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3: Empirical evidence.

Conceptually, the first research question to be addressed by empirical studies of liquidity and asset pricing is regarding the existence of aliquidity effect. As discussed in Section 2.1.3, the null hypothesis of standard asset pricing theory is that assets with the same cash flow d should have the same price. To test the existence of a liquidity effect, the researcher identifies two assets 1 and 2 with cash flows [d.sup.1] and [d.sup.2] and different measures of liquidity [L.sup.1] and [L.sup.2] and examines the asset prices, [P.sup.1] and [P.sup.2], at the same point in time. If asset 1 is more liquid, i.e., [L.sup.1] > [L.sup.2], but the assets have the same cash flow, [d.sup.1] = [d.sup.2], standard asset pricing theory implies the null hypothesis [P.sup.1] = [P.sup.2], whereas liquidity-based asset pricing implies the alternative hypothesis [P.sup.1] > [P.sup.2]. In some cases, asset 1 is a synthetic security designed to replicate the cash flow pattern [d.sup.2] of asset 2, so the price [P.sup.1] is only an estimate of the price of the synthetic security, typically based on theoretical considerations. Surely, the pricing differences between assets may also be estimated by looking at differences in their expected returns or yields, assuming the same cash flows or controlling for differences in other determinants of expected returns. In some cases, the researcher examines a family of assets with different cash flows and different levels of liquidity. Then, the analysis includes control variables that account for the differences that can be explained by the different cash flows, and then tests whether the price differential which is unexplained by the control variables is significantly related to differences in liquidity.

As we discuss below, the empirical evidence supports the existence of a liquidity effect, leading to a rejection of the null hypothesis. This leads to the second research question: What is the magnitude and functional form of the liquidity effect? This can be studied either cross-sectionally, comparing prices for a family of assets with different levels of liquidity (using adequate controls), or in a time-series study, where the liquidity of a given security changes over time and the researcher studies the price change associated with the liquidity change.

The empirical work on liquidity and asset pricing often combines the two research questions, focusing on the effects of liquidity on a family of financial instruments which vary in their liquidity. Accordingly, we classify the empirical literature based on the financial instruments used to test and estimate the liquidity effect. We start by examining the relationship between liquidity and asset prices for stocks, where the liquidity effect has been studied extensively. Within this class, we distinguish between cross-section tests and studies of the effect of changes in liquidity over time, examine separately studies that focus on the effects of liquidity risk (rather than the level of liquidity) on asset prices, and conclude with the effects of trading restrictions on stock prices. We then review empirical work that studies the effect of liquidity on bond yields, distinguishing between U.S. Treasury securities and corporate bonds, which pose the additional challenge of disentangling the effects of liquidity and default risk. We then review the literature on liquidity and asset prices for other financial instruments--options, index-linked bonds, American Depository Receipts (ADRs), hedge funds and closed-end funds.

We consider first the challenges of choosing a liquidity measure L.

3.1 Liquidity measures: Empirical issues

As pointed out in Section 2, liquidity has a many facets. A major problem in estimating the effect of liquidity on asset prices or returns is how to measure liquidity since there is hardly a single measure that captures all of its aspects. In addition, measures used in empirical studies are constrained by data availability. High-frequency data that enable the estimation of liquidity from the actual sequence of trades and quotes became available in the U.S. only recently and are thus available only for a relatively short period of time. Further, studies of the effect of liquidity on expected stock returns use ex-post or realized returns, whose variance around the expected return is high. Consequently, researchers need a large amount of data--long time series--to increase the power of their tests. Given the short duration of high-frequency data, this poses a problem. Researchers need then to find substitute measures of liquidity using low-frequency data, such as daily return data and perhaps trading volume. In stock markets outside the U.S., high frequency data are hardly available, and the researcher then needs to estimate liquidity from daily return data, and, if available, from volume data as well. The empirical studies we survey thus employ various measures of liquidity, obtained from both high frequency and daily data. Neither is a perfect measure of liquidity, but most of these measures are highly positively correlated.

These problems in the measurement of liquidity reduce the power of tests of the effect of liquidity on securities pricing. Any liquidity measure used clearly measures liquidity with an error, because (i) a single measure cannot capture all the different dimensions of liquidity, (ii) the empirically-derived measure is a noisy estimate of the true parameter, and (iii) the use of low-frequency data to create the estimates increases the measurement noise. It is well known that errors in the variables bias downward (towards zero) the estimated regression coefficients. This means that the effect of liquidity is hard to detect even when it exists and, further, this could aggrevate potential omitted-variable problems.

3.2 Equity markets

3.2.1 Cross-section tests

The effect of liquidity on asset pricing was first studied by Amihud and Mendelson (1986a), whose model produces two major empirical predictions (see Sections 2.2-2.3 above):

1. Expected asset return is an increasing function of illiquidity costs, and

2. The relationship is concave due to the clientele effect (Section 2.3): In equilibrium, less liquid assets are allocated to investors with longer holding periods, which mitigates the compensation that they require for the costs of illiquidity.

These predictions are tested using stock returns over the period 1961-1980 and data on quoted bid-ask spreads for 1960-1979. The relative spread is the ratio of the dollar spread to the stock price, where the spread is the average of the beginning- and end-of-year end-of-day quotes, collected from Fitch quote sheets for NYSE and AMEX stocks. Every year, stocks are grouped into 49 (7 x 7) portfolios sorted on previous-year relative spread and within that, sorted on previously-estimated beta, and monthly return is calculated for each portfolio. The estimation is done by a pooled time-series and cross-section GLS regression which employs an estimation of the variance-covariance matrix of the 49 portfolios.

The estimation model is a regression of the portfolio monthly return on the portfolios' previously-estimated betas and previous-year average relative spreads. The spread effect is estimated in a piece-wise linear fashion, using dummy variables for the seven spread groups and the mean spread for each portfolio in each year. Thus, the regression explicitly accounts for the effect of the spread on (a) the level of the portfolio's average return and on (b) the slope of the return-spread relationship. The model's predictions are that (1) the portfolio return increases with the bid-ask spread, which is the main prediction, and (2) the return-spread slope decreases in the bid-ask spread, reflecting concavity.

The results support both predictions. The alternative hypotheses--that average return is not increasing in the spread, and that the slope is not decreasing in the spread--are rejected. The following illustrates the effect of the spread. From spread-portfolio 1 to spread-portfolio 4, the average spread increases by 0.659% and the monthly stock return increases by 0.242% (roughly 3% per annum), a ratio of 0.37. From portfolio 4 to 7, the spread rises by 2.063% and the average return rises by 0.439%, a ratio of 0.21. That is, the return-spread relationship for low-spread portfolios is nearly twice as high as it is for high-spread portfolios.

In addition, the model estimates the effect of the firm's size (capitalization) on stock return. The hypothesis is that if size reflects an aspect of liquidity--it is less costly to trade stocks of larger companies--then the size effect should weaken once the equation includes the bid-ask spread, which is a more direct measure of liquidity costs. Indeed, the bid-ask spread is known to be negatively related to firm size, as shown by Stoll and Whaley (1983) and others. The results support this prediction. The negative effect of size is weakened--it becomes insignificant--once the spread is included in the equation. Note, however, that the results could accommodate the size effect in addition to the effect of the bid-ask spread since the relative spread alone does not capture all aspects of liquidity.

A convenient summary of the results is provided in Amihud and Mendelson (1986b). Given the concave effect of the spread on expected return, the following model is estimated:

[R.sub.j] = 0.0065 + 0.0010[[beta].sub.j] + 0.0021ln([S.sub.j]),

where [R.sub.j] is the monthly stock portfolio return in excess of the 90-day Treasury bill rate, [[beta].sub.j] is the systematic risk, estimated from data in the preceding period, and [S.sub.j] is the relative bid-ask spread in relative bid-ask spread in the preceding year. All coefficients significant. By this estimation, the return difference between a stock with a 1.5% spread and a stock with 1% spread (and the same [beta]) is 0.087% per month or roughly 1% per year. The return difference is greater--0.15% per month (or 1.8% annually) for a stock with 1% spread compared to a same-risk stock with 0.5% spread.

The estimated return-spread relationship is illustrated in Figure 3.1.


Amihud and Mendelson (1989) further estimate the return-spread relationship, accounting also for the effect of volatility. Constantinides (Constantinides, 1986, see Section 2.6) shows that the effect of trading costs may be confounded with that of risk. While in Constantinides (1986) model, trading costs have only second-order effect on asset returns, expected return rises with volatility because higher volatility induces more frequent trading, which makes investors incur higher trading costs. Amihud and Mendelson thus add to the estimation model, which includes the portfolio's beta and relative spread, the standard deviation of market-model residuals (unsystematic risk). The results show that while the bid-ask spread effect remains positive and significant, the effect of the unsystematic risk is generally negative but insignificantly different from zero.

For Nasdaq National Market System stocks, bid-ask spreads at the end of the day are available on the CRSP daily database, which facilitates the study of the return-spread relationship with more accurate data than in Amihud and Mendelson (1986b). Also, while on the NYSE and AMEX individual investors could trade through limit orders that had priority over the specialist's quotes and thus avoid the cost of the spread (though incurring the costs of risk and delay), on Nasdaq trading was done mostly through market makers, and investors had to incur the cost of the spread. (1) Consequently, the estimated effect of the bid-ask spread is expected to be stronger when using Nasdaq stocks. This is indeed the finding by Eleswarapu (1997), who estimates a model where the stock return is regressed on the stock's beta, relative spread, and log(size). The estimation is performed for individual stocks employing the Fama and MacBeth (1973) method. The only consistently significant effect is that of the relative spread, whose coefficient is positive and significant for both January and non-January months, whereas the coefficient of log(size) is negative and insignificant and that of beta is positive and significant only in January. (2) The liquidity effect in non-January months is inconsistent with an earlier finding by Eleswarapu and Reinganum (1993) that liquidity affects stock returns only in January. These authors replicate the Amihud-Mendelson study but employ the Fama-Macbeth method in the cross-section estimation and obtain that the bid-ask spread effect is significant only in the month of January but not in non-January months or in the year as a whole, and the size effect is never significant. Then, employing a looser data requirement that allows more small firms into the sample results again in the spread effect being significant only in the month of January but insignificant for the entire year, whereas the size effect is negative and significant both in January and in the entire year (but neither variable is significant in non-January months; the issue of the seasonality in the liquidity effect is revisited by Amihud (2002) and by Hasbrouck (2005), see below).

A finer measure of illiquidity is used by Brennan and Subrahmanyam (1996): Kyle (1985) [lambda] (see Section 2.7), estimated from intraday trade and quote data. Brennan and Subrahmanyam estimate [lambda] by regressing the trade-by-trade price change, [DELTA][p.sub.t], on the signed transaction size, [q.sub.t]. The slope coefficient from this regression (3) is Kyle's [lambda] which measures the price impact of a unit of trade size, being larger for less liquid stock. (4) The regression model also includes [D.sub.t] - [D.sub.t-1], where [D.sub.t] = 1 for a buy transaction and [D.sub.t] = -1 for a sell transaction. The coefficient of this differential, [psi], reflects the fixed cost of trading that is unrelated to the order size. The illiquidity variables that are used are the average of the marginal cost of trading, [C.sub.q] = [[lambda].sub.q]/P, where q and P are the monthly averages of trade size and price, respectively (or [C.sub.n] = [[lambda].sub.n]/P, where n is the monthly average of number of shares outstanding) and the relative fixed cost of trading, [psi]/P. These cost variables are estimated for the years 1984 and 1988.

