American Economic Association

Long Run Risks, the Macroeconomy, and Asset Prices Author(s): Ravi Bansal, Dana Kiku and Amir Yaron Source: The American Economic Review, Vol. 100, No. 2, PAPERS AND PROCEEDINGS OF THE One Hundred Twenty Second Annual Meeting OF THE AMERICAN ECONOMIC ASSOCIATION (May 2010), pp. 542-546 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/27805055 . Accessed: 01/08/2014 13:24 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp

. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].

.

American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review.

http://www.jstor.org

This content downloaded from 130.91.92.186 on Fri, 1 Aug 2014 13:24:32 PM All use subject to JSTOR Terms and Conditions

100 (May 2010): American Economie Review: Papers & Proceedings w w. aea web. org/a rticles.php ?doi=l0.1257/aer. 100.2.542 h ttp.V/w

542-546

LONG RUN RISKS AND ASSET MARKETS

and Asset Prices

Long Run Risks, theMacroeconomy, By Ravi

Dana

Bansal,

movements

in

with Robert E. Lucas Jr. (1987), who argues that

prices

and

and macroeconomic expected

returns.

those

on

Bansal

a

component

cyclical

asset

and

in this

case

the

once

10 percent,

to model

ble way view,

are

shocks

and

small

large.

5 years,

every

have

is via

macroeconomic

small

discrete

in our

crises,

reductions

in

long

run expected growth and/or a rise in aggregate These

uncertainty.

small

macroeco

discrete

nomic changes (i.e., jumps) in the generalized LRR model lead to large asset price movements and financial crises. Importantly, the model does not rely on implausible (over 20 percent) drops in consumption to trigger financialmarket

in consump

risk-free

are

little impact on the risk premium. A more plausi

volatility. We find that themagnitude of risk compensa tion for cyclical risks in consumption critically depends on themagnitude of the intertemporal elasticity of substitution (IES). When the IES is larger than one, cyclical risks carry a very small risk premium.When IES is close to zero, the risk compensation for cyclical variations is however,

of

growth

tion growth?this component is stationary in levels. To study financial market crises, we also entertain jumps in consumption growth and

large;

of transient

shocks

study financial market crises, we first explore jumps in the cyclical component of the generalized LRR model; Robert Barro, Emi Nakamura, Jon Steinsson, and Jos? Urs?a (2009) use a related LRR model for theiranaly sis of crises.We find thateven dramatic drops in

Yaron (2004) LRR model contains (i) a persis tent expected consumption growth component, (ii) long-run variation in consumption volatility, and (iii) preference for early resolution of uncer tainty.To evaluate the role of cyclical risks,we incorporate

for trend

To

consumption

crises The

costs

economic

growth rates and volatility, in accounting for a wide range of asset pricing puzzles. In this article we present a generalized LRR model, which allows us to study the role of cyclical fluctuations

and Amir Yaron*

Kiku,

Ravi Bansal and Amir Yaron (2004) devel oped the Long Run Risk (LRR) model which emphasizes the role of long run risks, that is, low-frequency

'

crises.

Consistent with theLRR model, Lars Hansen, John Heaton, and Nan Li (2008) and Bansal, Dana Kiku, and Yaron (2009) document pre dictable variation in consumption growth data at long horizons.

Lochstoer

rate

Georg

and Lars

(forthcoming) show that a standard model

production-based

is implausibly high (in excess of 10 percent). It is, therefore,unlikely that the compensation for cyclical risks is of economically significant magnitude. This implication is also consistent

Kaltenbrunner

endogenously

gener

ates long run predictable fluctuations in con sumption

growth.

zles?for

the term

Earlier work shows that the LRR model can explain an important set of asset pricing puz structure

and

related

puzzles

see Monika Piazzesi and Martin Schneider (2007) , for credit spreads see Hui Chen (forth coming), for option prices see Itamar Drechsler and Yaron (2007) and Bj0rn Eraker and Ivan Shaliastovich (2008), and for cross-sectional

