liquidity premium and consumptionliquidity premium and consumption 2 1. introduction it is well...

Liquidity Premium and Consumption

January 2011

Abstract

This paper studies the relationship between the liquidity premium and risk exposure

to the shocks that influence consumption in the long run. We find illiquid stocks do not

provide good hedge against the consumption fluctuation and have higher risk exposure to

the consumption shock. The observed liquidity premium can be explained by the difference

between such long-run risk exposure of liquid and illiquid stocks. The model implied liquidity

premium increases with the risk aversion of investors and is insensitive to the specification

of intertemporal substitution.

Keywords: Liquidity Premium, Long-Run Risk, Consumption-based Asset Pricing Model

Liquidity Premium and Consumption 2

1. Introduction

It is well documented that illiquid stocks command higher expected returns than

liquid stocks, but why investors require higher expected returns to hold illiquid stocks

remains an open question. In this paper, we study the trade-off between the risk and

return for liquid and illiquid stocks from a long-run perspective.

Amihud and Mendelson (1986) show a positive relationship between the stock ex-

pected return and the bid-ask spread. They further suggest that investors with longer

holding periods select illiquid stocks and earn higher expected returns as they have

less tendency to trade and are less sensitive to the transaction cost. Brennan and

Subrahmanyam (1996) find that stocks with larger price impact has higher required

rate of returns because of information asymmetry. Amihud (2002) proposes an illiq-

uidity measure based on the daily return and volume data, and shows this illiquidity

measure helps to explain both the cross-sectional and time-series variation of stock

returns. Liu (2006) uses a new liquidity measure based on the non-trading probability

and turnover rate, and shows that liquidity is an important risk factor. His liquidity-

augmented CAPM can explain a large part of the size and value premium. A recent

study by Amihud, Hameed, Kang, and Zhang (2010) suggests that liquidity premium

also exist for many of the emerging and developed markets.

While all these studies suggest that liquidity is priced in the stock market, there is

no consensus on what explains the observed liquidity premium. Amihud and Mendel-

son (1986) suggest that when there is finite liquidity in the market, the valuation

of stock can be decomposed into two parts, the expected discounted value of future

cash flows and terminal value, which is the liquidation value of the stock minus the

transaction cost. To motivate their empirical study of the liquidity premium, Amihud

and Mendelson (1986) focus on the second part, that is, the transaction cost incurred

during the stock liquidation, and they assume a constant discount rate to obtain the


present value of the cash flows during the stock holding periods. However, recent

study such as Hasbrouck (2009) finds that for the difference in transaction costs to

fully explain the observed liquidity premium in the stock market, an unrealistically

high turnover rate is required. This finding suggests that to better understand the

liquidity premium, we should study the pricing the cash flows of liquid and illiquid

stocks in an stochastic environment, with a focus on their different risk exposures.

Pastor and Stambaugh (2003) show that stocks whose returns have high sensitivity

to aggregate market liquidity outperform stocks with low sensitivity by around 7.5%

annually. Acharya and Pedersen (2005) suggest that the covariance between stock

return or liquidity and market return or liquidity produces considerable impact on the

stock’s expected return. Lee (2010) finds evidence of the pricing of liquidity risk in

global markets. In these studies, the liquidity risk is measured by the comovements

between either stock return/liquidity and market liquidity or other stock-market-based

variables. However, few studies have explored the relationship between liquidity pre-

mium and the risk exposure of stocks to the macroeconomic shocks.

In this study, we measure the long-run risk exposure of cash flows of stock port-

folios ranked by liquidity to the macroeconomic shocks, and study whether this risk

exposure can explain cross-sectional variation in the expected returns of liquidity-

based portfolios. Recent studies suggest that liquidity is closely related with market

and macroeconomic state variables. For example, Brunnermeier and Pedersen (2009)

suggest that the provision of liquidity on the stock market is related to the aggre-

gate market valuation level and the overall funding liquidity available for the financial

intermediaries. Hameed, Kang, and Viswanathan (2010) find liquidity decreases in

down markets and such effects are more pronounced with tighter funding liquidity.

Næs, Skjeltorp, and Ødegaard (2010) show that liquidity serves as a leading indicator

for the business cycle in the real economy. All these studies suggest that liquid and


illiquid stocks should respond differently to the macroeconomic shocks.

Recently, Bansal and Yaron (2004), Hansen, Heaton, and Li (2008) and others sug-

gest that the long-run risk-return trade-off has important implication on understanding

the cross-sectional variation in expected stock returns. Therefore, it is interesting to

study whether the long-run risk exposures of liquid and illiquid stocks to the macro-

economic shocks help to explain the observed liquidity premium. The consumption

based asset pricing models suggest that the macroeconomic shocks of interest in asset

pricing should be those that affect consumption in an important way, in particular,

the shocks that have permanent impact on the consumption. The responses of con-

sumption to these shocks and investors’ risk aversion determines the price of risk and

risk premium.

In this paper, we measure the stock illiquidity using the Amihud (2002) measure.

Our sample stocks are NYSE and AMEX common stocks over periods 1947 to 2009.

The sample stocks are sorted into five or ten portfolios based on the Amihud (2002)

illiquidity measures. The portfolio cash flows are dividends flowing to the investor who

holds the portfolio with infinite horizon, which are extracted from the monthly return

with and without dividends. We find that the growth rates of both consumption and

portfolio cash flows are procyclical. The annualized average growth rate of consump-

tion is 3.77% (1.34%) during the economic expansion (recession), while the growth rate

of market portfolio cash flow is 6.06% (-1.80%) in expansion (recession). The cash flows

of the most illiquid portfolio has not only the highest average growth rate but also

the highest volatility — the growth rates of its cash flows are 9.75% and -3.92% during

expansion and recession, respectively. In addition, the variation at long-period cycles

of the growth rates of consumption and portfolio cash flows contribute to the largest

proportion of their total variance. Hence, to better understand liquidity premium, it is

more appropriate to study the long-run risk exposure than the contemporaneous risk


exposure of the cash flows to the consumption shock.

