The Consumption of Active Investors and Asset Prices

Transcription

1 The Consumption of Active Investors and Asset Prices Department of Economics Princeton University June 6, 2009

2 Motivation does consumption asset pricing work with unconstrained active households? no reliable data on the consumption of wealthy households active households derive a large fraction of their income from the capital they own consumption of these households very volatile since their net worth is very volatile Idea: Use macro data to get aggregated consumption series of these households. valid stochastic discount factor that yields reasonable preference parameters with standard CRRA utility Econometric Society North American Summer Meeting, June 6,

3 Outline who are the active, unconstrained households? using macro data to construct consumption expenditure series estimating the Euler equation using GMM implications for the cross-section of asset returns importance of non-linearity of SDF time varying risk bearing capacity of active households related literature conclusions Econometric Society North American Summer Meeting, June 6,

4 active households Active households hold stocks, bonds directly, private business, sophisticated variable wage closely linked to equity, e.g. bonuses wealthy, derive large part of income from capital owned passive households wealth largely primary residence, vehicles, (human capital) financial wealth in deposits, pension and insurance funds income mostly fixed wages: life-cycle and precautionary savers top 1% of households (SCF data from Carroll (2000)) hold 60% of their net worth in equity (excl. pension funds) own 30% of total wealth and 50% of total equity Econometric Society North American Summer Meeting, June 6,

5 Total payout series (TP) Identifying assumption Total payout net of reinvestment by the business sector (corporate and non-corporate) finances consumption of active households. Formula T P = EP NBI + NINT + T P W + P ROP INC RoW + BDCB EP: net equity payout (div. and equity rep.) of non-fin. corp. NBI: net bond issuance of non-financial corporate NINT: net interest paid by non-financial corporate TPW: top percentile wage income (Piketty and Saez 2003) PROPINC: proprietors income net of reinvestment RoW: net flows to the rest of the world BDCB: net payout from commercial banks and brokers-dealers Econometric Society North American Summer Meeting, June 6,

6 Flow of Funds Accounts Data sources net equity issuance and dividends household net acquisition of different asset classes proprietor s capital expenditure National Income and Product Accounts personal consumption: includes durables, excludes housing investment interest paid by sector proprietor s income before capital consumption adjustment Internal Revenue Service (Piketty and Saez 2003) income of the top percentile of tax filers, before taxes average income of 1.1 million USD in 2005 Econometric Society North American Summer Meeting, June 6,

7 Total payout growth and excess market return year total payout growth (forward) market excess return Econometric Society North American Summer Meeting, June 6,

8 Top percentile income (TPI) Identifying assumption Realized income choice is optimal: active households do not realize income for tax purposes they do not consume. data from individual tax filings of top 1% earners also shows that assumption of TP is reasonable outliers: 1930, 1986, 1987 Econometric Society North American Summer Meeting, June 6,

9 Top percentile income and total payout growth ( ) top percentile income growth total payout growth Econometric Society North American Summer Meeting, June 6,

10 Summary statistics of log real growth cov. with market mean std autocorr backward forward total cons luxury ind. (61-01) total payout top perc. income all normalized to per capita luxury: sales of a few luxury retailers, up to 1991 only Tiffany (Aït-Sahalia et al. 2004) Econometric Society North American Summer Meeting, June 6,

11 Is it really consumption? if active households actively use e.g. deposits consumption series are not net of taxes consumption fluctuation could be due mostly to durables and housing all measure aggregate consumption of the group, while wealthy have substantial idiosyncratic risk (Carroll 2000): likely to overestimate risk-aversion wealthy might have different utility function, e.g. utility over spending Econometric Society North American Summer Meeting, June 6,

12 Luxury sales and total payout growth ( ) luxury expenditure growth total payout growth Econometric Society North American Summer Meeting, June 6,

13 for any return R t+1 : Euler equation E t [βu (c t+1 )R t+1 ] = u (c t ) using CRRA utility: for levels of returns: for excess returns: u(c) = cγ 1 γ 1 ( ) γ ct+1 E t [β R t+1 ] = 1 c t }{{} SDF ( ) γ ct+1 E t [ R c t+1] e = 0 t Econometric Society North American Summer Meeting, June 6,

14 Moment conditions for unconditional GMM moment conditions: E [ɛ] = 0, where ɛ t = [ɛ 1 t ɛ 2 t ɛ 3 t ɛ f t ] ( ) γ ct+1 ( ) Rt+1 i R f t+1 = ɛ i t+1 for i = 1..3 c t β ( ct+1 c t ) γ R f t+1 1 = ɛf t+1 GMM estimation using W = I 4 ( ) ɛ t W ɛ t min β,γ pricing 3 long-short portfolios (HML, SMB, market excess return) and the riskless rate covariance matrix calculated by VARHAC with own lags (den Haan and Levin 1996) t Econometric Society North American Summer Meeting, June 6,