'Discussants: Lars Lochstoer, Columbia University; Lukas Schmid, Duke University; George Tauchen, Duke University; Ivan Shaliastovich, University of Pennsylvania. :|:Bansal: Fuqua School of Business, Duke University, 1 Towerview Drive, NC 27708, and National Bureau of Economic Research Kiku: (e-mail: [email protected]); The Wharton 3620 School, University of Pennsylvania, Locust Walk, PA 19104 (e-mail: [email protected]); Yaron: The Wharton School, University of Pennsylvania, 3620 Locust Walk, PA 19104, and National Bureau of Economic Research (e-mail: [email protected]).

differences

Robert

in

expected

returns

see

Bansal,

F. Dittmar, and Christian Lundblad (2005); Kiku (2006); Hansen, Heaton, and Li (2008) and Bansal; Dittmar and Kiku (2009). Bansal, Ronald Gallant and George Tauchen

542

This content downloaded from 130.91.92.186 on Fri, 1 Aug 2014 13:24:32 PM All use subject to JSTOR Terms and Conditions

VOL.

100 NO.

2

LONG

RUN RISKS,

THE MACROECONOMY,

(2007) estimate theLRR model and find consid erable support for it. I. Generalized

Run

Long

Model

Risks

We generalize the Bansal and Yaron (2004) model and allow for cyclical variations in aggre gate consumption and dividends. Specifically, the level of log consumption (ct) consists of a deterministic trend, a stochastic trend (yt), and a transitorycomponent (st). That is, ct= fit+ yt+ sr The growth rate of the stochastic trend is assumed to follow: A yt+ ! = xt+ yv crtr}t+, + JVjt+,,

( 1)

rjtis iidN(0,

vation.

1), and J1htis a non-gaussian inno the

Thus,

of

evolution

growth is given by: =

(2) Acr+l

consumption

+ J1]J+{. p,+ xt+ As,+ 1+ ^7]crtrit+l

The dynamics of the state vector, denoted by Y't ? = (xn sn ctq), are described by: Yt+l

(3)

=

are

zeros.

Z',+

= 1

(et+l,

ut+u wt+l)

is a vector of iid standard gaussian shocks, and Jt+] is a vector of jumps. The jump component of = j-variable, j {77,x, sya2}, ismodeled as a com pound poisson process with a constant inten sity and mean jump size of JLr Dividends are to have

assumed

levered

to consump

exposure

tion components, i.e., the log level of dividends follows: dt= pdt + cbyyt + qbsst + ??where A?r+1

=

(fdat?t+h

and

et is an

idiosyncratic

dividend

innovation drawn from 7V(0, 1). While Bansal and Yaron (2004) focus on variation in the persistent growth component xt,we explore the asset pricing implications of cyclical variations in consumption driven by st. Following theLRR terminology,we refer to 77,, xt and

(jt as

to short-run,

long-run

and

volatility

risks respectively; innovations in st are labeled cyclical risks. For expositional simplicity, for the rest of this section, we assume that the jump component

PRICES

543

preferences. The log of the intertemporalmar ginal rate of substitution (IMRS), is given by: (4)

m,+1=0

where

+

1og5-^Ac,+1

rCJ+] is the continuous

return

(0-l)rCil on

the con

sumption asset, 0 < ? < 1 reflects the agent's time preference, 7 is the coefficient of risk aver sion, i/jis the intertemporal elasticity of substi

tution(IES) and 0 = (1- 7)/(l - (1/-0)).To

derive the dynamics of asset prices we rely on log-linear analytical solutions. Specifically, we conjecture that the log of the price to consump tion ratio follows, =

(5)

A0 + A'Y,

and solve forA' = (Ar,As, theEuler Aa2) using on return for the wealth. The equation loadings of the price-consumption ratio on the three state variables are given by:

(6) A'

1 - ?1 As

\l-?iAt'

*Y, + G,Z,+1+J,+1,

where diag($) = (px, ps, v\ diag(G,) = (
AND ASSET

is absent.

The representative agent has Larry G. Epstein and Stanley E. Zin (1989) type recursive

where k{ is the constant of log-linearization of thewealth return,and H > 0. Bansal and Yaron (2004) show that as long as IES is larger than one, asset valuations rise with higher long run expected growth x, and fall in response to an increase

in consumption

volatility.

