# Exchange-traded funds and information asymmetry

## Exchange-traded funds and information asymmetry

Journal of Finance and Accountancy Exchange-traded funds and information asymmetry Dan Zhou California State University at Bakersfield ABSTRACT The e...

Journal of Finance and Accountancy

AMEX was acquired by the NYSE in 2008 and the SPDRs are currently traded on the NYSE.

DIAMONDs are designed to track the performance of the Dow Jones Industrial 30 Average.

Journal of Finance and Accountancy The adverse selection component of the bid-ask spread is not directly observable, but it has been the subject of extensive study in recent years. To decompose the spread for measuring adverse selection costs, we use Glosten and Harris’s (1988) and Lin, Sanger and Booth’s (1995) models. Van Ness, Van Ness, and Warr (2001) examine the performance of five commonly used spread decomposition models in the finance literature. We conclude that the two models we choose operationally better than others when measuring adverse selection components. 2.2.1. Glosten and Harris (1988) Model In Glosten and Harris (1988), the bid-ask spread is divided into two components: a transitory component (order processing fee and inventory costs) and a permanent component (adverse selection cost). The transitory component is not related to the underlying value of the securities, which causes the transaction price changes to be negatively serially correlated (Roll, 1984). The permanent component reflects the market maker’s expected value of the security, which does not cause serial correlation in the transaction price changes. The Glosten and Harris model is represented as follows: Pt = mt + I t Ct (1) mt = mt −1 + I t Z t + et C t = c0 + c1Vt Z t = z 0 + z1Vt

(2) (3) (4)

where Pt is the transaction price at time t; mt is the unobserved ‘true’ price; Vt is the shares volume traded at time t; I t is a trade indicator that takes a value of +1 if the transaction is buyerinitiated and a value of –1 for seller-initiated; and et captures public information innovations and rounding errors. Based on the model, the adverse selection component is 2( z 0 + z1Vt ) , the transitory component is 2(c0 + c1Vt ) , and the quoted bid-ask spread is the sum of these two components. To obtain the value of I t , we followed the Lee and Ready (1991) procedure for trade classification.3 The parameters c0 , c1 , z 0 and z1 are estimated by OLS regression the following equation, which derived from the above model. ∆Pt = Pt − Pt −1 (5) = c0 ( I t − I t −1 ) + c1 ( I tVt − I t −1Vt −1 ) + z 0 I t + z1 I t Vt + et Using the average transaction volume for stock i, Vi , an estimate of the percentage adverse selection component ( Z i ) can be obtained: Zi =

2( z 0,i + z1,i V i ) 2(c0,i + c1,i V i ) + 2( z 0,i + z1,i V i )

(6)

2.2.2. Lin, Sanger and Booth (1995) Model

3

Classify the trades that occur in the middle of the spread using the tick test and other trades as buys (sells) is they are closer to the ask (bids). We compare the trades with their most recent quotes. The most recent quotes are defined as the quotes that were time stamped at least five second before the trades. This procedure is developed by Lee and Ready (1991) and is widely adopted.

(8)

where the disturbance terms et +1 and η t +1 are assumed to be uncorrelated. In the OLS regression to estimate the adverse selection component, we follow Lin, Sanger and Booth (1995)’s procedure to use the logarithms of the transaction price and the quote midpoint when we create the dependent and independent variables.

xt − E[ xt | Φ t −1 ] , which reflects the private information possessed by informed traders, where Φ t −1 is the public information set prior to the trade. The impact of the current trade innovation on the efficient price innovation, i.e. the trade related efficient price innovation, is E[ wt | xt − E[ xt | Φ t −1 ]] . If the absolute measure of trade informativeness is defined as the variance of trade related efficient price innovation, it should be represented by Var (E[ wt | xt − E[ xt | Φ t −1 ]]) = σ w2 , x . And the relative measure is 2

