether there is evidence of learning using the following equation: & (21) The trend is demeaned variable calculated from an observation number series. There would be evidence of learning if is positive and statistically significant or is negative and statistically significant. This would indicate the negative relation between industrial metals and stock return in expansions has weakened over time or the positive relation between industrial metals and stock return in contractions has weakened over time. 29 [Please insert Table 6 here] The Table 6 results indicate there is no evidence to support learning. The trend coefficient is not statistically different to zero in expansions and the trend coefficient in recessions is positive rather than negative. This suggests positive predictive power of industrial metals in recessions has strengthened over time, 4.2. Asset Pricing Models 4.2.1. ICAPM Another possibility is that an Industrial Metals factor model is a variant of the Intertemporal Capital Asset Pricing Model (ICAPM). Maio and Santa-Clara (2012) suggest there are three main conditions a factor model must meet in order to be consistent with the ICAPM. First, ICAPM candidate variables must forecast the first or second moments of aggregate stock returns. Second, a state variable that generates positive (negative) forecasts for expected aggregate returns should earn a positive (negative) risk price in cross-sectional tests. Third, the estimated relative risk aversion coefficients must be economically plausible. Maio and Santa-Clara (2012) find the Fama and French (1993) and Carhart (1997) models are the best at consistently meeting these ICAPM restrictions. Other models such as Pastor and Stambaugh’s (2003) do not. Following Merton (1973), the ICAPM equation is: E(Ri,t-Rf,t) = Cov(Ri,t - Rf,t,Rm,t - Rf,t) + z Cov(Ri,t - Rf,t,Zt) (22) 30 This equation suggests there are two sources of risk premium. The first is the market risk premium as per the CAPM. An average risk averse investor is assumed to only hold an asset if it offers a premium over the risk free rate, measures average relative risk aversion. The second risk premium component is intertemporal risk. An asset earns an intertemporal risk premium if it covaries positively with the changes in the state variable and therefore positively covaries with the future market expected return. Such an asset fails to hedge against future negative shocks against aggregate wealth and offers low returns when future aggregate wealth is expected to be low. We use z to denote the covariance risk price associated with the state variable Zt and Zt is the innovation or change in the state variable. The earlier results indicate the first Maio and Santa-Clara (2012) condition is satisfied. There is strong evidence that movements in industrial metal prices lead movements in equity prices. In order to determine whether their second and third conditions are met, we estimate the coefficient of risk aversion when the industrial metal price change is a state variable in the ICAPM using the GMM with the following moment conditions. 1 , , , , , , , , =0 , , (23) Where: Zt is industrial metal return, which is the state variable of interest. 31 We use 25 size and book-to-market sorted portfolios to estimate the coefficients of risk aversion and the intertemporal risk premium z via GMM with the Newey-West HAC robust t-statistics. The Table 7 results show that industrial metals is a state variable because it earns a significantly (negative) positive risk price in cross-sectional tests in (expansions) recessions. The negative z coefficient in expansion suggests a negative price risk with respect to a positive innovation in industrial metal return. On the other hand, the risk premium is generally negative during recession (see Appendix 1) so the covariance of risk premium and a positive industrial metal return innovation is negative. Given the negative z coefficient, industrial metals state variable earns positive risk price in recessions. The magnitude of estimated coefficients of risk aversion for the industrial metal price change state variable are economically reasonable. These range from 4.5 to 11.3 in expansions and from -12.2 to -2.6 in recessions. [Please insert Table 7 here] As a further test of whether the sign-switching predictive ability of industrial metal returns for stocks returns is related to an economy- or market-wide phenomenon, then sign-switching return predictability should apply across a range of portfolios. If, on the other hand, the signswitching return predictability is limited to a subset of portfolios, say growth and winner stocks, it would suggest a characteristic rather than an economic explanation prevails. The Appendix 6 results, which are based on ten size, book-to-market equity, momentum, and industry portfolios from Ken French’s website, show the sign-switching result is pervasive 32 across the vast majority of portfolios. The expansion coefficient is statistically significantly lower than the recession coefficient in all portfolios. The recession coefficient is positive and statistically significant in all portfolios while the expansion coefficient is negative and statistically significant in all but three of the portfolios. One of these is the smallest stock portfolio. As Kelly and Pruitt (2013) note, it is not surprising that this portfolio deviates from a model that explains stock returns (in our case, the sign switching model) given mispricing in small stocks are the most difficult to arbitrage away. 4.2.2. Consumption Asset Pricing The framework we use to test whether the results are consistent with either Consumption or Production Asset Pricing involves first creating a trading rule that uses information from industrial metal returns and economic states to time the market across various portfolios. The strategy involves going long the portfolio if the industrial metal return is negative during expansions or positive during recessions and investing in the risk free asset if the industrial metal return is positive during expansion or negative during recessions. We then determine if the trading rule’s Jensen and Fama and French (1993) three factor alphas are statistically significant. The Table 8 results the industrial metal trading rule consistently out-performs a buy-and-hold strategy in risk-adjusted terms. These results are based on 25 size and book-to-market portfolios, ten size, ten book-to-market, ten momentum, and ten industry portfolios. All 65 portfolios have larger Sharpe Ratios for the industrial metal trading rule than a buy-and-hold approach. The CAPM alphas average 0.36% per month and the Fama and French (1993) alphas average 0.33% per month. 