Moreover,

when IES is greater than one, the elasticity of the price-consumption ratio with respect to the cyclical component is negative (As < 0), cap turing

the

standard

mean-reversion

intuition

of business-cycle shocks. Note the difference between long run and cyclical effects?when s is high, consumption is expected to fall due to anticipated

mean-reversion

in

to

to its trend

(i.e.,

expected consumption growth is negative), whereas a positive innovation in x signals high consumption growth in the future.Thus, equity prices will react very differently to news about the long run and cyclical consumption com ponents. Similarly, real rates rise in response to positive x-shocks; however, they will drop response

positive

^-shocks.

Therefore,

in terms of real bonds, s-risk will contribute a positive risk premium, while x-riskwill contrib ute a negative

risk premium.

This content downloaded from 130.91.92.186 on Fri, 1 Aug 2014 13:24:32 PM All use subject to JSTOR Terms and Conditions

AEA PAPERS

544

Given the solution for zn the dynamics of the log IMRS are described by: mt+]

(7)

=

ries

a

separate

The

premium.

receive

separate

II.

Run

Long

0=

expressions

for

premia.

versus

Business

Cycle

Risks

Table 1 presents the calibration output of the model that incorporates cyclical fluctuations in consumption without any jumps. We simulate themodel on a monthly frequency and evalu ate its implications using time-averaged annual data. The configuration of model parameters for consumption and dividends, stated below the table, is chosen tomatch annual data for the 1929-2008 period. Our calibration of the bench mark LRR model parameters is fairly close to the one in Bansal, Kiku, and Yaron (2009). In themodel specification with cycle, the persis tence of the cyclical component is set at 0.96, and themagnitude of ^-shocks is half themagni tude of iid-innovations to consumption growth. The second column (labeled LRR) is the benchmark case without cyclical risks; the model closely matches the consumption growth data, data

equity

return,

counterparts

1?Asset Pricing Implications of the LRR Model with Cyclical Components

,

and themarket prices of risks, save for the cyclical component, are provided inBansal and Yaron (2004). The IMRS loading on st is equal to (1 ? ps)ip~\ and the cyclical risk price AM ? 1, AMis equals [7+ (1 6)kxAJ\ ip~l), the price of long run risks is positive. Finally, when jumps are incor porated, they also directly influence the IMRS and

Table

LRR

mo + M'Y,-A'C,+

A where CWi = (^r+h <^+i> crwwr+1). represents the vector of the corresponding mar ket prices of risks.Note thatdue to a separation between risk aversion and IES, each risk car M

MAY 2010

AND PROCEEDINGS

and

are

risk-free

reported

dynamics. below in Table

The

2.

The risk premium decomposition makes clear that the long run growth risk and consumption volatility risk contribute themost to the equity risk premia. In the next column we report the results from the augmented model that includes the cyclical component. As can be seen, with an IES greater than one, the market price of cyclical risks is essentially zero, and so is their

Risk premia short run risk long run risk

volatility risk cycle risk Risk-free rate mean volatility

LRR-cycle r - 1.5

1.5

6.24

6.23 1.39 2.05 2.79

0.25

1.39 2.05

-1.03

1.39

2.79 0.01

-0.39 0.28

1.24 1.14

1.25 1.04

10.5 8.13

2.66 0.39

2.39 0.44

LRR-cycle c 0.2

2.67 0.38

Notes:

The model is calibrated using the following config = = = uration: ? = 0.999, 7 = \.5e 1, 3, 10, // //,, = = = 0.035, = 3. 0.96,
contribution to the overall risk premia. The last column in Table 1 provides the model output when themodel contains the same cyclical pro cess but the IES is equal to 0.2. In this case, the risk price for cyclical risk rises, while themag nitude of the other risk prices decreases. Note that therisk premia contribution of volatility and long runrisk is negative, and therefore the over all risk premium is negligible. Importantly,with this low IES configuration, themean and volatil ityof the risk-free rate are implausible?11 per cent

and

8 percent,

respectively.

It follows that small values of IES raise the compensation for cyclical risk but fail to account for the observed dynamics of the risk-free rate. In addition, when IES is less than one, asset valuations rise with lower expected growth and higher consumption volatility. This configura tion implies a negative premium for long-run and volatility risks as reported in the last col umn of Table 1.Empirical evidence in Bansal, Varoujan Khatchatrian, and Yaron (2005) shows that in the data, price-dividend ratios drop in response sharply tion volatility, and

to an

increase

that asset

in consump antici

valuations

pate higher earnings growth; this evidence is consistent with an IES larger than one. In all, the empirical evidence and themodel implica tions point to an IES that is larger than one, and hence the compensation for business cycle risks is close

to zero.

