Relationship between Size and Liquidity

1. Ashok Bhardwaj Abbott
Presented at
Foundation for Accounting Education
Business valuation Conference , New York
May 21, 2012
© 2012 Ashok B. Abbott

2. Ashok B. Abbott is an Associate Professor of Finance at
West Virginia University in Morgantown, West Virginia.
Professor Abbott received his MBA in Finance at Virginia
Polytechnic Institute and State University (VPI&SU) in
1984, followed by a Ph.D. in finance also at VPI&SU, in
1987. His Ph.D. dissertation title was "The valuation
effects of tax legislation in corporate sell-offs".
He has published extensively in scholarly research journals
and made presentations at national and international
conferences. He serves on the editorial boards of The
Business Valuation Review and The Value examiner. The
Small Business administration recognized Professor
Abbott as the Small Business Advocate-Journalist for the
year 2002.
His focus area of research and consulting in valuation is the
level of price adjustments (discounts/premiums)
appropriate for liquidity, marketability, and control
attributes of the interests being appraised.
Professor Abbott consults for valuation divisions of well-
known firms, such as Standard & Poor's, Duff & Phelps,
Willamette Management Associates, Houlihan Valuation
Advisors, among others. He has served as an expert
witness in the business valuation arena for 15 years. You
can see his full CV at
www.be.wvu.edu/faculty_staff/cv/ashok_abbott_cv.pdf.

3. Research Questions
Q1. Is there a difference in returns among smaller and
larger firms?
Answer
Q2. Is there a difference in returns among low and high
liquidity firms?
Answer
Q3. Is there a difference in returns among low and high
liquidity firms within each size category?
Answer

4. Size Effect
Size effect, initially reported by Banz (1981) and
Reinganum (1981) has been researched extensively.
Research Indicates that smaller (measured by market
value) firms tend to exhibit higher returns than the
levels predicted by the Sharpe Lintner capital asset-
pricing model (CAPM).

5. Original Question by Banz
“It is not known whether size
per se is responsible for the
effect or whether size is just a
proxy for one or more true
unknown factors”.

6. Liquidity Effect
 Large Body of Academic Literature as well as the
recent Episodic Illiquidity amply illustrate that there
is a very substantial Cost associated with lack of
liquidity
 Business valuation profession has generally
incorporated lack of liquidity in to the Discount for
Lack of Marketability.

7. Intersection of Size and Liquidity
Is size is just a proxy for the
true unknown factor-
Liquidity?

8. Publicly Traded Equivalent Value
Capital Asset Pricing Model (CAPM),
Ibbottson premiums, or build-up rates
using capital market proxies provide
an estimate of the publicly traded
equivalent value (“PTEV”) of a
privately held company.

9. Liquidity Assumptions of the Publicly
Traded Equivalent Value
Finance literature recognizes four dimensions of
liquidity:
 Width (availability of a large number of buyers)
 Depth (ability to absorb large volume)
 Immediacy (ability to complete the transaction
quickly)
 Resiliency (absorbing large volume of trades without
moving the price)

10. Liquidity and Asset Prices
Liquidity is Priced
Liquidity is Systemic
Liquidity varies over time
Liquidity Premium is a major
factor in Asset Pricing

11. Measures of Liquidity
 Half Life
(Average Liquidation period)
 Bid Ask Spread
(Ask-Bid)/Ask
 Trading Cost
(Holding Return-Trading Return)
 Price Impact of Trading
(Amivest ratio)

12. Measuring Liquidity
Liquidity Measure (l) takes in to account both the trading volume and
shares outstanding. It is a natural log transformation on Turnover
measure.
Given
The stock issued and outstanding at Day 1 is S1
Trading Volume for one day is V1
The stock still in hands of original owners at beginning of Day 2 is S2 =
S1- V1
Assuming that the rate of deal flow is constant (l) at day 1
S2 = S1 e- l
Or l = Logn (S1) - Logn (S2)

13. Empirical Questions need
Empirical Analysis
Data Sample Used
Centre for Research in Security Prices (CRSP) equities
Data provides
Daily Price ( High Low Close Bid Ask), Return, Volume, and
Shares Outstanding among other data
Sample period 1926-2011
Covers periods of panic and Euphoria
80 Million Plus daily Observations
Three Million Plus monthly observations

14. Migration Issue Addressed
Fama and French suggest that ‘Migration’ is a significant
issue in size based studies. Firms tend to migrate to
higher size deciles following positive returns or lower
deciles/ get delisted following negative returns.
We form Portfolios based on MONTHLY levels of market
value and liquidity. Firms with IPO or delisting during
the month are excluded from the sample. This results
in reassigned monthly portfolios.

15. Removing Outlier Effect
 The data used in this analysis are
winsorized at 1% level.
 Values above the 99th percentile value
are set to the 99th percentile value.
 Values below the 1st percentile value are
set to the 1st percentile value.