These measures of illiquidity are then used in a cross-section regression of monthly NYSE stock returns for the years 1984-1991. The estimations are performed using pooled time series and cross section GLS regressions, where the dependent variable is the monthly portfolio return. Portfolios are formed annually by sorting stocks into 25 (5 x 5) portfolios on size and within that on [lambda]. In addition to the two liquidity cost variables, the regression model includes the three Fama and French (1993) factors: The market return index, the small-minus-big firm return indexes and the high-minus-low book-to-market return index. Thus, the returns are effectively the intercepts from the Fama-French three-index model.

The results show that [C.sub.q] (or [C.sub.n]) have a positive and significant effect on returns adjusted by the Fama-French factors, after controlling for firm size and price reciprocal. For example, the excess monthly return on the highest [C.sub.q] quintile is 0.55% higher than the respective return on the lowest [C.sub.q] quintile. In addition, [C.sup.2.sub.q] (or [C.sup.2.sub.n]) have a negative and significant effect, consistent with the Amihud and Mendelson (1986a) clientele effect that generates an increasing and concave relationship between return and illiquidity costs. Further, both [psi]/P and [([psi]/P).sup.2] have positive and significant effects. While the positive sign of [psi]/P is consistent with a positive illiquidity effect, the positive coefficient of [([psi]/P).sup.2] is inconsistent with the Amihud-Mendelson concavity prediction--instead, it suggests a convex illiquidity effect. When these finer measures of liquidity are used, both the bid-ask spread and the firm size become insignificant. In conclusion, Brennan and Subrahmanyam's results support the positive effect of illiquidity on expected stock returns.

As pointed out, liquidity is an elusive concept and is hard to measure. In addition, data such as bid-ask spread and intra-daily quotes and trades are hard to obtain. Even if such data are available, tests of asset pricing models require data that span a long periods of time to increase the power of the tests. Therefore, researchers often use alternative measures based on daily data on volume, shares outstanding and prices, which are available for most markets.

Brennan et al. (1998) use the stock's dollar trading volume as a measure of liquidity in a multi-factor asset pricing model, a version of the APT, where the stock's excess return is a function of the loadings of the stock return on the factors. The study uses excess returns from a factor model (using either the Connor and Korajczyk (1988) or the Fama and French (1993) approach), thus obtaining risk-adjusted returns. These risk-adjusted returns are regressed cross-sectionally on the stock's volume (in log) as well as on other characteristics: Size, book-to-market ratio, price, dividend yield and past returns (to capture the momentum effect). The study is performed using CRSP data for individual stocks over the period 1966-1995. As expected, the results show that volume has a negative and significant effect on risk-adjusted stock returns. Specifically, a one standard deviation increase in the dollar volume brings about a decline in the monthly excess return of 0.29% for Nasdaq stocks and 0.11% for NYSE/AMEX stocks.

Datar et al. (1998) use stock turnover (the ratio of stock volume to the number of shares outstanding) as a measure of liquidity. If in equilibrium less liquid stocks are allocated to investors with longer holding periods (Amihud and Mendelson, 1986b), or investors reduce their trading frequency of illiquid stocks (Constantinides, 1986), then even though liquidity is not directly observed, it can be inferred from the average holding period of the stock, which is the reciprocal of the stock turnover. (5) Datar et al. estimate the cross-section of NYSE stock returns (years: 1963-1991) on stock turnover, controlling for size, book-to-market ratio and beta, employing the Fama and MacBeth (1973) method. The prediction is that the longer the average holding period of the stock (which implies lower liquidity), or the lower the turnover, the higher the expected return. The results are consistent with this prediction: The cross section of stock returns is negatively related to stock turnover, with the effect being significant. The turnover coefficient was also negative and significant for each of the two subperiods. Similar results on the negative return-turnover relationship are obtained for the Tokyo Stock Exchange by Hu (1997).

Rouwenhorst (1999) examines the returns in 20 emerging markets over 10 or less years. Sorting each country's returns by turnover, he obtains no difference between high- and low-sorted returns. However, there are no controls for other variables, and the test period may be too short. He also finds that turnover is higher for small and high-beta firms; absent controls for size and risk in analyzing the return-turnover relationship, (6) there may be a confounding of the turnover effect with that of size and risk. Another study that uses turnover as a measure of liquidity is by Nguyen et al. (2005). They study the effect of turnover on stock returns in two ways, using 1970-2002 data. In one test, they use the intercepts from Fama and French (1993) three-factor model (the market and factors for size and book-to-market ratio) and aggregate them into 25 portfolios, obtained by sorting on size or book-to-market and within that on turnover. The average coefficients do not show a systematic relationship with the turnover portfolios, which is inconsistent with a liquidity effect. In the second test, Nguyen et al. perform a cross-section analysis using individual stocks (instead of portfolios), employing the Fama and MacBeth (1973) method with the GLS setup of Litzenberger and Ramaswamy (1979). Controlling for beta, size, book-to-market ratio or for beta and co-skewness with the market (to capture a skewness preference by investors), they find that turnover has a negative and significant coefficient, which is consistent with the liquidity effect.

Amihud (2002) examines the effect of illiquidity on the cross-section of stock returns using an illiquidity measure that is related to Kyle (1985) price impact coefficient [lambda]. The measure is called ILLIQ = |R|/(P * VOL), where R is daily return, P is the closing daily price and VOL is the number of shares traded during the day. Intuitively, ILLIQ reflects the relative price change that is induced by a given dollar volume. This ratio is averaged for each stock over a year to obtain the stock's ILLIQ for that period. (7) (As discussed later, ILLIQ varies over time.) The stock's ILLIQ is then used in cross-section regressions of monthly individual stock returns on their prior-year ILLIQ and other control variables: Beta, size, volatility, dividend yield and past returns (period: 1963-1996, NYSE stocks). The results show that ILLIQ has a positive and significant effect on stock returns, as suggested by the theory. This effect is positive and significant both in January and in non-January months and over both sub-periods of the entire period.

Gottesman and Jacoby (2005) consider the effect of the firm's pay-out policy and investors' personal taxes on the relationship between expected return and bid-ask spread in the Amihud and Mendelson (1986a) framework. Stock repurchase is tax-advantaged compared to dividend but it incurs transaction costs, thus a wider bid-ask spread reduces its attractiveness. Investors maximize expected net return-after transaction cost and after tax. Gottesman and Jacoby obtain that while for dividend-paying stock, return is an increasing and concave function of the bid-ask spread, for stock repurchases the function is increasing and it may be convex or concave, depending on the mass of investors' holding-period clientele. They test the theory using data from Nasdaq during 1993-1999, when stock repurchases were far more popular than in the 1961-1980 period studied by Amihud and Mendelson. The results show that in general, the return-spread relationship is positive and concave (controlling for other characteristics). This pattern also holds in a subsample of firms that pay dividends and do not repurchase their stock, whereas in the subsample of firms that repurchase their stock and pay no dividend the return-spread relationship is positive and possibly convex, but for this group the results are not statistically significant.

The papers considered so far have used liquidity measures that are based on trading costs or investors' holding periods. Chalmers and Kadlec (1998) consider the effect of amortized spread, the product of the effective relative spread (8) and the stock's turnover (whose reciprocal gives the average holding period) on returns using annual data on NYSE/AMEX stocks over the period 1983-1992. (9) In the context of the simplest liquidity model (Proposition 1 of Section 2.2), the slope coefficient of a regression of expected return on the amortized spread should be 1. In the regression of Chalmers and Kadlec, controlling for size, book-to-market ratio and volatility, they find that the coefficient on amortized spread is positive and large, 7.9, and statistically significant with all the control variables (though insignificant in other specifications). This large coefficient, while supporting the positive effect of amortized transaction costs on stock returns, is larger than would be predicted by the simplest liquidity theory. This can possibly result from the omission of a relevant variable which is correlated with the amortized spread. For instance, the liquidity clientele effect on excess return ([r.sup.*j] - [r.sup.f]) in Proposition 2 or the effect of liquidity risk described in Proposition 3.

Swan and Westerholm (2002) measure of the illiquidity of stocks relative to bonds is the difference in amortized bid-ask spread for stocks and bonds, deflated by unity minus the absolute value of the transaction cost elasticity with respect to turnover. The underlying model endogenizes trading, where investors trade until they are indifferent between trading further or not. Their estimation, using Finnish data for 1993-1998, shows that their measure of illiquidity has a strong positive effect on the cross-section of stock returns.

The difficulty of obtaining reliable liquidity measures from low-frequency (daily) data is addressed by Hasbrouck (2005) who examines three measures from daily data and correlates them with measures obtained from high-frequency microstructure data. The Gibbs sampler estimates the effective cost of trading from the square root of the (negative of the) serial covariance of daily price changes (following Roll, 1985), but truncating the negative outcomes, where the extent of truncation is determined by a Bayesian estimation. The Gibbs sampler is highly correlated with the effective spread estimated from transaction and quote data. The other two are [ILLIQ.sup.1/2] and Pastor and Stambaugh (2003) [gamma] that measures the return reversal in response to volume shocks, which is larger for less liquid stocks (see below). Hasbrouck then estimates the effects of these illiquidity measures on the cross-section of stock returns that are risk-adjusted by first employing the Fama and French (1993) three-factor model (following Brennan et al., 1998) (period: 1962-2003). The cross-sectional model that is estimated from monthly data using the Fama and MacBeth (1973) method, also includes market capitalization (in log) and past returns. The results show that both the Gibbs sampler and [ILLIQ.sup.1/2] have positive and significant effect on the cross-section of stock returns, with the effect being stronger for NYSE/AMEX stocks than for Nasdaq stocks. However, the estimated effect is not robust over January/non January time periods.

A problem that is revisited at this stage by Spiegel and Wang (2005) is the possible confounding between the effects of illiquidity and risk on stock returns. Given the strong positive relationship that they find between illiquidity and idiosyncratic risk (10) (the standard deviation of factor-model residuals), the estimated return-liquidity effects may be confounded with the positive relationship between return and idiosyncratic risk that obtains if investors are not well-diversified (see, e.g., Levy, 1978; Merton, 1987) or under the model of Constantinides (1986), where portfolio rebalancing is impeded by trading costs. The risk variable, EIDIO, is the conditional idiosyncratic standard deviation of Fama and French (1993) three-factor model residuals, estimated by EGARCH. Spiegel and Wang estimate the effect of EIDIO and of some measures of liquidity on stocks' risk-adjusted returns (following Brennan et al., 1998) in a cross-sectional model (period: 1962-2003). The illiquidity measures are Hasbrouck (2005) Gibbs sampler, Amihud (2002) ILLIQ and Pastor and Stambaugh (2003) [gamma]. The model also includes a measure of liquidity--trading volume in dollars and in logarithm (see Brennan et al., 1998)--as well as size (in log) and past returns, accounting for the momentum effect. The explanatory variables are lagged, reflecting the information investors had when making their investment decision. The results show that whereas the illiquidity variables have a positive and significant effect in a model without EIDIO, their effect becomes insignificant when EIDIO is included in the model, whereas the coefficient of EIDIO is positive and significant through all models. The coefficient of trading volume (particularly for NYSE/AMEX stocks), a measure of liquidity, is negative and significant in all models. The results highlight the problem of measuring illiquidity and disentangling it from other measures such as idiosyncratic risk.