We follow Hansen, Heaton, and Li (2008) to identify shocks that permanently

impact consumption in VAR models with aggregate consumption and earnings. Then

we measure the risk exposure of the cash flows of liquid and illiquid stock portfolios to

these shocks in a model features the separation between risk aversion and intertemporal

elasticity of substitution. We find that the cash flow risk exposure of the most illiquid

portfolio is two to three times of that of the most liquid portfolio. This difference in

the risk exposure implies a significant positive liquidity premium in the long-run for

reasonable value of risk aversion coefficient. For example, the model implied liquidity

premium is 5.12% per annum with risk aversion coefficient of 40, which is almost same

the observed liquidity premium of 5.53% per annum. We also find that the model

implied liquidity premium and risk premium are not sensitive to the variation in the

intertemporal elasticity of substitution (IES), but the risk free rate is very sensitive to

IES especially when risk aversion is large.

In summary, we find that the growth rates of both consumption and portfolio cash

flows are procyclical. In particular, this procyclical pattern is more pronounced in

the cash flows of illiquid portfolio. Furthermore, we show that the illiquid portfolio

has significantly higher cash-flow risk exposure to the shocks that impact consump-

tion permanently than the liquid portfolio, and the model implied long-run liquidity

premium is comparable to the observed sample average with plausible risk aversion

coefficient. These results imply that illiquid stocks are unlikely to be a good hedge

for the consumption fluctuation in the long run, and therefore investors require higher

rate of return to hold them.

The paper is organized as follows. Section 2 contains data description and the sam-

ple statistics of the liquidity-based portfolios. Section 3 introduces the methodology to

identify the shocks with long-run impact on the consumption and to measure the risk


exposure of the cash flows of the liquidity-based portfolios to these shocks. Section 4

presents the results from our empirical analysis. Section 5 concludes the paper.

2. Data Description and Liquidity Portfolios

In this paper we use the Amihud (2002) illiquidity ratio, which measures the price

impact for per dollar of stock trading volume, as our primary liquidity measure. The

Amihud measure is widely used in the literature, such as Acharya and Pedersen (2005)

and Avramov, Chordia, and Goyal (2006). In a study that compares the performance

of various liquidity measures in the U.S. market, Goyenko, Holden, and Trzcinka (2009)

show that the Amihud measure performs well in measuring the spread and price im-

pact. Furthermore, Zhang (2010) suggests that the Amihud measure is also highly

correlated with these high-frequency liquidity measures in global markets.

The daily return and volume data are retrieved from the Center for Research in

Security Prices (CRSP). The sample stocks are ordinary stocks listed on NYSE and

AMEX from 1947 to 2009. The NASDAQ stocks are excluded due to their different

trading protocols. We exclude ADRs, shares of beneficial interest, companies incor-

porated outside the U.S., Americus Trust components, close-ended funds, preferred

stocks, and REITs.

We first obtain the daily Amihud illiquidity measure as the absolute daily stock

return divided by the dollar trading volume for each stock in every trading day. Then

the monthly average Amihud measure is calculated as the average of the daily Amihud

illiquidity measure in each month. At the beginning of July in each year, the sample

stocks are sorted by their previous 12-month average Amihud illiquidity measure into

five liquidity-based portfolios. We filtering our sample by removing the outlier stocks

whose Amihud values is in the highest 5 percentile of the cross-sectional distribution

each year.


We follow Hansen, Heaton, and Li (2005) to construct monthly dividend yields

of each liquidity portfolio from the monthly gross portfolio return with and without

dividends. The dividend yields and return without dividends, which measures price

appreciation, are then used to construct the ratio of the date t cash flow to the date 01

cash flow. We normalize the date 0 cash flow to be unity and take 12-month trailing

average of the monthly cash flows to remove the pronounced seasonality in dividend

payments. The quarterly cash flows used in our empirical analysis are the geometric

average of the seasonally-adjusted monthly cash flows in each quarter.

Our measure of consumption is aggregate consumption of nondurables and services

taken from National Income and Product Accounts (NIPA). The corporate profit be-

fore tax taken from NIPA is our measure of aggregate corporate earnings. Aggregate

consumption and earnings measures are quarterly from 1947Q1 to 2009Q4, seasonally

adjusted and in real term. We take 90-day T-bill rate from CRSP as our measure of

risk free rate. We use the implicit price deflator of nondurables and services consump-

tion2 to deflate aggregate consumption, corporate earnings, risk free rate, returns and

cash flows of liquidity portfolio.

In Table 1, we report the summary statistics of equally weighted quintile portfolios

sorted by the sample stocks’ Amihud illiquid measure. We report both the sample

average portfolio return in excess of risk free rate and the real return, which is the

nominal portfolio return deflated by the implicit price deflator introduced above. Both

return measures suggest that illiquid stocks yield substantially higher return than

liquid stocks. We define the liquidity premium (IML) as the most illiquid portfolio

return minus the most liquid portfolio return. In our sample period, the liquidity

premium is 5.53% per annum, which is both economically and statistically significant.3

1Date 0 in our empirical analysis is 1947Q1.2Details of data contruction of price deflator is available at

http://www.bschool.nus.edu.sg/staff/biznl/3In this paper, we focus on the equally-weighted portfolios, following the literature on liquidity


We also find the illiquid stocks tend to have smaller size and higher book-to-market

ratio, and all these findings are with the stylized facts in the previous literature, such

as Amihud (2002) and Gopalan, Kadan, and Pevzner (2011).