56 and 54 of the CAPM and Fama and French alphas (out 33 of 65) are statistically significant at the 10% level. In sum, neither the CAPM or Fama and French three-factor model explain the returns to the industrial metal trading rule [Please insert Table 8 here] We follow habit-formation consumption CAPM specification of Campbell and Cochrane (1999) and Campbell and Cochrane (2000). Consumption growth is defined as follows: ∆ ; ~. . . 0, ) (24) Agents are assumed to be identical and to maximize the habit utility function: ∑ (25) Where is consumption, is the level of habit, and is the discount factor. The surplus consumption ratio is: (26) The log surplus consumption ratio is: 1 ̅ (27) 34 The sensitivity function which controls the sensitivity of contemporaneous consumption 1 2 and habit to is: 1, (28a) 0 where: ̅≡ , ≡ ̅ (28b) 1 ̅ (28c) Habit is assumed to be predetermined at the steady state ̅ and external. The log marginal rate of substitution is: ln ∆ ∆ (29) Following Campbell and Cochrane (2000), the assumed parameters are as follows: the subjective discount factor is 0.89, and the steady surplus consumption ratio ̅ is 0.057. [Please insert Table 9 here] Table 9 shows the results of the habit formation consumption CAPM in explaining the returns to trading rules based on industrial metals for 25 size and book to market sorted portfolios. The model test statistics are highly significant, which suggests that the strategy returns based 35 on industrial metal strategy is not fully explained by the habit formation consumption CAPM. Nevertheless, the risk aversion coefficient is significantly positive with reasonable magnitude, suggesting that the habit formation consumption is an important factor in the marginal of substitution and the habit consumption model offers a partial explanation. This result still holds when we include the market return as an additional factor in the marginal rate of substitution. We therefore conclude the consumption CAPM partially explains the industrial metal trading rule returns. 4.2.3. Production Asset Pricing Another possible explanation for the predictive ability of industrial metal returns for stock returns is production asset pricing. After all, industrial metals are important inputs in the production process. In production asset pricing, the expected asset return is related to its covariance with macro-economic factors. It is assumed that investors are comfortable with lower expected returns from a low risk asset because such an asset performs relatively well compared to other assets during the economic downturn. Alternatively, investors require a larger expected return from an asset that performs poorly in downturns. Cochrane (1991) shows there is an identity between consumption and the production based asset pricing and suggests that one can study macro-economic risk by examining a firm’s investment decisions instead of consumption decisions. Further, the production based asset pricing is more robust to the measurement error and frictions than the consumption based asset pricing model. We then investigate whether an investment factor can explain the trading rule returns. Following Cochrane (1996), we first estimate the investment return as follows: 36 1 (30) Where: i is an investment, and following Cochrane (1991) δ=0.05,andη 3. Mpk is the parameter to be estimated in the GMM, where i/k is investment to capital. We only observe i. We use private fixed investment residential and non-residential from the Bureau of Economic Analysis. We compute the investment to capital ratio, i/k, by cumulating the capital according to the equation below: 1 (31) where the steady-state investment to capital ratio is: / 1 1 (32) The moment condition is: 1 (37) Where: m is the stochastic discount factor is the portfolio returns from using industrial metals and the economic state to trade 37 (33) Where: and are resident and non-resident investment returns computed from the investment to capital ratio outlined above. [Please insert Table 10 here] In Table 10, we document results from the GMM estimation using the industrial metal trading rule returns on the investment factors. Both investment factors have a negative coefficient, but only the resident investment return is statistically significant. The negative coefficient is consistent with Cochrane (1991). We conduct a model test using J-statistics and the results indicate we can reject the null hypothesis that the investment based model explains the returns to the industrial metal trading rule. This suggests the investment model cannot explain all the cross-sectional variation. The null hypothesis that an investment factor and CAPM combined model can explain the trading rule returns is also rejected. While the model tests suggest that the marginal rate of substitution based on investment factors do not explain the trading rule, we perform further analysis to examine whether investment factors and the market returns are irrelevant in determining the pricing kernel. The results reject the null hypothesis that the investment factors and the CAPM factors contain no information. This implies that the production based asset pricing that uses investment factors as a marginal rate of substation can partially explain the industrial metal trading rule. 38 5. International Results In Tables 11 and 12, we present results for the ten international countries considered by Rapach, Strauss, and Zhou (2012). The Table 12 out-of-sample results require estimates of the business cycle in real time. We are not aware of such data for each international country so we use the real-time CFNAI US business cycle data as a proxy for the business cycles in each country. To the extent that that these data do not match the local business cycle, noise will be introduced which will make it more difficult to find a result of predictive power for equity market returns from industrial metal returns. The Table 11 results, which relate to the 1977 – 2013 period, indicate that industrial metal price increases are, on average, associated with price decreases the following month in expansions and price increases the following month in expansions. Given the added noise in these individual country estimations, we first consider a pooled overall result based on a panel regression. Pooling all our data we find a strong significant effect with the