All studies surveyed so far use historical returns to investigate the effects of liquidity on expected return. Clearly, realized return is a very noisy measure of expected return. Loderer and Roth (2005) depart from this method and investigate how stock prices are affected by liquidity. Clearly, controlling for future cash-flow growth and dividend payout, price is a measure of the expected return, and after controlling for risk, the results give the effect of liquidity on expected return. Loderer and Roth use data from the Swiss Stock Exchange for the years 1995-2001 and regress stock P/E, the price-earning ratio, on liquidity, measured by the relative bid-ask spread, after controlling for projected earnings growth obtained from analysts' reports, dividend payout ratio, risk and size (orthogonalized to the relative spread). The results show that the spread has a negative and significant effect on the cross-section of stock prices, as expected by the theory. A similar conclusion on the negative effect of illiquidity on stock prices is obtained when using trading volume as a measure of liquidity. The price discount is economically significant, being 12% for a median-spread stock compared to a zero-spread stock for the median year in the sample. Loderer and Roth replicate this methodology and examine the price discount, as a result of illiquidity, for Nasdaq stocks. The median discount there is 28% (for the median year).

3.2.2 Liquidity changes over time

If liquidity affects asset prices, it stands to reason that changes in liquidity should change asset prices (ceteris paribus). This hypothesis is examined by Amihud et al. (1990). They suggest that the stock market crash of October 19, 1987 can be partly explained by a decline in investors' perception of the market's liquidity. At the time, a popular investment strategy was "portfolio insurance," by which stockholdings are reduced when prices fall and increased when prices rise. In an infinitely liquid market, such a strategy would have no impact on prices even when exercised by many investors. However, in the days prior to the crash there were massive stock sales and price declines, which may have caused investors to adjust downward their beliefs about market liquidity. Liquidity asset pricing theory implies that a downward revision in liquidity should cause a decline in stock prices. Amihud, Mendelson and Wood test this hypothesis as follows. They regress cross-sectionally the risk-adjusted returns of NYSE stocks that are included in the S&P 500 index on October 19, 1987 on the change in liquidity during that day, measured by the average daily bid-ask spread or by depth (the number of shares that could be traded at the quoted bid and ask prices). The results show that stocks that suffered the greatest decline in liquidity on that day also suffered the greatest decline in prices. Further, stocks whose liquidity recovered more by the end of the month (October 30, 1987) also enjoyed a greater recovery in price.

A well-controlled case of changes in stock liquidity is the case of transfer of stocks in the Tel Aviv Stock Exchange from a once-a-day call auction to semi-continuous trading. Stocks were transferred in batches, an average of 7 stocks in each, at random times over the years 1987-1994, without company discretion--all transfer decisions were made by the Exchange. This avoids the self-selection problem that arises when stocks transfer voluntarily from one trading system to another, such as moving from the Nasdaq to the NYSE or AMEX (see below), which may reflect private information. This case is also different from the cases in European exchanges where an entire market, or most of it, was transferred from an auction market to continuous trading.

Stocks that were transferred to the semi-continuous trading system obviously enjoyed greater liquidity in general. Amihud et al. (1997) find that their trading volume increased significantly relative to the market's and their liquidity ratio (the ratio of average absolute daily return to average daily dollar volume) declined. Consequently, the prices of the transferred stocks rose by at least 5%-6% and remained high. Cross-sectionally, the price increase was greater for stocks that enjoyed a greater increase in liquidity. Moreover, there was a liquidity externality: The prices of closely-related stocks (stocks of the same company with different voting rights) that were not transferred also rose, although by less.

Similar results are obtained by Muscarella and Piwowar (2001) for the Paris Bourse's transfer of stocks from a call to a continuous market, and by Kalay et al. (2002) for a later improvement in the trading system at the Tel Aviv Stock Exchange. In both studies, stocks that were transferred to a more liquid trading system enjoyed an increase in prices. Interestingly, Muscarella and Piwowar as well as Lauterbach (2001) find that some thinly-traded stocks that are transferred from the call to the continuous market realize a decline in liquidity and a decline in price. Lauterbach finds that the price decline is positively associated with a decline in relative trading volume that measures liquidity. Stocks that were immediately returned to the call market realized both a price increase and a rise in liquidity. This suggests that for thinly-traded stocks, a call auction may be an efficient mechanism to consolidate trading which contributes to liquidity and value, and further reinforces the positive relationship between liquidity and stock prices. (11)

In another study on the effect of changes in the trading environment on stock prices, Berkman and Eleswarapu (1998) examined the effect of changes in the forward trading facility (Badla) for 91 stocks on the Bombay Stock Exchange--the abolition on 12/1993 and the reinstatement on 3/1994. The Badla enables trading without affecting delivery, which was attractive to short-term traders. When it was abolished, the liquidity of the affected stocks declined sharply and their price fell by about 15% compared to the price of non-Badla stocks. In a cross-section analysis, Berkman and Eleswarapu find the decline in prices of Badla stocks was significantly associated with the decline in their liquidity (controlling for the change in volatility).

Exogenous changes in stock liquidity occur when the composition of the S&P 500 index changes. Stocks included in the index are subject to a great deal of trading that is not based on stock-specific information, such as by index funds and by hedgers of index futures and index options. Thus, including the stocks in the S&P 500 index increases their liquidity. It has been documented that stocks that join the index enjoy a price increase whereas those that are deleted suffer a price decline. These changes have been attributed to demand pressures. Hegde and McDermott (2003) document increases in the liquidity of stocks that are added to the S&P 500 index, with liquidity being measured in a number of ways: bid-ask spread (quoted and effective), volume, trading frequency, and the estimated parameters from Kyle's model, [lambda]n/P and particularly [psi]/P (see above under the analysis of Brennan and Subrahmanyam, 1996). For deleted stocks, they find a decline in liquidity although the results are weaker since deletions are very noisy events. The authors then test in a cross-section regression the hypothesis that the price changes of these stocks are related to changes in their liquidity, measured by direct information cost. They find that the price increase of added stocks is positively and significantly associated with the improvement in liquidity.

Exchange listing generally induces improvement in liquidity and an increase in price. However, being voluntary, it may reflect self-selection due to favorable information. Kadlec and McConnell (1994) and Elyasiani et al. (2000) examine the effect of listing on both stock value and stock liquidity. The respective samples are 273 stocks that listed on the NYSE during 1980-1989 and 895 listings on NYSE and AMEX between 1971 and 1994. Both studies find that listing brought about a significant increase in stock price and at the same time a significant decline in the bid-ask spread. In a cross-section analysis, the studies find that price changes are negatively associated with changes in the spread, as would be predicted if liquidity enhances value. (In addition, the studies control for the change in number of shareholders and change in volatility). Bollen and Whaley (2004) too find that stocks that transferred from Nasdaq to the NYSE enjoyed greater liquidity and an increase in price, and they include controls to overcome the self-selection problem.

When a stock is delisted from an exchange, its liquidity dramatically declines. Involuntary delisting occurs because of violations of listing requirements, and the delisted stocks are subsequently traded in less liquid markets. Since delisting is involuntary, the delisting event per se does not convey new private information, and thus any observed price effect on the delisting day reflects the effect of the change in liquidity due to the change in the stock's trading arena. Angel et al. (2005) examine stocks that are involuntarily delisted from the Nasdaq Stock Market and are subsequently traded in the OTC Bulletin Board and in the Pink Sheets. They find a large and significant deterioration in liquidity, measured by trading volume, number of quotes per day and the bid-ask spread, and a large and significant price decline, about 18%, around the delisting day. This price decline understates the total effect of delisting because the event was partly anticipated. Similar results are obtained by Macey and O'Hara (2005) for 55 stocks that were delisted from the NYSE. For a sub-sample of 12 large stocks they find that stock prices fell along with a decline in trading volume and an increase in the percent bid-ask spread (the dollar bid-ask spread declined). (12)

Some corporate events may change the liquidity of the firm's stock and, if liquidity is priced, they can affect the stock price. Amihud et al. (1999) study a case where companies in Japan reduced the minimum trading unit of their stock and consequently increased the number of their individual shareholders. The greater breath of ownership led to significant increases in stock liquidity and in stock prices. (13) Amihud et al. (2003) examine the increase in stock liquidity that follows the exercise of outstanding stock warrants, which increases the stock's float without changing anything else in the firm. They find that this led to a decline in stock illiquidity (measured by Roll's (1985) bid-ask spread) and that stock prices abnormal returns being positively and significantly associated with the improvement in liquidity.

The time series effect of market-wide changes in stock liquidity on stock prices is examined by Amihud (2002) and Jones (2002). Amihud proposes that (i) expected stock return for period t + 1 is an increasing function of illiquidity for t + 1 as expected in period t, and (ii) an unexpected rise in illiquidity in period t lowers stock prices in the same period, producing a negative returns--unexpected liquidity relationship, consistent with the theoretical results in Acharya and Pedersen (Acharya and Pedersen 2005; see Proposition 4 in Section 2.4). To test these hypotheses, Amihud constructs a measure of aggregate illiquidity, AILLIQ (the average of stocks' ILLIQ, the daily ratio of absolute return to dollar volume), for NYSE stocks between 1962 and 1997. He finds that average stock excess return (monthly or annual) is an increasing function of lagged AILLIQ, which measures expected illiquidity (AILLIQ is highly autoregressive), and is a decreasing function of contemporaneous unexpected AILLIQ (the residual from an autoregressive model of AILLIQ). Both results are consistent with the liquidity theory of asset pricing.

Amihud further proposes that both effects of illiquidity should be stronger for less-liquid stocks. Liquid stocks, while being subject to the same effects, become more attractive when liquidity worsens--a "flight to liquidity"--which mitigates the negative effects of increased illiquidity. The results support this hypothesis. The negative effect on returns of market liquidity shocks, and the positive effect of lagged illiquidity on subsequent return, are both stronger for smaller firms, with the effect being monotonic in size, suggesting that the exposure to liquidity shocks is greater for less liquid stocks.

Jones (2002) examines the time series effects of market liquidity on stock prices over the twentieth century. He uses two measures of liquidity: transaction costs, measured by bid-ask spread and brokerage fees on the Dow Jones component stocks, and stock turnover. Jones finds that stock returns can be predicted a year or more ahead: High spreads predict high stock returns and high turnover predicts low stock returns.

The time-series liquidity-expected return relationship is further studied by Bekaert et al. (2005) using data from 19 emerging markets and the U.S. (which proxies the world index) and employing a VAR analysis. The measure of illiquidity used is the relative number of days of zero returns in each stock, averaged over all stocks used for the country index. This follows Lesmond et al. (1999) who suggest that higher transaction costs reduce the likelihood of trading for a given information signal. Indeed, the authors find that this measure (or a related measure of no-trade days) is highly correlated with other measures of illiquidity for U.S. data. The results show that (a) liquidity predicts return (monthly data) with the effect being negative, and (b) unexpected liquidity is positively correlated with contemporaneous returns. Both results are consistent with those of Amihud (2002) and Proposition 4 in Section 2.4. The results are qualitatively similar when returns are replaced by dividend yield. The use of data from emerging markets enables also to examine the effect of liquidity on stock returns when the market is closed to foreign investors and when it is opened up, the latter being measured by foreign investors' holdings relative to the market capitalization. The estimations then show that opening up a country's capital market to foreign investors reduces the effect (i.e., the coefficient) of liquidity on stock returns.

3.2.3 Pricing of liquidity risk

The studies reviewed in Section 2.2 examine the effects of the level of liquidity on stock returns. Since liquidity varies over time, as documented in Hasbrouck and Seppi (2001), Huberman and Halka (2001), Amihud (2002), and Chordia et al. (2002), it stands to reason that liquidity risk should also be priced.

