Natural Expectations, Macroeconomic Dynamics, and Asset Pricing

1. Natural Expectations,Macroeconomic Dynamics,and Asset Pricing

2. Two starting assumptions(cf. Fuster, Mendel, and Laibson 2010) Assume that macro fundamentals are hump-shaped. Earnings momentum in the short-run. Earnings mean reversion in the long run.

3. Second assumption 2. Agents do not know that fundamentals are hump-shaped and base their beliefs on parsimonious (simple) models that they fit to the data.

4. Economic reasons for parsimonious models Tradeoff between model flexibility and over-fitting To avoid over-fitting limit number of parameters in model, k Formalizations: Akaike Information Criterion (AIC) Bayesian (Schwarz) Information Criterion (BIC)

5. Psychological reasons for parsimonious models: Myopia: short-term predictions ? low k Recency bias: small samples ? low k Complexity aversion ? low k Preference for tractability ? low k Anchoring and Representativeness, also lead agents to underestimate mean reversion, which is similar to low k

6. Schematic for Economy Good news in aggregate earnings Asset price over-reacts parsimonious models predict earnings persistence Consumption and investment slowly rise Unanticipated mean reversion in earnings asset price falls debt overhang consumption falls investment falls

7. Consequences of parsimonious models: Agents recognize the short-term momentum but miss some of the long-run mean reversion Endogenous extrapolation bias and pro-cyclical excess optimism Asset returns are excessively volatile and exhibit overreaction Returns negatively predicted by lagged returns, P/E, and ?lnC Real economic activity has amplified cycles ?lnC negatively auto-correlated in medium run Equity premium is large, although long-run equity returns covary weakly with long-run consumption growth If agents had RE, equity premium nearly vanishes Rational agents should hold high equity allocations on average And follow counter-cyclical asset allocation policy

8. Related Literature Adam and Marcet (2011): learning and asset pricing Barberis, Shleifer, and Vishny (1998): extrapolative dividend forecasts Barsky and De Long (1993): extrapolation and excess volatility Benartzi (2001): extrapolation and company stock Black (1986): noise traders Campbell and Mankiw (1987): shocks are persistent in low-order ARIMA Campbell and Shiller (1988a,b): P/E ratio and return predictability Choi (2006): extrapolation and asset pricing Choi, Laibson, and Madrian (2009): positive feedback in investment Cutler, Poterba, and Summers (1991): return autocorrelations De Long, et al (1990): noise traders and positive feedback De Bondt (1993): extrapolation bias in surveys and experiments De Bondt and Thaler (1985, 1989, 1993): over-shooting in asset prices Gabaix (2010): sparse representations Hommes (2005, 2008): bubbles in the lab Hong and Stein (1999): forecasting biases

9. Some Related Literature

10. Model CARA habit preferences (Alessie and Lusardi)

11. Dynamic budget constraint for wealth, wt Elastic supply of foreign capital with gross return R Assume foreign agents don’t hold domestic capital Home bias Moral hazard

12. Quick review of time series models If growth in dividends (?lnD = ?d) is captured by an auto-regressive model with p lags, then: Refer to this as an AR(p) model.

13. Natural expectations

16. U.S. Log Real Capital Income (1947q1-2010q3)

17. Perceived IRF’s for real capital income

18. Calibration

19. Actual IRF’s for cumulative excess returnsderiving from a unit shock to dividends

20. Actual IRF’s for consumption

21. Covariance of consumption growth and cumulative return at different horizons

22. Empirical evaluation Annual data (1929-2010) Real per-capita consumption: US NIPA Excess returns P/E ratios Simulations annualized for comparisons Simulations generated for 82 years of data Monte Carlo to generate confidence intervals

23. Correlation of Excess Returns in Year t with Cumulative Excess Returns for Years t + 2 to t + 5, for Different AR(p) Models of Earnings

24. Correlation of P/E40 in Year t with Cumulative Excess Returns for Years t + 2 to t + 5, for Different AR(p) Models of Earnings

25. Correlation ?lnCt with Cumulative Excess Returns for Years t+2 to t+5, for Different AR(p) Models of Earnings

26. Correlation of P/E40 in Year t with (lnCt+6 - lnCt+2), for Different AR(p) Models of Earnings

27. Correlation of ?lnCt with (lnCt+6 - lnCt+2), for Different AR(p) Models of Earnings

28. Application to equity premium puzzle  

29. Equity Premium for Different AR(p) Models of Earnings

30. Standard deviation of equity returns for Different AR(p) Models of Earnings

31. Standard Deviation of Consumption Growth for Different AR(p) Models of Earnings

32. Covariance of consumption growth and cumulative return at different horizons

33. How would RE agents behave in this economy? Closed form solution for consumption function and asset allocation RE agents are relatively highly leveraged RE agents adjust their equity allocation counter-cyclically

34. Leverage of RE agents for Different AR(p) Models of Earnings

35. Summary Fundamentals follow hump-shaped dynamics: Short-run momentum Long-run (partial) mean reversion Agents estimate simple models Parsimonious, tractable Typical models chosen in economics literature

36. Summary Low order forecasting equations miss some of the mean reversion in fundamentals, so resulting asset prices exhibit excess volatility and long-run mean reversion Cycles in consumption (and investment) The covariance of returns and consumption growth rises and then falls with horizon h Equity is perceived as many times riskier than it actually is Rational investors should hold far more equity than typical investors Rational investors should follow a countercyclical investment strategy

37. Future work High earnings should be a bearish indicator Let’s test this by building a new predictor for bear markets. Procedure: Calculate book values using clean-surplus relation: Construct earnings to book ratio from 1872-2010. Calculate deviation of earnings to book ratio relative to ten-year moving average Call this deviation: Earnings cycle.

38. Earnings cycle

40. Real returns

42. Performance metrics In years: 11.5% real return Out years: -2.6% real return All years: 7.9% real return

43. Macro predictors of high future excess returns Low P/E40 Low equity returns Low consumption growth Low earnings Low real investment Low return expectations