To evaluate the ability of the LRR model to track the observed log price-dividend ratio, we utilize theLRR calibration of Table 1. Figure 1

This content downloaded from 130.91.92.186 on Fri, 1 Aug 2014 13:24:32 PM All use subject to JSTOR Terms and Conditions

VOL.

100 NO.

Table

2

2?Dynamics

of Growth

THE MACROECONOMY,

RUN RISKS,

LONG

AND ASSET

PRICES

1950

1970

545

and Prices

Rates

LRR model with jumps

Riskpremia Risk-free rate mean volatility Cons, growth volatility

Data

in s

6.65

6.74

0.90 1.85

2.53

2.10

0.47

AC(1)

in x and a2 6.73

1.00

1.21 1.02

5.44

0.11

2.48

0.43

Notes: The model configuration is the same as in Table 1with it = 1.5. In the "Jumps in j" column, themonthly = In the last column, the cycle com parameter /jv ?0.12. ponent is shut down, jumps in x and a2 occur simultane = ?2.5
displays the realized and the model implied price-dividend ratio. We first extract the two state variables xt and a} in the data by project ing annual consumption growth onto the lagged price-dividend ratio and the risk-free rate?see Bansal, Kiku, and Yaron (2007) for details. In an entirely analogous fashion, we estimate the state variables from inside themodel using time averaged annual quantities from the model based simulation. We then regress themodel's price-dividend ratio onto themodel's extracted annual state variables, xt and at. The line labeled "Model" in Figure 1 is the fitted log price-divi dend ratio using themodel-based price-dividend projection evaluated at the data based extracted state variables. Figure 1 shows that themodel price-dividend ratio tracks thatof the data quite well, including the declines in 1930 and 2008. Consistent with theLRR model, movements in measured expected growth and consumption volatility indeed drive asset prices. III. Long Run Risks and Crises Table 2 provides a quantitative evaluation of the asset pricing implications of the two alterna tive views of macroeconomic crises. In the first specification, an economic crisis ismodeled as a negative jump in the cyclical component (as inBarro et al. 2009). We refer to this specifica tion as

"Jumps

in s."

In the second

case,

macro

economic crises are associated with a small but persistent reduction in the long run consumption growth (jumps in x) and a small but sustained rise in economic uncertainty (jumps in a2).

2.0 p' 1930

1940

Figure

1.Data

1960

and Model

1980

1990

Price-Dividend

2000

2008

Ratio

This sp?cification is referred to as a model with "Jumps inx and cr2."Apart from jumps, we rely on the same baseline calibrations with and with out cyclical component as in Table 1with IES = 1.5. To facilitate the comparison between the twomodels, jump dynamics are chosen to yield a

half-a-percent

increase

in the annual

risk pre

mia relative to those reported inTable 1. As shown above, when IES is greater than one, any reasonably calibrated business cycle risks have a trivial effect on asset prices. Thus, generating a 50-basis-point increase in risk premia requires dramatically large declines in the cyclical component of consumption with a mean jump size of ?12 percent on a monthly basis. Since historically themagnitude and fre quency of such events are quite unlikely, this cri sis specification fails tomatch the dynamics of observed consumption, significantly overshoot ing the volatility and highermoments of annual growth rates.Moreover, the price-dividend ratio will rise in response to a negative jump in the cyclical component (as As is negative) ! The last column of Table 2 reports key moments of consumption and asset prices implied by a model where crises are set off by small negative jumps in the long run growth component and small positive jumps in thevola tility of consumption growth. Since both risks carry sizable risk premia, this specification does not entail extreme fluctuations in growth rates and easily matches the dynamics of aggregate consumption. Note that although jumps, on into are relatively small, average, they translate For example, asset prices. movements in large

a reduction in x that depresses consumption a growth by half a percent per annum, and

This content downloaded from 130.91.92.186 on Fri, 1 Aug 2014 13:24:32 PM All use subject to JSTOR Terms and Conditions