Next, Table 2 presents the growth rates of real consumption and that of the real

cash flows of the liquidity-based portfolios. The real consumption growth rate is 3.37%

per annum over the whole sample period. During the recession, consumption grows

only at 1.34% per annum, which is much lower than the average consumption growth

rate during the expansion (3.77%). In addition, we observe strong procyclicality in

the cash flows of the stock market. For example, the annualized growth rate of the

real cash flow from the equally weighted market portfolio is -2.86% during recession

and 6.06% during expansion. Moreover, this procyclical pattern of cash flow is more

pronounced for the illiquid portfolio. During the expansion, the real cash flow from the

illiquid portfolio grows rapidly at the annualized rate of 9.75%, which is the highest

among all the portfolios; while during recession, it declines at -3.92% per annum, which

is the lowest among all the portfolios. This is an interesting observation, which implies

that illiquid stocks are unlikely to be a good hedge against consumption risk, that is,

the growth rate of its cash flow is high (low) when consumption growth rate is high

(low) or marginal utility from consumption is low (high).

In Figure 1, we report the logarithm ratio of the portfolio cash flows to the aggre-

gate consumption. In general, the cash flows of each portfolio grow faster relative to

consumption during economic expansion, and grow slower during economic recession.

Over the whole sample period, the cash flow of illiquid portfolio exhibits higher average

growth rate as well as higher volatility of the growth rate.

premium studies, such as Amihud and Mendelson (1986), Brennan and Subrahmanyam (1996) andLiu (2006). We also examine the value-weighted liquidity-based portfolios. The sample average returndifference between the most illiquid and liquid quintile is 3.91% (t = 1.78) per annum, which is smallerthan the liquidity premium obtained from equally-weighted portfolios. This is consistent with thefindings in Liu (2006). As shown in Table 1, illiquid stocks are more likely to have small marketcapitalization, so the value-weighted method tends to underestimate the liquidity premium.


It is also interesting to note that cash flow of liquid stock grows much slower relative

to consumption, especially after 1970s. The real cash flow growth rate of the most

liquid portfolio is merely 2.55% as shown in Table 2, which is the lowest among all

the liquidity-based portfolios and even lower than the real consumption growth rate.

During the recession, the cash flow of liquid portfolio grows at a much lower rate

(-3.61%) than portfolios 2-4. This implies that the most liquid portfolio somehow

does not provide good hedge against consumption risk during recession, even it has

the lowest sample average return and cash flow growth rate. We will discuss later

in more detail whether investors who care about long-run consumption risk require

compensation for holding the liquid stock.

3. Long-Run Risk of Liquidity Portfolios

In the previous section, we show that the one-period average returns of illiquid

stocks are substantially larger than those of liquid stocks. Next we study whether the

observed liquidity premium can be explained by the heterogeneity in comovement of

the cash flows of illiquid and liquid portfolios with the macroeconomic shocks that

have important impact on consumption. We adopt the econometric model of Hansen,

Heaton, and Li (2008) to identify the macroeconomic shocks that have important

impact on consumption, and measure the risk exposure of the cash flows of illiquid

and liquid portfolios to these shocks in the long run.

3.1. Measure Risk Exposure and Price of Risk

In the capital asset pricing models, the stock expected excess return is usually

decomposed into the price of risk and the risk exposure. In the consumption-based

asset pricing model, the risk exposure is measured by the comovement between the

consumption and stock returns or cash flows. If the preference of investors is time


separable and state separable, then only the contemporaneous comovement between

the consumption growth and stock returns matters for the equilibrium price. However,

as summarized by Cochrane (2005), both the level and heterogeneity in the correla-

tion between consumption growth and stock returns are way too small to explain the

observed market equity premium and cross-sectional difference in the expected stock

returns. Suppose the utility function of investors is modelled as

U(Ct, Ct+1) =C1−γt

1− γ+ βEt

"C1−γt+1

1− γ

#(1)

where Ct is the investor consumption at time t, and γ > 0 denotes the relative risk

aversion coefficient; then the basic pricing equation is given as

E£mt+1R

it+1

¤= 1 (2)

where mt+1 = β³Ct+1Ct

´−γis the stochastic discount factor, and Ri

t+1 is the rate of

return on stock i. The expected return can be rewritten as4

E(Rit+1)−Rf ≈ γcov(Ri

t+1,∆ct+1) =cov(Ri

t+1,∆ct+1)

var(∆ct+1)· γvar(∆ct+1)

where ∆ct+1 is the logarithm of consumption growth and Rf is the risk free rate. The

risk exposure is measured bycov(Ri

t+1,∆ct+1)

var(∆ct+1). In Table 1 we report the covariance

between the returns of liquidity portfolios and consumption and the risk aversion

coefficient required to match the risk premium and liquidity premium. Table 1 shows

that the contemporaneous covariance between consumption growth and stock returns

are too small to generate sizable risk premium, for example, a risk aversion coefficient

of 190 is required get market risk premium. Furthermore, the heterogeneity in the

covariance is also too small to generate the observed liquidity premium, unless we set

risk aversion coefficient to be around 290!5

4We take a Taylor expansion of equation 2 to get this formula.5This depicts the famous equity premium puzzle first raised by Mehra and Prescott (1985) Even

if we are willing to believe that the investors are indeed extremely risk averse, the model implied risk


For investors with preferences specified as utility function (1), the risk aversion

coefficient is the inverse of the intertemporal elasticity of substitution (IES). However,

risk aversion of an investor reflects the preference for smoothing the consumption across

different states, while the IES measures the preference for smoothing the consumption

over different time periods. Hence it is more reasonable to specify the preference

of investors with a separation between risk aversion and intertemporal substitution.

As Hansen, Heaton, and Li (2008) argue, the recursive utility function proposed by

Epstein and Zin (1989) and others provides such separation that it is possible to study

the effects of changing risk exposure with modest impact on risk-free rate.