same sign as the US for both expansions and recessions. At the individual level, while more noisy, the expansion relation is negative in all ten countries and still statistically significant in three. The recession relation is positive in each individual country and is statistically significant in all but Japan. In all ten individual countries the difference between the two state estimates is statistically significant. [Please insert Table 11 here] The out-of-sample performance and economic significance of a trading rule based on industrial metal returns is presented in Table 12. These results are equivalent to those in the 39 first column of Table 2 for the US in that the CFNAI is used to measure the business cycle and the out-of-sample period is 2001 – 2013. The average is 4.30%. The strongest performances are in Switzerland (9.06%) and Canada (5.87%) while the weakest performances are in Italy (1.89%) and Japan (1.97%). The are highly statistically significant in each country on the bootstrap p-value and the MSPE test indicates the null hypothesis of industrial metal predictive ability that is no better than the historical mean can also be rejected for each country. [Please insert Table 12 here] 4. Conclusions We show that movements in industrial metal prices, such as aluminum and copper, predict stock returns. Increasing industrial metal prices suggest declines in the equity market the following month in expansions and increases in the equity market in recessions. The predictability is strong (out-of-sample R2 ranges from 3% to 8%) and robust. It holds when economic states are specified in alternative ways and exists in international equity markets. This paper makes several additional contributions. First, while researchers have recently documented that some predictors are more effective in recessions than expansions, we are, to our best knowledge, the first to show that increases in the same variable can signal future equity price increases in one state and future equity price declines in another. Second, we propose a modification to the predictive regression model to allow for different predictability in different states. This simple state-switching model is flexible enough to accommodate various specifications of states and is particularly useful for out-of-sample tests. 40 Third, we provide evidence regarding the nature of the linkage between industrial metal prices and stock returns. We show information from industrial metal returns gradually diffuses into stock returns. This occurs in both recessions and expansions but the diffusion is slower in recessions. Increasing industrial metal prices changes predict increased inflation and growth and decreased unemployment in both recessions and expansions. The fact that improvements in the economy are seen as positive news for the equity market in recessions and negative news in expansions is consistent with the findings of several macroeconomic announcement returns studies. The information from industrial metal returns works its way into stock returns through both the discount rate and cash flow channels, and both channels are consistent with the sign-switching result of increasing industrial metal prices being good (bad) news for stock returns in recessions (expansions). Other studies find that predictors lose some or all of their power as investors become more aware of them. We find no evidence of this for industrial metals. Fourth, we run a horse race of various asset price models to ascertain whether the industrial metal – stock return relation is consistent with any of these. Our results are consistent with the ICAPM, and are partially but not fully consistent with the habit formation consumption CAPM and the production-based asset pricing model. 41 References Awokuse., T.O., Yang, J. (2003). The informational role of commodity prices in formulating monetary policy: A reexamination. Economics Letters 79, 219–224 Bakshi, G., Panayotov, G., and Skoulakis, G. 2014. In search of explanation for the predictive ability of the Baltic Dry Index for global stock returns, commodity returns, and global economic activity. Working Paper - University of Maryland. Bernanke, B., 2008. Outstanding issues in the analysis of inflation. Speech at the Federal Reserve Bank of Boston’s 53rd Annual Economic Conference, Chatham, Massachusetts, June 9. Boyd, J. H., Hu, J., Jagannathan, R., 2005. The stock market’s reaction to unemployment news: Why bad news is usually good for stocks. Journal of Finance 60, 649-672. Campbell, J.Y., 1991. A variance decomposition for stock returns. The Economic Journal, 101, 157-179. Campbell, J.Y., Cochrane, J.H. 2000. Explaining the poor performance of consumption-based asset pricing models. Journal of Finance, 55(6), 2863-2878. Campbell, J.Y., Thompson, S.B., 2007. Predicting excess returns out of sample: Can anything beat the historical average. Review of Financial Studies 21, 1509-1531. Carhart, M., 1997. On Persistence in Mutual Fund Performance. Journal of Finance, 52(1), 57-82. Chauvet, M., Piger, J., 2008, A comparison of the real-time performance of business cycle dating methods. Journal of Business and Economic Statistics 26(1), 42-49. Clark, T. E., and McCracken, M. W. 2001. Tests of forecast accuracy and encompassing for nested models. Journal of Econometrics 105, 85–110. Clark, T.E., West, K.D., 2007. Approximately normal tests for equal predictive accuracy in nested models. Journal of Econometrics 138, 291–311. Cochrane, J.H., 1991. Production-based asset pricing and the link between stock returns and economic fluctuations. Journal of Finance, 46(1), 209-237. Cochrane, J.H., 1996. A cross-sectional test of an investment-based asset pricing model. Journal of Political Economy, 104(3), 572-621. Cooper, I., Priestley, R., 2009. Time-varying risk premiums and the output gap. Review of Financial Studies, 22(7), 2801-2833. Dangl, T., Halling, M., 2012. Predictive regressions with time-varying coefficients. Journal of Financial Economics, 106, 157-181. 