546 AEA PAPERSAND PROCEEDINGS MA Y 2010 20 percent increase in annualized volatility,will result in a ten percent drop in the price-dividend to the decline during 2008. ratio?comparable Thus, empirically plausible macroeconomic events that lead to financial market crises are quite likely due to reductions in long-term expected growth and/or a rise in consumption volatility. IV. Conclusions

present a generalized Long Run Risks model, which incorporates a cyclical component and jumps.We argue that the compensation for cyclical risk is small. Significant cyclical risk premium requires low values of the intertempo ral elasticity of substitution which are implau sible as those lead to counterfactually high and volatile risk-free rates.We show that financial crises triggeredby extreme declines in the cycli cal component of consumption are empirically implausible. A more plausible view is that small but long run declines in expected growth and/ We

or

an

in consumption

increase

trans

volatility

late into financial crises.We show that the long run risksmodel accounts for thedynamics of the observed price-dividend ratio quite well, includ ing the crisis periods.

REFERENCES

Bansal,

Ravi,

Ravi,

Robert

and Dana

Kiku.

2009. "Cointegration and Consumption Risks inAsset Returns." Review ofFinancial Studies, 22(3): 1343-75.

Bansal,

Ravi,

F. Dittmar,

and

Christian

T.

Lundblad. 2005. "Consumption, Dividends, and the Cross Section of Equity Returns." Journal ofFinance, 60(4): 1639-72.

Bansal,

Ravi,

Tauchen.

A. 2007.

Ronald

Gallant,

"Rational

and

Pessimism,

George Ratio

nal Exuberance, and Asset Pricing Models." Review ofEconomic Studies, 74(4): 1005-33. Bansal,

Ravi,

Varoujan

and Amir

Inference."

and Amir

Ravi,

Unpublished. Dana Kiku,

Bansal,

Ravi,

and Amir

Barro,

Robert,

Yaron.

2007.

Estimation and Yaron.

2009.

of the Long "An Empirical Evaluation Run Risks Model forAsset Prices." National Bureau of Economic Research Working Paper 15504. Yaron.

2004.

for

"Risks

theLong Run: A Potential Resolution ofAsset Pricing Puzzles." Journal of Finance, 59(4): 1481-509. Emi

and

Jon Steinsson,

Nakamura,

Jos? Urs?a. 2009. "Crises and Recoveries in an Empirical Model of Consumption Disas

ters." Unpublished. Chen, Hui. Forthcoming.

"Macroeconomic

Con

ditions and thePuzzles of Credit Spreads and Structure."

Capital Drechsler,

Journal

and Amir

Itamar,

Vol Got toDo With

Epstein,

and

G.,

Larry

of Finance. Yaron. 2007.

"What's

It."Unpublished. E.

Stanley

Zin.

1989.

"Substitution,Risk Aversion, and theTemporal Behavior of Consumption and Asset Returns:

A

Theoretical

Framework."

Econometrica,

57(4): 937-69. Eraker,

Bj0rn,

and

Lars

Peter,

Ivan

Shaliastovich.

"An

2008.

Equilibrium Guide toDesigning Affine Pricing Models." Mathematical Finance, 18(4): 519? 43.

F. Dittmar,

Robert

Kiku,

Bansal,

Hansen, Bansal,

Dana

"Risks for the Long Run:

Khatchatrian,

and

Amir

Yaron. 2005. "Interpr?tableAsset Markets?" European Economic Review, 49(3): 531-60.

John C. Heaton,

and Nan

Li.

2008. "Consumption Strikes Back? Measuring Risk."

Long-Run

Journal

of Political

omy, 116(2): 260-302.

Kaltenbrunner,

Georg,

and Lars

Lochstoer.

Econ Forth

coming. "Long-Run Risk throughConsump tion Smoothing." Review ofFinancial Studies.

Kiku,

Dana.

2006.

"Is

the Value

Premium

zle?" Unpublished. Lucas, Robert E. Jr. 1987. Models London:

Cycles. Piazzesi,

Monika,

a Puz

of Business

Blackwell. and Martin

Schneider.

2007.

"Equilibrium Yield Curves." InNBER Macro

economics

Annual

2006,

ed. Daron

Acemoglu,

Kenneth Rogoff andMichael Woodford, 389 442. Cambridge, MA: MIT Press.

This content downloaded from 130.91.92.186 on Fri, 1 Aug 2014 13:24:32 PM All use subject to JSTOR Terms and Conditions