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Growth Opportunities and Technology Shocks

Kogan and Papanikolaou (2009)

October 26th, 2009

Kogan and Papanikolaou (2009) Growth Opportunities and Technology Shocks

Introduction

Decompose firm value:

Vf ,t︸︷︷︸value of the firm

= VAPf ,t︸︷︷︸value of assets in place

+ PVGOf ,t︸︷︷︸present value of growth opportunities

(1)

If systematic risk of PVGO differs from VAP, heterogeneity infirms’ growth options could explain cross-sectional differencesin stock returns.

Q: How to measure growth opportunities?A: Covariance of stock returns with investment-specificproductivity shock.

High-growth firms respond more to the investment-specificproductivity shocks.


Consumption-Good Producers

Continuum of infinitely-lived, competitive firms producing ahomogeneous consumption good.

New projects arrive exogenously: Poisson process with arrivalrate λf ,t = λf λ̃f ,t , where λ̃f ,t follows 2-state Markov process.

Project j managed by firm f produces output yf ,j ,t at time t:

yf ,j ,t = εf ,t︸︷︷︸firm-specific

× uj ,t︸︷︷︸project-specific

× xt︸︷︷︸aggregate

× Kαj︸︷︷︸

capital

(2)

where α ∈ (0, 1)⇒ decreasing returns to scale.

If undertaken, choose capital Kj , pay investment cost ztxtKj

Cost of capital relative to average productivity, zt , followsGBM.

Projects expire according to Poisson process with intensity δ.


Productivity and SDF Dynamics

To value project, specify dynamics for productivity and SDF:

Components of projects’ productivity:

dεf ,t = −θε(εf ,t − 1)dt + σe√εf ,tdBf ,t (3)

duj ,t = −θu(uj ,t − 1)dt + σe√

uj ,tdBj ,t (4)

dxt = µxxtdt + σxxtdBx ,t (5)

xt and zt have constant prices of risk βx and βz . SDF follows:

dπt

πt= −rdt − βxdBx ,t − βzdBz,t (6)

(motivated by GE model in Papanikolaou (2008))


Optimal Investment

Time-t market value of project j for firm f :

p(εf ,t , uj,t , xt ,Kj) = Et

[∫ ∞t

exp−δ(s−t) πs

πtεf ,suj,sxsK

αj ds

](7)

= A(εf ,t , uj,t)xtKαj (8)

New projects arrive exogenously ⇒ apply NPV rule:

K∗(εf ,t , zt) ≡ argmaxKj

p(εf ,t , uj,t , xt ,Kj)︸︷︷︸value of output

− ztxtKj︸︷︷︸cost of input

(9)

=

(αA(εf ,t , 1)

zt

) 11−α

(10)

assuming uj,t = 1.


Decomposing the Value of the Firm

Vf ,t︸︷︷︸value of the firm

= VAPf ,t︸︷︷︸value of assets in place

+ PVGOf ,t︸︷︷︸present value of growth opportunities

(11)where

VAPf ,t =∑j∈If

p(ef ,t , uj ,t , xt ,Kj) (12)

= xt

∑j∈If

A(εf ,t , uj ,t)Kαj (13)

PVGOf ,t = zαα−1t xtG (εf ,t , λf ,t) (14)

PVGO depends on z , VAP does not.


Risk and Expected Returns

Regression betas different for 2 components of firm value:

VAP independent of cost of capital, loads only on aggregateproductivity.

PVGO depends negatively on cost of capital, and positively onaggregate productivity.

E [Rf ,t ]− rf = βxσx −α

1− αβzσz

PVGOf ,t

Vf ,t(15)

Low cost of new capital ⇒ high marginal valuation statesbecause of improved investment opportunities, so βz > 0.

Value premium: if low B/M ≈ highPVGOf ,t

Vf ,t, then growth

firms, with low B/M, have lower expected returns than valuefirms.


Investment-Good Producers

Continuum of investment-goods producers: producedemanded quantity of capital goods at price zt .

Profits are fraction φ of sales.

