heterogeneous gain learning and long swings in asset...
TRANSCRIPT
-
Heterogeneous Gain Learning and Long Swings in Asset Prices
Blake LeBaron!International Business School!
Brandeis University!www.brandeis.edu/~blebaron!
Microfoundations for Modern Macroeconomics
Center on Capitalism and Society
Columbia University
November, 2010
-
Long Swings: S&P Price/Dividend Ratio!
-
Gain Parameters!
ft = ft−1 + gj (xt − ft−1 )
-
Outline!
Model! Structure! Time series! Wealth distributions!
Learning dynamics! Summary!
-
Connections!
Adaptive learning! Agent-based markets!
-
Securities! Equity !
Risky dividend (Weekly U.S. Data)! Annual growth = 2%, std. = 12%! Macro shock!
Fixed supply (1 share)! Risk free!
Infinite supply! Constant interest: 0% per year!
-
Agents!
Myopic CRRA,!
Consumption!
Budget!
Equity fraction = α t ,i =Et ,i (rt+1 )− rf + (1 / 2)σ t ,i
2
γσ t ,i2 + t ,i
Ct ,i = λWt ,i
PtSt ,i + Bt ,i = (1− λ)(PtSt−1,i + Bt−1,i (1+ rf ))
γ = 3.5
-
Forecast Families! Adaptive: !
Adaptive expectations (log returns)! Fundamental:!
Log(P/D) regressions! Recursive least squares!
Short AR (autogressive) !! AR(3) on lagged returns! Recursive least squares!
Buy and hold! Low gain return mean and variance estimates!
-
Forecast Families!
Adaptive
Low Gain
High Gain
Fundamental
Low Gain
High Gain
Short AR
Low Gain
High Gain
Buy and Hold
Low Gain
High Gain
-
Variance Forecasts (Adaptive)!
σ̂ t , j2 = σ̂ t−1, j
2 + gj ,σ (et , j2 − σ̂ t−1, j
2 )
et , j2 = (rt − ft−1
j )2
gj ,σ = variance gain
-
Gain Levels 5 Discrete Values!
Low Gain: 50-45 years! All Gain: 50-1 year!
Discrete half-life: [50,18, 7,2.5,1] years
-
Forecast Selection!Agents
Forecasts
-
Learning and Wealth!
Active! Recursive parameter estimation! Active forecast rule selection!
Passive! Wealth moves to more successful
strategies!
-
Low Gain (long memory)!
-
All Gain!
-
Price/Dividend Ratios!
-
Annual Return Regressions R(t+1) on log(P/D(t))!
Series! Coefficient! R-squared!All Gain! -0.41! 0.19!
(0.03)!Low Gain! -0.01! 0.00!
(0.05)!S&P ! -0.13! 0.03!
(0.06)!
-
Weekly Return Density!
-
Weekly Return Autocorrelations!
-
Outline!
Model! Structure! Time series! Wealth distributions!
Learning dynamics! Summary!
-
Wealth Time Series!
-
Return Gain Wealth Distributions!
-
Variance Gain Wealth Distributions!
-
Utility Surfaces Annual Certainty Equivalent Returns!
-
Outline!
Model! Structure! Time series! Wealth distributions!
Learning dynamics! Summary!
-
Fundamental Portfolio Strategies by Gain!
-
Variance Forecasts!
-
Variance versus Log(P/D)!
-
Variance Forecast Comparisons!
-
High Gain Only Experiment!
Gain half-lives: [1-5] years!
-
High Gain Only!
-
Outline!
Model! Structure! Time series! Wealth distributions!
Learning dynamics! Summary!
-
Empirical Features!
Large and persistent fundamental deviations!
Fat tailed return series! Persistent volatility! Low gain convergence!
-
Necessary Components!
Multiple time scales! Risk and return! Active and passive learning!
-
Return Forecasts!
P/D regressions do not time market well! Difficult regressions, unstable learning! Is 50 year half-life long enough?!
Adaptive forecasts control large wealth share!
Short AR behaves predictably!
-
Variance Forecasts!
Forecast structure! Time series features give short gain
forecasts an edge! Range of gains survive!
Persistence in beliefs about risk!
-
Future!
Other forecast rules?! Estimation/validation! Fat tails/robust filtering! Macro dynamics!
-
Extra Figures/tables!
These tables may be useful for discussions!
-
Summary Statistics!Statistic S&P (1871-2008) All Gain Simulation Return mean (real) 7.9% 8.7% Return std. 0.17 0.25 P/E mean 15.3 15.2 P/E std. 6.0 4.2 P/E correlation (t,t+1) 0.68 0.64
-
Wealth over Utility Gain!
-
Forecast Comparisons!
-
Strategy Fractions!