Booms and Busts in Asset Prices. May 2010

Transcription

1 Booms and Busts in Asset Prices Klaus Adam Mannheim University & CEPR Albert Marcet London School of Economics & CEPR May 2010 Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 1 / 39

2 Introduction Present a simple asset pricing model with rationally investing in nitely lived agents in which Bayesian learning.gives rise to low frequency booms & busts in asset prices. Learning model replicates the low frequency behavior of PD ratio of US stocks Consistent with survey evidence that return expectations correlate positively with market valuation (unlike RE models) Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 2 / 39

3 Introduction Learning about price/return & long-standing asset price puzzles Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 3 / 39

4 Introduction Learning about price/return & long-standing asset price puzzles Implications for the behavior of price/return expectations... Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 3 / 39

5 Introduction Learning about price/return & long-standing asset price puzzles Implications for the behavior of price/return expectations... Implications for e ciency of asset price movements... Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 3 / 39

6 Relation to earlier work "Internal Rationality, Imperfect Market Knowledge and Asset Prices", Adam & Marcet, 2009 Decision theoretic foundations Risk neutral agents, heterogeneity & slight forms of market incompleteness Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 4 / 39

7 Relation to earlier work "Internal Rationality, Imperfect Market Knowledge and Asset Prices", Adam & Marcet, 2009 Decision theoretic foundations Risk neutral agents, heterogeneity & slight forms of market incompleteness Internal Rationality agents maximize IH utility under uncertainty consistent probability beliefs about payo -relevant external variables: prices & dividends Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 4 / 39

8 Relation to earlier work "Internal Rationality, Imperfect Market Knowledge and Asset Prices", Adam & Marcet, 2009 Decision theoretic foundations Risk neutral agents, heterogeneity & slight forms of market incompleteness Internal Rationality agents maximize IH utility under uncertainty consistent probability beliefs about payo -relevant external variables: prices & dividends External Rationality agents hold correct prior beliefs (RE) about external variables: prices & dividends Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 4 / 39

9 Relation to earlier work Relax External Rationality slightly subjective prior beliefs close to objective priors assumed under RE requires relaxing singularity in joint beliefs about prices&dividends Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 5 / 39

10 Relation to earlier work Relax External Rationality slightly subjective prior beliefs close to objective priors assumed under RE requires relaxing singularity in joint beliefs about prices&dividends Equilibrium asset price: one-step ahead equation P t = δe P m t t [P t+1 + D t+1 ] (& no dividend discount formula...) Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 5 / 39

11 Relation to earlier work Relax External Rationality slightly subjective prior beliefs close to objective priors assumed under RE requires relaxing singularity in joint beliefs about prices&dividends Equilibrium asset price: one-step ahead equation P t = δe P m t t [P t+1 + D t+1 ] (& no dividend discount formula...) Price beliefs not restricted by dividend beliefs + internal rationality: learning about price a potentially important source of price volatility! Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 5 / 39

12 Relation to earlier work "Stock Market Volatility & Learning", Adam, Marcet & Nicolini, 2009 Explore the quantitative performance of a learning model Learning moves (Lucas) AP model strongly in direction of data! strong return volatility ampli cation persistent, volatile and mean reverting PD ratio large equity premium Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 6 / 39

13 Quantitative Performance of Learning Model US Data Model (OLS) Statistics std t ratio E r s fi E r b fi E PDfi a r s a PD _ PD,? c R Parameters: N =.999, 1/J 1 = Coe cient of rel risk aversion: σ = 5. Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 7 / 39

14 Relation to earlier work Unsatisfactory aspects => could not discuss asset price booms & their end! Model with risk neutrality / exogenous stoch discount factor: IES in nite & too much momentum in price dynamics Projection facility: stop asset price booms in exogenous ways Ability to match unconditional second moments una ected but conditionally strong e ects What ends price booms? Should policy prevent booms? When? How? Exogenous projection facility subject to Lucas critique Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 8 / 39

15 Relation to earlier work This paper: non-linear utility & endogenous discount factor IES nite and no need for projection facility Technically more demanding: solve for optimal consumption plans implied by agents beliefs non-linear optimization problem in which beliefs are state variables & other complications Provide closed form solution for the case with vanishing risk. Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 9 / 39