Suppose the time t utility of the investor is a constant elasticity function of currently

consumption and utility in the time t+ 1,

Vt =

½(1− β)C1−ρ

t + β¡Et

£V 1−γt+1

¤¢ 1−ρ1−γ

¾1/(1−ρ)(3)

where β is the time discount rate, γ measures the risk aversion to wealth gambles in

the next period, and 1/ρ measures the intertemporal elasticity of substitution when

there is perfect certainty. Vt+1 is the time t+1 utility of investor or continuation value

of the consumption stream from time t + 1 forward. The basic pricing equation (2)

still holds in this recursive utility model, but the stochastic discount factor does not

only depend on the one-period consumption growth but also relies on the further value

of consumption, that is,

mt+1 = β

µCt+1

Ct

¶−ρ "Vt+1

Et

£V 1−γt+1

¤1/(1−γ)#ρ−γ

(4)

Consequently, investors who concern about long-run risk would require compensation

for the risk exposure to the shocks that affect contemporaneous consumption as well

as the consumption in the future. Hansen, Heaton, and Li (2008) show that if the

free rate would be to high for the risk aversion within this range, which leads to the risk free ratepuzzle, as discussed by Weil (1990)


representative investor has recursive utility (3) with unity intertemporal substitution

and growth rate of aggregate consumption is log-linear in the state vector xt,

xt+1 = Gxt +Hεt+1 (5)

ct+1 − ct = μc + Ucxt+1

then the value function Vt+1 and stochastic discount factor mt+1 are both log-linear in

the state vector xt+1.

Furthermore the long-run rate of return of a cash flow stream {dt}∞t=0 can be de-

composed to the exposure to the long-run risk and the price of risk, as summarized in

Theorem 1 in Hansen, Heaton, and Li (2008):

η + ν = ς∗ + π∗ · π (6)

where η denotes the long-run growth rate of cash flows, ν denotes the long-run rate

of return subtract of long-run growth rate η.6 ς∗ is the long-run risk free rate and

π∗ is the price of exposure to the long-run risk, both depend on the specification of

consumption dynamics and the preferences of the representative investors.

π∗ = λ(1) + (γ − 1)λ(β)

ς∗ = log β − μc −(1− γ)2λ(β) · λ(β)

2

where λ(β) is a vector of discounted responses of consumption growth from time t

onwards to the shocks at time t, that is,

λ(β) =∞Xj=0

βj∂∆ct+j∂εt

= Uc(I − βG)−1H

6Hansen, Heaton, and Li (2008) show that the time t price of a cash flow paid at time t + japproaches 0 as j gets larger and the value of ν governs the rate at which this time t price decays tozero. Furthermore, ν reflects the asymptotic rate of growth of the cash flow and the asymptotic riskadjusted rate of discount.


for all 0 < β ≤ 1. In particular, when we evaluate λ(β) at β = 1, we obtain λ(1).

Note that λ(1) measures the limiting response of date t+ j consumption ct+j to time

t shock when j goes to infinity.

π in Equation (6) measures the exposure of cash flows {dt}∞t=0 to long-run risk.

Suppose the cash flows dynamics is specified as

dt+1 − dt = μd + Udxt+1

Hansen, Heaton, and Li (2008) show that π equals to the limiting response of time

t+ j cash flows to the time t shock as j goes to infinity, that is,

π = ι(1) = limj→∞

∂dt+j∂εt

=∞Xj=0

∂∆dt+j∂εt

= Ud(I −G)−1H (7)

In Figure 2, we present the results of spectral analysis of the cash flows growth rates

and consumption growth rates. It is obvious that both consumption growth and cash

flows growth have important variation in the long-run, that is, low-frequency cyclical

variation with periods longer than 16 quarters. We examine the relationship between

low-frency variation of portfolio cash flows and that of consumption through the risk

exposure of cash flows (π).

3.2. Shock Identification

To measure the risk exposure of cash flows π in equation (7), we need to identify the

macroeconomic shocks that impact contemporaneous as well as future consumption.

Corporate earnings is an important predictor of consumption and provides information

on aggregate productivity in the economy. Figure 3 shows that both consumption

growth and earnings growth have important cyclical variation with periods longer

than 16 quarters. We follow Hansen, Heaton, and Li (2008) to add corporate earnings

in the VAR as another source of risk in addition to aggregate consumption.


Let yt+1 be a vector of the logarithm of consumption growth, ratio of earning to

consumption and dividend growth, that is

yt+1 =

⎡⎢⎢⎢⎢⎣ct+1 − ct

et+1 − ct+1

dt+1 − dt

⎤⎥⎥⎥⎥⎦we assume the process {yt+1} evolves as a VAR of order l7.

yt+1 = A1yt +A2yt−1 + ...+Alyt−l + V ωt+1 (8)

We impose two restrictions in this VAR. First, corporate earnings and aggregate con-

sumption are cointegrated, and the long-run responses of both series to the shocks are

the same. Secondly, dt+1 − dt does not Granger cause ct+1 − ct and et+1 − ct+1, hence

the risk exposure to the shocks that only affect dividend growth and do not affect

consumption and earnings is not priced in the market.

We adopt two orthogonalization schemes to identify shocks. Given our interests in

analyzing the exposure to the long-run risk, we follow Blanchard and Quah (1989) to

orthogonalize the shocks such that only one shock has permanent impact on consump-

tion and earnings, and we label this shock as the "permanent shock". As we will see

in the next section, exposure to the permanent shock by design dominates long-run

valuation. Investors with long-run risk concern only require compensation for the risk

exposure to the shock that affect current and future consumption. The other shock

that is uncorrelated with permanent shock only has transitory impact on consumption

and earnings, hence is not priced in the market.

In addition, we also follow Sims (1972) to normalize the shocks that only one shock

affect contemporaneous consumption growth. We call this shock as "Consumption7In the subsequent empirical analysis, we assume l = 5. Our results are not sensitive to the

variation in the value of l. It is straight forward to show that the xt+1 in VAR (5) contains the vectoryt+1 and its l lags.


Shock" and the other shock "Earnings Shock". More specifically, we restrict the matrix

V in VAR (8) to be lower triangular matrix. As Hansen, Heaton, and Li (2008)

pointed out, this recursive scheme to identify shocks allow us to use Bayesian method

to simulate the distribution of the risk exposure which is essentially measured by the

impulse responses.