42 Driesprong, G., Jacobsen, B., Maat, B., 2008. Striking oil: Another puzzle? Journal of Financial Economics 89(2), 307-327. Fama, E.F., French, K.R., 1989a. Business cycles and the behavior of metal prices. Journal of Finance 43(5), 1075-1093. Fama, E.F., French, K.R., 1989b. Business conditions and expected returns on stocks and bonds. Journal of Financial Economics 25, 23-49. Fama, E.F., French, K.R., 1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33, 3–56. Fama, E.F., Schwert, G.W., 1977. Asset returns and inflation. Journal of Financial Economics 5, 115-146. Fleming, J., Kirby, C. and Ostdiek, B., 2001. The Economic Value of Volatility Timing. Journal of Finance 56, 329-352. Forsyth, R.W., 2011. Rising commodities put profits through the wringer. Barrons: http://online.barrons.com/news/articles Garner, C.A., 1989. Commodity prices: Policy target or information variable?: Note Journal of Money, Credit and Banking 21(4), 508-514. Goyal, A., Welch, I., 2008. A comprehensive look at the empirical performance of equity premium prediction. Review of Financial Studies 21, 1455-1508. Henkel, S., Martin, J., Nardari, F., 2011. Time-varying short-horizon predictability. Journal of Financial Economics 99, 560-580. Hong, H., Stein, J., 1999. A unified theory of underreaction, momentum trading, and overreaction in asset markets. Journal of Finance 54, 2143-2148. Hong, H., Torous, W., Valkanov, R., 2007. Do industries lead stock markets? Journal of Financial Economics 83, 367-396. Jones, C., Tuzel, S., 2012. New orders and asset prices. Review of Financial Studies – forthcoming. Kelleher, J., Zieminski, N., 2011. More manufacturers warn of rising input costs. Reuters: http://www.reuters.com/assets/print?aid=USTRE7104YF20110201 Kelly, B., Pruitt, S., 2013. Market expectations in the cross-section of present values Journal of Finance 68(5), 1721-1756. Kilian, L., 1999. Exchange rates and monetary fundamentals: what do we learn from long– horizon regressions? Journal of Applied Econometrics 14(5), 491-510. 43 Maio, P., Santa-Clara, P., 2012. Multifactor models and their consistency with the ICAPM. Journal of Financial Economics 106, 586-613. Mandaro, L., 2009, Dr. Copper gets tested. MarketWatch. http://www.marketwatch.com/story/dr-coppers-forecasting-ability-tested-year Mark, N. C., 1995. Exchange rates and fundamentals: evidence on long–horizon predictability. American Economic Review 85(1), 201-218. Merton, R., 1973. An intertemporal capital asset pricing model. Econometrica, 41, 867-887. McLean, R.D., Pontiff, J., 2014. Does academic research destroy stock predictability? SSRN Working Paper: http://ssrn.com/abstract=2156623 McQueen, G., Roley, V. V., 1993. Stock prices, news, and business conditions. Review of Financial Studies 6, 683-707. Newey, W., West, K.D., 1987. A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, 55(3), 703-708. Pastor, L., Stambaugh, R.F., 2003. Liquidity risk and expected stock returns. Journal of Political Economy, 111, 642-685. Pesaran, M.H., Timmermann, A., 1995. Predictability of stock returns: Robustness and economic significance. Journal of Finance 50(4), 1201-1228. Perez-Quiros, G., Timmermann, A., 2000. Firm size, and cyclical variations and stock returns. Journal of Finance 55(3), 1229-1262. Pianalto, S., 2006. Inflation, inflation expectations, and monetary policy. Copper Development Association Global Market Trends Conference, September 8. Rapach, D., Strauss, J., Zhou, G., 2010. Out-of-sample equity premium prediction: combination forecasts and links to the real economy Review of Financial Studies 23(2), 861862. Rapach, D., Strauss, J., Zhou, G., 2013. International stock return predictability. What is the role of the United States? Journal of Finance 68(4), 1633-1662. Rapach, D., Zhou, G., 2012. Forecasting stock returns. Forthcoming in the Handbook of Economic Forecasting Tang, K., Xiong, W., 2012. Index investment and the financialization of commodities. Financial Analysts Journal 68, 54-74. 44 Table 1. Simple State Switching Model Expansion Recession Difference Panel A1: NBER Without Controls Industrial Metals -0.072 -2.310 0.219 1.731 -0.290 4.953 Panel A2: NBER With Controls Industrial Metals Dividend Yield Short Rate Term Spread Default Spread -0.073 -2.349 0.002 0.949 -0.001 -0.839 -0.001 -0.557 0.007 1.079 0.207 1.687 0.006 0.734 -0.001 -0.312 0.000 -0.034 -0.007 -0.516 -0.280 4.846 -0.004 0.240 0.000 0.000 -0.001 0.014 0.014 1.024 Panel C1: Macroeconomic Variables Without Controls Industrial Metals -0.139 -3.662 0.651 3.453 -0.790 14.540 Panel C2: Macroeconomic Variables With Controls Industrial Metals Dividend Yield Short Rate Term Spread Default Spread -0.133 -3.434 -0.002 -0.887 0.002 1.313 0.001 0.404 0.012 0.763 0.606 2.775 0.047 4.086 -0.016 -3.816 -0.014 -1.296 -0.028 -2.036 -0.739 9.515 -0.049 16.044 0.018 13.243 0.015 1.646 0.040 8.654 Expansion Recession Difference Panel B1: CFNAI Without Controls -0.078 -2.618 0.298 2.824 -0.376 11.816 Panel B2: CFNAI With Controls -0.078 -2.594 0.002 0.914 -0.001 -0.976 -0.001 -0.499 0.004 0.590 0.289 2.942 0.005 0.652 0.000 -0.018 0.002 0.463 -0.009 -0.925 -0.367 12.702 -0.003 0.145 -0.001 0.097 -0.003 0.440 0.013 1.276 Panel D1: Chauvet and Piger (2008) Probabilities Without Controls -0.082 -2.587 0.324 2.184 -0.406 6.726 Panel D2: Chauvet and Piger (2008) Probabilities With Controls -0.083 -2.618 0.001 0.614 -0.001 -0.958 -0.001 -0.477 0.008 1.134 0.299 2.255 0.016 1.342 -0.004 -0.876 -0.006 -0.671 -0.012 -0.819 -0.382 7.401 -0.015 1.423 0.003 0.371 0.005 0.310 0.020 1.690 The S&P GSCI Industrial Metals Index, and S&P 500 data are sourced from Thomson Reuters Datastream. The control variable data are sourced from David Rapach’s website. All analysis is for the period January 1977 – June 2013. The regression specified in equation 5 is run using four 45 different methods to define the states. The expansion and recession columns contain the coefficient for each variable with the Newey West t-statistic underneath. The difference columns contain the difference between expansion and recession coefficients with the Wald statistic underneath. Coefficients and differences that are statistically significant at the 10% level are in bold. 46 Table 2. Out-of-Sample Performance and Economic Significance 2001 - 2013 CFNAI RT Macro Variables OoS R2 Bootstrap OoS R2 p-value Bootstrap 95% Critical OoS R2 MSPE Difference MSPE Adjusted p-value CFNAI NRT 1994 - 2013 CFNAI NRT Macro Variables 7.11% 0.0000 1.36% -0.0144% 0.0025 2.64% 0.0070 1.27% -0.0054% 0.0557 8.83% 0.0000 1.04% -0.0179% 0.0017 6.94% 0.0000 0.69% -0.0135% 0.0005 2.96% 0.0020 0.95% -0.0058% 0.0147 Encompassing Bootstrap ENC p-value Bootstrap 95% Critical ENC 8.44 0.0000 1.98 3.87 0.0040 1.70 10.58 0.0000 1.45 12.37 0.0000 2.29 5.71 0.0050 2.65 Certainty Equivalent Return (p.a) 4.09% 1.87% 3.90% 3.07% 1.78% S&P GSCI Industrial Metals Index and S&P 500 data are sourced from Thomson Reuters Datastream. The results are generated from the state-switching model in equation 5. The first column of results is based on states specified by the CFNAI as it is released. The start date is 2001 as this is the first year these data were available in real time. The third and fourth columns use an extended CFNAI series which includes subsequent revisions so is not real time. The second and fifth columns are based states generated by the four macroeconomic variables employed by Henkel, Martin, and Nardari (2011). The out-of-sample (OoS) R2 is calculated in accordance with Campbell and Thompson (2008). The MSPE Difference is the difference between the meansquare prediction error for the forecast based on industrial metal returns and the naïve forecast. The MSPE adjusted p-value is as per Clark and West (2007). The Encompassing test proposed by Clark and MacCracken (2001) determines whether the historical mean model has predictive power for the state-switching model. The Certainty Equivalent Return is calculated following Fleming, Kirby and Ostdiek (2001). 