16 Learning: why relevant for boom and bust behavior? Fact 1: Stock market valuation (PD ratio) displays low frequency mean reversion Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 10 / 39

17 Euro Area: Quarterly Price Dividend Ratio Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 11 / 39

18 Japan: Quarterly Price Dividend Ratio Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 12 / 39

19 U.S.: Quarterly Price Dividend Ratio Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 13 / 39

20 Learning: why relevant for boom and bust behavior? Fact 2: Dividend growth is largely unpredictable Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 14 / 39

21 Learning: why relevant for boom and bust behavior? Facts => High market valuation predicts low future (excess) stock returns EMU(84-06) U.S.(74-06) Japan(74-06) k c 1 R 2 c 1 R 2 c 1 R (0.06) (0.02) (0.035) (0.06) (0.01) (0.02) (0.02) (0.01) (0.01) 0.54 Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 15 / 39

22 Learning: why relevant for boom and bust behavior? Facts & External Rationality (RE): Investors return expectations low when market valuation (PD) is high Available evidence suggests the opposite... Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 16 / 39

23 Learning: why relevant for boom and bust behavior? UBS/Gallup Survey, Source: Vissing-Jorgensen (2003 NBER Macro Annual). Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 17 / 39

24 Learning: why relevant for boom and bust behavior? Data suggests: boom & bust behavior (at least partly) driven by investors return expectations Investors observe high returns & become optimistic about future returns Return optimism drives up prices (IES>1) => high realized returns Return optimism positively associated with market valuation What causes mean reversions? Consumption plans... Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 18 / 39

25 Model Sketch Investors maximization problem: max fc i t 0,S i t 2[0,S]g t=0 s.t. E P i 0 " t=0 S i t P t + C t = S i t 1 (P t + D t ) for all t 0 S i 1 > 0 given # δ t Ct i 1 γ 1 γ (1) Su cient intertemporal elasticity of substitution (IES): γ 1 > 1 Standard dividend process: ln D t = ln D t 1 + ln β D + ln ε D t Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 19 / 39

26 Model Sketch P i : agents subjective probability measure de ned over space of outcomes Ω ω 2 Ω: ω = fp 0, D 0, P 1, D 1, P 2, D 2,...g ω t : history of ω up to period t Ω t : set of possible histories up to t Agents make fully contingent plans: S i t : Ω t! [0, S] P i : will be generated from some perceived law of motion + prior beliefs about unknown parameters in the law of motion Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 20 / 39

27 Rational Expectations Equilibrium REE returns: ln R t = ln R + ln ε D t (2) with β R = δ 1 D γ e γ(1 γ) σ2 D 2 Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 21 / 39

28 Relaxing External Rationality Keep rational dividend expectations => all price e ects from subjective beliefs about price behavior Di erentiates us from Bayesian RE learning literature: only subjective beliefs about dividends. Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 22 / 39

29 Relaxing External Rationality Relax agents prior beliefs ln R t = ln R t + ln ε t (3) ε t : transitory (iid) return component R t : persistent & time varying return component ln R t = ln R t 1 + ln ν t Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 23 / 39

30 Relaxing External Rationality Relax agents prior beliefs ln R t = ln R t + ln ε t (3) ε t : transitory (iid) return component R t : persistent & time varying return component ln R t = ln R t 1 + ln ν t Note: no mean reversion incoorporated into beliefs! Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 23 / 39

31 Relaxing RE Beliefs Learning... ln R t = ln R t + ln ε t {z } observed jointly... & need to attribute returns to persistent & transitory components. Prior beliefs updated using Bayes rule. ln R 0 N(ln m 0, σ 2 0) (4) σ 0 > 0 is stationary variance under the Kalman lter. Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 24 / 39

32 The Evolution of Beliefs Bayesian updating of beliefs ln m t = ln m t 1 + g ln R t + σ2 ε + σ 2 v 2 ln m t 1 Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 25 / 39

