Deviation of US Equity Return

1. Deviation of US Equity Return Are They Determined by Fundamental or Behavioral Variables? R. Bhar (UNSW), A. G. Malliaris (Loyola, Chicago) www.bhar.id.au

2. Background • Focus is on the intersection of financial markets and macro-economics • Cochrane (2006) is a brilliant survey of this area • Indicates long-run averages of GDP, dividend, equity – mostly with annual data www.bhar.id.au

3. Background • On a year by year basis deviations from long-run averages do not seem high • FRB St Louis (June 2007) shows S&P 500 return: • Stable (’92-’94) • Very high (’82-’83, ’97-’98) www.bhar.id.au

4. Recent Literature • Economists at FRB St Louis assert stock market boom takes place during above average GDP growth and below average inflation • They don’t find evidence of liquidity as a factor www.bhar.id.au

5. Recent Literature • Rapid economic growth increases corporate profitability that in turn leads to above normal increases in stock prices • Stock market boom reflects real positive macro fundamentals and monetary policy targeting price stability www.bhar.id.au

6. Recent Literature • A strong economy growing without concern for inflation most often induce stock price boom • They also find stock market boom ends within a few months of an increase in inflation www.bhar.id.au

7. Recent Literature • In addition to economic fundamentals, behavioral finance has offered valuable explanations for several asset pricing puzzles • Momentum return concept in the aggregate market refers broadly to continuation of short-term return www.bhar.id.au

8. Recent Literature • Barberis and Thaler (2005) suggest momentum return in the aggregate market in the form of persistence of above average return during periods of boom can be an important behavioral variable www.bhar.id.au

9. Aim & Hypothesis • Based on this literature review, we attempt to explain deviations of equity return from long-term average with the help of both fundamental and behavioral variables • Aim is to explain post WW II era • Use important macro-economic variables: inflation, funds rate and unemployment • Also, use behavioral variable – momentum return www.bhar.id.au

10. Data & Model • We use monthly data covering the period June 1965 to November 2005 • All economic data obtained from FRB St Louis website • S&P data obtained from DataStream • We use inverse unemployment rate as suggested in Ferrara (2003) www.bhar.id.au

11. Data & Model • Deviation from long-term average is computed as the difference between current return and the last eight months moving average • In order to understand the behavior of the variables we first tried a linear regression www.bhar.id.au

12. Data & Model • Linear regression • We use first differences of funds rate and inverse unemployment rate – these are non-stationary www.bhar.id.au

13. Regression Results • In linear regression not significant • Only and are significant • R-square only 6% • Residual CUSUM square test shows parameter and/or variance instability www.bhar.id.au

14. Regression Results • Linear model like this one simply captures the average effect • We need to account for structural instability in a meaningful way • Some of the insignificant parameters may be important during some ‘states’ www.bhar.id.au

15. Markov Switching Model • How do we define ‘states? • A popular approach in economic analysis is to let an unobserved Markov chain to drive transition between states • Question: How many states? What is the probability of transition? www.bhar.id.au

16. Markov Switching Model • We resort to the business cycle literature to decide on the number of states • Ferrara (2003) suggests three states for the US economy • Statistical alternative to this may not be computationally feasible www.bhar.id.au

17. Markov Switching Model • Transition probability between states inferred from the data • Computational complexity of such models is well known • We use maximum likelihood method together with Expectation Maximization (EM) algorithm www.bhar.id.au

18. Markov Switching Model • MS model without behavioral variable • Total of 30 parameters www.bhar.id.au

19. Markov Switching Model • Let us first look at the model inferred plots of the probability of being in a state for each month in the data (Figure 1) • A quick look at the estimation results (Table 1) www.bhar.id.au

20. Markov Switching Model • The three states are classified in term of the level of volatility • State volatility www.bhar.id.au

21. Markov Switching Model • Transition probability www.bhar.id.au

22. Markov Switching Model • Linear regression model did not find inflation significant • In the MS model inflation is significant for St=1 and 2 • State St=2 is particularly interesting • It has the lowest volatility • Positive average deviation in return www.bhar.id.au

23. Markov Switching Model • State St=2 and 3 show •  ‘ium’  ↓ ‘xsr’ • Intuitively ok • But the magnitude of the parameter is much smaller for St=2 • Being the lowest volatility state St=2 may be exhibiting irrational behavior www.bhar.id.au

24. Markov Switching Model • State St=2 has very high probability of occurring over the ’92 – ’96 period • It is about 59 months of positive ‘xsr’ • Nearly 4 times the average duration of St=2 • Now we add the behavioral variable www.bhar.id.au

25. Markov Switching Model • Define the momentum return as • The model is changed to incorporate this in addition to the previous variables www.bhar.id.au

26. Markov Switching Model • New model www.bhar.id.au

27. Markov Switching Model • New probability of states (Figure 2) • There are now 33 parameters and a quick look at the estimation results (Table 2) • Estimation results are similar to that in the previous model www.bhar.id.au

28. Markov Switching Model • Average positive ‘xsr’ in St=2 is nearly twice as much in the pervious model • St=2 has still the lowest volatility • ‘mmt’ parameter only significant for St=1 and 2 • Increasing ‘mmt’ reduces available ‘xsr’ www.bhar.id.au

29. Markov Switching Model • St=3 captures the most volatile periods of ’70s, ’80s and early 2000 • Has the shortest expected duration (7-8 months) www.bhar.id.au

30. Conclusions • Extensive statistical diagnostics prove the efficacy of the MS approach • Incremental explanatory power of the model with ‘mmt’ has been proved by Vuong (1989) statistic • Conclusively proves the influence of the behavioral variable for ‘xsr’ www.bhar.id.au

31. Conclusions • Markov regime based model brings out better understanding of the nature of interaction between return deviation from long-run average and macro-economic and behavioral variables www.bhar.id.au