Natural Expecta-ons, Macroeconomic Dynamics, and Asset Pricing Andreas Fuster Federal Reserve Bank of New York Benjamin Hebert Harvard University David Laibson Harvard University NBER Q-­‐Group April 2, 2012 The views expressed are those of the authors and do not necessarily represent the views of the Federal Reserve Bank of New York or the Federal Reserve System. Forthcoming: NBER Macroeconomics Annual Two starPng assumpPons (cf. Fuster, Mendel, and Laibson 2010) 1.  Assume that macro fundamentals are hump-­‐shaped. 
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Earnings momentum in the short-­‐run. Earnings mean reversion in the long run. 2.5 2 Long-­‐run trajectory 1.5 1 Long-­‐run trajectory 0.5 Unit shock Start here 0 Long-­‐run trajectory 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Time Second assumpPon 2. Agents do not know that fundamentals are hump-­‐shaped and base their beliefs on parsimonious (simple) models that they fit to the data. Economic reasons for parsimonious models •  Tradeoff between model flexibility and over-­‐fi^ng •  To avoid over-­‐fi^ng limit number of parameters in model, k
•  FormalizaPons:   Akaike InformaPon Criterion (AIC)   Bayesian (Schwarz) InformaPon Criterion (BIC) Psychological reasons for parsimonious models: •
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Myopia: short-­‐term predicPons → low k Recency bias: small samples → low k Complexity aversion → low k Preference for tractability → low k Anchoring and RepresentaPveness, also lead agents to underesPmate mean reversion, which is similar to low k SchemaPc for Economy 1.  Good news in aggregate earnings 2.  Asset price over-­‐reacts –  parsimonious models predict earnings persistence 3.  ConsumpPon and investment slowly rise 4.  Unan-cipated mean reversion in earnings –
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asset price falls debt overhang consumpPon falls investment falls Consequences of parsimonious models: 1.  Agents recognize the short-­‐term momentum but miss some of the long-­‐run mean reversion 
Endogenous extrapolaPon bias and pro-­‐cyclical excess opPmism 2.  Asset returns are excessively volaPle and exhibit overreacPon 
Returns negaPvely predicted by lagged returns, P/E, and ΔlnC
3.  Real economic acPvity has amplified cycles 
ΔlnC negaPvely auto-­‐correlated in medium run 4.  Equity premium is large, although long-­‐run equity returns covary weakly with long-­‐run consumpPon growth 
If agents had RE, equity premium nearly vanishes 5.  RaPonal agents should hold high equity allocaPons on average 
And follow counter-­‐cyclical asset allocaPon policy Related Literature Adam and Marcet (2011): learning and asset pricing Barberis, Shleifer, and Vishny (1998): extrapolaPve dividend forecasts Barsky and De Long (1993): extrapolaPon and excess volaPlity Benartzi (2001): extrapolaPon 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 raPo and return predictability Choi (2006): extrapolaPon and asset pricing Choi, Laibson, and Madrian (2009): posiPve feedback in investment Cutler, Poterba, and Summers (1991): return autocorrelaPons De Long, et al (1990): noise traders and posiPve feedback De Bondt (1993): extrapolaPon bias in surveys and experiments De Bondt and Thaler (1985, 1989, 1993): over-­‐shooPng in asset prices Gabaix (2010): sparse representaPons Hommes (2005, 2008): bubbles in the lab Hong and Stein (1999): forecasPng biases Some Related Literature Kahneman and Tversky (1973): representaPveness Keynes (1936): animal spirits Lansing (2010): extrapolaPon and asset pricing in a macro model LaPorta (1996): Growth expectaPons have insufficient mean reversion LeBaron, Arthur, and Palmer (1999): agent-­‐based modeling LeBaron and Tesfatsion (2008): agent-­‐based modeling Leroy and Porter (1981): excess volaPlity in stock prices Leiau and Ludvigson (1991): W/C correlates negaPvely with future returns Lo and MacKinlay (1988): variance raPo tests Loewenstein, O’Donoghue, and Rabin (2003): projecPon bias Malmendier and Nagel (2011): Recency bias and role of personal experience Parker (2001): Cov of returns and ΔlnC rises from short-­‐ to medium-­‐run Piazessi and Schneider (2009): extrapolaPve beliefs in the housing market Previtero (2010): extrapolaPve beliefs and annuity investment Shiller (1981): excess volaPlity in stock prices Summers (1986): power problems in financial econometrics Tortorice (2010): extrapolaPve beliefs in unemployment forecasts Model
CARA habit preferences (Alessie and Lusardi)
•  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
Quick review of time series models
If growth in dividends (ΔlnD = Δd) is captured
by an auto-regressive model with p lags, then:
Refer to this as an AR(p) model.