Pastor and Stambaugh (2003) propose that asset prices should reflect a premium for the sensitivity of stock returns to market-wide liquidity: Stocks with greater exposure to market liquidity shocks--i.e., with greater systematic liquidity risk--should earn higher returns.

Pastor and Stambaugh's market liquidity measure is based on Campbell et al. (1993) observation that in a regression of a stock's daily return on its signed lagged dollar volume, the coefficient which captures the bounce in the stock price following a given trading volume is more negative for less liquid stocks. Pastor and Stambaugh perform monthly estimations of the following model for each stock j:

[r.sup.e.sub.j,d+1] = [[theta].sub.j] + [[phi].sub.j][r.sub.d] + [[gamma].sub.j]sign([r.sup.e.sub.j,d]) x [v.sub.j,d] + [e.sub.j,d+1], (3.1)

where [r.sup.e.sub.j,d] is the return on stock j on day d in excess of the market return and [v.sub.j,d] is the daily dollar volume. (14) Stocks with more negative [[gamma].sub.j] are interpreted as less liquid. (15) The market's liquidity for month t, [[gamma].sub.t], is the average of the individual stocks' [[gamma].sub.j,t]. Finally, the liquidity measure [L.sub.t] is the residual from an AR1 model of [DELTA][[gamma].sub.t] = [[gamma].sub.t] - [[gamma].sub.t-1] (adjusted for variations in market capitalization over time), and it is serially uncorrelated. The stock's exposure to liquidity shocks is [[beta].sup.L], the regression coefficient of the stock returns on [L.sub.t], with the model also including the three Fama and French (1993) factors. The study eventually uses the predicted [[beta].sup.L], which is a function of seven stock characteristics, (16) or historical values of [[beta].sup.L]. The data are for NYSE, AMEX and Nasdaq over the period 1966-1999.

If liquidity risk is priced, stock returns should be increasing in their liquidity beta [[beta].sup.L]. Pastor and Stambaugh sort stocks in each year by their predicted [[beta].sup.L] (based on historical [[beta].sup.L] and other stock characteristics) and aggregate them into 10 portfolios. The return series of these portfolios are then linked over time to form a time series of returns, which are used to estimate portfolio alphas from the market model or from Fama-French three- or four-factors model. Pastor and Stambaugh find that these portfolio alphas are increasing over the 10 beta portfolios which are ranked from low to high [[beta].sup.L]. That is, the expected return is an increasing function of the stock's sensitivity to market-wide liquidity shocks, which means that liquidity risk is priced.

Acharya and Pedersen (2005) study a broad model of pricing liquidity level and liquidity risk. Expected excess return over the risk-free rate, E([r.sup.e.sub.j,t+1]), is a function of both the expected illiquidity, E([c.sub.j,t+1]), and four systematic risk variables: the ordinary return beta [beta] = cov([r.sub.j],[r.sub.m])/var([r.sub.m] - [c.sub.m]) and three liquidity-related betas, [[beta].sup.L1] = cov([c.sub.j],[c.sub.m])/var([r.sub.m] - [c.sub.m]), [[beta].sup.L2] = cov([r.sub.j],[c.sub.m])/var([r.sub.m] - [c.sub.m]) and [[beta].sup.L3] = cov([c.sub.j],[r.sub.m])/var([r.sub.m] - [c.sub.m]), where [c.sub.j] and [c.sub.m] are the illiquidity cost of stock j and of the market, respectively (see Section 2 above). The (unconditional version of the) model is:

E([r.sup.i.sub.t+1]) = [r.sup.f] + [kappa]E ([c.sup.i.sub.t+1]) + [lambda]([beta] + [[beta].sup.L1] - [[beta].sup.L2] - [[beta].sup.L3]) (3.2)

where [kappa] adjusts for the difference between the average holding period and the monthly estimation period. The liquidity risk [[beta].sup.L2] is analogous to that used by Pastor and Stambaugh (2003).

The empirical estimation of the model employs as a measure of illiquidity Amihud (2002) ILLIQ, calculated from daily CRSP returns and volume for NYSE/AMEX stocks for the period 1964-1999. Stocks are sorted every year by their ILLIQ or by their size and grouped into 25 portfolios. The monthly illiquidity of each portfolio and of the market is calculated as the residual from an autoregressive model of the portfolio (average) ILLIQ, adjusted for market capitalization. The four portfolio betas are estimated from the monthly data over the entire period. Naturally, [beta] is higher for less liquid stocks. As for the three liquidity betas, illiquid stocks have higher [[beta].sup.L1] and more negative [[beta].sup.L2] and [[beta].sup.L3]. Thus, the absolute values of the liquidity betas--the measures of exposure to liquidity risk--are greater for less liquid stock. The higher liquidity risk of illiquid stocks is consistent with the notion of "flight to quality" or "flight to liquidity": in times of liquidity crisis, the illiquid securities suffer the most.

Model (3.2) is estimated using GMM and the results show that the excess return is positively and significantly related to the portfolio's [[beta]] = [beta] + [[beta].sup.L1] - [[beta].sup.L2] - [[beta].sup.L3] as well as to its level of illiquidity E(c). The model's explanatory power in the cross-section is higher than the standard CAPM. Indeed, the liquidity-adjusted CAPM fairs better in specification tests and has a higher [R.sup.2].

To test the effect of liquidity risk over and above the effects of market risk and liquidity level, the authors estimate

E([r.sup.i.sub.t+1]) = [r.sup.f] + [kappa]E ([c.sup.i.sub.t+1]) + [[lambda].sup.1][beta] + [[lambda].sup.2] ([[beta].sup.L1] - [[beta].sup.L2] - [[beta].sup.L3])

The estimated coefficient on liquidity risk [[lambda].sup.2] is positive and significant in several, but not all, specifications. This is consistent with liquidity risk being priced.

Finally, Acharya and Pedersen assess the relative economic significance of liquidity level and liquidity risk by considering the return premium required to hold the most illiquid stocks rather than the liquid ones. Under the restriction of one risk premium [lambda] and with [kappa] calibrated to the average turnover, the total annual liquidity risk premium is estimated to 1.1% while the premium for liquidity level is 3.5%. When the risk premium on each kind of liquidity risk is estimated freely, the effect of liquidity risk rises, but the statistical significance is limited. Pastor and Stambaugh (2003) find a larger effect of liquidity risk, but they do not control for liquidity level.

Another specification of a model with systematic liquidity risk is proposed by Martinez et al. (2005). Beginning with the pricing kernel [E.sub.t-1][[M.sub.t](1 + [R.sub.j,t])], they assume that [M.sub.t] = [d.sub.0,t-1] + [d.sub.1,t-1][r.sub.m,t] + [d.sub.2,t-1][L.sub.t], where [L.sub.t] is a replicating liquidity portfolio, and [d.sub.k,t] = [d.sub.k,0] + [d.sub.k,1][bm.sub.t] for k = 0,1,2, with [bm.sub.t] being the book-to-market ratio. This gives rise to the asset pricing model

E([r.sub.j]) = [c.sub.0] + [c.sub.1][[beta].sub.j,m] + [c.sub.2][[beta].sub.j,bm] + [c.sub.3][[beta].sub.j,mbm] + [c.sub.4][[beta].sub.j,L] + [c.sub.5][[beta].sub.j,Lbm], (3.3)

where [[beta].sub.j,x] = cov([r.sub.j,t],[x.sub.t])/var([x.sub.t]) and [[beta].sub.j,xbm] = cov([r.sub.j,t], [bm.sub.t-1][x.sub.t])/var([bm.sub.t-1][x.sub.t]) for x = [r.sub.m] or L. It is expected that [[beta].sub.j,L] < 0 and [[beta].sub.j,Lmb] < 0. Notably, [[beta].sub.j,L] is related to Pastor and Stambaugh's liquidity beta and to Acharya and Pedersen (2005) [[beta].sup.L2]. The focus of the test is on whether liquidity is priced, i.e., whether [c.sub.4] and [c.sub.5] are significantly different from zero.

For the factor L, the study uses three measures of liquidity: Pastor and Stambaugh (2003) market liquidity, Amihud (2002) ILLIQ and the return differential between portfolios of stocks with high and low sensitivity to changes in their relative bid-ask spread. The data are obtained from the Spanish stock market for the years 1993-2000. The results show that when L is measured as ILLIQ, the coefficients [c.sub.4] and [c.sub.5] are negative and significant, that is, higher (absolute) liquidity-related betas lead to higher expected returns.

The pricing of liquidity risk in nineteen emerging markets is studied by Bekaert et al. (2005) in a model that extends Acharya and Pedersen (2005). They model the effects of liquidity factors--both a country and a global (U.S.-based) factor, as well as a country and a global (U.S.) return factor, allowing for different prices for the two risks, market and liquidity. Further, their model enables to study the differences in the effects on expected return of segmented and integrated markets, with the difference being whether or not the risks due to the global return and liquidity factors are present. The results show that while the price of the local market risk is not significant, the price of local liquidity risk is positive and significant. The positive and significant effect of the local liquidity risk is preserved in a mixed model that allows for both segmentation and integration. In the latter model, the price of global liquidity risk is positive but only marginally significant (the same applies to the pricing of the global return factor). The best fitting model assumes a locally-segmented market and estimates a compensation for local liquidity risk of 85 basis points per month. (17) This suggests that opening up the local market to foreign investors does not eliminate the effect of local liquidity risk, which remains the most important priced factor.

Sadka (2003) examines the pricing of liquidity risk in a factor model that includes the three Fama-French factors and a liquidity factor L, calculated as an average of the stocks' permanent market impact coefficient. This coefficient is similar to Kyle's e as estimated by Glosten and Harris (1988) but it separates permanent from transitory price impact effects, and the measure that is eventually used reflects only the permanent price impact (period: 1983-2001). For each portfolio, formed based on a 5 x 5 momentum/liquidity sorting or size/book-to-market sorting, the factor loadings ([beta] coefficients) are estimated in a model that includes L and the three Fama-French factors. Notably, the [beta] coefficient of factor L is related Acharya and Pedersen (2005) [[beta].sup.L2]. Finally, the asset pricing relationship is estimated by a cross-section regression of monthly returns on the factor loadings, employing the Fama and MacBeth (1973) method. The results show that the liquidity factor is priced, with a positive risk premium, whereas the other factors are not. This supports the importance of liquidity risk in asset pricing. However, Sadka reports that the return on high-minus-low price impact is statistically insignificant, which is inconsistent with the results of Brennan and Subrahmanyam (1996). This may be due to the use of different measures of price impact or a different study period.

Fujimoto and Watanabe (2005) propose that the effects on stock returns of liquidity--both level and risk--on stock returns varies over time across identifiable states. They estimate the liquidity beta from a regression of portfolio return on a liquidity index (the negative of the residuals of an AR(2) model of modified ILLIQ) by a regime-switching model. This liquidity beta is analogous to that in Pastor and Stambaugh (2003) and to [[beta].sup.L2] in Acharya and Pedersen (2005). Fujimoto and Watanabe find that the liquidity betas are higher--for both large and small firm portfolios--in states when investors may expect liquidity needs, especially when turnover is abnormally high. (18) The high liquidity-beta states are identified to be during 43-47 months (depending on the portfolio sorting method) out of the 480 months of the study period, 1965-2004. They subsequently find that in states of high liquidity betas, there is a greater effect on stock returns of the level of liquidity and of the price of liquidity risk (measured by the coefficients of the liquidity betas).