47 Table 3. Industrial Metals and Economic Variables Expansion Recession Difference Panel A: Growth and Employment Durable Goods Orders ISM Manufacturing Industrial Production Unemployment Rate Capacity Utilization Overall 0.064 1.761 0.124 2.901 0.013 3.456 -0.034 -1.799 0.007 1.838 0.040 2.206 0.267 2.841 0.497 2.608 0.039 1.349 -0.167 -2.669 0.049 3.353 0.191 5.260 -0.204 4.149 -0.372 3.824 -0.026 0.779 0.133 3.985 -0.042 7.606 -0.152 13.895 0.095 1.913 0.017 0.782 0.032 1.983 0.048 8.276 -0.071 2.024 -0.011 0.260 -0.028 2.705 -0.037 32.081 Panel B: Inflation Producers Price Index Consumers Price Index Personal Consumption Expenditures Overall 0.023 3.848 0.006 1.933 0.005 1.551 0.011 3.926 S&P 500 data are sourced from Thomson Reuters Datastream. The growth and employment results are based on five series. These include the Durable Goods Orders, ISM Manufacturing New Orders Index, Industrial Production, Capacity Utilization, and the inverse of the Civilian Unemployment Rate. The inflation series are based on the Consumers Price Index, Producers Price Index, and Personal Consumption Expenditures. All economic series are sourced from the Federal Reserve Bank of St. Louis, with the exception of Producer Price Index (PPI), which we obtain from the Bureau of Labor Statistics. The overall regression results relate to a panel fixed effect model based on the specification in equation 5 (with the monthly change in the economic series rather than the S&P 500 return on the left hand side and no control variables) is estimated. All analysis is for the period January 1977 – June 2013. The expansion and recession columns contain the coefficient for each variable with the Newey West t-statistic underneath. The difference columns contain the difference between expansion and recession coefficients with the Wald statistic underneath. Coefficients and differences that are statistically significant at the 10% level are in bold. 48 Table 4. Gradual Information Diffusion Expansion & , Expansion Recession & , Recession & , & , 0.6411 0.2068 0.1331 0.0496 Panel A: NBER Coefficient Standard Error 0.7434 0.1219 -0.0638 0.0162 Panel B: CFNAI Coefficient Standard Error 0.8603 0.1528 -0.0583 0.0165 0.6941 0.1022 0.2814 0.0463 Expansion Expansion Expansion : & , Recession : & , : & , 1 : & , 0 & , 1, 0 Recession 1 : & , 0 Recession : & , 1, & , 0 Panel C: NBER Coefficient Standard Error 4.4292 0.0353 15.4804 0.0001 15.6072 0.0004 3.0123 0.0826 7.1977 0.0073 9.1123 0.0105 8.9649 0.0028 36.971 0.000 42.6258 0.000 Panel C: CFNAI Coefficient Standard Error 0.8356 0.3607 12.5047 0.0004 15.1786 0.0005 49 The gradual information diffusion model is as per Rapach, Strauss, and Zhou (2013). & , impact of industrial metal return shock contemporaneously incorporated into S&P return, S&P. The null hypotheses of no information diffusion therefore are: : & , 0, : June 2013. is a diffusion parameter measuring the proportion of the is total impact of industrial metal return shock on & , 1. All analysis is for the period January 1977 – & , 50 Table 5. Bond Return Predictability and Cash Flow Versus Discount Rate Channel NBER NBER CFNAI CFNAI Expansion Recession Expansion Recession Panel A: Bond Return Predictability Bond Return Coefficient t-statistic -0.045 -1.721 -0.182 -3.072 -0.069 -1.835 -0.088 -1.849 Panel B: Cash Flow Versus Discount Rate Channel , Coefficient t-statistic -0.104 -2.642 0.192 2.414 -0.111 -2.888 0.275 3.234 , Coefficient t-statistic -0.013 -2.643 0.023 2.422 -0.013 -2.884 0.033 3.234 The Panel A results relate to the use of industrial metal returns to predict 10-year Government Bond returns In Panel B, following Campbell (1991) we decompose stock price impact into cash flow and discount rate channels. , reflects the discount rate channel and , represents the cash flow channel. All analysis is for the period January 1977 – June 2013. Coefficients and differences that are statistically significant at the 10% level are in bold. 51 Table 6. Learning Expansion Expansion Trend Recession Recession Trend 0.189 2.888 0.001 3.338 0.177 2.734 0.001 3.246 Panel A: NBER Coefficient t-statistic -0.073 -2.315 0.000 -0.373 Panel B: CFNAI Coefficient t-statistic -0.084 -2.802 0.000 -0.997 These results are equivalent to those in Table 1. However, a trend variable, which is a demeaned variable calculated from an observation number series, is added in both recessions and expansions. All analysis is for the period January 1977 – June 2013. Coefficients and differences that are statistically significant at the 10% level are in bold. 52 Table 7. ICAPM Risk Premiums Expansion Recession NBER NBER Expansion CFNAI Recession CFNAI 11.275 4.053 5.921 71.872 9.844 3.823 4.540 14.978 t-statistic -9.050 -2.979 -12.163 -113.630 -7.254 -2.716 -2.635 -11.426 J-stat p(J-stat) 67.286 0.000 2,505.900 0.000 t-statistic z 82.860 10,799.000 0.000 0.000 All analysis are for the period January 1977 – June 2013. ICAPM states that the risk premium is determined by the market risk and the intertemporal risk. E(Ri,t-Rf,t) = Cov(Ri,t - Rf,t,Rm,t - Rf,t) + z Cov(Ri,t - Rf,t,Zt) where measures average relative risk aversion and z to denotes the intertemporal risk price associated with the state variable Zt which is the industrial metal return. The moment conditions ∑ , , , , , , , , , , . Coefficients are estimated from the GMM and those are statistically significant at the 10% level are in bold. The J-statistics tests whether the model error is significantly different from zero. 53 Table 8. Trading Based on Industrial Metals and Business Cycles Port MeanRule SDRule SRRule