Liquidity Premium and Consumption

Transcription

1 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 betweensuchlong-runriskexposureofliquidandilliquid 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

2 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 remainsanopenquestion.inthispaper,westudythetrade-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 expected 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 illiquidity 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 liquidityaugmented 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 Mendelson (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

3 Liquidity Premium and Consumption 3 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 premium 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 portfolios ranked by liquidity to the macroeconomic shocks, and study whether this risk exposure can explain cross-sectional variation in the expected returns of liquiditybased 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 aggregate 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

4 Liquidity Premium and Consumption 4 illiquid stocks should respond differently to the macroeconomic shocks. Recently, Bansal and Yaron (2004), Hansen, Heaton, and Li (2008) and others suggest 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 macroeconomic 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 consumption 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 Thesamplestocksaresortedintofive or ten portfolios based on the Amihud (2002) illiquidity measures. The portfolio cash flows are dividends flowingtotheinvestorwho 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 consumption 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

5 Liquidity Premium and Consumption 5 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 riskexposuretotheshocksthatimpactconsump- 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 sample 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

6 Liquidity Premium and Consumption 6 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 impact. 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 The NASDAQ stocks are excluded due to their different trading protocols. We exclude ADRs, shares of beneficial interest, companies incorporated 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.

7 Liquidity Premium and Consumption 7 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 0 1 cash flow. Wenormalizethedate0 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 flowsineachquarter. Our measure of consumption is aggregate consumption of nondurables and services taken from National Income and Product Accounts (NIPA). The corporate profit before 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 consumption 2 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 1 Date 0 in our empirical analysis is 1947Q1. 2 Details of data contruction of price deflator is available at 3 In this paper, we focus on the equally-weighted portfolios, following the literature on liquidity

8 Liquidity Premium and Consumption 8 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, thegrowthrateofitscashflow 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 aggregate 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) and Liu (2006). We also examine the value-weighted liquidity-based portfolios. The sample average return difference between the most illiquid and liquid quintile is 3.91% (t =1.78) per annum, which is smaller than the liquidity premium obtained from equally-weighted portfolios. This is consistent with the findings in Liu (2006). As shown in Table 1, illiquid stocks are more likely to have small market capitalization, so the value-weighted method tends to underestimate the liquidity premium.

9 Liquidity Premium and Consumption 9 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 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

10 Liquidity Premium and Consumption 10 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 correlation 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(C t,c t+1 )= C1 γ t C 1 γ 1 γ + βe t+1 t 1 γ where C t is the investor consumption at time t, andγ>0 denotes the relative risk aversion coefficient; then the basic pricing equation is given as (1) E m t+1 R i t+1 =1 (2) ³ γ where m t+1 = β Ct+1 C t is the stochastic discount factor, and R i t+1 istherateof return on stock i. The expected return can be rewritten as 4 E(R i t+1) R f γcov(r i t+1, c t+1 )= cov(ri t+1, c t+1 ) var( c t+1 ) γvar( c t+1 ) where c t+1 is the logarithm of consumption growth and R f istheriskfreerate.the risk exposure is measured by cov(ri t+1, c t+1 ). In Table 1 we report the covariance var( c t+1 ) 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 4 We take a Taylor expansion of equation 2 to get this formula. 5 This 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

11 Liquidity Premium and Consumption 11 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, V t = ½ (1 β)c 1 ρ t + β ¾ E t V 1 γ 1/(1 ρ) 1 ρ 1 γ t+1 (3) where β isthetimediscountrate,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. V t+1 is the time t+1 utility of investor or continuation value of the consumption stream from time t +1forward. 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, µ " # ρ ρ γ Ct+1 V t+1 m t+1 = β C t E t V 1 γ 1/(1 γ) (4) t+1 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 rate puzzle, as discussed by Weil (1990)

12 Liquidity Premium and Consumption 12 representative investor has recursive utility (3) with unity intertemporal substitution and growth rate of aggregate consumption is log-linear in the state vector x t, x t+1 = Gx t + Hε t+1 (5) c t+1 c t = μ c + U c x t+1 then the value function V t+1 and stochastic discount factor m t+1 are both log-linear in the state vector x t+1. Furthermore the long-run rate of return of a cash flow stream {d t } t=0 can be decomposed 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 = logβ μ c (1 γ)2 λ(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) = X j=0 β j c t+j ε t = U c (I βg) 1 H 6 Hansen, Heaton, and Li (2008) show that the time t price of a cash flow paid at time t + j approaches 0 as j gets larger and the value of ν governs the rate at which this time t price decays to zero. Furthermore, ν reflects the asymptotic rate of growth of the cash flow and the asymptotic risk adjusted rate of discount.