Whereas all previous studies used a measure of liquidity as a factor, Liu (2004b) uses a factor-mimicking stock portfolio that reflects the liquidity premium, constructed in a similar way to the Fama-French SMB and HML factors. Liu measures stock illiquidity in each month as the sum of the number of no-trading days and the average reciprocal of daily turnover (scaled) over the prior 250 trading days. Illiquid stocks have both more non-trading day and higher value of the reciprocal of turnover, which proxies the stock's holding period (see Amihud and Mendelson, 1986a; Datar et al., 1998). Stocks are then sorted by this illiquidity measure into 10 portfolios. The sample includes NYSE, AMEX and Nasdaq stocks over 41 years, 1963-2003. The results are that return alphas from the Fama-French model increase almost monotonically in the rank of illiquidity, with the difference in alphas between high and low illiquidity being significant. Liu's novel construction of a factor-mimicking portfolio of high-minus-low illiquidity reinforces the earlier results: Liquidity risk is priced. Liu then proposes a model with only two factors: excess market return and the illiquidity factor. The alphas from this model are not significantly related to stock size or to book-to-market ratio, supporting the adequacy of the liquidity-based two-factor asset pricing model. This model also renders the momentum effect insignificant after adjusting for trading costs.

Another form of liquidity risk is studied by Chordia et al. (2001) who extend the Brennan et al. (1998) approach to estimate a model of cross-sectional risk-adjusted returns on stock characteristics. As liquidity they use trading activity measured either as dollar trading volume (as in Brennan et al., 1998) or turnover (as in Datar et al., 1998). A novel aspect of their analysis is the inclusion of the volatility of trading activity. The results show that both the level and volatility of trading activity have a negative and significant effect on risk-adjusted stock returns. Their finding that investors demand a compensation for liquidity volatility is contrary to the authors' initial hypothesis. The authors suggest that the effect of liquidity volatility may be due to its correlation with some omitted and unknown risk factor. Alternatively, volatility in trading activity may imply larger investor following which, by Merton (1987), should lead to lower expected return. Yet another hypothesis would be that liquidity volatility could be helpful to investors if they can choose to trade when liquidity is favorable. The finding of Chordia et al. is not directly comparable to the above studies by Pastor and Stambaugh (2003) and Acharya and Pedersen (2005) that focus on systematic liquidity risk, not total volatility.

The above papers study the effects of liquidity costs which result in part from asymmetric information (see Section 2.7 above). Easley et al. (2002) suggest that information risk affects asset returns since asymmetric information exposes uninformed investors to the risk of being unable to infer information from prices, and this risk is priced. They test this hypothesis on the cross-section of asset returns, employing their measure PIN, the probability of informed trading, estimated by maximum likelihood from a structural model, following Easley et al. (1997). PIN is an estimate of the fraction of information-based orders, based on the imbalance between buy and sell trades. They indeed find that across stocks, PIN is negatively correlated with size and positively correlated with the bid-ask spread. Using data for NYSE stocks over the years 1983-1998, the effect of PIN is examined in a cross-section regression of stock returns with controls for beta, size and book-to-market ratio, employing the methods of Fama and MacBeth (1973) and Litzenberger and Ramaswamy (1979). The results show that PIN has a positive and significant coefficient. The positive effect of PIN survives when other variables--bid-ask spread, return standard deviation, turnover and the coefficient of variation of turnover--are included in the equation. In a multiple regression, the liquidity measures have the expected signs (positive for the bid-ask spread, negative for turnover), yet the positive and significant effect of PIN means that it contains information beyond other liquidity-related variables. (The paper finds some puzzling results for the spread in certain specifications.) The results thus suggest that the risk of informed trading is priced.

3.2.4 Restricted stock

The existence of a liquidity effect may be tested directly by comparing two assets that are identical in every respect except in their liquidity. As pointed out in the introduction to this section, the price difference between such two assets can be attributed to the effect of liquidity. This is the case with restricted stocks. In the United States, restricted or "letter" stocks that are issued by publicly-traded companies are not registered with the SEC for trading in public markets, (19) but they can sometimes be traded privately, and the private transaction prices are reported to the SEC. Until 1990, the SEC required that restricted stocks would not be traded in the public markets for at least two years after issuance. Thereafter, the holder could sell the stock in the public market subject to some restrictions, and block sales of restricted stocks following the 2-year period required registration with the SEC. In 1990, the SEC dropped the registration requirement for block sales and in 1997 it lowered the minimum holding period from two years to one year, which consequently increased the liquidity of restricted stocks.

The 1971 Institutional Investor Study conducted by the SEC examines the discounts on 398 letter stock transactions over the 1966-1969 period compared to their publicly-traded counterparts. The study finds a mean discount of 26% and a median discount of 24%, with smaller companies associated on average with larger discounts. Gelman (1972) studies the prices of restricted stocks purchased by investment companies that specialized in the purchase of such stock using 89 transactions over the 1968-1970 period and finds a mean and median discount of 33%. Trout (1977, study period 1968-1972, 60 transactions) finds an average discount of 33%, and Maher (1976, study period 1969-1973, 34 transactions) finds restricted stock discount of 35% (both mean and median). Solberg (1979) analyzes the discounts approved by courts (based on a number of underlying studies) for the lower marketability of restricted stock, finding a median discount of 39%.

Silber (1991) studies 69 restricted stock issues over the 1981-88 period, finding a mean discount of 34%. Silber also finds that the discount is an increasing function of the size of the restricted block transaction relative to the total common stock, and a decreasing function of the company's size and its profitability, controlling for special relationship between the company and the restricted stock holder. That is, greater liquidity of the traded shares generates a positive externality on the value of the restricted stock (see also Amihud et al., 1997), and the discount is greater for "problem firms" (with low profitability).

Generally, restricted stock discounts over the pre-1990 period were around 1/3 of the value of the equivalent--but publicly traded-stock. Post-1997 studies find similar behavior but lower discounts ranging between 13% and 21%, consistent with the less-stringent restrictions on restricted stock during the later period (Pratt, 2003). To illustrate the meaning of a discount of 1/3 of value in terms of excess return, consider the following. Assume that the annual return on the publicly-traded stock is 10%, and that the restriction period is 2.5 years (including restrictions on the rate of unwinding the position). Then, the annual excess return due to the illiquidity of the restricted stock is 19%.

The value effect of restrictions on trading is studied by Chen and Xiong (2001) for restricted stocks in China. There, a typical listed company has, in addition to its traded stock, two classes of restricted stock: Institutional stocks that can be transferred only in irregularly scheduled auctions and state shares that are only privately transferable. The study obtains data on auction prices of institutional shares and the prices of private transactions for the state shares. Chen and Xiong find that the discounts on the two types of restricted shares compared to their publicly-traded counterparts is 78% and 86%, respectively. As in Silber (1991), the illiquidity discount decreases in the firm's size (measured by book value) and increases if it has problems, such as a low price-to-book ratio. The discount also declines in the firm's age.

3.3 Fixed-income markets

The fixed income markets provide a fruitful area for examining the effects of liquidity on asset prices, since the cash flows for fixed-income instruments are typically known with greater certainty than in the case of stocks. Studies of the effects of liquidity on bonds examine the effect of liquidity on the bond's yield to maturity, which--for riskless bonds, such as government securities--measures the expected return if the bond is held to maturity. For corporate bonds which can default, the yield to maturity after controlling for the effect of default provides a low-noise estimate of the expected return, compared to the case of stocks where realized returns are used to estimate expected returns.

3.3.1 U.S. treasury securities

A key advantage of using U.S. Treasury securities is that they are risk-free, thus it is unnecessary to separate the default premium from a liquidity premium, as is the case with corporate bonds. This provides relatively "clean" tests of the effects of liquidity on bond yields (although one must be mindful of repo and tax effects as discussed below). Amihud and Mendelson (1991a) directly test the effect of bond liquidity on yields, without the need to control for risk. They compare the yields on Treasury notes and bills with the same time to maturity. With less than six months to maturity, both are discount instruments with identical payoffs. However, the two instruments are traded in different markets with bills being far more liquid. This is because notes with a short time left to maturity are "off-the-run," having been issued long ago and locked in investors' portfolios, whereas bills are issued frequently for short maturities and are actively traded throughout their life, being effectively "on-the-run" instruments. The brokerage fee per $1 million was $12.50-$25 for bills compared with $78 1/8 for notes; bid-ask spreads for bills were of the order of $ 1/128 compared to $ 1/32 for notes, both per $100 face value; and the search for a counterparty for notes took significantly longer than for bills. This gives rise to the hypothesis that bills should have a lower yield to maturity than notes with the same time to maturity.

The hypothesis is tested on the yield differential of 489 pairs of notes and bills with less than 6 months to maturity over 37 trading days during the period April-November 1987, using actual quotes "pulled off the screen." The pairs are constructed by matching a note with bills whose maturities straddled the note's. The average bid-ask spread on the notes and bills are, respectively, 3 basis points and 0.78 basis point. The average note yield is 6.52% compared to 6.09% for the bills, a difference of 43 basis points, which is significant both economically and statistically. This suggests a yield premium due to illiquidity. (20) In addition, given the higher fixed cost of trading notes, Amihud and Mendelson hypothesize that the yield differential should be larger for shorter maturities. They indeed find that the notes-bills yield differential is increasing in the reciprocal of the time to maturity. The notes-bills yield differential is also found to be declining in the note's coupon, reflecting constraints on some institutions to distribute only accrued interest. This liquidity constraints on these institutions makes them pay a premium for the liquidity afforded by the notes' coupon.

It would seem that the notes-bills yield differential provides a profitable and riskless arbitrage opportunity: buy the high-yield note and short a similar-maturity low-yield bill, holding them to maturity. However, this exercise ignores the very essence of the illiquidity: Arbitrage trades also entail transaction costs. Amihud and Mendelson simulate this arbitrage transaction, taking into account the associated transaction costs: The bid-ask spread, brokerage fees and cost of carrying the short position. At the end, the apparent arbitrage profit disappears (it is insignificantly different from zero). This suggests that the price differential between securities of different liquidity is bounded by arbitrage.

Kamara (1994) studies the determinants of the yield differentials for matched-maturity note-bill pairs using 91 observations of bid and ask prices for Treasury bills and notes with about 14 weeks to maturity over the period January 1977-July 1984. He posits that the notes-bills yield differential reflects differences in liquidity, tax treatment and dealer inventories. Kamara proposes to measure the liquidity difference between notes and bills as the product of the volatility of the underlying rate (estimated from a GARCH model) by the ratio of the bills' turnover to the notes' turnover, where turnover is calculated using the ratio of dealer transactions to the absolute value of their net positions. This measure of "liquidity risk" of a trade reflects the variance of the security's value between the point in time when a trader wishes to trade and the point when she actually trades (Garbade and Silber, 1979; Mendelson, 1982). This variance is proportional to the time needed to find a counterparty and execute the transaction, and to the security's underlying return volatility. Since the average time to transact is not available, the turnover ratio is used as a proxy for the time ratio.

Kamara finds an average notes-bills bid yield differential of 34 basis points, a statistically and economically significant difference. The notes-bills bid yield differential is found to be increasing in the liquidity risk, supporting the role of liquidity in the pricing of bonds, as in (Amihud and Mendelson, 1991). In addition, Kamara finds a significant tax effect, reflecting the asymmetric tax treatment of notes priced above par value vs. notes priced below par value, and a transient effect of dealers' inventories: An increase in dealers' inventories of notes, which are the less-liquid asset, reduces the notes-bills yield differential. (21)

While Amihud and Mendelson (1991a) and Kamara (1994) compare "on-" and "off-the-run" short-term U.S. Treasury securities, other studies examine this issue in the context of long-maturity Treasury bonds. In general, Treasury bonds are actively traded right after they are issued, as a large part of them are initially bought not by their ultimate investors but by dealers and speculators. However, once a new Treasury of the same maturity is issued--which may be a month or two later, the now older security goes "off-the-run," as most trading interest shifts to the newly issued security and much of the old security's units are already included in portfolios of their ultimate investors who are less likely to trade them before maturity. Off-the-run securities are almost always less liquid than on-the-run securities of the same class, and this difference may be exploited to study whether and how illiquidity differences translate into a yield difference.