MeanBH SDBH SRBH αCAPM αFF3 0.03 0.13 0.16 0.20 0.20 0.08 0.14 0.19 0.19 0.17 0.10 0.16 0.17 0.18 0.22 0.13 0.14 0.15 0.17 0.16 0.12 0.14 0.12 0.13 0.13 0.08 0.37 0.44 0.51 0.55 0.23 0.34 0.42 0.44 0.42 0.24 0.37 0.34 0.41 0.51 0.31 0.34 0.39 0.40 0.42 0.35 0.34 0.28 0.31 0.42 0.10 0.33 0.37 0.41 0.41 0.28 0.30 0.33 0.32 0.27 0.31 0.34 0.27 0.30 0.37 0.40 0.32 0.33 0.31 0.31 0.47 0.38 0.26 0.25 0.32 0.13 0.13 0.14 0.14 0.15 0.15 0.16 0.14 0.15 0.12 0.32 0.35 0.35 0.32 0.35 0.31 0.35 0.32 0.33 0.33 0.25 0.29 0.30 0.27 0.32 0.29 0.34 0.32 0.34 0.38 Panel A: 25 Size / BM Portfolios 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0.82 1.05 1.09 1.14 1.19 0.97 1.02 1.08 1.08 1.08 0.96 1.05 1.00 1.05 1.15 1.02 1.01 1.06 1.04 1.07 1.02 0.98 0.90 0.92 1.04 5.00 4.22 3.58 3.32 3.54 4.55 3.73 3.34 3.26 3.53 4.24 3.49 3.19 3.12 3.24 3.77 3.22 3.34 3.02 3.35 3.17 2.93 2.84 2.84 3.24 0.08 0.15 0.19 0.22 0.22 0.12 0.16 0.20 0.20 0.19 0.13 0.18 0.18 0.20 0.23 0.16 0.18 0.19 0.21 0.19 0.19 0.19 0.17 0.18 0.19 0.63 1.30 1.36 1.47 1.58 0.98 1.24 1.40 1.41 1.40 1.05 1.29 1.28 1.29 1.57 1.19 1.14 1.17 1.22 1.27 0.97 1.07 0.98 1.00 1.09 7.96 6.73 5.69 5.30 5.74 7.19 5.84 5.25 5.12 5.85 6.65 5.44 4.93 4.84 5.29 5.98 5.20 5.14 4.70 5.27 4.74 4.61 4.53 4.40 5.09 Panel B: 10 Size Portfolios 1 2 3 4 5 6 7 8 9 10 0.97 1.04 1.04 1.00 1.04 0.98 1.03 0.99 0.99 0.97 3.78 3.97 3.77 3.64 3.60 3.32 3.22 3.21 2.99 2.83 0.15 0.16 0.16 0.16 0.17 0.17 0.19 0.18 0.19 0.20 1.20 1.21 1.27 1.20 1.26 1.20 1.22 1.15 1.11 0.95 6.07 6.28 5.94 5.75 5.64 5.22 5.14 5.08 4.69 4.34 Panel C: 10 BM Portfolios 54 1 2 3 4 5 6 7 8 9 10 0.95 1.08 0.99 1.00 0.94 0.95 0.98 0.94 1.06 1.18 3.45 3.04 2.97 3.06 2.86 2.92 2.93 2.72 2.96 3.75 0.15 0.22 0.19 0.19 0.18 0.18 0.19 0.19 0.22 0.20 0.90 1.06 1.09 1.11 1.08 1.04 1.14 1.07 1.25 1.38 5.19 4.73 4.69 4.86 4.59 4.57 4.41 4.44 4.67 5.83 0.09 0.13 0.14 0.14 0.14 0.14 0.16 0.15 0.18 0.16 0.26 0.42 0.34 0.35 0.31 0.31 0.35 0.33 0.43 0.52 0.40 0.47 0.38 0.35 0.28 0.28 0.28 0.24 0.34 0.36 -0.01 0.07 0.11 0.13 0.11 0.12 0.15 0.18 0.16 0.17 0.01 0.32 0.41 0.37 0.32 0.35 0.39 0.39 0.41 0.44 -0.05 0.28 0.36 0.34 0.28 0.35 0.40 0.41 0.45 0.53 0.20 0.08 0.13 0.13 0.09 0.12 0.14 0.16 0.14 0.12 0.45 0.36 0.34 0.30 0.26 0.32 0.47 0.50 0.21 0.40 0.46 0.26 0.32 0.28 0.41 0.38 0.49 0.58 0.17 0.36 Panel D: 10 Momentum Portfolios 1 2 3 4 5 6 7 8 9 10 0.78 1.03 1.08 1.02 0.95 0.99 1.02 1.03 1.05 1.16 5.58 4.23 3.69 3.10 2.91 2.93 2.89 2.96 3.06 4.26 0.07 0.14 0.18 0.19 0.18 0.20 0.21 0.21 0.21 0.17 0.31 0.87 0.99 1.02 0.89 0.98 1.06 1.24 1.22 1.52 8.36 6.27 5.31 4.72 4.44 4.49 4.41 4.49 4.97 6.43 Panel E: 10 Industry Portfolios NoDur Durbl Manuf Enrgy HiTec Telcm Shops Hlth Utils Other 1.05 1.06 1.00 0.90 1.00 0.95 1.13 1.12 0.74 1.08 2.82 4.50 3.15 3.61 4.43 3.31 3.47 3.24 2.65 3.41 0.22 0.14 0.18 0.13 0.13 0.16 0.21 0.22 0.12 0.19 1.25 0.96 1.09 1.17 1.02 0.99 1.16 1.18 0.98 1.04 4.19 6.67 5.05 5.65 6.92 4.94 5.11 4.72 3.93 5.26 The table contains trading rules results for a strategy that involves going long the portfolio if the industrial metal return is negative during expansions or positive during recessions and investing in the risk free asset if the industrial metal return is positive during expansion or negative during recessions. The characteristic portfolios are from Ken French’s website. All analysis is for the period January 1977 – June 2013. Mean, SD, and SR, are the monthly means, standard deviations, and Sharpe Ratios for the trading rule (Rule) and Buy and Hold (BH) approaches respectively. αCAPM and αFF3 are monthly CAPM and Fama and French three-factor alphas. Coefficients and differences that are statistically significant at the 10% level are in bold. 55 Table 9. Consumption Asset Pricing Panel A: CCAPM Only Model Test J-stat p-value Coefficient t-statistic p-value 0.996 2.863 0.004 193.310 0.000 Panel B: CCAPM + CAPM Coefficient t-statistic p-value m 3.170 2.781 0.005 -6.751 -5.587 0.000 Model Test J-stat p-value 67.297 0.000 All analysis are for the period January 1977 – June 2013. The marginal rate of substitution is ∆ and excess market return RM. ln ∆ ∆ a linear function of ∆ where the subjective discount factor is assumed to be 0.89, is the log surplus consumption ratio and is the log consumption. is the coefficient of risk aversion. m is the coefficient of a market factor in determining the marginal rate of substitution. Coefficients are estimated from the GMM and those that are statistically significant at the 10% level are in bold. The J-statistics tests whether the pricing error is significantly different from zero. 56 Table 10. Production Asset Pricing Panel A: Production Asset Pricing and CAPM in Isolation Variables 0 Coefficient t-statistic p-value 94.376 1.272 0.203 0 Coefficient t-statistic p-value r nr -66.823 -2.299 0.022 -31.460 -0.454 0.650 Model Test J-stat p-value 30.629 Model Test J-stat p-value Variables 0.963 24.731 0.000 0.06 rmrf 0.241 0.121 0.903 35.792 0.043 Panel B: Production Asset Pricing and CAPM Together Variables 0 r nr rmrf Coefficient t-statistic p-value 118.872 1.491 0.136 -58.621 -2.062 0.039 -65.687 -0.848 0.396 -0.512 -0.214 0.831 H0: r=nr =0 H0: rmrf =0 LR 41.423 67.181 Model Test J-stat p-value 32.170 0.023 #restrictions p-value 2 0.000 1 0.000 All analysis are for the period January 1977 – June 2013. The marginal rate of substitution m is a linear function of the residential investment return , nonresidential investment return , and . . Coefficients that are the excess stock market return statistically significant at the 10% level are in bold. The J-statistics tests whether the pricing error is significantly different from zero. LR is the likelihood ratio test. LR = 2*T*(Jrestricted – Junresticted) 57 Table 11. International Results Expansion Overall Australia Canada France Germany Italy Japan Netherlands Sweden Switzerland United Kingdom -0.056 -4.074 -0.036 -0.876 -0.037 -1.069 -0.114 -2.338 -0.107 -2.404 -0.069 -1.445 -0.003 -0.088 -0.046 -1.519 -0.060 -1.406 -0.105 -3.075 -0.039 -0.899 Recession Difference 0.210 7.490 0.274 3.386 0.298 3.203 0.324 3.671 0.294 2.444 0.297 2.137 0.162 1.072 0.287 2.754 0.310 3.600 0.266 3.368 0.195 2.507 0.267 72.200 -0.309 11.617 -0.335 11.492 -0.438 18.520 -0.401 9.694 -0.365 6.134 -0.165 1.137 -0.333 9.412 -0.370 14.710 -0.371 17.767 -0.234 6.831 S&P GSCI Industrial Metals Index and MSCI international equity indices in local currency are sourced from Thomson Reuters Datastream. The expansion and recession columns contain the coefficient for each variable with the Newey West t-statistic underneath. The difference columns contain the difference between expansion and recession coefficients with the Wald statistic underneath. Coefficients and differences that are statistically significant at the 10% level are in bold. The “overall” results are from the panel-regression. 