An Analysis of Stock Returns and Aggregate Earnings Yunhao Chen Xiaoquan Jiang Bong Soo Le School of Accounting Dept of Finance Dept of Finance Florida International University Florida State University

Earnings Response Coefficient (ERC) Firm level: earnings changes are positively associated with stock returns (e.g., Ball and Brown 1968, etc) Aggregate level: stock prices react negatively to aggregate earnings news –Kothari, Lewellen, and Warner (KLW), 2006 –Sadka and Sadka (SS), 2009 –Choi, Kalay and Sadka, 2011 –Cready and Gurun (CG), 2010 Puzzling 2

Research Question 1 Whether and how the aggregate earnings response coefficient (ERC) varies over time Is negative aggregate ERC robust over time? –KLW (2006): from 1960 to 2000 –SS (2009): from 1965 to 2005 –CG (2010): from 1973 to 2006 Our sample period: 1881 to

Research Question 2 What drives aggregate ERCs? Campbell (1991) return decomposition: (1) expected return: + (2) changes in expected cash flows (cash flow news): + (3) changes in expected discount rates (discount rate news): – KLW (2006) conjecture that discount rate news dominates SS (2009) show that “Price leads earnings” (i.e., expected return dominates). Contemporaneous vs. dynamic relations We estimate all three components and provide a comprehensive picture of the relation between aggregate earnings and all three return components. 4

Research Question 3 We further decompose discount rate news into risk and mispricing subcomponents following Campbell and Vuolteenaho (2004). What drives discount rate news? Risk or mispricing? What drives the time-varying ERC? –Business cycles and macroeconomic activities –the stock market regulations: Securities Exchange Act of 1934, Fair Disclosure of 2000, the Sarbanes-Oxley Act in

Research Design - Return decomposition Campbell (1991) decomposes return into expected return, cash flow news and discount rate news: a dynamic accounting identity (6) 6

7 Campbell and Vuolteenaho (2004) decompose discount rate news into risk premium (fitted value) and mispricing (residual). The subjective risk premium and mispricing components can be generated from the regression of the objective revision in the expectations of the future discount rates on the revision in the future cross-sectional equity risk premium: where N SRC,t denotes the revision in the expected future cross-sectional risk premium. The fitted value of is a proxy for the subjective revision in the risk premium, and the residual, ε n,t, is a proxy for the revision in the mispricing.

In sum, we decompose the stock return into the following four components: 1.one-period-ahead objective expected returns, 2.the objective revision in the expected long-term cash flows, 3.the subjective revision in the expected risk premium, and 4.the revision in the expected mispricing component. 8

Research Design Contemporaneous returns and earnings relation r t = α + β  Y t + e t, –Return components and earnings (dE/P) relation –Alternative measures of aggregate earnings: earnings changes scaled by book value of equity (dE/B), and earnings surprise as a residual from an autoregressive regression of earnings on lagged earnings and lagged returns. Dynamic relation - Granger causality tests 9

–Vector Autoregressive (VAR) model Z t = A 0 +AZ t-1 + u t, where Z t is a vector of log market returns (r), the cross-sectional equity risk premium (λ), the log book- to-market ratio (bp), and log return on equity (roe), describing the economy at time t. the components of return in (6) is obtained by: E t-1 r t = e1’(A 0 + AZ t-1 ), (10a) N CF,t = [e1’ + e1’ρA(I-ρA) -1 ]u t, (10b) N DR,t = e1’ ρA(I-ρA) -1 u t, (10c) where ei’ = [0 0 1 … 0], picking the i th state variable in the state vector, and I is an identity matrix. 10

Further, in the spirit of Campbell and Vuolteenaho (2004), the subjective revision in the risk premium and the revision in the mispricing components can be expressed by (10e) (10f) This allows us to examine whether risk or mispricing or both determines the relation between stock return and earnings changes. 11

- regression of returns on earnings changes: r t = α + β  Y t + e t, (11) - Using the decomposition of Campbell (1991), E t-1 r t = α 1 + β ER  Y t + e ER,t, (12a) N CF,t = α 2 + β CF  Y t + e CF,t, (12b) N DR,t = α 3 + β DR  Y t + e DR,t. (12c) - Since N DR,t can be further decomposed into subjective risk premium and mispricing, N RISK,t = α 31 + β RISK  Y t + e RISK,t, (13a) N MIS,t = α 32 + β MIS  Y t + e MIS,t. (13b) 12

Sample and Data Robert Shiller's website provides historical earnings, price, and dividend information on the S&P 500 index Moody’s, CRSP, Compustat Sample period: 1881 Q1 to 2009 Q4 (128 years) 13

Aggregate Earnings-Returns Relation Five-year (20-quarter) rolling regressions Figure 1 –Panel A: overall ERC –Panel B to D: component ERC (Expected return ERC, Cash flow news ERC, Discount rate news ERC) 14

