Understanding Predictability (JPE, 2004)

Transcription

1 Understanding Predictability (JPE, 2004) Lior Menzly, Tano Santos, and Pietro Veronesi Presented by Peter Gross NYU October 19, 2009 Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

2 Introduction Market returns forecastable by the dividend yield However, relation not stable (such as in the 1990s) Price dividend ratio does not forecast dividend growth Combination of time-varying risk tolerance and time-varying dividend growth rates can solve this problem Increase in dividend growth leads to Increase in expected return (due to greater duration risk) Increase in price dividend ratio This can weaken forecasting power of dividend yield for dividend growth and expected returns Need to correct usual predictive regressions by augmenting with consumption price ratio Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

3 Overview 1 Model 2 Price Consumption Ratio 3 PD Ratios, Expected Returns, and Dividend Growth Homogeneous Cash Flow Risk Heterogeneous Cash Flow Risk 4 Empirical Evaluation 5 Conclusion 6 Discussion Predictability of Dividend Growth Predictability of Stock Returns Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

4 Model (1) - Agents Continuous Time, t 2 [0, ). One perishable consumption good Representative agent has preferences given by: Z E e ρt log(c t 0 X t )dt C t is current consumption, X t external habit level De ne the surplus ratio as S t = C t C t X t Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

5 Model (2) - Consumption Process The inverse surplus ratio, Y t = 1 S t processes and log consumption, c t follow the dy t = k(ȳ Y t )dt α(y t λ)(dc t E t [dc t ]) dc t = µ c dt + σ c db 1 t α > 0 ensures that positive innovations in consumption growth will lead to negative innovations in the inverse surplus λ 1 ensures lower bound for inverse surplus ratio k controls spead of mean reversion Furthermore, restrict α so that Cov t (dc t, dx t ) > 0 Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

6 Model (3) - Cash Flow Process n risky nancial assets, paying Dt i n units of consumption good at i=1 time t Other income cash ow Dt 0 (labor income, government transfers,...) Consumption shares are given by st i = D t i, i = 1, 2,..., n and governed Ct i by ds i t = φ i ( s i s i t)dt + s i t σ i (s t )db 0 t σ i (s t ) = v i n st j v j j=0 Here, B t is a N dimensional standard Brownian motion (N n + 1), and v i is a vector of constants for each i = 1, 2,..., n. The v i n need to be normalized to be identi ed: s j v j = 0 j=0 Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

7 Model (4) - Cash Flow Process Log dividends, δ i t = log(d i t), are governed by dδ i t = µ i D (s t)dt + σ D (s t )db 0 t s µ i D (s t) = µ c + φ i i σi (s t )σ(s t ) s i t σ D (s t ) = σ c + σ i (s t ), σ c = (σ c, 0, 0,..., 0) Quantity of economic importance is Cov(dδ i t, dc t ) = σ 2 c + θ i CF where θ i CF = v i 1 σ c If negative, asset pays o in bad times and is hence worth more to agent Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

8 Price Consumption Ratio (1) - Total Wealth Portfolio Price/Consumption ratio of total wealth portfolio is given by P TW t C t = 1 ρ ρ + kȳ St ρ + k If S t is at average, then everything collapses to standard case Decrease in risk aversion (increase in S t ) pushes ratio up The excess return is given by dr TW t = µ TW µ TW σ TW R (S t ) = R (S t )dt + σ TW R (S t )dbt 1, where R (S t ) R = [1 + α(1 λs t )] σ TW 1 + kys t(1 λs t )α kys t + ρ σ c Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

9 Price Consumption Ratio (2) - Figure 1 Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

10 PD Ratios and Expected Returns (1) - Homogeneous Cash Flow Risk Let θ i CF = 0 for all i so that Cov(dδ i t, dc t ) = σ 2 c. Then Pt i Dt i = a0 i + a1s i t + a2 i s i st i + a3 i s i st i S t ( ) E t [drt i kys t (1 λs t ) ] = [1 + α(1 λs t )] 1 + kys t + ρ 1 + f ( s i /st) i Here, f (1) = 0, and f 0 < 0. Also, all the coe cients a i j are positive. PD ratio is increasing in relative share and surplus, but expected return goes in opposite directions as these move σ 2 c Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

11 PD Ratios and Expected Returns (2) - Homogeneous Cash Flow Risk Expected return and dividend growth regressions can be corrected as follows: E t [dr i t ] = b i 0(S t ) + b i 1(S t ) Di t P i t E t [dδ i t] = m i 0(S t, s t ) + m i 1(S t ) Pi t D i t + b i 2(S t ) C t P i t Intuition for this: D t i more sensitive to relative share changes and C Pt i t Pt i more sensitive to surplus consumption changes Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