4. Empirical Analysis

In this section, we present the estimates of long-run return and risk exposure of

liquidity-based portfolios.

4.1. Long-Run Liquidity Premium

In Table 3, we report the model implied long-run rates of return of liquidity-

ranked portfolios for different parameter values of risk aversion coefficients (γ). The

long-run rate of return of the most illiquid portfolio is higher than that of the most

liquid portfolio, and this return difference is enlarged by increasing the risk aversion

coefficient γ. For example, when γ is five, the implied liquidity premium in the long-run

is merely 0.64% per annum; when γ is forty the implied liquidity premium increases

to 5.12% per annum, which almost matches the sample average liquidity premium of

5.53%. In addition, the implied long-run rate of return of equally weighted market

portfolio increases from 6.6% to 7.46% when γ increases from 5 to 40. These results

suggest that the long-run consumption risk exposure of liquid stocks and illiquid stocks

differs in an important way. However, only when the risk aversion coefficient is sizable,

this difference can explain the observed cross-section return variation between liquid

and illiquid stocks. The last column of Table 3 reports the long-run cash flow growth

rates of the liquidity-based portfolio which is independent of the choices of IES and

risk aversion. The dispersion in the growth rates of the liquidity-based portfolios is


large. The illiquid stock portfolio has higher expected return because its cash flows

grow much faster and have higher exposure to the long-run risk.

We noticed that in Table 3, the long-run rate of return of portfolio 1 (most liquid

portfolio) is higher than that of portfolios 2 and 3, while the growth rate of most liquid

stocks is much lower than other portfolios. This result is consistent with Table 2, in

which we show that portfolio 1 has a significantly low growth rate during recession

when consumption growth rate is low, and hence it is not a good hedge against con-

sumption risk. Table 3 shows that investors who care about long-run risk does require

compensation for holding such kind of stocks. However, this compensation for risk

is not reflected in the sample average return for portfolio 1. We conjecture that the

difference between the sample average return and model implied long-run return of

portfolio 1 could be explained as follows. First, the most liquid stock portfolio might

hedge some other aggregate shocks that are not identified in our model. Next, liquid

stocks have substantially less information asymmetry and therefore investors are will-

ing to accept a lower rate of returns. Another possible explanation is that institutional

investors could overinvest in these liquid stocks, which are large stocks and likely to

be popular index components.

In Table 4 and 5, we decompose the risk premium of liquidity-based portfolios as the

price of risk times the risk exposure to aggregate shocks. We adopt two identification

methods to decompose the aggregate shocks. In Table 4, we follow Blanchard and Quah

(1989) to decompose the aggregate shocks into permanent and transitory components,

where the permanent shock captures all the components of the aggregate shocks that

have a permanent impact on the level of consumption and aggregate earnings, while

the transitory shocks are the component orthogonal to permanent shock. Panel A

shows that the permanent shock commands a significant positive price of risk, which

increases proportionally with the risk aversion coefficient γ. In a sharp contrast, the


price of risk for the transitory shock is virtually zero. Panel B presents the risk

exposure of liquidity-based portfolios to the permanent and transitory shocks. As we

can observe, the most illiquid portfolio has the highest exposure to the permanent

shock. In addition, we also present the model implied compensation for the long-run

risk exposure to these two shocks. We show that the risk exposure to permanent

shock contributes to almost all of the long-run return difference between the liquid

and illiquid stocks. For example, when γ = 40, the difference in the compensation for

the risk exposure to permanent shock between the most liquid and illiquid portfolios

is 5.29%, which is able to explain the entire model implied liquidity premium of 5.12%

as shown above in Table 3.8 This result implies that when the representative agent

cares about the long-run risk, only the shocks that can affect the consumption level in

the long-run is priced in the market, while the price of the risk exposure to transitory

shock is negligible.

In Table 5, we use Sims’ orthogonalization to decompose the aggregate shocks to

two components: consumption and earning shocks. Panel A shows that both shocks

are positively priced in the market and their prices increase with risk aversion coeffi-

cient γ. More importantly, the price of risk for the consumption shock is much higher

than that for the earnings shock. Panel B in Table 5 shows that the risk exposure to

consumption shock explains about 80% of liquidity premium in the long run, while the

rest 20% can be explained by the risk exposure to the earning shock. The consumption

shock is constructed to capture all the shocks that directly influence the contempora-

neous consumption growth rate. On the other hand, the earnings shock is orthogonal

to the consumption shock and does not have any impact on the contemporaneous

consumption growth rate. Instead, it indirectly affects the consumption growth in the

8As a robustness check, we also analyze the cash flows from the value-weighted portfolios. Themodel implied liquidity premium in the long run is 3.95% per annum when the risk aversion coefficientis 20.


future periods through the lagged effect in the VAR system. Our results suggest that

the direct impact from the consumption shock on the consumption growth is more

important than the indirect impact from the earnings shock in explaining the liquidity

premium.

4.2. Specification Sensitivity

The results reported in the previous sections are based on the benchmark scenario

of unity intertemporal elasticity of substitution (IES). In Table 6, we report the model

implied long-run return of liquidity-based portfolios in excess of risk free rate for

different values of IES, that is, 1/ρ. We show that the model implied liquidity premium

is always positive and increases with the risk aversion coefficient for different values of

IES. Furthermore, the model implied liquidity premium only slightly increases with

IES (or decreases with ρ) when the risk aversion coefficient (γ) is large. For small

values of γ, and the liquidity premium is insensitive to the change in the IES.

In addition, Table 6 shows that the risk free rate declines (increases) with increases

in risk aversion when ρ < 1 (>1). In the literature, Campbell argues for IES smaller

than 1 while Bansal and Yaron (2004) argue for IES more than 1. The results presented

in Table 6 are consistent with the arguments of Bansal and Yaron (2004). Only when

IES is greater than 1(ρ < 1), the increases in risk aversion enlarges the risk premium,

liquidity premium and depresses the risk free rate.

