Business Cycles, Macro Business Cycles, Macro Variables, and Stock Market Variables, and Stock Market

ReturnsReturns

William Carter, David Nawrocki, William Carter, David Nawrocki, and Tonis Vagaand Tonis Vaga

AgendaAgenda

Introduction and literature review (Jon)Introduction and literature review (Jon) Relationships between real activity and Relationships between real activity and

stock returns (Jordan)stock returns (Jordan) Multiple phases of the business cycle Multiple phases of the business cycle

(Danielle)(Danielle) Linear regression analysis (Dmitry)Linear regression analysis (Dmitry) Application of neural network (Raegen)Application of neural network (Raegen) Conclusion (Jon)Conclusion (Jon)

IntroductionIntroduction

Business cycle indicators: relevant issueBusiness cycle indicators: relevant issue Chen, Roll, and Ross; Fama and French; and Chen, Roll, and Ross; Fama and French; and

SchwertSchwert Risk premium embedded in expected returns Risk premium embedded in expected returns

moves inversely with business conditionsmoves inversely with business conditions WhitelawWhitelaw

Conditional returns and conditional volatility Conditional returns and conditional volatility change over time with changes in the cyclechange over time with changes in the cycle

Nawrocki and ChauvetNawrocki and Chauvet Find dynamic relationship between stock market Find dynamic relationship between stock market

fluctuations and cyclesfluctuations and cycles

Intro. Con’t.Intro. Con’t.

Perez-Quiros and TimmermanPerez-Quiros and Timmerman Asymmetries in conditional mean and volatility of Asymmetries in conditional mean and volatility of

excess stock returns around cycle turning pointsexcess stock returns around cycle turning points Chauvet and PorterChauvet and Porter

Suggest non-linear risk measure that allows risk-Suggest non-linear risk measure that allows risk-return relationship to not be constant over Markov return relationship to not be constant over Markov statesstates

DeStafanoDeStafano Tests four-state model of cycle and dividend Tests four-state model of cycle and dividend

discount model to provide evidence that expected discount model to provide evidence that expected stock returns vary inversely with economic stock returns vary inversely with economic conditions conditions

This all suggests…This all suggests…

Nonlinear financial market dynamic Nonlinear financial market dynamic Thus requiring a nonlinear methodologyThus requiring a nonlinear methodology

Between business cycle and stock market Between business cycle and stock market

DeStafano (2004)DeStafano (2004) Arbitrarily defined four phases Arbitrarily defined four phases

Period between NBER peaks and troughs into two Period between NBER peaks and troughs into two equal periods equal periods

Where the authors differWhere the authors differ

Utilizes simple linear models Utilizes simple linear models Looks for phase transitions Looks for phase transitions

Provides preliminary definitions of phasesProvides preliminary definitions of phases Then used in the neural network methodology for final Then used in the neural network methodology for final

estimates of the phasesestimates of the phases

Independent of NBER peaks and troughsIndependent of NBER peaks and troughs Not announced until 9-18 months after the Not announced until 9-18 months after the

factfact

Multiple Phases of the Business Multiple Phases of the Business CycleCycle

Chauvet and Potter (1998) and Perez-Quiros and Chauvet and Potter (1998) and Perez-Quiros and Timmermann (2000) study two phases: expansions and Timmermann (2000) study two phases: expansions and recessionsrecessions Consistent with the NBER’s definition of business cycle peaks Consistent with the NBER’s definition of business cycle peaks

and troughsand troughs

Chauvet and Potter (1998) note changes in conditional Chauvet and Potter (1998) note changes in conditional means and variances well before the peak and trough, means and variances well before the peak and trough, suggesting additional phases of the business cyclesuggesting additional phases of the business cycle

Four/five-stage models have been proposed by Hunt Four/five-stage models have been proposed by Hunt (1987), Stovall (1996), DeStefano (2004), Guidolin and (1987), Stovall (1996), DeStefano (2004), Guidolin and Timmermann (2005), Guidolin and Ono (2006)Timmermann (2005), Guidolin and Ono (2006)