Var (E[ wt | xt − E[ xt | Φ t −1 ]]) σ w, x = 2 = Rw2 . Var ( wt ) σw

Journal of Finance and Accountancy

Because the variables, such as efficient price innovations, are unobservable, the estimation adopts Hasbrouck’s (1991a) vector autoregressive (VAR) model, which is: rt = a1rt −1 + a 2 rt −2 + L + b0 xt + b1 xt −1 + L + υ1,t (9) xt = c1rt −1 + c 2 rt −2 + L + d1 xt −1 + d 2 xt −2 + L + υ 2,t where rt = qt − qt −1 . The innovations υ1,t and υ 2,t are zero-mean, serially uncorrelated disturbances with Var (υ1,t ) = σ 12 , Var (υ 2,t ) = Ω , and E (υ1,tυ 2,t ) = 0 . Under the assumption of invertibility, the trades and quote revisions may be expressed as a linear function of current and past innovations, i.e. the vector moving average (VMA) corresponding to the above VAR model: rt = υ1,t + a 1∗υ1,t −1 + a ∗2 υ1,t −2 + L + b ∗0υ 2,t + b1∗υ 2,t −1 + L (10) ∗ ∗ ∗ ∗ xt = c 1 υ1,t −1 + c 2 υ1,t −2 + L + υ 2,t + d 1 υ 2,t −1 + d 2 υ 2,t −2 + L

Then, the variance of efficient price innovation σ w2 and the absolute (relative) measure of trade informativeness σ w2 ,x ( Rw2 ) can be estimated by:

 

′ 

t =1

2

σ w2 =  ∑ bi∗ Ω ∑ bi∗  + 1 + ∑ ai∗  ⋅ σ 12 σ w2 , x Rw2 =

 t =0   t = 0    ∞   ∞ ′ =  ∑ bi∗ Ω ∑ bi∗   t =0   t =0 

σ w2 , x σ w2

In our estimation, we adopt a four-variable VAR model, i.e. the trade variable becomes a

[

column vector of xt0 have xtk = sign( xt ) xt

x1t k

]

xt2 in this model. Assuming xt is the signed trading volume we

. For the quote revision, we use rt = log(qt / qt −1 ) instead of

rt = qt − qt −1 , where q t is the quote midpoint. We followed the Lee and Ready (1991) procedure to classify the trade as a purchase or a sale. Then the signed trade volume can be obtained by multiplying the trade volume with –1 (or +1) if the trade is a sale (or purchase). Following Hasbrouck (1991b), VAR is truncated at lag 5 and VMA is truncated at lag 10.

3. DATA AND SAMPLE SELECTION 3.1. Sample Selection We compare the information asymmetry between SPDRs and its 90 underlying sample stocks. To estimate the proxies of information asymmetry, we select the sample period over the three-month period of February, March and April in 1993, 1995, 1997 and 2000. The reason we choose the month of February, March and April is because SPDRs began to trade on the AMEX on January 29th, 1993. And also there is no stock split for SPDRs and its 90 sample underlying individual securities, and there is no tick size change either over these periods.

Journal of Finance and Accountancy The S&P 500 index consists of 500 stocks chosen for market size, liquidity, and industry group representation. We excluded the stocks that added or deleted from the S&P 500 index composition during the sample period. Our initial sample size is 266 common stocks, which last at least 8 years in the S&P 500 index. Due to the time-consuming estimation process, we further decrease our sample size to 90 common stocks. They were selected by using the following procedure: First, we rank the 266 stocks based on their average market capitalization, then we divide them into three groups4. In each group, we pick the median 30 stocks. Of these 90 stocks, 87 are traded on the NYSE and three are traded on the NASDAQ. To exclude the effect of different trading mechanism we substitute the NASDAQ listed stocks with NYSE listed stocks of similar size. We also compare the information asymmetry between DIAMONDS and its underlying individual securities and we choose its sample period from February 1, 1998 through December 20005. We obtained the Dow Jones Industry Average 30 component stocks list and change history over the sample period from Dow Jones & Company, Inc.6 We estimate the asymmetric information cost for each component stock in the index every month. Then a price-weighted cost is computed for a synthetic portfolio of the underlying stocks and it is used to compare with the estimated cost of DIAMONDS.

( At − At −1 )

At −1 > 0.10 ; 8) quotes with bid price Bt if (Bt − Bt −1 ) Bt −1 > 0.10 .