Natural expectations
Data generating process
Natural expectations
We will study cases 1 ≤ p ≤ 40.
Model matches the data for p ≤ 20.
Consumption is a weighted average of ct-1 and Yt
Permanent income
Shift term
Value function:
Price of the equity tree:
U.S. Log Real Capital Income (1947q1-­‐2010q3) U.S. NIPA (BEA): net opera=ng surplus of private enterprises. Perceived IRF’s for real capital income Unit shock Quarters Calibration
Actual IRF’s for cumulaPve excess returns deriving from a unit shock to dividends Actual IRF’s for consumpPon Covariance of consumpPon growth and cumulaPve return at different horizons Empirical evaluaPon •
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Annual data (1929-­‐2010) Real per-­‐capita consumpPon: US NIPA Excess returns P/E raPos •  SimulaPons annualized for comparisons •  SimulaPons generated for 82 years of data •  Monte Carlo to generate confidence intervals CorrelaPon of Excess Returns in Year τ with CumulaPve Excess Returns for Years τ + 2 to τ + 5, for Different AR(p) Models of Earnings CorrelaPon of P/E40 in Year τ with CumulaPve Excess Returns for Years τ + 2 to τ + 5, for Different AR(p) Models of Earnings CorrelaPon ΔlnCτ with CumulaPve Excess Returns for Years τ+2 to τ+5, for Different AR(p) Models of Earnings CorrelaPon of P/E40 in Year τ with (lnCτ+6 - lnCτ+2), for Different AR(p) Models of Earnings CorrelaPon of ΔlnCτ with (lnCτ+6 - lnCτ+2), for Different AR(p) Models of Earnings ApplicaPon to equity premium puzzle •  Equity Premium for Different AR(p) Models of Earnings Standard deviaPon of equity returns for Different AR(p) Models of Earnings Standard DeviaPon of ConsumpPon Growth for Different AR(p) Models of Earnings Covariance of consumpPon growth and cumulaPve return at different horizons Simulated data Empirical data How would RE agents behave in this economy? •  Closed form soluPon for consumpPon funcPon and asset allocaPon •  RE agents are relaPvely highly leveraged •  RE agents adjust their equity allocaPon counter-­‐cyclically Leverage of RE agents for Different AR(p) Models of Earnings Summary 1.  Fundamentals follow hump-­‐shaped dynamics: •  Short-­‐run momentum •  Long-­‐run (parPal) mean reversion 2.  Agents esPmate simple models –  Parsimonious, tractable –  Typical models chosen in economics literature Summary 1.  Low order forecasPng equaPons miss some of the mean reversion in fundamentals, so resulPng asset prices exhibit excess volaPlity and long-­‐run mean reversion 2.  Cycles in consumpPon (and investment) 3.  The covariance of returns and consumpPon growth rises and then falls with horizon h
4.  Equity is perceived as many Pmes riskier than it actually is 5.  RaPonal investors should hold far more equity than typical investors 6.  RaPonal investors should follow a countercyclical investment strategy 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 relaPon: –  Construct earnings to book raPo from 1872-­‐2010. –  Calculate deviaPon of earnings to book raPo relaPve to ten-­‐year moving average –  Call this deviaPon: Earnings cycle. -­‐0.01 -­‐0.04 1881 1886 1891 1896 1901 1906 1911 1916 1921 1926 1931 1936 1941 1946 1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001 2006 0.04 Earnings cycle 0.03 0.02 0.01 0 -­‐0.02 -­‐0.03 Source: Fuster, Hebert, and Laibson In years 0.04 0.03 Out years 0.02 Earnings cycles 0.01 -­‐0.01 1881 1886 1891 1896 1901 1906 1911 1916 1921 1926 1931 1936 1941 1946 1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001 2006 0 -­‐0.02 -­‐0.03 -­‐0.04 Source: Fuster, Hebert, and Laibson Exit if earnings cycle was above 0.0085 within last two years (unless you’re in a deep bear market) 1872 1877 1882 1887 1892 1897 1902 1907 1912 1917 1922 1927 1932 1937 1942 1947 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 2002 2007 0.6 -­‐0.4 Real returns 0.4 0.2 0 -­‐0.2 Source: Fuster, Hebert, and Laibson 1872 1877 1882 1887 1892 1897 1902 1907 1912 1917 1922 1927 1932 1937 1942 1947 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 2002 2007 0.6 0.4 0.2 0 -­‐0.2 -­‐0.4 Source: Fuster, Hebert, and Laibson Performance metrics •  In years: 11.5% real return •  Out years: -­‐2.6% real return •  All years: 7.9% real return Source: Fuster, Hebert, and Laibson Macro predictors of high future excess returns •
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Low P/E40 Low equity returns Low consumpPon growth Low earnings Low real investment Low return expectaPons