Business Cycles, Macro Variables, and Stock Market Returns

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

2. 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)

3. 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

4. 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

5. 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

6. 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

7. 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)

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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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)

16. 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

17. 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

18. 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

19. Linear regression analyses • Two regression analyses performed on monthly time series for the period 1970-1997 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)

20. Regression results for 1971-1997 • Industrial production, manufacturing orders, and housing starts are significant at 10% confidence level • The correlation between independent variables is quite low below 0.40. Only two correlation coefficients were as high as 0.60 • Adjusted R2 below 0.0386 indicates little relationship between variables

21. Individual regression results for four business cycle phases

22. 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 R2 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

23. 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.

24. 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.

25. Studying Economic Phases with a Neural Network

26. 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.”

27. Studying Economic Phases with a Neural Network …Since 1997

28. 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

29. 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

30. 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

31. 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