58 Table 12. International Out-of-Sample Performance and Economic Significance Australia Canada France Germany Italy OoS R2 Bootstrap OoS R2 p-value Bootstrap 95% Critical OoS R2 MSPE Difference MSPE Adjusted p-value Encompassing Bootstrap ENC p-value Bootstrap 95% Critical ENC Certainty Equivalent Return (p.a) Japan Netherlands Sweden Switzerland UK 5.371% 0.001 1.343% -0.008% 0.008 5.874% 0.000 1.180% -0.010% 0.008 5.755% 0.000 1.206% -0.016% 0.005 4.159% 0.001 1.116% -0.018% 0.005 1.893% 0.000 1.429% -0.007% 0.084 1.967% 0.000 1.072% -0.006% 0.022 4.646% 0.001 1.143% -0.015% 0.002 1.510% 0.000 1.360% -0.006% 0.043 9.062% 0.000 1.410% -0.016% 0.000 2.750% 0.000 1.255% -0.005% 0.017 5.747 0.002 1.841 7.598 0.000 1.625 8.237 0.000 1.812 4.900 0.001 1.555 2.651 0.000 1.852 2.347 0.000 1.435 4.846 0.002 1.654 4.054 0.000 1.830 11.287 0.000 2.225 2.730 0.000 1.712 1.127% 3.453% 3.418% 2.539% 1.635% 1.220% 4.174% 2.946% 3.344% 0.504% S&P GSCI Industrial Metals Index and S&P 500 data are sourced from Thomson Reuters Datastream. The results are generated from the stateswitching model in equation 5 and relate to the 2001 – 2013 period. States are specified according to the CFNAI. The out-of-sample (OoS) R2 is calculated in accordance with Campbell and Thompson (2008). The MSPE Difference is the difference between the mean-square prediction error for the forecast based on industrial metal returns and the naïve forecast. The MSPE adjusted p-value is as per Clark and West (2007). The Encompassing test proposed by Clark and MacCracken (2001) determines whether the historical mean model has predictive power for the state-switching model. The Certainty Equivalent Return is calculated following Fleming, Kirby and Ostdiek (2001). 59 Appendix 1. Data Summary Statistics Mean Median Max Min Std. Dev. Skewness Kurtosis N Panel A: All Data IM Index Aluminum Copper S&P 500 0.005 0.002 0.006 0.007 0.003 -0.004 0.002 0.010 0.288 0.165 0.303 0.132 -0.292 -0.162 -0.356 -0.218 0.068 0.056 0.076 0.044 0.148 0.178 0.030 -0.620 5.821 3.359 5.720 5.040 437 269 437 437 0.517 0.255 0.446 -0.617 5.527 3.236 4.997 5.741 381 241 381 381 -0.779 0.333 -1.009 -0.263 4.984 2.335 5.720 2.666 56 28 56 56 Panel B: NBER Expansions IM Index Aluminum Copper S&P 500 0.008 0.004 0.009 0.009 0.005 -0.003 0.004 0.011 0.288 0.165 0.303 0.132 -0.248 -0.162 -0.248 -0.218 0.065 0.051 0.072 0.041 Panel C: NBER Recessions IM Index Aluminum Copper S&P 500 -0.016 -0.012 -0.014 -0.004 -0.019 -0.032 -0.007 -0.002 0.146 0.151 0.171 0.116 -0.292 -0.162 -0.356 -0.169 0.083 0.087 0.094 0.061 This Table contains summary statistics for the entire data period and NBER expansions and contractions. 60 Appendix 2. Model Specification and Hypothesis Testing This appendix shows the relation between the state-switching return predictability model and the standard return predictability model in terms of model misspecification and hypothesis testing. To or the de-meaned S&P500 return. By simplify the notation, let be a column vector of using the de-meaned return, we do not need the intercept in the regression. Similarly, we let column vector of and and be a column vector of are dummy variables and column vector of be a . Given this definition, 1 . . Let be a . The standard return predictability model and state-switching model can then be written as: Standard model: (A1) State-switching model: (A2) then from A2 we obtain: The regression A1 and A2 are nested. If = Therefore, in this special case, both regressions are equivalent in population. Also, under the null hypothesis of no predictability, this restriction is valid. 61 Model Misspecification and Hypothesis Testing when the State-switching Model is Correct If we assume that the state-switching model in A2 is correct, then the standard model in A1 is misspecified in a way similar but not equivalent to an omitted variables problem. We can estimate the coefficient for regression A1 as follows. ′′ Substitute from the state-switching model ′ Because ′ , we have ′ ′ ′ ′ There are three terms. Taking the expectation of the first term, we get the third term, we get 0 because manipulation. Let is uncorrelated with be the total sample size; and expansion and recession, respectively. Note that ′ ′ ; ′ ′ If the variance of ; ′ ′ . Taking the expectation of . The second term needs further are the size of the sample that is in ′ ′ ; . The expectation of the second term is . Then, is the same in expansions as in recessions, then 62 This suggests that is simply the weighted average of and , with weights depending on the amount of time the economy is in expansion or recession, respectively. In summary, if the stateswitching model is assumed to be correct, then the standard model is misspecified. Model Misspecification and Hypothesis Testing when the Standard Model is Correct Now we assume that the standard return predictability model is correct. Let ′ ′ ′ ′ ′ ′ 0 and ′ and ′ ′ ′ ′ ′ Note that ′ ′ ′ . Then ′ ′ ′ ′ ′ 0 0 This shows that even if the standard model is assumed to be correct, the state-switching regression still gives a consistent estimator for . In terms of estimation efficiency, we have where is the standard error of the regression. Given 0 and = 0, 1 0 0 0 0 1 63 If the variance of is the same in expansions as in recessions, 1 0 where is the or than from the regression of . Given that and 1 0 1 on then 0 0 1 . The are less than , both 1 from the standard model is and are greater . These results are in line with the usual case for nested models: having too many redundant variables still gives consistent but less efficient estimates. 