Advantages of the Neural NetworkAdvantages of the Neural Network

Eliminates problems from traditional Eliminates problems from traditional approachesapproaches Linearity assumptionsLinearity assumptions Data-pooling issuesData-pooling issues Data miningData mining Pre-specification of the modelPre-specification of the model

Relationships between Real Activity Relationships between Real Activity and Stock Returnsand Stock Returns

Prior Research:Prior Research: Moore (1976) and Sherman (1986) found certain economic Moore (1976) and Sherman (1986) found certain economic

indicators are leading indicators for the business cycle and indicators are leading indicators for the business cycle and security marketssecurity markets

Chen, Roll, Ross (1986) modeled equity returns using Chen, Roll, Ross (1986) modeled equity returns using macroeconomic factors:macroeconomic factors: Industrial ProductionIndustrial Production Monetary AggregatesMonetary Aggregates Debt Market YieldsDebt Market Yields

Fama & French (1989) measured stock return volatility using the Fama & French (1989) measured stock return volatility using the relationship between returns and real activityrelationship between returns and real activity

SkewnessSkewness

Skewness and volatility has also been tied to the Skewness and volatility has also been tied to the business cyclebusiness cycle

Schwert (1989) finds stock market volatility increases Schwert (1989) finds stock market volatility increases during recessionsduring recessions

Other research has found high variability in the Other research has found high variability in the skewness of stock returns and that it varies skewness of stock returns and that it varies systematically with business conditionssystematically with business conditions

Skewness becomes more negative during expansions Skewness becomes more negative during expansions and less negative or positive during contractionsand less negative or positive during contractions

Prior ResearchPrior Research Whitelaw (1994) finds that the relationship Whitelaw (1994) finds that the relationship

between the conditional mean and volatility of between the conditional mean and volatility of stock returns is nonstationarystock returns is nonstationary Using a linear relationship between mean and Using a linear relationship between mean and

volatility can lead to incorrect results from GARCH volatility can lead to incorrect results from GARCH and ARCH modelsand ARCH models

Utilizing a Nonlinear Markov switching Utilizing a Nonlinear Markov switching regression:regression: Volatility increases during recessions Volatility increases during recessions Conditional means rise before the end of recessionsConditional means rise before the end of recessions Conditional means decrease before the peak of Conditional means decrease before the peak of

expansionsexpansions Sharpe ratios are negative in troughs, positive in Sharpe ratios are negative in troughs, positive in

peakspeaks

Prior ResearchPrior Research

Whitelaw (1994) et al. find conditional variance is Whitelaw (1994) et al. find conditional variance is countercyclical countercyclical

Fama and French (1989) et al. find conditional means Fama and French (1989) et al. find conditional means move with the business cyclemove with the business cycle

Rapach (2001) finds real stock returns are related to Rapach (2001) finds real stock returns are related to changes in money supply, aggregate supply, aggregate changes in money supply, aggregate supply, aggregate spendingspending

This research suggests that stock market phases are This research suggests that stock market phases are related to economic fluctuationsrelated to economic fluctuations

Prior ResearchPrior Research

Recent research finds that the power of the Recent research finds that the power of the economic factors used for predictions varies economic factors used for predictions varies over time and volatilityover time and volatility

Small firms are shown to be strongly affected Small firms are shown to be strongly affected during recessionsduring recessions

Fundamental factors such as DDM are affected Fundamental factors such as DDM are affected by the business cycleby the business cycle Investors discount earnings using short term T-Bill Investors discount earnings using short term T-Bill

when the economy is slowing downwhen the economy is slowing down Discount using long term T-Bond rate in the other Discount using long term T-Bond rate in the other

states of economystates of economy

MethodMethod Time-invariant forecasting models will not work under Time-invariant forecasting models will not work under

sudden large changes in time seriessudden large changes in time series

Previous research was determined using the NBER Previous research was determined using the NBER cycle dates, which have a lag of 9 – 18 months cycle dates, which have a lag of 9 – 18 months

