I collect daily return, price and trading volume of common shares listed in AMEX and NYSE from CRSP daily stock file for July 1, 1962 to December 31, 2004. Monthly return and price are collected from CRSP monthly stock file for the corresponding periods. Stocks are required to have at least 100 positive trading volume days (Chor- dia, Roll, and Subrahmanyam (2000)). To prevent any disruptive influence from extremely large or small stocks, if any end-month price of stocks in a given year is less than or equal to $2 or great than or equal to $1000, that stock is dropped from the sample for that year.5 If a stock shifts from one trading venue to another in any given year, that stock is dropped from the sample for that year. As previous studies pointed out, stock splits affect liquidity (Conroy, Harris, and Benet (1990), Schultz (2000), Dennis and Strickland (2003), Gray, Smith, and Whaley (2003), Goyenko, Holden, and Ukhov (2005)), thus I exclude stocks for the year when splits occur.
Since the LCAPM is built based on trading cost, illiquidity, rather than on liquid- ity, the following illiquidity measures are used in this study. First, I use the reversal- measure of illiquidity based on Pastor and Stambaugh (2003). It is estimated in the following way.
ri,d+1,t−rM,d+1,t =αi,t+βi,tri,d,t+γi,tsign(ri,d,t−rM,d,t)ãdvoli,d,t+ǫi,d,t
5This criterion is also used in Chordia, Roll, and Subrahmanyam (2000) and other papers from the same authors. More recently, Huang (2005) applied the same criterion.
whereri,d,tis a return of stockion dayd in montht,rM,d,t is a market return (CRSP value-weighted return) on a day d in a month t, and dvoli,d,t is a dollar trading volume (in million dollar unit). The coefficient of signed dollar trading volume (γi,t), the liquidity measure, is expected to be negative reflecting price reversals due to large trading volume. To give precision, I require stocks to have at least 15 days with valid observations within a month.6 To convert the liquidity measure to an illiquidity measure, I multiply it by -1. Our illiquidity measure, P S, is:
P Si,t≡γi,t×(−1). (2.4)
Our next illiquidity measure is a price impact measure by Amihud (2002).
RVi,d,t≡ |ri,d,t| Pi,d,tãV Oi,d,t
×106
where,Pi,d,tandV Oi,d,tare a price and a daily share trading volume (in one share unit) of stock i on day d in month t, respectively. Note that this measure is defined only for positive volume days. Monthly illiquidity measure is constructed as an equally- weighted average of dailyRVs.
RVi,t = 1 Ti,t
Ti,t
X
i=1
RVi,d,t (2.5)
where Ti,t is a number of daily observations of stock i in month t. I also restrict the stock to have at least 15 days with valid observations within a month as inP S.
Turnover has been a popular liquidity measure in the previous literature (e.g.
Rouwenhorst (1999), Chordia and Swaminathan (2000), Dennis and Strickland (2003)).
We may attribute the reason for using turnover as a liquidity measure to Demsetz
6Due to 9/11 terrorist attack, the number of total available trading days in September 2001 is 15. Thus, I require stocks to have at least 14 days only in September 2001.
(1968), Glosten and Milgrom (1985) and Constantinides (1986) among others. Dem- setz (1968) shows that the price of immediacy would be smaller for stocks with high trading frequency since frequent trading reduces the cost of inventory controlling.
Glosten and Milgrom (1985) shows that stocks with high trading volume would have lower level of information asymmetry to the extent that information is revealed by prices.7 Constantinides (1986) shows that investors would increase their holding pe- riods (thus, reduce turnover) when a stock is highly illiquid. To be consistent with other measures, I convert turnover into an illiquidity measure by multiplying it by -1:
T Vi,d,t = V Oi,d,t
NSHi,d,t
×(−1)
where NSHi,d,t is a number of shares outstanding (in one share unit) of stock i on day dof month t. Monthly turnover is constructed as an equally-weighted average of dailyT Vs.
