The Great Divorce between Investment and Pro tabilityMay 27, 2020 · The Great Divorce between Investment and Pro tability Mete Kilic Louis Yang Miao Ben Zhang University of Southern

The Great Divorce between Investment andProfitability

Mete Kilic Louis Yang Miao Ben Zhang

University of Southern California

May 27, 2020

SFS Cavalcade

Investment, profitability, and the stock market

• Firm investment and profitability are related to expected returns in the cross-section

I High investment predicts lower returnsI Titman, Wei, and Xie (2004), Cooper, Gulen, and Schill (2008), Xing (2008) ...

I High profitability predicts higher returnsI Novy-Marx (2013), Ball et.al. (2015), Ball et.al. (2016) ...

I Investment and profitability factors explain the cross-section of expected returnsI Fama and French (2015), Hou, Xue, and Zhang (2015)

• Investment and profitability premia only significant in recent decades

I Linnainmaa and Roberts (2018)

• Basic investment-based model with persistent productivity predicts corr(inv , prof ) > 0

• This paper:

I novel facts about differences between two episodes in the U.S. stock market history

I investigate the joint cross-section of investment and profitability, and

I the relation between investment and profitability factors using these episodes

Kilic, Yang, Zhang (USC Marshall) Investment and Profitability May 27, 2020 1 / 18

Investment and profitability factors over the last century

-.5

-.25

0

.25

.5

.75

1M

onth

ly p

erce

nt re

turn

1930 1940 1950 1960 1970 1980 1990 2000 2010 2020Year

CMA (L−H Investment)RMW (H−L Profitability)

• 10-year moving average of investment and profitability factors

• Pre 1980: corr(RMW ,CMA) < 0, RMW and CMA averages are not significant

• Post 1980: corr(RMW ,CMA) > 0, RMW and CMA averages are both significant


Investment and profitability in the cross-section

-.2

0

.2

.4

Corr

elat

ion(

OP,

INV)

1930 1940 1950 1960 1970 1980 1990 2000 2010 2020Year

• The cross-sectional correlation between investment and profitability in each year

• Pre 1980: corr(inv , prof ) > 0 in most years

• Post 1980: corr(inv , prof ) < 0 in most years

By industry By characteristic


Decomposing the investment-profitability relation

What drives the change in the sign ofcorr(inv , prof )?

• A change in firm investmentpolicy, or

• The composition of firms in thestock market

Decomposition of the cross-sectionalcorrelation:

corr(uj,t , ij,t) =cov(uj + uj,t , ij + ij,t)

σu(t)σi (t)

=cov(uj , ij )

σu(t)σi (t)︸︷︷︸Between-firm component

+ Within-firm component

Between-firm component

-.2

-.1

0

.1

.2

.3

Corr

elat

ion(

OP,

INV

)

1960 1970 1980 1990 2000 2010Year

Within-firm component

-.2

-.1

0

.1

.2

.3

Corr

elat

ion(

OP,

INV

)

1960 1970 1980 1990 2000 2010Year


A simple model• Individual firm investment with quadratic costs as in Abel (1983)

• CapitaldKt = (it − δKt)dt

• DividendDt = utKt −

c

2i2t

• Optimal investment

maxit

p(ut)it −c

2i2t

it =p(ut)

c

• Firm value

Vt = Et

[∫ ∞t

e−r(s−t)Dsds

]