Warga (1992) studies holding period returns on constant duration portfolios of U.S. Treasury notes and bonds, and measures the yield premium generated by liquidity differences in bonds. He constructs portfolios of off-the-run and on-the-run bonds using durations within narrow ranges over the sample period 10/1982-12/1988, and finds a consistent, positive and significant yield differential between them of 55 basis points per annum.

Krishnamurthi (2002) studies the price difference between the on-the-run and the most recent off-the-run 30-year bond. The price difference follows a systematic pattern over the auction cycle: It is highest right after the auction date and it declines to a small spread by the following auction date. To test whether the old bond-new bond yield difference results from a demand for liquid assets, Krishnamurthy regresses it on the yield spread between commercial paper and Treasury bills (both for three months), which represent demand for liquidity since commercial paper is less liquid than bills. Studying all 30-year bond auctions in the 1990s, he finds that the yield difference increases when the yield spread between commercial paper and bills increases, and that the relation is stronger far from an auction date, when the liquidity demand is strongest.

Further, Treasury bonds are often "on special" in the repo market which means that an owner can earn a "lending fee" by lending his bond to a short seller who must pay this fee. Krishnamurthy finds that new Treasury bonds are more special than old bonds. Hence, owners of new Treasury bonds can earn larger lending fees, which provides a partial explaination for why new bonds are more expensive (i.e. have lower yields). The differences in pricing, liquidity, and repo specialness between new and old bonds are consistent with the theories of Duffie et al. (2002) and Vayanos and Weill (2005) as described in Section 2.8.3.

Goldreich et al. (2003) study the varying value of liquidity over time, analyzing the liquidity and yields of two-year U.S. Treasury notes, comparing the very liquid on-the-run note with the most recent off-the-run note over the entire on/off-the-run cycle between the issue of the bond and the issue of the next bond. While the note is very liquid after issue and its buyer can expect to sell it to another buyer who will pay a premium for its liquidity, a buyer towards the end of the cycle may expect to sell the note when it goes off-the-run and becomes less liquid. Correspondingly, the yield difference between the off-the-run and the on-the-run notes decreases during the on-the-run cycle and approaches zero by the end of the cycle. Thus, the yield difference is driven by differences in expected future liquidity, rather than contemporaneous liquidity, where future liquidity is estimated by the average liquidity over the remainder of the cycle.

Goldreich et al. use GovPX data for 1/1994-12/2000, resulting in 56 two-year notes that were issued and matured through the period. The average yield difference between the on-the-run and off-the-run notes (adjusting for differences in the coupon rate and the yield curve) is about 1.5 basis point at the beginning of the cycle and it declines to zero by the end of the month. The liquidity variables that they consider are the quoted and effective bid-ask spread, the quote and trade size, the number of quotes and trades per day and the daily trading volume. The contemporaneous value of each such variable, denoted C, is [C.sub.t], and the expected future value is [[bar.C].sub.t] = ([C.sub.t+1] + [C.sub.t+2] + ... + [C.sub.T])/(T - (t + 1)), obtained by averaging the future values of the variable over the remaining life of the security (t = t + 1, t + 2, ..., T). Goldreich et al. find that the difference in future liquidity, [[bar.C],t] - [[bar.C].sub.on,t], has strong explanatory power for the yield differential. When they consider both the contemporaneous and future liquidity variables jointly, future liquidity dominates. Finally, they find that the best explanatory liquidity variables are the quoted bid-ask spread and the quoted depth.

In Japan, an old government bond issue is effectively made to be on-the-run by designating it as the benchmark bond. It usually has a coupon similar to the coupon rate on newly-issued bonds and has large size, and following the designation, the benchmark bond becomes very liquid. Boudoukh and Whitelaw (1991) find that the yield on benchmark bonds is lower by about 30 to 100 basis points than the yield on bond issues with similar maturities and coupons, suggesting a sizable liquidity premium, especially in light of the fact that the average maturity of the benchmark bonds was 9.7 years over their study period.

Elton and Green (1998) examine the effect of liquidity on Treasury securities, where liquidity is measured by the trading volume in the interdealer market, obtained from the GovPX database for the period 1/1991-9/1995. Controlling for the tax type of the securities, they find significant differences between similar-maturity bonds that differ in their trading volumes. The difference between the price of a low-volume bond and the weighted average of a pair of high-volume bond with the same maturity but different coupons is negative and highly significant, meaning that the low-volume bond is cheaper and has a higher yield to maturity. However, their estimated price differential due to the liquidity difference for a sample of new bonds is small, 5 cents per $100 face value, and it is smaller for a sample of old bonds. In another test of the liquidity effect, Elton and Green fit a cubic spline price model to the after tax term structure, using the variable log(volume) to represent the bond's liquidity. The coefficient of this term is mostly positive, implying a higher price for more liquid bonds. The liquidity effect is small, though, amounting to 2.25 basis points, and it has been declining over the sample period. Notably, even after controlling for the liquidity effect (using the volume variable), there is a positive and significant price deviation for on-the-run bonds, perhaps reflecting an aspect of liquidity of these bonds not captured by volume such as repo specialness.

Longsta. (2004) provides another test of the effect of liquidity on bond yields by comparing yields on U.S. Treasury bonds with those on bonds issued by the Resolution Funding Corporation (Refcorp), a government agency. These bonds are effectively guaranteed by the U.S. Treasury and have the same default-free status as Treasury bonds. The difference between these bonds and Treasuries is in their liquidity: Refcorp bonds are less liquid than U.S. Treasury bonds. Longsta. compares the yield differential between zero-coupon Treasury and Refcorp bonds and finds that the average yield premium on Refcorp bonds ranges from 10 to 16 basis points, the differences being statistically significant (period: 4/1991-3/2001). This is a large liquidity premium which, for longer-term bonds, can represent 10%-15% of the value of the Treasury bond. There are considerable variations over time in this liquidity premium. Longstaff finds that it is negatively related to consumer confidence and to the change in the BBB-AAA credit spread, and positively related to Treasury buybacks. This means that the liquidity premium reacts to varying market conditions.

3.3.2 Corporate bonds

It has been suggested that the yield spread on corporate bonds--the yield in excess of the yield on Treasury bonds of the same maturity--is "too high" to be explained by default risk alone (Elton et al., 2001; Huang and Huang, 2003). Given that corporate bonds are generally less liquid than Treasury bonds, it stands to reason that the yield spread reflects in part a compensation for illiquidity. In analyzing corporate bonds, there is a problem of separating the risk premium from the illiquidity premium. Low-rated corporate bonds typically have both greater risk and lower liquidity, as is the case for stocks of risky and small companies. The results on the effects of liquidity depend, then, on the quality of the model that controls for the bond's risk.

Fisher (1959) studies the determinants of corporate bond "risk premium"--the yield spread--in cross-sectional regressions for the years 1927, 1932, 1937, 1949 and 1953. The determinants of the yield spread are default risk--proxied by the coefficient of variation of the firm's earnings, the period of solvency (the time it has been operating without a default) and its debt/equity ratio--and marketability, proxied by the market value of the firm's outstanding publicly-traded bonds (for lack of data on volume and bid-ask spreads). He finds a negative relationship between the logarithm of the risk premium and the marketability variable, as well as the expected signs for the variables proxying for default risk. These results mean that corporate bond yields reflect both risk and liquidity premiums.

The effect of liquidity on bond yields, using explicit measures for the cost of illiquidity, is studied by Chen et al. (2005). They measure illiquidity in three ways. One is the bound around the bond price within which new information would not trigger a transaction, estimated from daily data by the limited dependent variable model of Lesmond et al. (1999) (see Section 3.2.2 above), where the information variables are the daily change in the ten-year risk-free interest rate and the daily change in the S&P 500 index, both scaled by the bond's duration. The two other measures of illiquidity are the quoted bid-ask spread and the percent of zero spread and the percent of zero returns for a given year. The study examines a few thousand U.S. corporate bonds between 1995 and 2003 (the estimations use varying numbers of observations, depending on data availability). As may be expected, lower-rated bonds are more illiquid. Chen et al. then estimate a cross-sectional model of the corporate yield spread as a function of the three illiquidity variables as well as a number of variables that control for the bond's risk and its characteristics as well as the issuing firm's characteristics. The results show a significant positive effect of illiquidity on the yield spread, after controlling for the other variables (bond characteristics). The liquidity effect holds for both investment grade and speculative grade bonds, with the coefficient being larger for speculative-grade bonds. For example, in one estimate the authors divide the bonds in each category into three groups by their liquidity cost. They find that moving from one liquidity cost to a lower liquidity cost increases the yield spread by 37 basis points for investment-grade bonds and 128 basis points for speculative-grade bonds. The study further finds in a cross-section regression that annual changes in the bonds' yield spread are an increasing function of changes in the bond's illiquidity variables for both investment grade and speculative grade bonds (again, the regression controls for the changes in all other variables that reflect the bond and firm characteristics as well as macroeconomic factors). In conclusion, this study shows in a comprehensive way that the yield spread on corporate bonds reflects compensation for illiquidity as well as for risk.

The effect of liquidity risk on corporate bond yields is studied by De Jong and Driessen (2005), following Pastor and Stambaugh (2003) and Acharya and Pedersen (2005) (see section 3.2.4 above), using data from the U.S. and Europe (1/1993-2/2003). They employ a two-step multifactor procedure using two market risk factors, the equity market index return and the change in the implied volatility of equity index options, and two liquidity risk factors: Amihud (2002) illiquidity measure for equity, ILLIQ, and quoted bid-ask spreads on long-maturity U.S. Treasury bonds. In the first step they estimate the factor loadings and the liquidity betas of bond portfolios, aggregated by credit rating and maturity, by regressing the excess bond returns (over appropriate government bonds) on the market factors and the liquidity factor. The liquidity beta here is similar to the liquidity exposure coefficient in Pastor and Stambaugh (2003) and to fL2 in Acharya and Pedersen (2005). They find that lower-rated and longer-maturity bonds have greater exposure to the two indices of liquidity as well as greater exposure to the equity and risk factors. In the second step, they estimate whether the liquidity betas are priced by estimating a cross-section regression of the expected bond returns on the liquidity betas obtained from the first step, pegging the equity risk premium at some reasonable level. The two resulting liquidity exposures for their U.S. bond portfolios are highly correlated, but both are priced in the returns on corporate bonds. That is, corporate bonds with a higher exposure to stock and bond market illiquidity have higher expected returns. For the U.S. market, the total estimated liquidity premium is around 45 basis points for long-maturity investment grade bonds. For speculative grade bonds, which have higher exposures to the liquidity factors, the liquidity premium is around 100 basis points. The results for a sample of European corporate bonds are similar in spirit but insignificant in the cross-section analysis, perhaps due to small sample limitations (there are only 7 bond portfolios).