4. EMPRICIAL RESULTS 4.1. Market Liquidity 4

For each common stock, we calculate its market capitalization at the end of each year (from 1992 to 2000) and average them over this time period. The market capitalization is measured as the product of the stock price and the number of shares outstanding at the end of each year. The stock price and the number of shares outstanding at the end of each year are retrieved from the CRSP Daily Database. 5 DIAMNONS was introduced on January 20, 1998. 6 We adjust the underlying 30 stocks every month based on the component list at the end of each month.

4.2. Adverse Selection Cost Because there is less information asymmetry in markets for ETFs than in markets of their underlying individual securities, we predict that the adverse selection component of the bid-ask spread is lower for ETFs than their underlying individual securities. We choose Glosten and Harris (1988), and Lin, Sanger and Booth (1995)’s models to decompose the bid-ask spread for SPDRs, DIAMONDS and their underlying stocks. The estimation results are presented in Table 2 and Table 3.

The summary statistics of adverse selection component for SPDRs’ 90 sample stocks are available upon request, both for LSB and GH model.

Journal of Finance and Accountancy

Journal of Finance and Accountancy

Journal of Finance and Accountancy

Table 1

Market Liquidity of Exchange-Traded Funds and Their Underlying Individual Securities

The variables are defined as follows: Denote At, Bt, and Pt as the ask, bid and trade prices at time t. The quoted dollar spread is At − Bt; the relative quoted spread is (At − Bt)/ Qt, where Qt = (At + Bt)/2; the effective dollar spread is 2|Pt − Qt|; the effective relative spread is 2|log(Pt / Qt)|. Depth and dollar depth are the average of quoted depth in number of shares and dollars per quotation. Depth and dollar depth in half-hour period are the average of total quoted depth in number of shares and dollars over a half-hour period.

Panel A

SPDRs and it 90 Underlying Sample Stocks

The Trade and Quote data for SPDRs and its 90 underlying sample stocks are retrieved from TAQ database over the period from February 1 to April 30 in 1993, 1995, 1997 and 2000. All variables are equally weighted for the underlying sample stocks.

1993

1995

1997

2000

Quoted Spread (\$) SPDRs Underlying Sample Stocks

0.0313 0.2057

0.0314 0.1777

0.1183 0.1761

0.2015 0.1421

Relative Quoted Spread (%) SPDRs Underlying Sample Stocks

0.0702 0.5411

0.0635 0.5087

0.1515 0.4116

0.1404 0.4156

Effective Spread (\$) SPDRs Underlying Sample Stocks

0.0325 0.1184

0.0301 0.1099

0.0878 0.1176

0.1313 0.0888

Relative Effective Spread (%) SPDRs Underlying Sample Stocks

0.0730 0.3236

0.0607 0.3268

0.1126 0.2822

0.0919 0.2591

Depth (000's) SPDRs Underlying Sample Stocks

132.0 17.9

198.1 23.1

191.8 20.2

713.0 11.5

Dollar Depth (\$000's) SPDRs Underlying Sample Stocks

5873.9 646.8

9814.3 770.6

15029.8 823.3

102215.5 393.0

Depth in Half-Hour Period (000,000's) SPDRs Underlying Sample Stocks

1425.5 162.2

3159.3 264.5

9526.0 563.9

116043.1 771.1

63.4 6.6

156.5 9.6

746.5 27.8

16635.0 32.4

Dollar Depth in Half-Hour Period (\$000,000,000's) SPDRs Underlying Sample Stocks

Journal of Finance and Accountancy

Table 1

(Cont.)

Panel B

DIAMONDS and its Underlying securities

The estimates use the intra-day transaction and quotation data retrieved from TAQ Database over the period from February 1, 1998 to December 1, 2000. Quoted and effective spreads are price weighted and all other variables are equally weighted for underlying individual securities.