• Expected return

Et

[dVt + Dtdt

Vt

]= rdt


Classic and boom firms• Two firm types that differ in the process for u and in r

1. Classic firms

I Discount rate is rsI Profitability process

dut

ut= σdBt

I Optimal investment

ic (ut) =1

c(rs + δ)ut

2. Boom firms

I Discount rate is rlI Profitability process

dut

ut= σdBt + (eZt − 1)dNt

I Nt is a Poisson process with intensity λ and µz = E[eZt]− 1 > 0

I Optimal investment

ib(ut) =1

c(rl + δ − λµz )ut


Examples of profitability booms

02468

10

Prof

itabi

lity

Rank

ing

1995 2000 2005 2010Year

Amazon.com

02468

10

Prof

itabi

lity

Rank

ing

1990 1995 2000 2005Year

Biogen

02468

10

Prof

itabi

lity

Rank

ing

1985 1990 1995 2000Year

Comverse Technology

02468

10Pr

ofita

bilit

y Ra

nkin

g

1980 1985 1990 1995 2000Year

Amgen

02468

10

Prof

itabi

lity

Rank

ing

2000 2005 2010 2015Year

Booking Holdings

02468

10

Prof

itabi

lity

Rank

ing

1990 1995 2000 2005Year

SICOR

IPO IPO

IPOIPO

IPO IPO BoomBoom

Boom Boom

BoomBoom

“Because of our emphasis on thelong term, we may make deci-sions and weigh tradeoffs differ-ently than some companies. [...]We will continue to make invest-ment decisions in light of long-term market leadership considera-tions rather than short-term prof-itability considerations ...”— Jeffrey P. Bezos, “Amazon.com 1997 Letter to

Shareholders” (page 1)


The stock market

• Case 1: Only classic firms

I i and u are perfectly positively correlated in the time-series and cross-section

I Expected returns do not vary as a function of investment and profitability

• Case 2: Classic and boom firms

I For the same level of profitability u, optimal investment of a classic and a boom firmdiffer by a factor of q:

q =rs + δ

rl + δ − λµz

I i and u are perfectly positively correlated in the time-series, not in the cross-section

I q > 1 can hold both due to λµz > 0 and rs > rl

• Example for Case 2

I Compare a classic and a boom firm with ub,t = φuc,t with φ < 1

I Optimal investments are ib,t = qφic,tI Boom firm’s investment is higher despite lower profitability if qφ > 1

I Both investment and profitability premia are rs − rl with these two firms


Investment and profitability with classic and boom firms• A cohort of classic and boom firms born T years ago with ub,0 = φuc,0

• Variation within firm types gives rise to positive cross-sectional correlation

• Variation across firm types gives rise to negative cross-sectional correlation

Fitted Line

• If q is large enough, the negative correlation can dominate

Parameters and expected growth


Investment and profitability premia

• Boom firms have higher cash flow duration compared to classic firms

• The cross-section of expected returns is fully characterized by the “duration premium”rs − rl across classic and boom firms

• Under the assumption that the mass of boom firms is tilted towards lower currentprofitability:

I Profitability premium (RMW)

rR − rW = ξ(rs − rl ),

I Investment premium (CMA)

rC − rA = ψ(rs − rl )

where ξ, ψ > 0.


Mapping to data

• Case 1: Only classic firms

I Data prior to 1980 (Early period)

• Case 2: Classic and boom firms

I Data since 1980 (Later period)


Distribution of expected cash flow duration

Den

sity

12 14 16 18 20 22 24 26 28 30 32Duration [years]

Early PeriodLater Period

• Duration following Dechow, Sloan, Soliman (2004) and Weber (2018)

• Realized duration mapped onto firm characteristics to obtain expected duration

• Later (early) period characterized by presence (absence) of long duration firms

• Consistent with Case 1 (Case 2) representing early (later) period

Duration calculation


Distribution of investment by profitability

0

.1

.2

.3

.4

.5

.6

1 2 3 4 5 6 7 8 9 10Operating Profitability

1. Asset GrowthLater PeriodEarly Period

0

.1

.2

.3

.4


2. Asset Growth(controlling for industry)

Later PeriodEarly Period

0

.1

.2

.3

.4

.5


3. Asset Growth(controlling for size)

Later PeriodEarly Period

.1

.2

.3


4. Future Asset GrowthLater PeriodEarly Period

.2

.3

.4

.5

.6

.7


5. Tangible InvestmentLater PeriodEarly Period

.2

.3

.4

.5


6. Intangible InvestmentLater PeriodEarly Period

• Investment increasing in profitability in early period as in Case 1

• The rise in long duration firms flips this relation in later period as in Case 2


Investment and profitability of newly listed firms

-.15

-.1

-.05

0

.05

Indu

stry

-adj

uste

d pr

ofita

bilit

y

1960 1970 1980 1990 2000 2010 2020Year

0

.2

.4

.6

.8

Indu

stry

-adj

uste

d in

vest

men

t

1960 1970 1980 1990 2000 2010 2020Year

• Newly listed firms since 1980 characterized by low profitability and high investment