The Markov switching VAR is used in this study along The Markov switching VAR is used in this study along with a neural networkwith a neural network It does not require the form of the regression to be previously It does not require the form of the regression to be previously

specifiedspecified

Allows for a state switching nonlinear model that tests Allows for a state switching nonlinear model that tests the significance of the various macroeconomic variablesthe significance of the various macroeconomic variables The neural network must be provided with an initial set of dates The neural network must be provided with an initial set of dates

for the phases and macroeconomic variables for the transistionsfor the phases and macroeconomic variables for the transistions

Multiple Phases of the Business Multiple Phases of the Business CycleCycle

Chauvet and Potter (1998) and Perez-Quiros and Chauvet and Potter (1998) and Perez-Quiros and Timmermann (2000) study two phases: expansions and Timmermann (2000) study two phases: expansions and recessionsrecessions Consistent with the NBER’s definition of business cycle peaks Consistent with the NBER’s definition of business cycle peaks

and troughsand troughs

Chauvet and Potter (1998) note changes in conditional Chauvet and Potter (1998) note changes in conditional means and variances well before the peak and trough, means and variances well before the peak and trough, suggesting additional phases of the business cyclesuggesting additional phases of the business cycle

Four/five-stage models have been proposed by Hunt Four/five-stage models have been proposed by Hunt (1987), Stovall (1996), DeStefano (2004), Guidolin and (1987), Stovall (1996), DeStefano (2004), Guidolin and Timmermann (2005), Guidolin and Ono (2006)Timmermann (2005), Guidolin and Ono (2006)

Stovall’s Business Cycle PhasesStovall’s Business Cycle Phases

Expansion in 3 phases:Expansion in 3 phases: Recovery from recession – slow growthRecovery from recession – slow growth Economic growth picks up vigorouslyEconomic growth picks up vigorously Inflation increasesInflation increases

Recession in 2 phases:Recession in 2 phases: Decline in economic productionDecline in economic production Economy flattens out and begins to recoverEconomy flattens out and begins to recover

A simplistic model – Stovall uses the time period A simplistic model – Stovall uses the time period between NBER peaks and troughs, divides each time between NBER peaks and troughs, divides each time period evenly into three and two periodsperiod evenly into three and two periods

Finds that certain sectors perform well during certain Finds that certain sectors perform well during certain stagesstages

Hunt’s Business Cycle PhasesHunt’s Business Cycle Phases Hunt suggests economic variables that drive the transition between phasesHunt suggests economic variables that drive the transition between phases EaseoffEaseoff

Industrial production slowsIndustrial production slows Initial unemployment claims increaseInitial unemployment claims increase Non-farm payrolls turn downNon-farm payrolls turn down University of Michigan Consumer Sentiment index fallsUniversity of Michigan Consumer Sentiment index falls

PlungePlunge Federal Funds rate decreasesFederal Funds rate decreases Real monetary base increasesReal monetary base increases Interest rate spread narrowsInterest rate spread narrows

Revival Revival Industrial production increasesIndustrial production increases Initial unemployment claims fallInitial unemployment claims fall Non-farm payrolls increaseNon-farm payrolls increase

AccelerationAcceleration Real monetary base increasesReal monetary base increases Consumer Price Index risesConsumer Price Index rises

Early Revival – transition between Plunge and RevivalEarly Revival – transition between Plunge and Revival

Hunt’s Business Cycle PhasesHunt’s Business Cycle Phases Implemented his model using 12-month rate of change Implemented his model using 12-month rate of change

statistics, followed monthlystatistics, followed monthly One complete cycle measured from Easeoff to Easeoff One complete cycle measured from Easeoff to Easeoff

phasephase Each phase exhibited different investment behaviorEach phase exhibited different investment behavior