Figure 1- Panel A (Overall ERC) Figure 1 beta_Ret date1 JAN1880JAN1890JAN1900JAN1910JAN1920JAN1930JAN1940JAN1950JAN1960JAN1970JAN1980JAN1990JAN2000JAN2010JAN2020 Panel A: Rolling regression of betas of SP Ret on dE/P 15

Figure 1- Panel B (Expected ERC) beta_expR date1 JAN1880JAN1890JAN1900JAN1910JAN1920JAN1930JAN1940JAN1950JAN1960JAN1970JAN1980JAN1990JAN2000JAN2010JAN2020 Panel B: Rolling regression of betas of expected S&P Ret on dE/P 16

Figure 1- Panel C (Cash flow news ERC) beta_NE date1 JAN1880JAN1890JAN1900JAN1910JAN1920JAN1930JAN1940JAN1950JAN1960JAN1970JAN1980JAN1990JAN2000JAN2010JAN2020 Panel C: Rolling regression of betas of S&P Ncf on dE/P 17

Figure 1- Panel D (Discount rate news ERC) beta_-NR date1 JAN1880JAN1890JAN1900JAN1910JAN1920JAN1930JAN1940JAN1950JAN1960JAN1970JAN1980JAN1990JAN2000JAN2010JAN2020 Panel D: Rolling regression of betas of S&P Ndr on dE/P 18

Aggregate Earnings-Returns Relation Overall ERC –Mostly positive before 1960s –Negative from mid-1960s to mid-1990s –Positive after mid-1990s –Overall, time varying Component ERCs - The component ERCs are generally less volatile –Expected return ERCs mostly hover near zero. –Cash flow news ERCs are mostly positive – : discount rate news ERC matches that of the overall ERC –Overall, time varying 19

Aggregate Earnings-Returns Relation Panel A: 1881:Q1-2009:Q4 αβR2R2 RmPARMS T ERPARMS T NcfPARMS T NdrPARMS T Rm t+1 = α + β dE/P t +e t+1 20

Aggregate Earnings-Returns Relation Panel B: 1881:Q1-1969:Q4 RmPARMS T ERPARMS T NcfPARMS T NdrPARMS T Rm t+1 = α + β dE/P t +e t+1 21

Aggregate Earnings-Returns Relation Panel C: 1970:Q1-2000:Q4 RmPARMS T ERPARMS T NcfPARMS T NdrPARMS T Rm t+1 = α + β dE/P t +e t+1 22

Aggregate Earnings-Returns Relation Panel D: 2001:Q1-2009:Q4 RmPARMS T ERPARMS T NcfPARMS T NdrPARMS T Rm t+1 = α + β dE/P t +e t+1 23

Aggregate Earnings-Returns Relation (Multivariate regression) Panel A: 1881:Q1-2009:Q4 αβ1β2β3R2R2 PARM S T Panel B: 1881:Q1-1969:Q4 PARM S T Panel C: 1970:Q1-2000:Q4 PARM S T Panel D: 2001:Q1-2009:Q4 PARM S T dE/P = α + β 1 *ER + β 2 *Ncf - β 3 *Ndr 24

Aggregate Earnings-Returns Relation 25 Overall ERC –Whole and sub period 1: + not significant from zero – : negative significant (KLW, 2005) –Beyond 2000: positive significant Components ERC –Whole period: CF_ERC and DR_ERC significantly positive; offset each other –KLW period: DR_ERC dominates –Beyond 2000: E_ERC dominates Multivariate analysis results - similar

the relation between earnings and return components is time-varying. The time-varying ERCs are determined by the relative importance of the expected returns, cash flow news, and discount rate news. Discount rate news dominates cash flow news before However, in years after 2000, expected return dominates both cash flow news and discount rate news. This can be due to the improvement in the quality of firm disclosure (FD) and the investor confidence after the enactment of the Sarbanes-Oxley Act. Our evidence also reconciles both stories provided by KLW and SS. 26

Dynamic Earnings-Returns Relation (Granger Causality test 1) Panel A: Granger causality test (1881:Q1-2009:Q4) VARqHypothesisCommentsF-statsp-value [Rm, dE]1Ho:A12(L)=0dE→Rm [ER, dE]2Ho:A12(L)=0dE→ER [Ncf, dE]2Ho:A12(L)=0dE→Ncf [Ndr, dE]1Ho:A12(L)=0dE→Ndr Panel B: Granger causality test (1881:Q1-1969:Q4) [Rm, dE]1Ho:A12(L)=0dE→Rm [ER, dE]3Ho:A12(L)=0dE→ER [Ncf, dE]2Ho:A12(L)=0dE→Ncf [Ndr, dE]2Ho:A12(L)=0dE→Ndr Panel C: Granger causality test (1970:Q1-2000:Q4) [Rm, dE]1Ho:A12(L)=0dE→Rm [ER, dE]1Ho:A12(L)=0dE→ER [Ncf, dE]1Ho:A12(L)=0dE→Ncf [Ndr, dE]1Ho:A12(L)=0dE→Ndr Panel D: Granger causality test (2001:Q1-2009:Q4) [Rm, dE]1Ho:A12(L)=0dE→Rm [ER, dE]1Ho:A12(L)=0dE→ER [Ncf, dE]1Ho:A12(L)=0dE→Ncf [Ndr, dE]1Ho:A12(L)=0dE→Ndr