15 Cross section of asset returns Theoretical result for excess returns ( E[R e i ] = R f cov Factor pricing approach β ( ct+1 c t ) γ, R e i take linear factor and estimate factor loadings β i of R e i E[R e i ] = α + λ β i α = 0 usually rejected: cannot price the levels of returns strongly criticized by Lewellen et al. (2007) use the SDF derived from consumption directly with parameter estimates from the GMM exclude 11: the small growth portfolio is likely to be mispriced ) Econometric Society North American Summer Meeting, June 6,

16 Cross section: 25 Fama-French portfolios with TP series 25 two period total payout 20 realized return (%) predicted return (%) Econometric Society North American Summer Meeting, June 6,

17 Estimates timing adj. ˆγ ˆβ J-stat R 2 R 2 (s.e.) (s.e.) (p-value) excl. 11 total payout (TP), two-period (20.82) (2.344) (0.216) backward (38.38) (2.394) (0.002) forward (105.91) (7.077) (0.050) Econometric Society North American Summer Meeting, June 6,

18 Estimates timing adj. ˆγ ˆβ J-stat R 2 R 2 (s.e.) (s.e.) (p-value) excl. 11 top percentile income (TPI), two-period (10.16) (0.836) (0.172) backward (12.34) (1.380) (0.393) forward (6.81) (0.856) (0.007) Econometric Society North American Summer Meeting, June 6,

19 Reduced noise estimates timing adj. ˆγ ˆβ J-stat R 2 R 2 (s.e.) (s.e.) (p-value) excl. 11 TP and TPI average, two-period (12.19) (0.679) (0.188) two-period timing maximizes signal to noise (measurement error) ratio average of two data sources: attenuates strong non-linear effect of outliers due to measurement error Econometric Society North American Summer Meeting, June 6,

20 Importance of non-linearity, the SDF (TP+TPI, two-period) SDF year Econometric Society North American Summer Meeting, June 6,

21 Share of total consumption by active households year cash flow of portfolio share top percentile income share total payout share Econometric Society North American Summer Meeting, June 6,

22 Who bears aggregate risk? year residual consumption growth total payout growth Econometric Society North American Summer Meeting, June 6,

23 Some preliminary data The crisis of 2008 total payout close to 4 trillion in 2007 non-financial dividend almost unchanged non-financial net equity repurchase: 831 billion in 2007 to 395 billion in 2008, 106 billion offset by decrease in net bond issuance financial: net equity repurchase and dividends 300 billion in 2007, in 2008 reversed to influx of 900 billion bonuses fell substantially 20-30% drop in total payout not unconceivable. Econometric Society North American Summer Meeting, June 6,

24 Related literature Malloy et al. (forthcoming) find 4.1% annual consumption volatility for top 1 3 group of stockholders in the CEX, 12.9% at the individual level, uses Epstein-Zin preferences to get γ 10 Aït-Sahalia et al. (2004) shows luxury goods consumption covaries strongly with returns γ 5-10, but do not price levels of returns Basak and Cuoco (1998) show in a simple theoretical model that the consumption of active households has to be around 20 30% to yield reasonable risk aversion Guvenen (2008) shows that Campbell and Cochrane (1999) habit level can be interpreted as the consumption of non-participants in the market Econometric Society North American Summer Meeting, June 6,

25 Conclusions implications for risk sharing: active households bear substantially more risk than passive, both aggregate and redistributional importance of non-linearity of the Euler equation focus on stochastic discount factor, not factor models: Lewellen et al. (2007) argues for such an approach consumption based asset pricing works: do not necessarily need generalized preferences Implication for further research: both risk and risk bearing capacity fluctuates over time: could effect P D ratio Econometric Society North American Summer Meeting, June 6,

26 References Aït-Sahalia, Y., J. A. Parker, and M. Yogo, Luxury Goods and the Equity Premium, Journal of Finance, 2004, 59 (6), Basak, Suleyman and Domenico Cuoco, An equilibrium Model with Restricted Stock Market Participation, Review of Financial Studies, 1998, 11 (2), Campbell, John Y. and John H. Cochrane, By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior, Journal of Political Economy, 1999, 107 (2), Carroll, C. D., Portfolios of the Rich, NBER Working Paper 7826, den Haan, W. J. and A. Levin, Inferences from Parametric Econometric Society North American Summer Meeting, June 6,

27 and Non-Parametric Covariance Matrix Estimation Procedures, NBER Technical Working Paper 195, Guvenen, Fatih, A Parsimonious Macroeconomic Model for Asset Pricing, University of Minnesota, Working Paper, Lewellen, J., S. Nagel, and J. Shanken, A Skeptical Appraisal of Asset-pricing Tests, Stanford University, Working Paper, Malloy, C., T. Moskowitz, and A. Vissing-Jørgensen, Long-Run Stockholder Consumption Risk and Asset Returns, Journal of Finance, forthcoming. Piketty, Thomas and Emmanuel Saez, Income Inequality in the United States, , Quarterly Journal of Economics, 2003, 118 (1), Econometric Society North American Summer Meeting, June 6,