3.3.3 Rule 144A bonds

Some corporate bonds are traded in restricted markets. Rule 144A, approved by the Securities and Exchange Commission (SEC) on April 1990, allows firms to raise capital from "Qualified Institutional Buyers" (QIBs) without requiring registration of the securities and compliance with U.S. disclosure rules. The rule thus restricts trading in these securities to a purely-institutional market. Most of the securities issued under Rule 144A are corporate bonds. If liquidity affect asset prices, the yield spread (relative to Treasuries) on bonds that trade on Rule 144A markets should be higher than on bonds that trade on public markets. This is because public markets are more transparent and subject to disclosure rules that reduce informational asymmetries and increase liquidity.

Chaplinsky and Ramchand (2004) study the impact of Rule 144A on the cost of debt for international firms (1991-1997). They find, in a pooled cross-section regression of the yield spread on the Rule 144A dummy variable, as well as bond characteristics as controls, that Rule 144A bonds require a yield premium of 49 basis points on average. This pattern holds particularly for investment grade bonds.

Fenn (2000) too examines the difference between the yield spreads on bonds traded in the private and public markets. He posits that the yield differential declines over time, thus adding in his model an interaction variable, the product of a Rule 144A dummy variable and a time trend. He finds that the coefficient on the Rule 144A dummy variable is positive and significant (33 to 41 basis points, depending on specification), but the interaction variable is negative and significant (-8 basis points a year). However, Livingston and Zhou (2002), who study a later time period, find that the yield premium is strong and persistent, and Fenn's results are not robust to model specification. Livingston and Zhou estimate the yield differential between Rule 144A bonds and publicly-traded bonds, controlling for a number of variables: the first time the firm issued debt, the (log of) its issuing frequency, bond ratings, maturity, call protection, the default risk premium and indicators for senior debt and utility firms. They obtain that Rule 144A bonds have a higher yield, and dividing the sample by credit rating they obtain a yield differential of 35 basis points for the high-yield sample and 14 basis points for the investment grade sample. This is consistent with the notion that moving from the private to the public markets is a bigger step for high-yield than for investment-grade bonds, which is consequently worth more.

One may wonder why firms choose to issue less liquid debt under Rule 144A and incur the associated illiquidity cost. Fenn (2000) concludes that Rule 144A serves as a quick and convenient vehicle en route to issuing public securities: Rather than incur the delay of registering the securities with the SEC, firms sell them first to sophisticated investors who do not require registration, and after collecting the proceeds, they get to work at their leisure on registering the securities so they can be publicly traded.

3.4 Other financial instruments

In addition to stocks and bonds, liquidity affects the expected returns on other financial assets. In what follows, we discuss the effect of liquidity illiquid options, index-linked bonds, American Depository Receipts, hedge funds and closed-end funds. In each case, the price or expected return of the asset under study is compared to a benchmark asset with different liquidity, and the differences show the magnitude of the illiquidity discount and its determinants.

3.4.1 Illiquid options

The effect of liquidity on option prices is unclear. The buyer and the seller may each demand a liquidity premium, but since the option value sums to zero between the two parties, it is unclear that the equilibrium price would reflect any liquidity premium. However, if the seller (writer) of the option does not demand a liquidity premium, the equilibrium price may reflect the liquidity premium demanded by the buyer. In Israel, the Bank of Israel issues European call options on the U.S. dollar paid in NIS (the Israeli currency), which are non-negotiable. Brenner et al. (2001) compare these options to ordinary options traded on the Tel Aviv Stock Exchange that are similar in their payoff but differ in their liquidity, the latter being far more liquid than the former. Brenner et al. compare the prices of three- and six-month at-the-money-forward options auctioned by the Bank of Israel, which are illiquid, to the same-day prices of synthetic publicly-traded options with a similar strike price and expiration date that they generate using the liquid options (period: 4/1994-6/1997, 272 and 127 options of 3 and 6 months, respectively). Because of the limited number of strike prices and expiration dates, it is impossible to exactly replicate the illiquid Bank of Israel option, and emulating its performance using publicly-traded option contracts entails transaction costs that total about 12%. They propose that the price (option premium) of the (synthetic) liquid option should be higher than the price of the illiquid option issued by the Bank of Israel. They find that the illiquid Bank of Israel option trades at a mean discount of 18% to 21% to the liquid (synthetic) option, highly significant. (22) The results are virtually unchanged when the estimation is performed separately for three- and six-month options. As the transaction costs to replicate the position have declined so did, later in time, the liquidity premium.

Empirical asset-pricing puzzles related to options are that index options are "expensive" (i.e. have high implied volatility relative to actual volatility), especially out-of-the-money put options, and that individual stock options are priced differently (i.e., are inexpensive and have less steep smile curves). Garleanu et al. (2004) address these puzzles using a model of demand pressure in which market makers can only hedge imperfectly. They show empirically that "end users" of options are net long index options, especially out-of-the-money puts, and net short individual stock options, and--employing the model--these demand pressures can help explain the option pricing puzzles. Equivalently, market makers are net short index volatility and net long individual stock options, and they want to be compensated for the risks associated with these positions, which helps explain the puzzles. Also, Bollen and Whaley (2004) show that signed order flow in options markets is related to changes in implied volatility, again reflecting market makers' inability to perfectly absorb demand pressures, and discuss the option-pricing implications.

3.4.2 Index-linked bonds

Dimson and Hanke (2002) test the existence of a liquidity effect by comparing instruments with similar cash flows that differ only in their liquidity. They analyze equity index-linked bonds which provide the same payoff as an investment in an equity index (23) but have finite (typically 10-15 year) maturities and their trading volume and transaction frequencies are low, i.e., they have low liquidity. Because they are issued in small quantities and are immediately repayable if the asset cover drops below a pre-specified level, their default risk is very low. Dimson and Hanke use transaction data for all equity index-linked bonds traded on the London Stock Exchange for their entire history (through 2001). They find that the prices of these bonds is discounted by an average of 2.71% relative to their underlying value, with the discount being an increasing function of bonds' bid-ask spread. Using the time series of the discounts, discounts, they show that liquidity risk has a systematic component, and relate this market-wide factor to a number of macroeconomic variables that have previously been shown to be related (at least partially) to illiquidity: The small-firm premium and the changes in closed-end fund discounts, the bond maturity premium, U.S. stock market turnover, credit spread over Treasuries and futures basis for the FTSE 100 contract.

3.4.3 American depository receipts (ADRs)

ADRs (American Depository Receipts) enable to compare two identical securities with the same payoffs but with different liquidity. ADRs are negotiable certificates of ownership of shares for foreign securities which may be listed on a U.S. stock market. They entitle the holders to the same cash flows as does the underlying stock in the foreign country but due to the difference in their trading venue, there may be a difference between the liquidity of the ADR and of its underlying stock.

Chan et al. (2005a) study 401 pairs of ADRs and underlying stocks, relating the price difference between them to differences in their liquidity. (24) The study uses ADRs that were listed on the New York Stock Exchange, the American Stock Exchange or the NASDAQ stock market from 23 countries for the period 1981-2003. (25) They propose that the ADR premium--the price differential relative to the underlying stock's price (all converted to U.S. dollars)--is an increasing function of the ADR liquidity in the U.S. market and a declining function of the liquidity of the underlying stock and of the liquidity of the market in the foreign country. The study employs three liquidity measures: (i) Amihud (2002) ILLIQ (see Section 3.2.1 above), (ii) the security's turnover (the ratio of volume to shares outstanding), and (iii) the trading infrequency (the percentage of days on which the security did not trade over the month). The measures are calculated for each ADR for each month, and the first two measures are also calculated for the underlying stock and for the home country by averaging each over the stocks from each country (trading frequency did not vary for the underlying stocks in their home country because these stocks were frequently traded).

Chan et al. (2005a) estimate cross-sectional monthly regressions of the ADR premium over the different liquidity measures, and calculate the coefficients by the Fama and MacBeth (1973) method. The results support the hypothesis of a positive price-liquidity relationship. The coefficients of the ADR premium on ADR liquidity (illiquidity) are positive (negative) and significant for all three measures. The coefficient of the underlying stock's ILLIQ is positive and significant, and that of the underlying stock's turnover is negative and significant--again, consistent with the hypothesis that liquidity is priced. These results are robust and continue to hold with controls for the ADR size, 1- and 6-month home stock market return, and 1- and 6-month exchange rate returns. The home country's ILLIQ has the expected sign but with lower explanatory power, and it is statistically insignificant in some models. In summary, the liquidity of the ADR vis-a-vis the underlying stock appears to be an important driver of the ADR premium. The effect of the ADR's illiquidity on its premium continue to hold in a cross-sectional regression of the monthly changes in these variables, particularly for the turnover and trading frequency measures; changes in the underlying stock's liquidity, as well as in the home country's liquidity, are insignificant.

3.4.4 Hedge funds

Hedge funds are private investment partnerships which can follow flexible investment strategies, take both long and short positions, use leverage and derivatives and invest in a variety of assets and markets. Liang (1999) studies how hedge fund characteristics affect their returns using a sample of 385 hedge funds that reported monthly returns over the 1/1994-12/1996 period. One of his explanatory variables is the fund lockup period, the number of days since the initial investment the investor's shares are "locked up" and cannot be redeemed, which constrains the investors' liquidity (other fund characteristics included in his regressions are the fund's incentive fee, management fee, log(assets) and age since the fund's inception). While most funds in the sample did not have a lockup period, the mean lockup period across all funds (including the zeros) was 84 days, with a standard deviation of 164 days. (26) The results show that the coefficient of monthly return on the lockup period is positive and significant, consistent with a positive liquidity premium. Liang concludes that "the lockup period is critical in determining fund returns" (p. 78).

In a comprehensive analysis of the effects of liquidity on hedge fund returns, Aragon (2004) studies the relationship between the liquidation restrictions on hedge funds and their returns. The study considers two liquidity variables: (i) the lockup provision, indicated by a lockup dummy (the lockup period is usually the same, around one year), which applies to 18% of the funds, and (ii) the fund's redemption notice period, which is the number of days investors are required to give advance notice before redeeming their shares. The redemption period averages 26 days across the entire sample (28% of sample funds do not have an advance notice requirement). The study uses monthly data from the TASS Tremont database for 2,871 hedge funds over the period 1/1994-12/2001.

Aragon finds that the annual return on a portfolio of funds with lockup provisions is higher than the return on a portfolio of funds without such provision (within a multifactor model). The difference is 7%-8% for equally-weighted portfolios and 4%-5% for value-weighted portfolios. (27) In a pooled time-series and cross-section factor model of the monthly returns as a function of the lockup dummy and the notice period as well as the minimum investment size, the coefficients of both liquidity variables are positive and significant. The coefficient of the lockup dummy is 6.2%-7.6%, and the excess annual return associated with the notice period is about 2% per month of advance notice. After controlling for these variables, the constant coefficients are not statistically different from zero. That is, the excess returns on hedge funds may be fully attributable to the special liquidation restrictions that they impose. As a further test of the theory, Aragon (2004) estimates the pooled regression with quadratic forms for the notice period and minimum investment variables. Because of the clientele effect discussed in Section 2.3, expected return should be a concave function of illiquidity, suggesting a negative coefficient of the squared illiquidity variables. The results show that the coefficients on the squared illiquidity variables are indeed negative and significant, again confirming the theoretical predictions. (28)

3.4.5 Closed-end funds

Closed-end funds, unlike their open-end counterparts, have a fixed number of shares, they trade like ordinary stocks and are priced in the market. Funds that hold domestic securities typically trade at a discount to their net asset value, or a negative premium, where the premium is the excess value of the fund's price over its NAV (net asset value). The negative premium is typically explained by investor sentiment and other behavioral factors, or by a capitalization of the management fee. Another explanation is the difference between the liquidity of closed-end funds and that of their underlying securities. Then, liquidity differences across funds between the liquidity of the fund's stock and the liquidity of the stocks in its portfolio may explain differences in fund premiums.