64 Appendix 3. Aluminum Simple State Switching Model Results Expansion Recession Difference Expansion Panel A: NBER Aluminum Dividend Yield Short Rate Term Spread Default Spread -0.113 -2.581 0.002 0.767 0.001 0.591 -0.001 -0.354 0.013 0.751 0.346 1.990 0.004 0.299 -0.007 -0.983 0.011 0.795 -0.010 -0.451 Dividend Yield Short Rate Term Spread Default Spread -0.153 -3.095 -0.002 -0.598 0.004 1.616 -0.001 -0.542 0.011 0.500 1.009 7.515 0.053 5.130 -0.075 -2.709 -0.045 -2.141 0.007 0.331 Difference Panel B: CFNAI -0.459 6.285 -0.001 0.011 0.008 1.595 -0.012 0.797 0.022 0.999 Panel C: Macroeconomic Variables Aluminum Recession -1.161 57.449 -0.055 22.892 0.078 7.312 0.044 4.026 0.005 0.061 -0.132 -3.020 0.002 0.776 0.001 0.339 -0.001 -0.514 0.004 0.247 0.354 2.452 -0.002 -0.216 -0.001 -0.131 0.002 0.237 0.002 0.141 -0.487 10.171 0.005 0.166 0.001 0.094 -0.004 0.173 0.002 0.015 Panel D: Chauvet and Piger (2008) probabilities -0.148 -3.490 0.001 0.298 0.001 0.611 -0.002 -0.585 0.010 0.593 0.651 5.478 0.011 0.737 -0.020 -2.286 0.008 0.563 -0.007 -0.357 -0.799 37.813 -0.010 0.420 0.022 6.390 -0.009 0.460 0.017 0.662 The aluminum and S&P 500 data are sourced from Thomson Reuters Datastream. The control variable data are sourced from David Rapach’s website. All analysis is for the period 1991 – 2013. The state-switching regression is run using four different methods to define the states. The expansion and recession columns contain the coefficient for each variable with the Newey West tstatistic underneath. The difference columns contain the difference between expansion and recession coefficients with the Wald statistic underneath. Coefficients and differences that are statistically significant at the 10% level are in bold. 65 Appendix 4. Copper Simple State Switching Model Results Expansion Recession Difference Expansion Panel A: NBER Copper Dividend Yield Short Rate Term Spread Default Spread -0.063 -2.242 0.002 0.967 -0.001 -0.877 -0.001 -0.559 0.008 1.116 0.192 2.078 0.006 0.680 -0.001 -0.225 0.001 0.074 -0.008 -0.596 Dividend Yield Short Rate Term Spread Default Spread -0.083 -2.587 -0.002 -0.703 0.001 0.790 0.000 -0.109 0.004 0.405 0.419 3.342 0.045 2.763 -0.013 -2.453 -0.009 -0.676 -0.037 -2.460 Difference Panel B: CFNAI -0.255 6.908 -0.004 0.189 0.000 0.006 -0.002 0.053 0.015 1.206 Panel C: Macroeconomic Variables Copper Recession -0.502 13.819 -0.047 7.129 0.015 5.469 0.009 0.362 0.042 8.034 -0.068 -2.510 0.002 0.936 -0.001 -1.006 -0.001 -0.499 0.004 0.639 0.252 3.695 0.004 0.590 0.000 0.092 0.003 0.575 -0.010 -1.006 -0.321 18.919 -0.003 0.105 -0.001 0.189 -0.004 0.609 0.015 1.521 Panel D: Chauvet and Piger (2008) probabilities -0.072 -2.539 0.001 0.640 -0.001 -1.012 -0.001 -0.496 0.008 1.194 0.257 2.928 0.015 1.278 -0.003 -0.788 -0.004 -0.521 -0.014 -0.946 -0.328 12.107 -0.014 1.277 0.002 0.263 0.003 0.163 0.022 2.069 The copper and S&P 500 data are sourced from Thomson Reuters Datastream. The control variable data are sourced from David Rapach’s website. All analysis is for the period 1977 - 2013. The stateswitching regression is run using four different methods to define the states. The expansion and recession columns contain the coefficient for each variable with the Newey West t-statistic underneath. The difference columns contain the difference between expansion and recession coefficients with the Wald statistic underneath. Coefficients and differences that are statistically significant at the 10% level are in bold. 66 Appendix 5. Aluminum and Copper Out-of-Sample Performance and Economic Significance OoS R2 Bootstrap OoS R2 p-value Bootstrap 95% Critical OoS R2 MSPE Difference MSPE Adjusted p-value Encompassing Bootstrap ENC p-value Bootstrap 95% Critical ENC Certainty Equivalent Return (p.a.) Aluminum Copper 5.270% 0.005 1.496% -0.011% 0.006 7.958% 0.000 1.135% -0.016% 0.005 9.958 0.000 1.711 10.399 0.000 1.671 3.596% 3.597% S&P GSCI Aluminum, Copper, and S&P 500 data are sourced from Thomson Reuters Datastream. The results are generated from the state-switching model in equation 5 based on CFNAI states. The start date is 2001 as this is the first year these data were available in real time. The out-of-sample (OoS) R2 is calculated in accordance with Campbell and Thompson (2008). The MSPE Difference is the difference between the mean-square prediction error for the forecast based on industrial metal returns and the naïve forecast. The MSPE adjusted p-value is as per Clark and West (2007). The Encompassing test proposed by Clark and MacCracken (2001) determines whether the historical mean model has predictive power for the state-switching model. The Certainty Equivalent Return is calculated following Fleming, Kirby and Ostdiek (2001). 67 Appendix 6. Characteristic Portfolios Expansion Recession Difference Expansion Panel A: Size Small 2 3 4 5 6 7 8 9 Large -0.036 -1.021 -0.078 -2.073 -0.069 -1.854 -0.074 -2.081 -0.076 -2.198 -0.077 -2.280 -0.075 -2.459 -0.087 -2.802 -0.077 -2.419 -0.078 -2.617 0.507 3.948 0.468 4.217 0.448 3.905 0.408 3.589 0.420 3.443 0.342 3.252 0.367 2.903 0.360 3.178 0.357 2.741 0.278 2.953 2 3 4 5 6 7 8 9 -0.102 -2.305 -0.103 -2.787 -0.101 -2.759 -0.095 -2.896 -0.078 -2.412 -0.080 -2.729 -0.093 -2.817 -0.056 -1.808 -0.069 -2.148 0.778 2.772 0.596 3.082 0.458 2.824 0.432 4.038 0.389 3.285 0.359 3.559 0.213 3.115 0.250 2.596 0.263 2.213 Difference Panel B: B/M -0.542 16.475 -0.546 21.340 -0.517 18.158 -0.481 16.330 -0.495 15.219 -0.418 14.191 -0.442 11.541 -0.447 14.448 -0.435 10.479 -0.355 13.054 Growth 2 3 4 5 6 7 8 9 Value Panel C: Momentum Losers Recession -0.099 -3.075 -0.099 -3.217 -0.086 -2.914 -0.070 -2.305 -0.056 -1.810 -0.076 -2.562 -0.075 -2.269 -0.068 -2.330 -0.051 -1.502 -0.053 -1.568 0.288 2.584 0.281 2.989 0.229 4.047 0.379 3.119 0.297 2.872 0.373 2.931 0.279 2.633 0.491 2.840 0.412 3.710 0.607 3.698 -0.388 11.144 -0.380 14.701 -0.316 24.244 -0.450 12.848 -0.353 10.670 -0.449 11.777 -0.354 10.294 -0.558 10.226 -0.463 15.918 -0.660 15.582 Panel D: Industry -0.880 9.586 -0.700 12.504 -0.559 11.140 -0.528 22.141 -0.468 14.259 -0.439 17.398 -0.306 16.358 -0.305 9.300 -0.333 7.328 Con N-Dur Con Dur Manu Energy Tech Telecom Retail Healthcare Utilities -0.083 -3.044 -0.076 -1.672 -0.076 -2.611 0.001 0.016 -0.085 -2.089 -0.068 -1.832 -0.112 -3.353 -0.117 -3.612 -0.058 -1.527 0.218 2.445 0.486 2.297 0.376 3.007 0.231 2.248 0.333 2.675 0.300 4.291 0.249 2.716 0.166 1.852 0.158 2.567 -0.301 10.461 -0.562 6.708 -0.452 12.370 -0.231 4.320 -0.418 10.283 -0.368 21.533 -0.361 13.805 -0.283 8.694 -0.216 8.865 68 Winners -0.074 -1.838 0.268 2.129 -0.341 6.617 Other -0.107 -3.034 0.474 3.303 -0.582 15.522 The S&P GSCI Industrial Metals Index are sourced from Thomson Reuters Datastream while the characteristic portfolios are from Ken French’s website. All analysis is for the period January 1977 – June 2013. The expansion and recession columns contain the coefficient for each variable with the New West t-statistic underneath. The difference columns contain the difference between expansion and recession coefficients with the Wald statistic underneath. Coefficients and differences that are statistically significant at the 10% level are in bold. 69