12 PD Ratios and Expected Returns (3) - Figure 2 Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

13 PD Ratios and Expected Returns (4) - Heterogeneous Cash Flow Risk Without habit persistence, the price dividend ratio of ith asset is: Pt i Dt i = 1 ρ + φ i 1 + φi ρ s i The expected excess return in turn is given by s i t E t [dr i t ] = σ 2 c + θi CF n j=0 θ j CF sj t 1 + (φ i /ρ)( s i /s i t) = b 0 + b i 1(s t ) Di t P i t Perfect linear relation between expected returns and dividend yield. Increase in relative share increases price dividend ratio/expected return (more so if φ i /ρ is small) Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

14 PD Ratios and Expected Returns (5) - Heterogeneous Cash Flow Risk With habits in place, no closed form solutions available However, very good approximations (error around 0.1 per cent) can be obtained: Pt i Dt i â0 i + â1s i t + â2 i s i s i t + â3 i s i st i S t E t [dr i t ] ˆb i 0(S t ) + ˆb 1 (S t ) Di t P i t E t [dδ i t] ˆm i 0(S t, s t ) + ˆm i 1(S t ) Pi t D i t + ˆb 2 (S t ) C t P i t Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

15 Empirical Evaluation (1) - Data Quarterly dividends, returns, and market equity from CRSP Sample: value-weighted industry portfolios Cash ows include both dividends and share repurchases Per capita consumption (NDS) from NIPA, de ated by PCE Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

16 Empirical Evaluation (2) - Calibration of Preferences Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

17 Empirical Evaluation (3) - Calibration of Cash Flows Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

18 Empirical Evaluation (4) - Predictability of Dividend Growth Cash ow predictive regressions: d i t,t+τ = β i o + βi X X t + ɛ i t,t+τ, τ = 1, 4, or 7 years X t is si st i, Pi t Dt i, or both PD ratio is never signi cant when market dividends are used, and only weakly when industries are used The relative share is a strong predictor of dividend growth, with R 2 up to 41 percent for market at the 7 year horizon In individual regressions, relative share is signi cant predictor for 15 out of 20 industries, with R 2 above 30 percent in 10 cases Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

19 Empirical Evaluation (5) - Predictability of Dividend Growth Regressions on simulated data also fail to nd predictability of dividend growth rates by price dividend ratio Coe cients in simulated regressions are similar to those in the data Presence of small sample bias since simulated data regressions has lower R 2 than actual data regressions Actual R 2 s are mostly within 90 percent con dence interval of simulated ones when taking into account small sample Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

20 Empirical Evaluation (6) - Predictability of Stock Returns Augmented expected return regression: r i t,t+τ = β i 0 + βi D /P Dt i Pt i + β i C /P C t Pt i + ɛ i t,t+τ, τ = 1, 4, or 7 years With market return, no signi cance for consumption price ratio, due to very slow mean reversion of market With industry returns, the consumption price ratio becomes signi cant if mean reversion of dividends is quick R 2 for some industries jumps dramatically (e.g., from 3 to 37 percent for mining) when this is included Simulated data regression results mostly agree with empirical ones, with small sample bias present in data Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

21 Empirical Evaluation (7) - Relation between Dividends and Return Predictability Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

22 Conclusion An increase in dividend growth increases both expected returns and price dividend ratios An increase in risk aversion increases expected returns while decreasing price dividend ratios This makes dividend yield less reliable forecaster of future returns By including consumption price ratio, one can decouple these two sources of return predictability The extent to which dividends are predictable in uences predictability of returns by the dividend yield Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

23 Discussion (1) - Share Process The share process for each security assumed to be mean-reverting to long run share Secular trends in industries can be seen as convergence to long-run share However, equilibrium share of sectors is likely time-varying itself Introducing time varying long run share could make cash ows riskier Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

24 Discussion (2) - Portfolio Selection The model works well with the industry portfolios selected What about other portfolios? In particular, HML and SMB portfolios to nd out the whether value premium goes away Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25

25 Discussion (3) - Cash Flow Homogeneity Are industries homogeneous enough for cash ows to be similar? Sorting across similar cash ows characteristics would be a useful exercise See if resulting portfolios largely line up with industry ones Presented by Peter Gross (NYU) Understanding Predictability October 19, / 25