1998

1999

2000

Quoted Spread (\$) DIAMONDS Underlying Individual Stocks

0.1093 0.1265

0.1628 0.1335

0.1718 0.1247

Relative Quoted Spread (%) DIAMONDS Underlying Individual Stocks

0.1273 0.1852

0.1568 0.1890

0.1603 0.1999

Effective Spread (\$) DIAMONDS Underlying Individual Stocks

0.0922 0.0898

0.1224 0.0877

0.1322 0.0887

Relative Effective Spread (%) DIAMONDS Underlying Individual Stocks

0.1075 0.1335

0.1176 0.1228

0.1236 0.1357

Depth (000's) DIAMONDS Underlying Individual Stocks

191.2 11.7

178.0 12.5

142.4 16.8

Dollar Depth (\$000's) DIAMONDS Underlying Individual Stocks

16607.3 755.3

18536.9 757.3

15283.4 849.0

Depth in Half-Hour Period (000,000's) DIAMONDS Underlying Individual Stocks

3401.8 314.8

3495.7 446.9

4881.5 882.5

294.1 20.0

364.2 27.8

523.4 48.6

Dollar Depth in Half-Hour Period (\$000,000,000's) DIAMONDS Underlying Individual Stocks

Journal of Finance and Accountancy

Table 2

Lin, Sanger and Booth (1995)’s Estimates of the Adverse Selection Cost

The adverse selection cost is estimated by the regression: Qt +1 − Qt = λX t + et +1 , where Qt is the log quoted midpoint and X t = Pt − Qt is the signed effective half-spread and Pt is the log transaction price at time t. λ is the percentage adverse selection cost. The adverse selection cost in cents is the product of λ and the absolute effective spread in cents.

Panel A SPDRs and its 90 Underlying Sample Stocks The estimates use the intra-day transaction and quotation data retrieved from TAQ Database over the period from February 1 to April 30 in 1993, 1995, 1997 and 2000. The percentage adverse selection cost and the absolute adverse selection cost in cents are all equally weighted for the underlying sample stocks.

Year

SPDRs

Underlying Stocks

SPDRs

Underlying Stocks

1993

23.93

28.74

0.78

3.58

1995

13.38

29.30

0.40

3.25

1997

8.91

36.36

0.78

4.35

2000

10.29

39.51

1.35

3.57

Average

14.12

33.48

0.83

3.69

Journal of Finance and Accountancy

Table 2 Panel B

(Cont.) DIAMONDS and its Underlying Individual Stocks

The estimates use the intraday trade and quote data retrieved from TAQ Database over the period from February 1, 1998 to December 1, 2000. The percentage adverse selection cost is equally weighted and the absolute adverse selection cost in cents is price weighted for the underlying individual stocks.

Month 1998. 02 1998. 03 1998. 04 1998. 05 1998. 06 1998. 07 1998. 08 1998. 09 1998. 10 1998. 11 1998. 12 1999. 01 1999. 02 1999. 03 1999. 04 1999. 05 1999. 06 1999. 07 1999. 08 1999. 09 1999. 10 1999. 11 1999. 12 2000. 01 2000. 02 2000. 03 2000. 04 2000. 05 2000. 06 2000. 07 2000. 08 2000. 09 2000. 10 2000. 11 2000. 12 Average

Adverse Selection Cost (%) DIAMONDS Underlying Stocks 14.08 13.15 12.50 4.22 9.73 2.67 10.69 7.08 3.94 8.42 8.54 2.83 5.90 5.06 9.63 13.55 9.80 14.33 12.34 8.60 9.26 7.66 10.10 10.27 17.26 8.56 8.81 11.69 17.00 19.19 21.92 21.17 17.22 18.18 15.73 11.17

33.25 34.21 34.31 35.78 36.04 36.37 38.91 27.81 39.98 36.73 36.59 37.00 36.74 34.69 34.96 36.22 35.15 34.64 34.63 35.34 36.71 30.99 30.45 31.21 31.65 31.52 33.77 31.33 28.89 28.69 26.86 27.43 29.77 29.33 29.19 33.35

Adverse Selection Cost (¢) DIAMONDS Underlying Stocks 0.72 0.68 0.74 0.26 0.70 0.24 1.25 0.89 0.58 0.98 1.03 0.37 0.75 0.63 1.27 1.71 1.17 1.69 1.53 1.03 1.01 0.86 1.29 1.38 2.19 1.11 1.52 1.72 2.46 2.56 2.35 2.21 2.16 2.34 2.10 1.30

2.69 2.78 2.99 3.05 2.96 3.13 3.64 3.77 3.77 3.25 3.41 3.61 3.55 3.29 3.64 3.58 3.21 3.14 3.18 3.19 3.73 2.75 2.81 3.11 3.14 3.22 3.68 2.92 2.43 2.44 2.35 2.51 2.82 2.66 2.84 3.12