VI ,t = Γxtzαα−1t

1ρI


IMC Portfolio

Data on investment-goods prices only available at annualfrequency ⇒ use mimicking portfolio:

(Investment Minus Consumption) IMC portfolio ≡ longinvestment sector, short consumption sector

Proxy for investment-specific shock sensitivity:

βimcf ,t ≡

covt(Rf ,t ,RIt − RC

t )

vart(R It − RC

t )(16)

= β0,t

(PVGOf ,t

Vf ,t

)(17)

where β0,t = V̄t¯VAPt

So βimcf ,t is a measure of growth opportunities.


Estimating β imcf ,t

Classify industries as producing investment or consumptiongoods according to NIPA Input-Output tables.

Sample period: 1965-2007

Exclude financial firms, utilities, those producinginvestment-goods, and those with missing, or excessive, datavalues.

For consumption-good producing firms, estimate βimcf ,t based

on weekly returns within year t:

rf ,t,w = αf ,t + βimcf ,t r imc

t,w + εf ,t,w (18)

w = 1,...,52


Characteristics of β imc-sorted Firms

High-βimc firms: have higher investment rates, higher Tobin’sQ, higher R&D, pay less in dividends, smaller, higher βmkt .⇒ βimc measure of growth opportunities.


Response of inv. rate to R̃ imc : Firms sorted by β imc

Firms with high βimc invest more on average; investment respondsmore to investment-specific shock.


Other Results and Robustness

Table Conclusion6 High-βimc firms invest relatively more when equipment

gets cheaper.

8 Firms increase increase investment when credit spreads fall,and sensitivity highest for high-βimc firms.

9, 10 Using Tobin’s Q or βmkt as measures of growth optionsyields weaker results than βimc .

11 Using Tobin’s Q as measure of growth options yields noquintile differences in response to credit shocks.

Web 1. βimc not just measure of financial constraints.Appendix 2. Results not due to leverage.

3. Results due to intra- rather than inter-industry variation.

Alternative measure of growth opportunities:

Tobin’s Q ≡ market value of firmreplacement cost of its capital

βmkt (in real options literature: PVGO = levered claim on VAP)


Simulation: Calibration

Parameters How Chosen

dist’n of λf , average and cross-section of investment rate,projects’ cash-flows market-to-book and return to capital (ROE)

dynamics of λ̃f ,t firms grow 2× as fast as average in high growthphase, and 1

3× as fast in low growth phase

δ depreciation rate

xt and zt first 2 moments of agg. div. and inv. growth

φ relative size of consumption/investment sectors

βx and βz average excess returns on market, IMC portfolios

λf ≡ E [λf ,t ] = µλδ − σλδ log(Xf ) (19)

where Xf ∼ U[0, 1]


Simulation: Parameters and Moments


Simulation

Simulate 2,500 firms for 100 years at weekly frequency,aggregate to annual observations

First half = burn-in

Repeat to get 1,000 samples

Lower average return on IMC portfolio may be due to sizeeffect: investment-good firms tend to be smaller thanconsumption-good firms

Investment = Expenses = If ,t =∑

s∈t xszsK∗f ,s

Book value = replacement cost of capital =Bf ,t = ztxt

∑j∈If ,t

Kj ,t


Sim: Response of inv. rate to R imc : Firms sorted by β imc


The Value Premium


Conclusion

Firms with abundant growth opportunities benefit more frominvestment-specific technological improvements.

⇒ Stock returns of high-growth firms have higher exposure toinvestment-specific technology shocks.

Investment rates of high-growth firms are relatively high, andmore sensitive to investment-specific shocks.

Generates value premium.


Discussion

Calibration: not much detail on how parameters are chosen.- ”We set the interest rate r to 2.5%, which is close to thehistorical average risk-free rate (2.9%).”- Simulate 2,500 firms for 100 years, vs 6,831 firms over 42years in data sample.- βz and βx chosen to match average excess return on marketand IMC portfolios. βz (=0.35? =0.40?) must be positive togenerate value premium: how precise is estimate?

What are examples of investment-good producing firms, anddo they really not have any growth opportunities?

Partial equilibrium: zt specified exogenously.


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