33 In which sense a small deviation from RE priors? RE prior ln R t = ln R + ln ε D t Agents prior beliefs ln R t = ln R t + ln ε t (5) ln R t = ln R t 1 + ln ν t (6) Small noise limit: σ 2 ln ε D! 0, σ 2 ln v, σ2 ln ε! 0, σ2 ln v! 0 As long as lim σ 2 ln ε /σ2 ln v 2]0, [ learning well de ned in the limit If initial beliefs ln m 0 = ln R, as we assume, then agents P arbitrarily close to PF-REE beliefs (in distribution) Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 26 / 39

34 Asset Demand under Learning about Return Behavior Determine asset demand function S(S 1 1, P t D t, ln m t ) solves the FOCs of the investment problem under the perceived state dynamics S t = S(S 1 1, P t, ln m t ) D t P t+1 = R t+1p t D t+1 D t+1 D t+1 ln m t+1 = ln m t + g ln R t+1 + σ2 ε + σ 2 v 2 ln m t Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 27 / 39

35 Equilibrium Prices under Learning Behavior If all agents hold the same beliefs, the market clearing condition is 1 = S(1, (P t /D t ), ln m t ) which de nes equilibrium asset price as a function of beliefs PD (ln m t ) Su cient intertemporal elasticity (γ 1 > 1): PD increases with return expectations Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 28 / 39

36 Analytical Solution with Vanishing Risk Proposition Proposition: Under vanishing uncertainty, i.e., equilibrium PD is given by P t D t + 1 = δ γ 1 j j i=1 j=0 σ 2 ε, σ 2 ν, σ 2 ε D! 0, the 1 γ Et P γ R t+i (7) Holds for all beliefs P whether externally rational or not. Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 29 / 39

37 Analytical Solution with Vanishing Risk For the speci c beliefs above, realized returns: R t = 1 1 δ (m t 1 ) 1 γ γ 1 δ (m t ) 1 γ γ 1 1 δ (m t 1 ) 1 γ γ 1 D t D t 1 (8) Constant beliefs: m t 1 = m t Changing beliefs: m t 1 6= m t Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 30 / 39

38 Booms & Busts in the Learning Model Simulate the learning model: low frequency boom and bust dynamics? Baseline parameterization (quarterly model): δ = β D = γ = 0.8 g = Agents attribute 1,4% of any return observation to the persistent component and 98,6% to the transitory component. Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 31 / 39

39 Booms & Busts in the Learning Model Impulse response to a 10 basis points change of the quarterly real return expectations from its PF-REE value (78 bp) Positive and negative impulse responses: non-linear model. Plausibly sized impulse given the data: generated by observation of +8% (-7%) quarterly real return Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 32 / 39

40 Booms & Busts in the Learning Model IR of the PD Ratio to a 10bp increase in permanent return exp (m t ) Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 33 / 39

41 Booms & Busts in the Learning Model IR of the PD Ratio to a 10bp decrease in permanent return exp (m t ) Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 34 / 39

42 Booms & Busts in the Learning Model At the peak of the boom: return expectations very optimistic Positive comovement between market valuation & return expectations consistent with survey data Agents make very optimistic consumption plans = δe P i t 6 4 R t+1 γ Ct+1 C t 7 5 Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 35 / 39

43 Matching the US PD Ratio & Survey Expectations Assess the ability of the learning model to replicate the time series of US PD Ratio the survey data Learning model parameters g = m 0 : to match PD ratio in 1926:4 δ = γ = 0.72 Historical return process & initial belief m 0 => time series of model-implied beliefs fm t g Compare PD ratio in the data to the model implied PD ratio: P t /D t = δ (m t ) 1 γ 1 γ / 1 δ (m t ) 1 γ 1 γ Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 36 / 39

44 Matching the US PD Ratio & Survey Expectations Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 37 / 39

45 Matching the US PD Ratio & Survey Expectations Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 38 / 39

46 Summary Endogenous expectations driven boom and bust cycles in a model with rationally investing agents Agents are internally rational but have insu cient knowledge about the equilibrium behavior of returns/market discount factor Bayesian learning about return behavior causes booms + busts: momentum and mean reversion Asset prices comove positively with return expectations, unlike in RE models Price uctuations potentially ine cient (but no welfare implications in current model) Adam & Marcet ( Mannheim Booms University and Busts & CEPR London School of Economics May 2010 & CEPR) 39 / 39