13 Liquidity Premium and Consumption 13 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 c t+j to time t shock when j goes to infinity. π in Equation (6) measures the exposure of cash flows {d t } t=0 to long-run risk. Suppose the cash flowsdynamicsisspecified as d t+1 d t = μ d + U d x t+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, d t+j X d t+j π = ι(1) = lim = = U d (I G) 1 H (7) j ε t ε t j=0 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) 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.

14 Liquidity Premium and Consumption 14 Let y t+1 be a vector of the logarithm of consumption growth, ratio of earning to consumption and dividend growth, that is y t+1 = c t+1 c t e t+1 c t+1 d t+1 d t we assume the process {y t+1 } evolvesasavaroforderl 7. y t+1 = A 1 y t + A 2 y t A l y t l + Vω t+1 (8) We impose two restrictions in this VAR. First, corporate earnings and aggregate consumption are cointegrated, and the long-run responses of both series to the shocks are the same. Secondly, d t+1 d t does not Granger cause c t+1 c t and e t+1 c t+1, hence theriskexposuretotheshocksthatonlyaffect 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 consumption 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 "Consumption 7 In 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 x t+1 in VAR (5) contains the vector y t+1 and its l lags.

15 Liquidity Premium and Consumption 15 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 Long-Run Liquidity Premium In Table 3, we report the model implied long-run rates of return of liquidityranked 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

16 Liquidity Premium and Consumption 16 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 consumption 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 hedgesomeotheraggregateshocksthatarenotidentified in our model. Next, liquid stocks have substantially less information asymmetry and therefore investors are willing 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. InTable4and5,wedecomposetheriskpremiumofliquidity-basedportfoliosasthe 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

17 Liquidity Premium and Consumption 17 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 thelong-runispricedinthemarket,whilethepriceoftheriskexposuretotransitory 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 coefficient 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 contemporaneous 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 8 As a robustness check, we also analyze the cash flows from the value-weighted portfolios. The model implied liquidity premium in the long run is 3.95% per annum when the risk aversion coefficient is 20.

18 Liquidity Premium and Consumption 18 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 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, themarketriskpremiumisonlyaportion ofthesampleaverage. Forthemodelimpliedmarketriskpremiumtomatchthe observed value of 8.71% per annum, an even higher value of the risk aversion coefficient around 125 should be used 9. However, at the same time the model implied liquidity premium would become unrealistically high as 32.04% per annum. Our results suggest 9 This result is obtained in the benchmark case of ρ =1.

19 Liquidity Premium and Consumption 19 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 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. InTable8,wereportthemodelimpliedlong-runrateofreturnof10liquidityportfolios. 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 unreported 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 macroeconomic 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-

20 Liquidity Premium and Consumption 20 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 aversion 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 liquid 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

21 Liquidity Premium and Consumption 21 explore the possible explanations for this empirical finding.

22 Liquidity Premium and Consumption 22 References Acharya, V. V. and L. H. Pedersen (2005). Asset pricing with liquidity risk. Journal of Financial Economics 77, Amihud, Y. (2002). Illiquidity and stock returns:cross-section and time-series effects. Journal of Financial Markets 5, Amihud, Y., A. Hameed, W. Kang, and H. Zhang (2010). Liquidity and stock returns: International evidence. Working Paper, National University of Singapore. Amihud, Y. and H. Mendelson (1986). Asset pricing and the bidűask spread. Journal of Financial Economics 17, Avramov, D., T. Chordia, and A. Goyal (2006). Liquidity and autocorrelations in individual stock returns. Journal of Finance 61, Bansal, R. and A. Yaron (2004). Risks for the long run: A potential resolution of asset pricing puzzles. Journal of Finance 59, Blanchard, O. J. and D. Quah (1989). The dynamic effects of aggregate demand and supply disturbances. American Economic Review 79, Brennan, M. J. and A. Subrahmanyam (1996). Market microstructure and asset pricing: On the compensation for illiquidity in stock returns. Journal of Financial Economics 41, Brunnermeier, M. K. and L. H. Pedersen (2009). Market liquidity and funding liquidity. Review of Financial Studies 22 (6), Cochrane, J.(2005). Asset Pricing, Revised Edition. Princeton University Press. Epstein, L. G. and S. E. Zin (1989). Substitution, risk aversion, and the temporal behavior of consumption and asset returns: A theoretical framework. Econometrica 57,