Earnings-Returns Relation (Granger Causality test 2) Panel A: Granger causality test (1881:Q1-2009:Q4) HypothesisCommentsF-stats(p-value) Ho:A21(L)=0Rm→dE Ho:A21(L)=0ER→dE Ho:A21(L)=0Ncf→dE148.96<.0001 Ho:A21(L)=0Ndr→dE Panel B: Granger causality test (1881:Q1-1969:Q4) Ho:A21(L)=0Rm→dE Ho:A21(L)=0ER→dE Ho:A21(L)=0Ncf→dE90.45<.0001 Ho:A21(L)=0Ndr→dE Panel C: Granger causality test (1970:Q1-2000:Q4) Ho:A21(L)=0Rm→dE Ho:A21(L)=0ER→dE Ho:A21(L)=0Ncf→dE Ho:A21(L)=0Ndr→dE56.56<.0001 Panel D: Granger causality test (2001:Q1-2009:Q4) Ho:A21(L)=0Rm→dE Ho:A21(L)=0ER→dE Ho:A21(L)=0Ncf→dE36.37<.0001 Ho:A21(L)=0Ndr→dE

Dynamic Earnings-Returns Relation (Granger Causality tests) 29 Dynamic effect of earnings changes on returns and its components –Earnings do not forecast future market returns (returns follow random walk) –However, earnings have information contents for return components. Dynamic effect of returns and its components on earnings changes –“Prices lead earnings” (prices contain information for future earnings)

Discount rate news decomposition (risk or mispricing) Risk= α + β 1 *dE/P Mis= α + β 2 *dE/P Panel A: αβ1β1 β2β2 R2R2 1927:Q1-2009:Q4 PARMS T PARMS T

Discount rate news decomposition (risk or mispricing) 1927:Q1-1969:Q4 α β 1 β 2 R 2 PARMS T PARMS T :Q1-2000:Q4 PARMS T PARMS T :Q1-2009:Q4 PARMS T PARMS T Risk= α + β 1 *dE/P and Mis= α + β 2 *dE/P 31

Discount rate news decomposition (risk or mispricing) – multivariate dE/P = a + β 1 *ER + β 2 *Ncf + β 3 *Risk + β 4 *Mis Panel B: α β1 β2 β3 β4 R :Q1-2009:Q4 PARMS T :Q1-1969:Q4 PARMS T :Q1-2000:Q4 PARMS T :Q1-2009:Q4 PARMS T

Discount rate news decomposition (risk or mispricing) 33 Overall, discount rate news contain both time- varying risk premium and mispricing Before 2000, mispricing dominates discount rate news After 2000, risk premium dominates discount rate news With improved quality in firm disclosure after 2001, the market’s mispricing may be reduced. Multivariate analysis results - similar

The business cycles, macroeconomic activities and disclosure on ERC We document that the business cycles, macroeconomic activities and fair disclosure and SOA help determine the time-varying ERC. –the aggregate ERC (CF_ERC and DR_ERC ) is affected by the business cycle: more significantly negative when the economy is in recession. –aggregate ERC is affected by macroeconomic activities and/or information environment changes: Positive ERC in latest sample is due to FD 34

Summary 1 We document that the relation between aggregate earnings and returns (aggregate ERC) is time-varying. –positive before the 1960s –became negative from 1960 to mid-1990s –turned to positive again after mid-1990s 35

Summary 2 Discount rate news dominates the relation between aggregate earnings and returns over the time period from 1970 to The expected return component mainly drives the relation in the more recent sample period. 36

Summary 3 Mispricing component seems to play an important role in the sample period before Risk component is the main determinant for the discount rate news in the more recent sample period. the switch around 2000 is due to the improved firm disclosure quality and information environment in the stock market 37

Summary 4 The business cycles, macroeconomic activities helps understand the time-varying ERC. We attribute the change in ERC and the relative importance of components of ERC in recent years to the improved quality of firm disclosure after Regulation Fair Disclosure and the enactment of the Sarbanes-Oxley Act in 2002 (Increased reporting requirements and responsibility of corporate directors) and to macroeconomic conditions. 38

Thank you! 39