Easeoff had significant negative skewnessEaseoff had significant negative skewness Consistent with Alles and Kling’s (1994) finding that skewness Consistent with Alles and Kling’s (1994) finding that skewness

becomes strongly negative during contractionsbecomes strongly negative during contractions Plunge had insignificant skewnessPlunge had insignificant skewness Revival had initial insignificant skewness, followed by positive Revival had initial insignificant skewness, followed by positive

significant skewnesssignificant skewness Acceleration exhibited poor risk-return behavior (high inflation Acceleration exhibited poor risk-return behavior (high inflation

period)period) Easeoff and revival exhibited the best risk-return behaviorEaseoff and revival exhibited the best risk-return behavior

Linear regression analysesLinear regression analyses

Two regression analyses performed on monthly time Two regression analyses performed on monthly time series for the period 1970-1997 to study relationships series for the period 1970-1997 to study relationships between S&P 500 and variablesbetween S&P 500 and variables

Macroeconomic variables consideredMacroeconomic variables considered CPI rate of change (CPIROC)CPI rate of change (CPIROC) Industrial production rate of change (IP)Industrial production rate of change (IP) Spread between 90-days T-bill and 30-year T note (SPREAD)Spread between 90-days T-bill and 30-year T note (SPREAD) Difference between AAA and BAA corporate bonds (AAA_BAA)Difference between AAA and BAA corporate bonds (AAA_BAA) Rate of change in real adjusted monetary base lagged 4 month Rate of change in real adjusted monetary base lagged 4 month

(REAL_MB)(REAL_MB) Level of housing starts (STARTS)Level of housing starts (STARTS) Level of manufacturing orders excluding aircraft and parts Level of manufacturing orders excluding aircraft and parts

(ORDERS)(ORDERS)

Regression results for 1971-1997Regression results for 1971-1997 Industrial production, manufacturing orders, and housing starts are Industrial production, manufacturing orders, and housing starts are

significant at 10% confidence levelsignificant at 10% confidence level The correlation between independent variables is quite low below 0.40. The correlation between independent variables is quite low below 0.40.

Only two correlation coefficients were as high as 0.60Only two correlation coefficients were as high as 0.60 Adjusted RAdjusted R22 below 0.0386 indicates little relationship between variables below 0.0386 indicates little relationship between variables

Individual regression results for four Individual regression results for four business cycle phasesbusiness cycle phases

Individual regression results for four Individual regression results for four business cycle phases (cont.)business cycle phases (cont.)

Impact of variables changes through the phases Impact of variables changes through the phases of the business cycleof the business cycle

All of the phase regressions have higher All of the phase regressions have higher adjusted Radjusted R22 compared to the base regression compared to the base regression

The four phase regressions exhibit different The four phase regressions exhibit different significant independent variables both from each significant independent variables both from each other and the base regressionother and the base regression

Conclusion: strong support for the hypothesis Conclusion: strong support for the hypothesis that S&P 500 has different phasesthat S&P 500 has different phases

Studying Economic Phases with a Studying Economic Phases with a Neural NetworkNeural Network

What is a neural network?What is a neural network? Mimics the structure of the brain. Output is produced Mimics the structure of the brain. Output is produced

by interconnected nodes in a parallel fashion as by interconnected nodes in a parallel fashion as opposed to traditional sequential processing.opposed to traditional sequential processing.

This operation makes the NN more robust and This operation makes the NN more robust and adaptable to fuzzy logic.adaptable to fuzzy logic.

Here, a neural network is used as computational Here, a neural network is used as computational architecture to learn from past economic phases and architecture to learn from past economic phases and performance variables. And, then predict unseen performance variables. And, then predict unseen phases in the economy.phases in the economy.