Datar (2001) studies the impact of market liquidity on the premium (= fund's price/NAV--1) on closed-end funds, based on the relationship between the liquidity of the fund's shares and the liquidity of the assets held in the fund's portfolio. He tests the hypothesis that within a group of funds that hold similar assets (stocks or bonds), the closed-end fund premium increases as the liquidity of the funds' shares increases. Using weekly data for closed-end funds listed on the NYSE, Datar tests this hypothesis and indeed finds the expected positive relationship between the fund premium and the liquidity of the funds' shares. As liquidity measures, Datar uses (the logarithms of) the funds' share and dollar trading volumes, shares outstanding and fund size, turnover and volatility. Using a number of alternative specifications, he shows the results are robust. The results thus support the liquidity explanation for the closed-end fund discount.

Manzler (2004) shows that the discounts on closed-end funds are driven by both liquidity and liquidity risk differentials between the fund stocks and the stocks in the underlying portfolio. First, he calculates the portfolio liquidity--the value-weighted average of the liquidity of its component stocks--and the liquidity of the fund's shares using two measures, a modified ILLIQ measure and the quoted bid-ask spread. The study spans the 1995-2003 period, where data on the portfolios of 37 funds were compiled from quarterly reports. Manzler finds that the closed-end fund premium increases (or its discount decreases) in the difference between the illiquidity on the fund's portfolio and the illiquidity of the fund's shares (the results are significant only when using ILLIQ).

Next, Manzler proposes that as the liquidity risk of closed-end funds increases relative to the liquidity risk of their portfolios, the fund premium should be lower (or the discount greater). To that end, he constructs an illiquidity factor, the return series on illiquid-minus-liquid (IML) stocks, obtained by ranking stocks into deciles by the magnitude of the residuals from an AR(2) model of their ILLIQ measure and then taking the difference between the returns on the extreme portfolios. He then regresses the returns on the funds and their NAV on a three-factor Fama-French model that has an additional illiquidity factor, IML. Finally, the average three-year premia are regressed across funds on the differences between the fund betas and the underlying portfolio betas. Focusing on the IML betas, the results are that the fund premium declines in the difference between the fund's illiquidity beta and the illiquidity beta of its portfolio. That is, the higher the liquidity risk of a closed-end fund relative to its underlying portfolio, the larger the closed-end fund discount.

Cherkes et al. (2005) develop a liquidity-based model of closed-end funds that shows they provide investors a way to buy illiquid securities at lower illiquidity costs. Their model predicts that closed-end fund IPOs take place in waves, a sector at a time, with the fund share initially issued at a premium to net asset value that often turns later into a discount. They show, using Morningstar data over the 1986-2004 period, that the behavior of closed-end fund premiums generally conforms with the predictions of their model. Empirically, they find that in a time series regression of the closed-end fund premium on the Pastor and Stambaugh (2003) liquidity measure, the coefficient is negative, suggesting that closed-end funds are more valuable when market liquidity worsens.

Liquidity differences are accentuated for closed-end country funds which issue shares in the U.S. and invest the proceeds in the shares of companies in a foreign country or region. Unlike domestic funds, country funds tend to have positive fund premiums which vary substantially over time and across countries. Similar to the case of ADRs, closed-end country funds enable to test the liquidity effect, in this case--the relationship between liquidity differences and fund premiums. This task is undertaken by Chan et al. (2005b), who study a sample of 41 single-country closed end funds from 29 different countries that traded in the U.S. over the 8/1987-12/2001 period. The hypothesis is that if the home and U.S. market are segmented, lower home market liquidity should decrease only the NAV, which will increase the fund premium, whereas lower liquidity in the U.S. market should reduce only the fund's price, thereby decreasing the fund premium. In an integrated market, however, where liquidity shocks in one market spill over to the other market, the prices of the fund and its underlying assets should converge. The study distinguishes between segmented and integrated markets using the Edison and Warnock (2003) measure of capital control. In all, 16 funds are in integrated markets and 26 funds in segmented markets. The illiquidity of a country's market is calculated using Amihud (2002) ILLIQ measure: A country ILLIQ is an equally-weighted average of the illiquidity of all qualifying individual stocks in the representative market index for that market (which is usually quite broad-based). The illiquidity measure is calculated every month (values are in logs).

Chan et al. (2005b) first estimate a pooled model with fixed fund effects where the fund premium is a function of the illiquidity of the U.S. market and the illiquidity of the foreign market as key explanatory variables, in addition to control variables (capital controls, the fund's expense ratio, size, dividend yield, fund age, degree of institutional ownership, market returns in the U.S. and in the home market and the foreign exchange appreciation rate). A monthly time-series control variable is the average premium of all funds, thus capturing any investor sentiment effect. The results are consistent with the hypothesis for the segmented markets: The fund premium declines in the U.S. market's illiquidity and increases in the foreign market's illiquidity, with the coefficients being statistically significant. For the integrated market, the effect is reversed although the significance of the coefficients is not robust to model specification.

Next, a cross-sectional test regresses the monthly fund premiums on the explanatory variables, employing the Fama and MacBeth (1973) method. Since the illiquidity of the U.S. market is constant across all funds in every month, the study uses instead the exposure of the fund's premium to the U.S. market's illiquidity, consistent with Pastor and Stambaugh (2003) [gamma] and with Acharya and Pedersen (2005) [[beta].sup.L2]. This is obtained as the beta coefficient from a regression of the fund's premium on the U.S. illiquidity. (Also, the U.S. market return is replaced by the beta coefficient of the fund's return on the U.S. market return.) The U.S. liquidity beta, which is negative, has a negative and significant coefficient, implying that the liquidity risk is priced in the fund's premium. The coefficient is larger and significant for the integrated markets funds and is insignificant for the segmented markets funds. Country illiquidity has a positive and statistically significant coefficient for the segmented markets funds, and it is insignificantly different from zero for the integrated markets funds. In sum, Chan et al. (2005b) conclude that the premiums on closed-end country funds are largely explained by illiquidity considerations: Their empirical results show that market illiquidity accounts for 35% of the time-series and 12% of the cross-sectional variation in fund premiums.

(1) Until 1997, customer limit orders were not displayed in Nasdaq and were not incorporated in market-makers' quotes even when the limit price was better than the best displayed quote.

(2) The separation between January and non-January is due to the "January Effect": Small-firm stocks tend to outperform the market only in January. See Keim (1983).

(3) For these regressions, the authors use two models, one by Glosten and Harris (1988) and the other by Hasbrouck (1991) which mainly differ in the specification of the order quantity: The latter uses residual transaction size obtained from a regression model. The results from the two models are qualitatively similar.

(4) In Kyle (1985), [lambda] is an increasing function of the variance of information and a decreasing function of the variance of uninformed trading.

(5) Indeed, ? find a positive relationship across stocks between the bid-ask spread and the average holding period, defined as the reciprocal of turnover, after controlling for size.

(6) In Datar et al. (1998), using U.S. data, turnover alone was negatively related to return.

(7) Hasbrouck (2005) estimates the cross-stock correlation between the Kyle's [lambda], estimated from intraday data aggregated into 5-minutes intervals, and ILLIQ. The Pearson (Spearman) correlation across stocks is 0.54 (0.76). The correlations are higher for ILLIQ1/2 and for stock portfolios.

(8) The effective relative spread is the difference between a transaction price and the preceding mid-point of the bid-ask spread, divided by price.

(9) The annual sample consists of only ten time periods--a small number and a short sample compared to other studies.

(10) Inventory models of the bid-ask spread suggest a positive relationship between the bid-ask spread and risk, see Stoll (1978a,b). The positive relationship between the bid-ask spread and idiosyncratic risk is estimated by Benston and Hagerman (1974). See also (Amihud and Mendelson, 1987, Section VIII) on the positive relationship between idiosyncratic risk and the bid-ask spread.

(11) If the estimated price increase when stocks were transferred to a continuous market was due to some reason other than the increase in liquidity, this would likely result in the opposite price pattern.

(12) Delisting, however, while involuntary, may not be totally beyond the firm's control. Reasons for delisting include the stock price being below some minimum, too little ownership dispersion and delinquency in meeting SEC filing requirements. These problems can be rectified by the firm if it chooses. If it fails to do so, the delisting that ensues due to these reasons may reflect information and ought to be treated separately.

(13) The positive effect of increased ownership breath on stock price can also be explained by Merton (1987) model.

(14) On a day of zero stock return, the volume obtains the sign of the market return.

(15) Pastor and Stambaugh find that [[gamma].sub.j] increases in firm size, as expected if [[gamma].sub.j] measures liquidity. However, Hasbrouck (2005) finds a small and unstable correlation between [[gamma].sub.j] and a measure of Kyle's [[lambda].sub.j] that is estimated from microstructure data.

(16) The characteristics with the most stable effect over time (and the sign of their coefficients) are historical beta (+), return volatility (-) and price (+).

(17) In this model, the estimated effect of the level of liquidity on expected return is positive, which is contrary to theory.

(18) The study identifies other variables that indicate liquidity needs. The liquidity beta is also high in states of high volatility, high probability of recession, low growth of the index of leading indicators and low consumer expectations.

(19) Such stocks may be issued when a public firm raises private capital or as part of an acquisition. Restricted stocks may also be held by company founders or insiders who are prohibited from selling their shares in the open market for a period of time.

(20) A similar observation on the yield differential between notes and bills is made by Garbade (1984). The notes-bills difference has considerably shrunk recently (Strebulaev, 2002), which may be attributed at least in part to structural changes in the fixed-income market.

(21) The inventory effect is consistent with the optimal dealer pricing policies derived by Amihud and Mendelson (1980).

(22) There is a range of discounts because they use three different methods to create the synthetic option.

(23) Equity-linked index bonds have a principal that is linked to an equity market index and a coupon that equals the dividend yield of the underlying equity index. At maturity, investors receive a payment equal to the level of the index.

(24) See also Rabinovitch et al. (2003) on the relationship between ADR liquidity and returns on ADRs versus the return on the underlying stocks.

(25) Foerster and Karolyi (1999) show that foreign firms that cross-list their shares as ADRs earn on average cumulative abnormal returns of 19% during the year before listing, and an additional 1.2% during the listing week, of which they lose 14% in the year following listing. They focus, however, on Merton (1987) investor recognition hypothesis.

(26) The lockup periods for funds that have them are generally around a year. Liang (1999) statistics are consistent with about a quarter of the funds having a lockup period around one year, and about three quarters of the funds having no lockup period.

(27) Aragon (2004) explains the return difference between equally-weighted and value-weighted portfolios by the dependence on fund age.

(28) Aragon obtains similar results when he uses a two-pass approach which first estimates the multifactor model for each fund separately, and then uses a cross sectional regression with the fund's a as the dependent variable and the above variables as independent variables.

Yakov Amihud (1), Haim Mendelson (2) and Lasse Heje Pedersen (3)

(1) Stern School of Business, New York University,

(2) Graduate School of Business, Stanford University

(3) Stern School of Business, New York University
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Title Annotation:Liquidity and Asset Prices
Author:Amihud, Yakov; Mendelson, Haim; Pedersen, Lasse Heje
Publication:Foundations and Trends in Finance
Geographic Code:1USA
Date:Jul 1, 2005
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