Download Stock Market Predictability and Industrial Metal Returns

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
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http://online.barrons.com/news/articles
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of Money, Credit and Banking 21(4), 508-514.
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43
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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