16. Markets are Self Synchronizing
Observed synchronization between
the measures of
Liquidity
Volatility
Market Returns

17. 500
900
600
0
800
200
100
400
700
300
1
22
43
64
85
106
127
148
169
190
211
232
253
274
295
316
337
358
379
400
421
442
463
484
505
526
547
1926 January = 100
568
589
610
Mean half Life Index
631
652
673
694
715
736
757
778
799
820
841
862
883
Mean Half Life Months Index :
904
925
946
967
988
10…
HLFMeanIndex

18. 0.05
0.1
0.2
0
0.25
0.15
1
21
41
61
81
101
121
141
161
181
201
221
241
261
281
301
321
341
361
381
401
421
441
461
481
501
521
541
sprd_Mean
561
581
Bid Ask Spread 1926-2011 :
601
621
Response to Market Liquidity
641
661
681
701
721
741
761
781
801
821
841
861
881
901
921
941
961
981
1001
1021

19. 0.25
0
0.15
0.05
0.1
0.2
0.3
1
22
43
64
85
106
127
148
169
190
211
232
253
274
295
316
337
358
379
400
421
442
463
484
505
526
547
568
Trading Cost
589
610
631
652
673
694
715
736
757
778
799
820
Trading Cost ( 1926-2011)
841
862
883
904
925
946
967
988
1009
ltcost_Mean
1030

20. 0.0001
0
0.00005
0.0002
0.0003
0.00015
0.00025
1
22
43
64
85
106
127
148
169
190
211
232
253
274
295
316
337
358
379
400
421
442
463
484
505
526
547
Amivest ratio
568
589
610
631
652
673
694
715
736
757
778
799
820
841
862
883
904
925
946
967
988
Price Impact of Trading(1926-2011)
10…
amivest_Mean
1030

21. 0.006
0
0.005
0.004
0.001
0.002
0.003
1
21
41
61
81
101
121
141
161
181
201
221
(1926-2010)
241
261
281
301
321
341
361
381
401
421
441
461
481
501
521
Market Returns Volatility
541
561
581
Market Volatility
601
621
641
661
681
701
721
741
761
781
801
821
841
861
881
901
921
941
961
981
1001
lpretw_Var_Mean

22. Liquidity and Returns ( 1926-2010)
Annual 95%
Liquidity
returns Compares Confidence
Mean equal to Interval
Liquid 0.1193None ( 0.118: 0.120)
Illiquid 0.1455None ( 0.145: 0.146)
Liquidity
Premium 0.0262

23. Liquidity Impact on Value
No Growth Relative
Liquidity
Annual returns Value Valuation
Mean $100 Cash Flow
Liquid 11.93% $ 838.22 100%
Illiquid 14.55% $ 687.29 82%
Liquidity Liquidity
Premium 2.62% Discount Value 18%

24. Size and Returns(1926-2010)
95%
Size
Annual returns Compares Confidence
Mean equal to Interval
Large 0.1222None ( 0.121: 0.123)
Small 0.1433None ( 0.142: 0.144)
Size
Premium 0.0211

25. Size Impact on Value
No Growth Relative
Size
Annual returns Value Valuation
Mean $100 Cash Flow
Large
12.22% $ 818.33 100%
Small
14.33% $ 697.84 85%
Size Discount
Size Premium
2.11% Value 15%

26. Liquidity and Size Impact
( 1926-2010)
Liquidity sorted Annual
by size Return Compares 95% Confidence
Mean equal to Interval
Liquid and Large 0.1179None ( 0.117: 0.119)
Liquid and Small 0.1208None ( 0.119: 0.122)
Illiquid and
Large 0.1241None ( 0.123: 0.125)
Illiquid and
Small 0.1669None ( 0.166: 0.168)
Size
premium
Aggregate Adjusted
Difference
0.049
for
Liquidity 0.02285

27. Interaction Liquidity and Size
Liquidity sorted by
size Annual Return No Growth Value Relative Valuation
Mean $100 Cash Flow
Liquid and Large
11.79% $ 848.18 100%
Liquid and Small
12.08% $ 827.81 98%
Illiquid and Large
12.41% $ 805.80 95%
Illiquid and Small
16.69% $ 599.16 71%
Aggregate Aggregate
Differential 4.90% Differential 29.36%

28. Size and Liquidity Impact
(1926-2010)
Size sorted by Annual
Liquidity returns Compares95% Confidence
Mean equal to Interval
Large and Liquid 0.1191None ( 0.118: 0.120)
Large and
Illiquid 0.1254None ( 0.124: 0.127)
Small and Liquid 0.1281None ( 0.127: 0.129)
Small and
Illiquid 0.1586None ( 0.157: 0.160)
Liquidity
premium
Aggregate
Adjusted
Difference
0.0395
for Size
0.0184

29. Interaction Size and Liquidity
Size sorted by
Liquidity Annual returns No Growth Value Relative Valuation
Mean $100 Cash Flow
Large and Liquid
11.91% $ 839.63 100%
Large and Illiquid
12.54% $ 797.45 95%
Small and Liquid
12.81% $ 780.64 93%
Small and Illiquid
15.86% $ 630.52 75%
Aggregate Aggregate
Differential 3.95% Differential 24.91%

30. Distribution of Impact :
Liquidity Sorted by Size
Annual
Returns large Small Difference
Illiquid 0.1241 0.1669 0.0428 87%
Liquid 0.1179 0.1208 0.0029 6%
Difference 0.0062 0.0461
13% 94%

31. Distribution of Impact:
Size sorted by Liquidity
Annual
Returns large Small Difference
Illiquid 0.1281 0.1586 0.0305 77%
Liquid 0.1191 0.1254 0.0063 16%
Difference 0.009 0.0332
23% 84%

32. Questions?
Please do not hesitate to contact us for any clarifications.
Ashok Bhardwaj Abbott Ph.D. MBA
Email abbott.ashok@gmail.com
Phone 304 692 1385