Journal of Finance and Accountancy

Table 3 Glosten and Harris (1988)’s Estimates of the Adverse Selection Cost The estimates use the intra-day transaction and quote data from TAQ Database from February 1 to April 30 in 1993, 1995, 1997 and 2000. Based on the model, the percentage adverse selection component of the quoted bid-ask spread is 2( z 0,i + z1,i V i ) , 2(c 0,i + c1,i V i ) + 2( z 0,i + z1,i V i ) where Vi is the average trading volume for stock i, and the parameters of

c0 , c1 , z 0 and z1 are estimated by OLS

regression the following equation: ∆Pt = Pt − Pt −1 = c 0 ( I t − I t −1 ) + c1 ( I t Vt − I t −1Vt −1 ) + z 0 I t + z1 I t Vt + et

Pt is the transaction price at time t; Vt is the shares volume traded at time t; I t is a trade indicator that takes a value of +1 if the transaction is buyer-initiated and a value of –1 for seller-initiated; and

ε t captures

public

information innovations and rounding errors. The adverse selection cost in cents is the product of percentage adverse selection cost and the absolute quoted spread in cents.

Panel A SPDRs and its 90 Underlying Sample Stocks The estimates use the intra-day transaction and quotation data retrieved from TAQ Database over the period from February 1 to April 30 in 1993, 1995, 1997 and 2000.

Year

SPDRs

Underlying Stocks

SPDRs

Underlying Stocks

1993

15.56

20.44

0.49

4.61

1995

18.64

18.52

0.59

3.53

1997

15.41

26.43

1.82

5.00

2000

16.52

36.82

3.33

5.62

Average

16.53

25.55

1.56

4.69

Journal of Finance and Accountancy

Table 3

(Cont.)

Panel B

DIAMONDS and its Underlying Individual Stocks

The estimates use the intra-day transaction and quotation data retrieved from TAQ Database over the period from February 1, 1998 to December 1, 2000. The percentage adverse selection cost is equally weighted and the absolute adverse selection cost in cents is price weighted for the underlying individual stocks.

Month 1998. 02 1998. 03 1998. 04 1998. 05 1998. 06 1998. 07 1998. 08 1998. 09 1998. 10 1998. 11 1998. 12 1999. 01 1999. 02 1999. 03 1999. 04 1999. 05 1999. 06 1999. 07 1999. 08 1999. 09 1999. 10 1999. 11 1999. 12 2000. 01 2000. 02 2000. 03 2000. 04 2000. 05 2000. 06 2000. 07 2000. 08 2000. 09 2000. 10 2000. 11 2000. 12 Average

Adverse Selection Cost (%) DIAMONDS Underlying Stocks 30.55 28.95 26.48 29.44 27.23 31.61 28.63 32.27 20.72 32.43 19.53 33.34 22.18 37.35 13.26 82.34 14.14 39.15 14.12 33.80 14.15 33.97 6.46 35.26 11.06 34.82 11.00 31.53 20.69 34.44 24.87 35.34 22.08 32.28 17.12 31.02 19.60 30.93 14.18 31.79 10.83 32.30 8.58 27.72 13.98 27.64 16.06 30.35 18.22 30.01 15.19 30.23 15.56 33.12 17.21 28.58 21.58 24.53 25.79 2356 26.45 21.92 28.16 22.76 23.30 26.26 23.89 24.98 21.06 25.65 18.97 32.05

Adverse Selection Cost (¢) DIAMONDS Underlying Stocks 1.87 3.69 1.61 3.82 1.77 4.35 1.90 4.38 1.72 4.16 1.76 4.59 3.01 5.74 1.99 11.60 2.39 5.94 2.15 4.84 2.39 5.22 1.17 5.58 1.96 5.51 1.83 4.89 3.67 6.01 4.10 5.81 3.53 4.98 2.63 4.77 3.23 4.73 2.15 4.73 1.64 4.81 1.29 4.07 2.17 4.31 2.74 4.99 2.98 5.04 2.52 5.18 3.34 5.92 3.37 4.37 4.15 3.36 4.73 3.37 4.05 3.25 4.01 3.50 3.62 4.05 3.87 3.71 3.45 4.11 2.71 4.84