We should note that even when γ = 40, the market risk premium is only a portion

of the sample average. For the model implied market risk premium to match the

observed value of 8.71% per annum, an even higher value of the risk aversion coefficient

around 125 should be used9. However, at the same time the model implied liquidity

premium would become unrealistically high as 32.04% per annum. Our results suggest

9This result is obtained in the benchmark case of ρ = 1.


that we should be cautious when applying the high risk aversion coefficient in the

consumption-based asset pricing models to explain the observed risk premiums in the

stock market.

4.3. Liquidity-based Decile Portfolios

In this section, we test whether our results can be replicated when the sample

stocks are sorted into ten portfolios based on the Amihud illiquidity measure. In Table

7 Panel A, we reports the summary statistics of the liquidity-based decile portfolios.

The liquidity premium (IML) increases to 7.9% (t = 2.70) per annum based on the

finer portfolio sorting. Again the most illiquid decile portfolio has the smallest size and

the highest book-to-market ratio. Panel B presents the real consumption and real cash

flow growth rates of the liquidity-based deciles. We still find strong procyclical pattern

in the cash flow growth rates of the most illiquid decile portfolio, with annualized rates

of 12.04% during the expansion and -5.69% during the recession.

In Table 8, we report the model implied long-run rate of return of 10 liquidity port-

folios. The observed liquidity premium of 7.9% is within the range of the model implied

long-run liquidity premium of 5.14% when γ is 20 and 10.26% when γ is 40. The un-

reported results show that the risk exposure to the permanent shock and consumption

shock still contribute to most of the long-run liquidity premium obtained from cash

flows of the liquidity-based decile portfolios. Likewise, most of our results remain the

same qualitatively when the stocks are sorted into 10 liquidity-based portfolios.

5. Conclusion

In this paper, we examine the risk exposure of liquid and illiquid stocks to macro-

economic shocks that affect current and future consumption. We find that the cash

flows growth rate of liquidity-based portfolios is procyclical, and such procyclical pat-


tern is more pronounced for illiquid stocks. We test whether the difference in such

risk exposure can explain the liquidity premium observed in the stock market. We

extract the component of the aggregate shocks that has a permanent impact on the

consumption and earning, and find positive market price of the risk exposure to this

permanent shock. More importantly, illiquid stocks has higher risk exposure to the

permanent shock than liquid stocks, and the difference in this risk exposure explains

almost all of the liquidity premium. We decompose the aggregate shocks in another

way to extract the shock that has a direct effect on the contemporaneous consumption

growth rate, and find that the risk exposure of liquidity portfolios to this consumption

shock explains about 80% of the liquidity premium. These results imply that investors

command higher rate of return to hold illiquid stocks, because illiquid stocks are not

a good hedge against the consumption risk in the long run.

We compute the long-run risk premium in the model with separation of risk aver-

sion and intertemporal substitution. We examine the model implications with the

different values of risk aversion and intertemporal substitution. We find that the

model implied long-run liquidity premium increases with risk aversion and matches

the observed liquidity premium when the risk aversion coefficient is around 40. On the

other hand, the model implied liquidity premium is not sensitive to the change in the

intertemporal substitution. In addition, we sort the sample stocks into liquidity-based

decile portfolios and most of our results remains qualitatively unchanged.

We find that the model implied rate of return increases with the portfolio liquidity

ranking, except for the most liquid portfolio (Portfolio 1). Although the most liq-

uid portfolio has the lowest average cash flow growth rate, it is not necessarily the

best hedge for the consumption fluctuation, especially during the economic recession.

Therefore, the model implied long-run rate of return of the most liquid portfolio is

higher than the second most liquid portfolio (Portfolio 2). It should be interesting to


explore the possible explanations for this empirical finding.


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1950 1960 1970 1980 1990 2000 20101950 1960 1970 1980 1990 2000 2010−1

−0.5

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Portfolio 1 (Liquid)234Portfolio 5 (Illiquid)Market

Figure 1: Logarithm of ratios of the real cash flows to the real consumption for theequally weighted market portfolio and liquidity-based quintile portfolios. The yellowshaded area depicts the NBER business recession periods.


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Figure 2: Sample periodogram of the real cash flow growth and the real consumptiongrowth. The solid line plots the sample periodogram of the real cash flow growth withthe scale shown on the left vertical axis. The dashed line plots the sample periodogramof the real consumption growth with the scale shown on the right vertical axis.


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Figure 3: Sample periodogram of the real corporate earning growth and the realconsumption growth. The solid line plots the sample periodogram of the real corporateearning growth with the scale shown on the left vertical axis. The dashed line plotsthe sample periodogram of the real consumption growth with the scale shown on theright vertical axis.


Table 1: Summary Statistics of Liquidity-Based Portfolios

This table presents the descriptive statistics of the liquidity-based quintile portfolios and the market portfolio. Our sample covers the ordinary stocks listed on NYSE and AMEX from 1947 to 2009. The sample stocks are sorted by their previous-year Amihud illiquidity measure, which is defined as the 12-month average of the absolute daily stock return divided by the dollar trading volume, into five quintile portfolios. Portfolio 1 (5) is the most liquid (illiquid) portfolio, and “5-1” stands for the difference of the descriptive statistics between the most liquid and illiquid portfolio. For each liquidity-based portfolio, as well as the market portfolio, the portfolio returns and other statistics are calculated by the equally-weighted method. The sample average return is the annualized portfolio return in excess of risk free rate, and the real return is the annualized portfolio return deflated by the implicit price deflator of nondurable and services consumption. The average book-to-market ratio is the average of the ratio of book value to the market value for the sample stocks in the portfolio. The average size is average of the log-value of the market capitalization for the sample stocks in the portfolio. The average liquidity is the average of the Amihud illiquidity measure for the sample stocks in the portfolio. We also report the contemporaneous covariance between portfolio returns and logarithm of real consumption growth, where the consumption is defined as the aggregate consumption of nondurables and services from the National Income and Product Accounts (NIPA) data.