Studying Economic Phases with a Studying Economic Phases with a Neural NetworkNeural Network

Advantages of using a Neural NetworkAdvantages of using a Neural Network Captures all relationships (linear and non)Captures all relationships (linear and non) A pre-specified regression equation is not requiredA pre-specified regression equation is not required

This study uses a PNNThis study uses a PNN PNN’s use estimated “probability functions to train the PNN’s use estimated “probability functions to train the

network with a data set.”network with a data set.” It is an adaptive PNN, meaning that an algorithm It is an adaptive PNN, meaning that an algorithm

determines a smoothing function for each variable. determines a smoothing function for each variable. The variables can be weighted and insignificant The variables can be weighted and insignificant variables eliminated.variables eliminated.

Studying Economic Phases with a Studying Economic Phases with a Neural NetworkNeural Network

Studying Economic Phases with a Studying Economic Phases with a Neural NetworkNeural Network

How it worksHow it works The neural network was trained, using 1971 to 1988, to specify The neural network was trained, using 1971 to 1988, to specify

the phase for the next year.the phase for the next year. After each 12 month period was added on the network retrainedAfter each 12 month period was added on the network retrained

Testing the neural networkTesting the neural network Known economic phases for Dec 1989 through Dec 1997 were Known economic phases for Dec 1989 through Dec 1997 were

compared to the neural network’s defined phasescompared to the neural network’s defined phases Linear and nonlinear models differ 37% of the time…indicating Linear and nonlinear models differ 37% of the time…indicating

that there is some nonlinear dynamic captured by the NN. that there is some nonlinear dynamic captured by the NN. ““There are significant variables and processes in the S&P data There are significant variables and processes in the S&P data

stream that are not strictly linear. Linear models can only stream that are not strictly linear. Linear models can only approximate the actual nonlinear process.”approximate the actual nonlinear process.”

Studying Economic Phases with a Studying Economic Phases with a Neural NetworkNeural Network

……Since 1997Since 1997

Summary and ConclusionsSummary and Conclusions

Previous researchPrevious research Two market states in economy and US stock Two market states in economy and US stock

market returns (S&P 500 index)market returns (S&P 500 index) Four, possibly five Markov states have been Four, possibly five Markov states have been

identified in the business cycleidentified in the business cycle Regression analysis and neural network Regression analysis and neural network

provide evidence of four distinct market statesprovide evidence of four distinct market states Supports empirical research that delineates 4-5 Supports empirical research that delineates 4-5

market statesmarket states

Summary and Conclusion Con’t.Summary and Conclusion Con’t.

Instead of a fundamental variable Instead of a fundamental variable approach using earnings and discount approach using earnings and discount rates (DeStafano)rates (DeStafano)

Macroeconomic variable approach was Macroeconomic variable approach was usedused Real time approach Real time approach Even though independent of NBEREven though independent of NBER

NBER peak occurs in Easeoff/Plunge phasesNBER peak occurs in Easeoff/Plunge phases NBER trough occurs in Plunge/Revival phasesNBER trough occurs in Plunge/Revival phases

Summary and Conclusion Con’t.Summary and Conclusion Con’t.

This methodology closely corresponds to the This methodology closely corresponds to the “growth cycle” methodology defined by “growth cycle” methodology defined by Geoffrey H. MooreGeoffrey H. Moore

Also supports studies that discovered Also supports studies that discovered nonlinear relationships in financial marketsnonlinear relationships in financial markets Chauvet and Potter (1998)Chauvet and Potter (1998) Perez-Quiros and Timmermann (2000)Perez-Quiros and Timmermann (2000)

Echo LeBaron’s warningEcho LeBaron’s warning Results with nonlinear measures are not as robust Results with nonlinear measures are not as robust

as results obtained from linear modelsas results obtained from linear models

Step Back…..Step Back…..

These different business cycles could be These different business cycles could be used for the Coleman Fundused for the Coleman Fund To switch out of potentially underperforming To switch out of potentially underperforming

sectors sectors QInsight has the economy in the plunge QInsight has the economy in the plunge

phasephase In general, if these criteria were used we would be In general, if these criteria were used we would be

invested in a slightly different combination of invested in a slightly different combination of sectorssectors