23 Liquidity Premium and Consumption 23 Gopalan, R., O. Kadan, and M. Pevzner (2011). Asset liquidity and stock liquidity. Journal of Financial and Quantitative Analysis forthcoming. Goyenko, R. Y., C. W. Holden, and C. A. Trzcinka (2009). Do liquidity measures measure liquidity? Journal of Financial Economics 92, Hameed, A., W. Kang, and S. Viswanathan (2010). Stock market declines and liquidity. Journal of Finance 65(1), Hansen, L. P., J. Heaton, and N. Li (2005). Intangible risk? In C. Corrado, J. Haltiwanger, and D. Sichel (Eds.), Measuring Capital in the New Economy. The University of Chicago Press. Hansen, L. P., J. Heaton, and N. Li (2008). Consumption strikes back? measuring long-run risk. Journal of Political Economy 116, Hasbrouck, J. (2009). Trading costs and returns for u.s. equities: Estimating effective costs from daily data. Journal of Finance 64(3), Lee, K. (2010). The world price of liquidity risk. Journal of Financial Economics 99, Liu, W. (2006). A liquidity-augmented capital asset pricing model. Journal of Financial Economics 82, Mehra, R. and E. Prescott (1985). The equity premium: A puzzle. Journal of Monetary Economics 15, Næs, R., J. A. Skjeltorp, and B. A. Ødegaard (2010). Stock market liquidity and the business cycle. Review of Financial Studies forthcoming. Pastor, L. and R. F. Stambaugh (2003). Liquidity risk and expected stock returns. Journal of Political Economy 111,

24 Liquidity Premium and Consumption 24 Sims, C. A. (1972). Money, income, and causality. American Economic Review 62 (4), Weil, P. (1990). Nonexpected utility in macroeconomics. Quarterly Journal of Economics 105, Zhang, H. (2010). Measuring liquidity in emerging markets. Working Paper, National University of Singapore.

25 Liquidity Premium and Consumption Portfolio 1 (Liquid) Portfolio 5 (Illiquid) Market Figure 1: Logarithm of ratios of the real cash flows to the real consumption for the equally weighted market portfolio and liquidity-based quintile portfolios. The yellow shaded area depicts the NBER business recession periods.

26 Liquidity Premium and Consumption 26 4 x 10 4 Portfolio 1 x x 10 4 Portfolio 2 x cash flow Consumption cash flow Consumption cash flow 8 x Portfolio x Consumption cash flow 1.5 x Portfolio x Consumption cash flow 5 x Portfolio x Consumption cash flow 8 x Market x Consumption Periods in Quarters Periods in Quarters Figure 2: Sample periodogram of the real cash flow growth and the real consumption growth. The solid line plots the sample periodogram of the real cash flow growth with the scale shown on the left vertical axis. The dashed line plots the sample periodogram of the real consumption growth with the scale shown on the right vertical axis.

27 Liquidity Premium and Consumption x 10 4 x Earnings Consumption Figure 3: Sample periodogram of the real corporate earning growth and the real consumption growth. The solid line plots the sample periodogram of the real corporate earning growth with the scale shown on the left vertical axis. The dashed line plots the sample periodogram of the real consumption growth with the scale shown on the right vertical axis.

28 Liquidity Premium and Consumption 28 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 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) (Illiq) Market 5-1 Sample average return (%) * Excess return (%) * Covariance with consumption growth Average book-to-market ratio Average size Average liquidity Average price-dividend ratio

29 Liquidity Premium and Consumption 29 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) (Illiq) Market Whole sample standard deviation Recession standard deviation Expansion standard deviation

30 Liquidity Premium and Consumption 30 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 γ = 5 γ = 10 γ = 20 γ = 40 Rate 1(Liq) (Illiq) Market

31 Liquidity Premium and Consumption 31 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 = γ = γ = γ = Panel B: Risk Exposure and Risk Premium 1(Liq) (Illiq) Market 5-1 Permanent Shock Risk Exposure Risk Premium (γ = 5) Risk Premium (γ = 10) Risk Premium (γ = 20) Risk Premium (γ = 40) Transitory Shock Risk Exposure Risk Premium (γ = 5) Risk Premium (γ = 10) Risk Premium (γ = 20) Risk Premium (γ = 40)

32 Liquidity Premium and Consumption 32 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 liquiditybased portfolios to the consumption and earnings shocks. Panel A: Price of Risk Consumption Shock Earnings Shock γ = γ = γ = γ = Panel B: Risk Exposure and Risk Premium 1(Liq) (Illiq) Market 5-1 Consumption Shock Risk Exposure Risk Premium (γ = 5) Risk Premium (γ = 10) Risk Premium (γ = 20) Risk Premium (γ = 40) Earnings Shock Risk Exposure Risk Premium (γ = 5) Risk Premium (γ = 10) Risk Premium (γ = 20) Risk Premium (γ = 40)