1(Liq) 2 3 4 5(Illiq) Market 5-1 Sample average return (%) 7.56 8.84 9.17 9.71 13.10 9.83 5.53* Excess return (%) 6.45 7.73 8.06 8.60 11.98 8.71 5.53* Covariance with consumption growth 0.040 0.041 0.042 0.048 0.059 0.046 0.019 Average book-to-market ratio 0.87 1.03 1.20 1.60 3.54 2.67 1.64 Average size 3.90 0.61 0.26 0.11 0.05 -3.85 1.00 Average liquidity 0.15 0.63 1.52 3.36 8.82 8.67 2.85 Average price-dividend ratio 33.57 38.36 44.23 49.50 82.20 48.63 43.99


Table 2: Growth Rates of Cash Flows of Portfolios and Real Consumption

This table presents the average growth rates of the real consumption and the real cash flows of liquidity-based portfolios. The real consumption growth rate is the annualized growth rate of the aggregate consumption of nondurables and services. The real cash flow growth rate is the annualized growth rate of the cash flow to the stock holders for each liquidity-based portfolio and the market portfolio. Besides the average of the whole sample periods, we also report the average growth rates conditional on the NBER business cycle.

Mean Growth Rates Consumption 1(Liq) 2 3 4 5(Illiq) Market Whole sample 3.37 2.55 3.72 3.69 4.06 7.52 4.61 standard deviation 0.14 0.64 0.95 0.89 1.26 2.51 0.78 Recession 1.34 -3.61 -1.82 -2.39 -3.28 -3.92 -2.86 standard deviation 0.38 1.72 2.36 1.75 3.89 4.62 1.80 Expansion 3.77 3.75 4.81 4.87 5.49 9.75 6.06 standard deviation 0.13 0.66 1.03 0.99 1.29 2.84 0.83


Table 3: Long-Run Rate of Return

This table reports the model implied long-run rate of returns of liquidity-based portfolios for different parameter values of risk aversion coefficients (γ). Portfolio 1 (5) is the most liquid (illiquid) portfolio, and “5-1” stands for the difference between the most liquid and illiquid portfolio. The model implied rate of returns is expressed as the annualized rate of returns in percentage points. In this table we assume the intertemporal elasticity of substitution to be unity (ρ = 1).

Portfolio Rate of Return (ρ = 1) Growth Rate γ = 5 γ = 10 γ = 20 γ = 40

1(Liq) 6.62 6.77 7.06 7.65 2.75 2 6.37 6.26 6.05 5.62 3.95 3 6.52 6.57 6.67 6.87 4.15 4 6.86 7.24 8.00 9.52 5.04

5(Illiq) 7.27 8.05 9.62 12.77 10.89 5-1 0.64 1.28 2.56 5.12 8.14

Market 6.60 6.72 6.97 7.46 5.20


Table 4: Risk Exposure and Price of Risk: Permanent versus Transitory Shocks

This table presents risk exposure of liquidity-based portfolios to the permanent shock and transitory shock. We follow Blanchard and Quah (1989) to construct the permanent shock as the components of the aggregate shocks that have a permanent impact on the aggregate consumption and aggregate earnings. The transitory shock is the component orthogonal to the permanent shock. Panel A shows the risk price of the exposure to the permanent shock and the transitory shock. Panel B presents the risk exposure of liquidity-based portfolios to the permanent and transitory shocks.

Panel A: Price of Risk

Permanent Shock Transitory Shock γ = 5 0.0633 -0.0013 γ = 10 0.1158 -0.0025 γ = 20 0.2207 -0.0050 γ = 40 0.4306 -0.0101

Panel B: Risk Exposure and Risk Premium

1(Liq) 2 3 4 5(Illiq) Market 5-1 Permanent Shock

Risk Exposure 0.018 0.006 0.013 0.029 0.049 0.017 0.031 Risk Premium (γ = 5) 0.46 0.15 0.34 0.74 1.24 0.43 0.78 Risk Premium (γ = 10) 0.84 0.28 0.62 1.35 2.26 0.79 1.42 Risk Premium (γ = 20) 1.60 0.54 1.19 2.58 4.31 1.50 2.71 Risk Premium (γ = 40) 3.13 1.05 2.32 5.04 8.41 2.93 5.29

Transitory Shock Risk Exposure 0.013 0.014 0.013 0.012 0.023 0.011 0.010 Risk Premium (γ = 5) -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 0.00 Risk Premium (γ = 10) -0.01 -0.01 -0.01 -0.01 -0.02 -0.01 -0.01 Risk Premium (γ = 20) -0.03 -0.03 -0.03 -0.02 -0.05 -0.02 -0.02 Risk Premium (γ = 40) -0.05 -0.06 -0.05 -0.05 -0.09 -0.04 -0.04


Table 5: Risk Exposure and Price of Risk: Consumption versus Earnings Shocks

This table presents risk exposure of liquidity-based portfolios to the consumption shock and earnings shock. We use Sims’ orthogonalization to decompose the aggregate shocks to the consumption shock and the earnings shock. The consumption shock is constructed to capture all the shocks that directly influence the contemporaneous consumption growth rate. The earnings shock is orthogonal to the consumption shock and does not have any impact on the contemporaneous consumption growth rate. Panel A shows the risk price of the exposure for the consumption shock and the earnings shock. Panel B presents the risk exposure of liquidity-based portfolios to the consumption and earnings shocks.