Journal of Finance and Accountancy

Table 4

Trade informativeness is computed as σ w2 , x σ w2 , where σ w2 is the variance of efficient price change and σ w2 ,x is trade-correlated component of σ w2 . They are defined as 10 10 10 ′ σ w2 = ( ∑ bi∗ )Ω( ∑ bi∗ ) + (1 + ∑ a i∗ ) 2 ⋅ σ 12 and t =0

where

a i∗ ,

bi∗

t =0

t =1

10

10

t =0

t =0

σ w2 , x = ( ∑ bi∗ )Ω( ∑ bi∗ )

Ω, σ 12

and are come from the Hasbrouck (1991a, 1991b)’s VAR and VMA model: rt = a1 rt −1 + a 2 rt − 2 + L + b0 x t + b1 x t −1 + L + υ1,t x t = c1 rt −1 + c 2 rt − 2 + L + d 1 x t −1 + d 2 x t − 2 + L + υ 2,t

rt = υ1,t + a1∗υ1,t −1 + a 2∗υ1,t − 2 + L + b0∗υ 2,t + b1∗υ 2,t −1 + L x t = c1∗υ1,t −1 + c 2∗υ1,t − 2 + L + υ 2,t + d 1∗υ 2,t −1 + d 2∗υ 2,t − 2 + L

[

]

where rt = 100 × log(q t / q t −1 ) , qt is the quote midpoints; x t is the trade variable column vector x t0 x1t x t2 , where x t0 is trade indicator (+1 if the market order is a purchase and -1 if a sale), x 1t is signed trading volume in 100 shares (positive if the market order is a purchase and negative if a sale), and x t2 is signed square of x 1t . VAR is truncated at lag 5 and VMA is truncated at lag 10.

Panel A

SPDRs and its 90 Underlying Sample Stocks

The estimates use the intra-day transaction and quotation data retrieved from TAQ Database over the period from February 1 to April 30 in 1993, 1995, 1997 and 2000.

SPDRs

1993

Underlying stocks Maximum

28.76

3rd Quartile 36.62

29.67

36.46

41.46

53.39

1.46

38.79

43.43

48.70

73.46

13.00

32.35

37.27

41.88

56.76

st

Mean

Minimum

1 Quartile

Median

1.57

29.00

0.61

20.26

1995

1.65

35.43

2.31

1997

3.30

43.56

2000

3.45

36.70

64.99

Journal of Finance and Accountancy

Table 4

(Cont.)

Panel B

DIAMONDS and its Underlying Individual Stocks

The estimates use the intra-day transaction and quotation data retrieved from TAQ Database over the period from February 1, 1998 to December 1, 2000. The percentage adverse selection cost is equally weighted for the underlying individual stocks.

Informativeness (%)

Informativeness (%)

Month

DIAMONDS

Stocks

Month

DIAMONDS

Stocks

1998. 02

2.27

42.31

1999. 08

3.59

43.36

1998. 03

3.25

41.68

1999. 09

2.98

43.86

1998. 04

2.49

40.86

1999. 10

3.23

39.03

1998. 05

1.95

42.94

1999. 11

4.39

38.07

1998. 06

1.21

42.68

1999. 12

3.07

37.97

1998. 07

1.11

38.90

2000. 01

2.55

38.94

1998. 08

2.22

42.53

2000. 02

5.49

41.17

1998. 09

6.77

38.58

2000. 03

3.44

36.91

1998. 10

1.37

43.06

2000. 04

3.93

41.93

1998. 11

1.66

43.42

2000. 05

5.22

38.96

1998. 12

1.50

40.48

2000. 06

8.48

38.27

1999. 01

0.63

42.87

2000. 07

11.59

40.83

1999. 02

0.78

45.02

2000. 08

14.33

39.34

1999. 03

0.98

41.66

2000. 09

9.08

39.91

1999. 04

4.01

38.35

2000. 10

11.00

36.28

1999. 05

7.93

37.40

2000. 11

8.49

39.51

1999. 06

3.97

43.16

2000. 12

9.21

40.09

1999. 07

2.10

41.05

Average

4.46

40.61