Business Cycles, Macro Variables, and Stock Market Returns William Carter, David Nawrocki, and Tonis Vaga

Agenda  Introduction and literature review (Jon)  Relationships between real activity and stock returns (Jordan)  Multiple phases of the business cycle (Danielle)  Linear regression analysis (Dmitry)  Application of neural network (Raegen)  Conclusion (Jon)

Introduction  Business cycle indicators: relevant issue  Chen, Roll, and Ross; Fama and French; and Schwert  Risk premium embedded in expected returns moves inversely with business conditions  Whitelaw  Conditional returns and conditional volatility change over time with changes in the cycle  Nawrocki and Chauvet  Find dynamic relationship between stock market fluctuations and cycles

Intro. Con’t.  Perez-Quiros and Timmerman  Asymmetries in conditional mean and volatility of excess stock returns around cycle turning points  Chauvet and Porter  Suggest non-linear risk measure that allows risk- return relationship to not be constant over Markov states  DeStafano  Tests four-state model of cycle and dividend discount model to provide evidence that expected stock returns vary inversely with economic conditions

This all suggests…  Nonlinear financial market dynamic  Thus requiring a nonlinear methodology  Between business cycle and stock market  DeStafano (2004)  Arbitrarily defined four phases  Period between NBER peaks and troughs into two equal periods

Where the authors differ  Utilizes simple linear models  Looks for phase transitions  Provides preliminary definitions of phases  Then used in the neural network methodology for final estimates of the phases  Independent of NBER peaks and troughs  Not announced until 9-18 months after the fact

Multiple Phases of the Business Cycle  Chauvet and Potter (1998) and Perez-Quiros and Timmermann (2000) study two phases: expansions and recessions  Consistent with the NBER’s definition of business cycle peaks and troughs  Chauvet and Potter (1998) note changes in conditional means and variances well before the peak and trough, suggesting additional phases of the business cycle  Four/five-stage models have been proposed by Hunt (1987), Stovall (1996), DeStefano (2004), Guidolin and Timmermann (2005), Guidolin and Ono (2006)

Advantages of the Neural Network  Eliminates problems from traditional approaches  Linearity assumptions  Data-pooling issues  Data mining  Pre-specification of the model

Relationships between Real Activity and Stock Returns  Prior Research:  Moore (1976) and Sherman (1986) found certain economic indicators are leading indicators for the business cycle and security markets  Chen, Roll, Ross (1986) modeled equity returns using macroeconomic factors:  Industrial Production  Monetary Aggregates  Debt Market Yields  Fama & French (1989) measured stock return volatility using the relationship between returns and real activity

Skewness  Skewness and volatility has also been tied to the business cycle  Schwert (1989) finds stock market volatility increases during recessions  Other research has found high variability in the skewness of stock returns and that it varies systematically with business conditions  Skewness becomes more negative during expansions and less negative or positive during contractions

Prior Research  Whitelaw (1994) finds that the relationship between the conditional mean and volatility of stock returns is nonstationary  Using a linear relationship between mean and volatility can lead to incorrect results from GARCH and ARCH models  Utilizing a Nonlinear Markov switching regression:  Volatility increases during recessions  Conditional means rise before the end of recessions  Conditional means decrease before the peak of expansions  Sharpe ratios are negative in troughs, positive in peaks

Prior Research  Whitelaw (1994) et al. find conditional variance is countercyclical  Fama and French (1989) et al. find conditional means move with the business cycle  Rapach (2001) finds real stock returns are related to changes in money supply, aggregate supply, aggregate spending  This research suggests that stock market phases are related to economic fluctuations

Prior Research  Recent research finds that the power of the economic factors used for predictions varies over time and volatility  Small firms are shown to be strongly affected during recessions  Fundamental factors such as DDM are affected by the business cycle  Investors discount earnings using short term T-Bill when the economy is slowing down  Discount using long term T-Bond rate in the other states of economy

Method  Time-invariant forecasting models will not work under sudden large changes in time series  Previous research was determined using the NBER cycle dates, which have a lag of 9 – 18 months  The Markov switching VAR is used in this study along with a neural network  It does not require the form of the regression to be previously specified  Allows for a state switching nonlinear model that tests the significance of the various macroeconomic variables  The neural network must be provided with an initial set of dates for the phases and macroeconomic variables for the transistions

Multiple Phases of the Business Cycle  Chauvet and Potter (1998) and Perez-Quiros and Timmermann (2000) study two phases: expansions and recessions  Consistent with the NBER’s definition of business cycle peaks and troughs  Chauvet and Potter (1998) note changes in conditional means and variances well before the peak and trough, suggesting additional phases of the business cycle  Four/five-stage models have been proposed by Hunt (1987), Stovall (1996), DeStefano (2004), Guidolin and Timmermann (2005), Guidolin and Ono (2006)