Panel A: Price of Risk

Consumption Shock Earnings Shock γ = 5 0.0604 0.0189 γ = 10 0.1106 0.0343 γ = 20 0.2110 0.0652 γ = 40 0.4116 0.1269

Panel B: Risk Exposure and Risk Premium

1(Liq) 2 3 4 5(Illiq) Market 5-1 Consumption Shock

Risk Exposure 0.013 0.001 0.009 0.024 0.039 0.013 0.026 Risk Premium (γ = 5) 0.31 0.03 0.21 0.58 0.94 0.30 0.63 Risk Premium (γ = 10) 0.57 0.06 0.38 1.05 1.72 0.56 1.15 Risk Premium (γ = 20) 1.10 0.12 0.73 2.01 3.29 1.06 2.19 Risk Premium (γ = 40) 2.14 0.23 1.43 3.92 6.42 2.08 4.28

Earnings Shock Risk Exposure 0.018 0.015 0.017 0.021 0.037 0.016 0.019 Risk Premium (γ = 5) 0.14 0.11 0.12 0.16 0.28 0.12 0.14 Risk Premium (γ = 10) 0.25 0.21 0.23 0.29 0.51 0.22 0.26 Risk Premium (γ = 20) 0.48 0.39 0.43 0.55 0.98 0.41 0.50 Risk Premium (γ = 40) 0.94 0.76 0.84 1.06 1.90 0.81 0.97


Table 6: Long-Run Excess Return and Risk Free Rate

This table presents the model implied long-run rate of return of market portfolio and liquidity-based portfolios in excess of risk free rate and long-run risk free rate for different values of intertemporal elasticity of substitution (ρ) and risk aversion (γ). “5-1” stands for the difference between the excess return of most illiquid portfolio (portfolio 5) and the most liquid portfolio (portfolio 1). “Rf” stands for the model implied long-run risk free rate.

Excess Return Portfolio ρ = 0.9 ρ = 1 ρ = 1.1

γ = 5 Market 0.36 0.35 0.35

5-1 0.65 0.64 0.64 Rf 5.87 6.24 6.62

γ = 10 Market 0.71 0.71 0.70

5-1 1.29 1.28 1.28 Rf 5.50 6.02 6.54

γ = 20 Market 1.43 1.41 1.39

5-1 2.59 2.56 2.53 Rf 4.42 5.56 6.70

γ = 40 Market 2.95 2.81 2.67

5-1 5.34 5.12 4.90 Rf 0.84 4.65 8.34


Table 7: Summary Statistics of Liquidity-Based Decile Portfolios

This table presents the summary statistics and the average growth rates of the real cash flows of the liquidity-based decile portfolios. The sample stocks are sorted into ten portfolios based on their Amihud illiquidity measure. Panel A reports the descriptive statistics of the liquidity-based decile portfolios, including the portfolio sample average return and real return, the portfolio average book-to-market ratio, size, and liquidity. Panel B reports the growth rates of the real cash flows of the liquidity-based decile portfolios, including the real cash flow growth rates in the whole sample periods and during the business expansion and recession periods respectively. For each liquidity-based portfolio, as well as the market portfolio, the portfolio returns and other statistics are calculated by the equally-weighted method.

Panel A: Portfolio Descriptive Statistics 1(Liq) 2 3 4 5 6 7 8 9 10(Illiq) Market 10-1

Sample average return (%) 6.81 8.26 8.57 9.06 9.11 9.20 9.81 9.54 11.33 14.71 9.83 7.90 Excess return (%) 5.69 7.15 7.46 7.95 8.00 8.09 8.70 8.42 10.21 13.60 8.71 7.90 Average book-to-market ratio 0.67 0.82 0.85 0.93 1.03 1.08 1.29 1.60 1.86 2.95 0.76 2.29 Average size 6.33 1.46 0.76 0.45 0.30 0.21 0.14 0.08 0.06 0.04 1.00 -6.30 Average liquidity 0.08 0.22 0.48 0.79 1.21 1.84 2.71 4.02 6.19 11.53 2.85 11.45 Average price-dividend ratio 33.04 34.25 38.25 38.85 43.48 45.60 45.88 54.72 62.91 133.94 43.99 100.90

Panel B: Mean Growth Rates of Portfolio Cash Flows

1(Liq) 2 3 4 5 6 7 8 9 10(Illiq) Market 10-1 Whole sample 3.37 1.83 3.20 3.44 3.95 3.82 3.51 4.12 3.90 5.55 9.14 4.61 standard deviation 0.14 0.60 0.98 1.20 1.26 1.20 1.33 1.72 1.32 2.24 4.64 0.78 Recession 1.34 -3.66 -3.59 -2.53 -1.38 -1.24 -3.31 -1.56 -4.87 -4.21 -5.69 -2.86 standard deviation 0.38 1.58 2.75 3.30 2.98 2.03 2.70 5.47 3.43 5.33 6.00 1.80 Expansion 3.77 2.90 4.52 4.61 4.99 4.81 4.84 5.23 5.61 7.46 12.04 6.06 standard deviation 0.13 0.62 1.03 1.26 1.39 1.37 1.48 1.75 1.40 2.45 5.40 0.83


Table 8: Long-Run Rate of Return of Liquidity-Based Decile Portfolios

This table reports the model implied long-run rate of returns of liquidity-based decile portfolios for different parameter values of risk aversion coefficients (γ). The sample stocks are sorted into ten portfolios based on their Amihud illiquidity measure. Portfolio 1 (10) is the most liquid (illiquid) portfolio, and “10-1” means the difference between the most liquid and illiquid portfolio. The model implied rate of returns is expressed as the annualized rate of returns in percentage points.

Portfolio Rate of Return (ρ=1) γ = 5 γ = 10 γ = 20 γ = 40 1(Liq) 6.54 6.60 6.72 6.97 2 6.76 7.04 7.60 8.72 3 6.44 6.40 6.33 6.18 4 6.30 6.13 5.80 5.12 5 6.34 6.22 5.96 5.45 6 6.64 6.80 7.12 7.76 7 6.55 6.62 6.78 7.08 8 7.07 7.66 8.84 11.21 9 6.99 7.51 8.55 10.62 10(Illiq) 7.83 9.17 11.86 17.23 10-1 1.29 2.57 5.14 10.26 Market 6.60 6.72 6.97 7.46

liquidity premium and consumptionliquidity premium and consumption 2 1. introduction it is well...

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