• Consistent with the evidence that negative correlation is due to between-firm variation

• The addition of boom firms is the source of the negative correlation in Case 2


Cash flow duration and expected returns

• Monthly average returns of portfolios sorted on duration

Early period

Sorted by duration Sorted by duration within size group

1 5 10 10−1 1 5 10 10−1

Dur 15.83 17.01 18.75 16.05 16.93 18.48Ret 0.59∗∗ 0.81∗∗ 0.79 0.19 0.83∗∗ 1.02∗∗∗ 0.83 0.00SE (0.29) (0.38) (0.54) (0.36) (0.34) (0.38) (0.53) (0.26)

Later period

Sorted by duration Sorted by duration within size group

1 5 10 10−1 1 5 10 10−1

Dur 15.28 19.08 23.43 16.05 18.25 21.38Ret 0.94∗∗∗ 1.21∗∗∗ 0.13 −0.81∗∗ 1.04∗∗∗ 1.07∗∗∗ 0.41 −0.64∗∗

SE (0.24) (0.32) (0.51) (0.35) (0.25) (0.29) (0.47) (0.29)

• Little variation in duration and expected returns in early period

• Long duration firms in later period have lower expected returns (as in Weber (2018))

• Corresponds to the duration premium rs > rl in the model


Reconciling theory and evidence

• Assumptions

1. Only classic firms in the early period (Case 1), both classic and boom firms in thelater period (Case 2)

2. Duration premium between the expected returns of classic and boom firms

• Results

1. Cross-sectional correlation between investment and profitability

I Positive in earlier period (Case 1), negative in later period (Case 2)

2. Cross-sectional correlation between investment and profitability after firm FE

I Always positive in both early and later periods (Cases 1 and 2)

3. Insignificant (significant) investment and profitability premia in early (later) period

I Driven by absence (presence) of boom firms in the early (later) period

I Empirically consistent with Linnainmaa and Roberts (2018)

4. Investment and profitability premia are driven by the same source when significant

I Both driven by the duration premium in Case 2

I Empirically consistent with Gormsen and Lazarus (2020) and Goncalves (2020)


Venture capital and the investment/profitability factorsPanel A: North American

(InvVC/InvTOT = 1.27%)

-.5

-.25

0

.25

.5

.75

1

Mon

thly

per

cent

retu

rn

1990 1995 2000 2005 2010 2015 2020Year


ρ = 0.79

Panel B: Asian Pacific Except Japan


-.5

-.25

0

.25

.5

.75

1

Mon

thly

per

cent

retu

rn

1990 1995 2000 2005 2010 2015 2020Year


ρ = 0.64

Panel C: Europe


-.5

-.25

0

.25

.5

.75

1

Mon

thly

per

cent

retu

rn

1990 1995 2000 2005 2010 2015 2020Year


ρ = -0.66

Panel D: Japan


-.5

-.25

0

.25

.5

.75

1

Mon

thly

per

cent

retu

rn

1990 1995 2000 2005 2010 2015 2020Year


ρ = -0.91

• VC investments are usually long-term oriented (Gompers and Lerner (2001))

• Similar to boom firms in the stock market: valuable due to upside potential

• Investment/profitability factor correlation is positive where of VC investment share is high

Rise of VC in the US


Conclusion

• Two periods in the U.S. stock market over the last century exhibit a completely differentjoint distribution of investment and profitability

• Our analysis

I reveals several novel facts about what is different before and after 1980

I guides theories of the cross-section of firm characteristics and expected returns

• Crucial to acknowledge the joint presence of classic and boom firms to understandpost-1980 U.S. stock market and new asset pricing factors

• Differences between pre-1980 and post-1980 serve as a laboratory

I Cross-sectional relation between investment and profitability

I Significance of investment and profitability premia

I Relation between investment and profitability factors

“If you’re a shareowner in Amazon, you may want to take a seat, because we’re not thinkingsmall. [...] I’m confident that our long-term oriented shareowners will understand and embraceour approach, ...”