Stovall’s Business Cycle Phases  Expansion in 3 phases:  Recovery from recession – slow growth  Economic growth picks up vigorously  Inflation increases  Recession in 2 phases:  Decline in economic production  Economy flattens out and begins to recover  A simplistic model – Stovall uses the time period between NBER peaks and troughs, divides each time period evenly into three and two periods  Finds that certain sectors perform well during certain stages

Hunt’s Business Cycle Phases  Hunt suggests economic variables that drive the transition between phases  Easeoff  Industrial production slows  Initial unemployment claims increase  Non-farm payrolls turn down  University of Michigan Consumer Sentiment index falls  Plunge  Federal Funds rate decreases  Real monetary base increases  Interest rate spread narrows  Revival  Industrial production increases  Initial unemployment claims fall  Non-farm payrolls increase  Acceleration  Real monetary base increases  Consumer Price Index rises  Early Revival – transition between Plunge and Revival

Hunt’s Business Cycle Phases  Implemented his model using 12-month rate of change statistics, followed monthly  One complete cycle measured from Easeoff to Easeoff phase  Each phase exhibited different investment behavior  Easeoff had significant negative skewness  Consistent with Alles and Kling’s (1994) finding that skewness becomes strongly negative during contractions  Plunge had insignificant skewness  Revival had initial insignificant skewness, followed by positive significant skewness  Acceleration exhibited poor risk-return behavior (high inflation period)  Easeoff and revival exhibited the best risk-return behavior

Linear regression analyses  Two regression analyses performed on monthly time series for the period to study relationships between S&P 500 and variables  Macroeconomic variables considered  CPI rate of change (CPIROC)  Industrial production rate of change (IP)  Spread between 90-days T-bill and 30-year T note (SPREAD)  Difference between AAA and BAA corporate bonds (AAA_BAA)  Rate of change in real adjusted monetary base lagged 4 month (REAL_MB)  Level of housing starts (STARTS)  Level of manufacturing orders excluding aircraft and parts (ORDERS)

Regression results for  Industrial production, manufacturing orders, and housing starts are significant at 10% confidence level  The correlation between independent variables is quite low below Only two correlation coefficients were as high as 0.60  Adjusted R 2 below indicates little relationship between variables

Individual regression results for four business cycle phases

Individual regression results for four business cycle phases (cont.)  Impact of variables changes through the phases of the business cycle  All of the phase regressions have higher adjusted R 2 compared to the base regression  The four phase regressions exhibit different significant independent variables both from each other and the base regression  Conclusion: strong support for the hypothesis that S&P 500 has different phases

Studying Economic Phases with a Neural Network  What is a neural network?  Mimics the structure of the brain. Output is produced by interconnected nodes in a parallel fashion as opposed to traditional sequential processing.  This operation makes the NN more robust and adaptable to fuzzy logic.  Here, a neural network is used as computational architecture to learn from past economic phases and performance variables. And, then predict unseen phases in the economy.

Studying Economic Phases with a Neural Network  Advantages of using a Neural Network  Captures all relationships (linear and non)  A pre-specified regression equation is not required  This study uses a PNN  PNN’s use estimated “probability functions to train the network with a data set.”  It is an adaptive PNN, meaning that an algorithm determines a smoothing function for each variable. The variables can be weighted and insignificant variables eliminated.

Studying Economic Phases with a Neural Network

 How it works  The neural network was trained, using 1971 to 1988, to specify the phase for the next year.  After each 12 month period was added on the network retrained  Testing the neural network  Known economic phases for Dec 1989 through Dec 1997 were compared to the neural network’s defined phases  Linear and nonlinear models differ 37% of the time…indicating that there is some nonlinear dynamic captured by the NN.  “There are significant variables and processes in the S&P data stream that are not strictly linear. Linear models can only approximate the actual nonlinear process.”

Studying Economic Phases with a Neural Network …Since 1997

Summary and Conclusions  Previous research  Two market states in economy and US stock market returns (S&P 500 index)  Four, possibly five Markov states have been identified in the business cycle  Regression analysis and neural network provide evidence of four distinct market states  Supports empirical research that delineates 4-5 market states

Summary and Conclusion Con’t.  Instead of a fundamental variable approach using earnings and discount rates (DeStafano)  Macroeconomic variable approach was used  Real time approach  Even though independent of NBER  NBER peak occurs in Easeoff/Plunge phases  NBER trough occurs in Plunge/Revival phases

Summary and Conclusion Con’t.  This methodology closely corresponds to the “growth cycle” methodology defined by Geoffrey H. Moore  Also supports studies that discovered nonlinear relationships in financial markets  Chauvet and Potter (1998)  Perez-Quiros and Timmermann (2000)  Echo LeBaron’s warning  Results with nonlinear measures are not as robust as results obtained from linear models

Step Back…..  These different business cycles could be used for the Coleman Fund  To switch out of potentially underperforming sectors  QInsight has the economy in the plunge phase  In general, if these criteria were used we would be invested in a slightly different combination of sectors