T Vi,t= 1 Ti,t
Ti,t
X
i=1
T Vi,d,t (2.6)
I also restrict stocks to have at least 15 days with valid observations in a given month.
A relatively recent and popular measure of illiquidity is the zero-return proportion measure proposed by Lesmond, Ogden, and Trzcinka (1999).
ZRi,t ≡ Ni,t
Tt
(2.7) whereTt is a number of trading days in montht andNi,t is the number of zero-return days of stock i in month t. The economic intuition is as follows: when the trading cost is too high to cover the benefit from informed trading, informed investors would
7Consistent with this argument, Hasbrouck (1991) found that the information asymmetries are more significant for small stocks.
choose not to trade and this non-trading would lead to an observed zero return for that day. The zero return measure has been used to evaluate the impact of trading costs in a momentum strategy (Lesmond, Schill, and Zhou (2004)), the relation between market liquidity and political risks in emerging markets (Lesmond (2005)), liquidity contagion across international financial markets (Stahel (2004a)), and the implication of liquidity on asset pricing in emerging markets (Bekaert, Harvey, and Lundblad (2003)). Importantly, ZRis defined over zero-volume days as well as positive volume days since this measure assumes that a zero-return day with positive volume is a day when noise trading induces trading volume.
Our last illiquidity measure is from Roll (1984). Roll proposed a proxy for effec- tive spread based on bid-ask bounce: 2p
−Cov(ri,d−1,t, ri,d,t). However, the measure cannot be defined if the covariance term is positive. In that case, I force covariance terms to have negative values by taking absolute values with a negative sign added (Harris (1989), Lesmond (2005)). Thus, Roll’s measure is defined as:
ROi,t= 2 q
|Cov(ri,d−1,t, ri,d,t)|. (2.8)
Figure B.1 shows market return and market illiquidity, which is formed as an equally-weighted average of individual stocks’ illiquidity. Following Pastor and Stam- baugh (2003), Porter (2003) and Acharya and Pedersen (2005), P S and RV are multiplied by the scaling factor, which is computed as a ratio of total market value at the end of montht divided by that in August 1962. This is to adjust the time-trend of the measures due to different values of currency over time.
As manifested in Pastor and Stambaugh (2003), the time-series of market illiq- uidity based onP S adequately captures anecdotal events in liquidity. It shows peaks on November 1973 (Oil shock), October 1987 (stock market crash) and September
1998 (LTCM). The same is true for RV and RO. However, T V and ZR show that the stock market was highly liquid on October 1987, when the stock market crash occurred.
Table A.1 shows summary statistics of daily percentage returns and our illiquidity proxies by 25 size groupings. Each size group is formed based on the total market value of each stock at the end of previous year. Average and standard deviations are obtained as time-series average or standard deviation of medians in each size group.
We see some interesting patterns in the table. Most importantly, we find that illiquidity is higher for small stocks than for large stocks. This is consistent with the previous literature (Amihud and Mendelson (1986), Amihud (2002)) and fits well with our intuition. Except for turnover, all illiquidity proxies show a monotonic relation between illiquidity and size. For example, P S is 0.067 for the smallest size group, while it is almost zero for the largest size group. A similar pattern is shown forRV, RO andZR. RV is 6.55 for the smallest size group and it is 0.005 for the largest size group. RO (ZR) is 0.028 (0.28) for the smallest size group and it is 0.011 (0.07) for largest size group. However, T V does not show a clear monotonic pattern. Though the smallest size group has a turnover of -0.0015, which is larger than -0.0016 for the largest size group, there is increasing pattern of T V from the 23rd largest size group to the largest.
Turning to standard deviation, small stocks have higher volatility of returns and illiquidity across all illiquidity proxies except T V. Standard deviation of returns for the smallest stocks is 7.77% while it is 4.17% for the largest stocks. Standard deviation of P S is 0.41 for the smallest size group while it is 0.0003 for the largest
size group. In sum, Table A.1 shows that the returns and illiquidity and their volatility are negatively correlated with size, which is consistent with the previous literature.