— Jeffrey P. Bezos, “Amazon.com 2020 Q1 Earning’s Report” (page 1)


Correlation by industry Back

Panel A: Manufacturing

-.2

0

.2

.4

Cor

rela

tion(

OP,

INV

)

1960 1970 1980 1990 2000 2010Year

Panel B: Transportation

-.4

-.2

0

.2

.4

Cor

rela

tion(

OP,

INV

)

1960 1970 1980 1990 2000 2010Year

Panel C: Wholesale & Retail

-.4

-.2

0

.2

.4

Corr

elat

ion(

OP,

INV)

1960 1970 1980 1990 2000 2010Year

Panel D: Service & Finance

-.2

0

.2

.4

Corr

elat

ion(

OP,

INV)

1960 1970 1980 1990 2000 2010Year

Correlation by other characteristics Back

Panel A: NASDAQ firms

-.3

-.15

0

.15

.3

Corr

elat

ion(

OP,

INV

)

1960 1970 1980 1990 2000 2010Year

Panel B: NYSE&Amexfirms

-.3

-.15

0

.15

.3

Cor

rela

tion(

OP,

INV)

1960 1970 1980 1990 2000 2010Year

Panel C: Small cap firms

-.3

-.15

0

.15

.3

Corr

elat

ion(

OP,

INV)

1960 1970 1980 1990 2000 2010Year

Panel D: Large cap firms

-.3

-.15

0

.15

.3

Corr

elat

ion(

OP,

INV)

1960 1970 1980 1990 2000 2010Year

Panel E: Growth firms

-.3

-.15

0

.15

.3

Corr

elat

ion(

OP,

INV)

1960 1970 1980 1990 2000 2010Year

Panel F: Value firms

-.3

-.15

0

.15

.3Co

rrel

atio

n(O

P, IN

V)

1960 1970 1980 1990 2000 2010Year

Expected dividend growth Back

The parameter values are:rs = 0.16, rl = 0.03, δ = 0.1, c = 4, φ = 0.75, σ = 0.04, u0 = 0.2, λ = 0.01. Z has a normaldistribution with mean µz = 0.15 and σz = 0.1. We simulate 1,000,000 firms and use τ = 10and mc = mb = 0.5. The correlation between i and u is -28%. The model implied values areq = 2.026 and q = 1.714 satisfying the negative covariance condition q > q.

1 2 3 4 5 6 7 8 9 10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Classic firms

Boom firms

Duration calculation Back

• Estimate realized cash flows for each firm(Clean Surplus Accounting)

CFi,t+s = BVi,t+s−1

(ROEi,t+s − ∆BVi,t+s

)

• Estimate an ex-post duration for each firm(Dechow, Sloan, and Soliman (2004) and Weber (2018))

Duri,t =

∑Ts=1 s × CFi,t+s/(1 + r)s

Pi,t

+

(T +

1 + r

r

) Pi,t −∑T

s=1 CFi,t+s/(1 + r)s

Pi,t

• Estimate ex-ante duration for each firm using projection(Da (2009) and Hou, Mo, Xue, and Zhang (2018))

log(Duri,t) = αt + β1,t log(MEi,t) + β2,tROEi,t + β3,t∆BVi,t + εi,t

Et [log(Duri,t)] = αt + β1,t log(MEi,t) + β2,tROEi,t + β3,t∆BVi,t

• T = 10 years, r = 0.12

Institutional VC investment Back

Institutional investors targeting venture capital funds

.5

.6

.7

.8

.9

Prop

ortio

n of

VC

New

Com

mitm

ents

from

Inst

itutio

nal I

nves

tors

1970 1980 1990 2000 2010Year

Institutional investors targeting long-duration stocks

-.2

-.15

-.1

-.05

0

Rela

tive

Prob

abili

ty o

f Bee

n H

eld

by In

stitu

tiona

l Inv

esto

rs

1970 1980 1990 2000 2010Year

Documents

The Great Divorce between Investment and Pro tabilityMay 27, 2020 · The Great Divorce between Investment and Pro tability Mete Kilic Louis Yang Miao Ben Zhang University of Southern