Ashok Bhardwaj Abbott

Presented at

ASA Business Valuation Seminar Philadelphia

April 20, 2012

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.

Size Effect Size effect, initially reported by Banz (1981) and

Reinganum (1981) has been researched extensively.

Research Indicates that smaller (measured by market value) ( Check with Roger on other measures of size)firms tend to exhibit higher returns than the levels predicted by the Sharpe Lintner capital asset-pricing model (CAPM).

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”.

Intersection of Size and Liquidity

Is size is just a proxy for the true unknown factor- Liquidity?

Research Questions Q1. Is there a difference in returns among smaller and

larger firms?

Q2. Is there a difference in returns among low and high liquidity firms?

Q3. Is there a difference in returns among low and high liquidity firms within each size category?

Why do we care about liquidity Recent events in the financial markets have pointed

out how much the financial system depends on the ability to trade assets continuously.

The current failures in the Auction Rate Market demonstrate what happens when the market for an asset disappears. Even in the event of no underlying default securities become non-tradable.

7

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.

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)

Time Varying Liquidity Liquidity conditions change rapidly.

Cost of Liquidity is a function of liquidity and volatility.

Low Liquidity and high volatility combine to increase the cost of liquidity.

10

11

Characterized by infrequent shocks in which the bottom drops out of previously well functioning market.

No bids, no asks. Fire-sale pricing.

Securities suddenly become “toxic waste”.

Episodic Illiquidity

Core Issue in Liquidity :Immediacy

Assumption: Market orders have immediate execution.

Reality: Small at -the -market transactions of high trading volume public securities approach immediate execution.

Large block transactions of thinly traded public securities are likely to occur off the floor or may need to dribble out.

Substantial execution delay and Liquidity discount are relevant to asset pricing.

Liquidity and Returns in Public markets

Research shows significant difference between returns on liquid and illiquid publicly traded securities.

Brennan and Subrahmanyam (1996) show the return difference of the most liquid and least liquid shares on the New York Stock Exchange is 6.62% per year.

This difference roughly translates to a discount for lack of liquidity (DLOL) of 35.5%.

Liquidity and Asset Prices

Liquidity is Priced

Liquidity is Systemic

Liquidity varies over time

Liquidity Premium is a major factor in Asset Pricing

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)

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)

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

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.

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.

Markets are Self Synchronizing

Observed synchronization between the measures of

Liquidity

Volatility

Market Returns

Mean Half Life Months Index : 1926 January = 100

0

100

200

300

400

500

600

700

800

900

1

22 43

64 85

106

127

148

169

190

211

232

253

274

295

316

337

358

379

40

0

421

44

2

46

3

48

4

505

526

547

568

589

610 631

652

673

69

4

715

736

757

778

799

820 84

1

86

2

88

3

90

4

925

94

6

96

7

98

8

100

9

Mean half Life Index

HLFMeanIndex

Median Half Life Months Index : 1926 January = 100

0

200

400

600

800

1000

1200

1400

1600

1

22 43

64 85

106

127

148

169

190

211

232

253

274

295

316

337

358

379

40

0

421

44

2

46

3

48

4

505

526

547

568

589

610 631

652

673

69

4

715

736

757

778

799

820 84

1

86

2

88

3

90

4

925

94

6

96

7

98

8

100

9

Median Half Life Index

HLFMedianIndex

Bid Ask Spread 1926-2011 : Response to Market Liquidity

0

0.05

0.1

0.15

0.2

0.25

1 21 41

61

81

101

121

141

161

181

201

221

241

261

281

301

321

341

361

381

40

1

421

44

1

46

1

48

1

501

521

541

561

581

60

1

621

64

1

66

1

68

1

701

721

741

761

781

80

1

821

84

1

86

1

88

1

90

1

921

94

1

96

1

98

1

100

1

1021

sprd_Mean

Trading Cost ( 1926-2011)

0

0.05

0.1

0.15

0.2

0.25

0.3

1

22 43

64 85

106

127

148

169

190

211

232

253

274

295

316

337

358

379

40

0

421

44

2

46

3

48

4

505

526

547

568

589

610 631

652

673

69

4

715

736

757

778

799

820 84

1

86

2

88

3

90

4

925

94

6

96

7

98

8

100

9

1030

Trading Cost

ltcost_Mean

Price Impact of Trading(1926-2011)

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

1

22 43

64 85

106

127

148

169

190

211

232

253

274

295

316

337

358

379

40

0

421

44

2

46

3

48

4

505

526

547

568

589

610 631

652

673

69

4

715

736

757

778

799

820 84

1

86

2

88

3

90

4

925

94

6

96

7

98

8

100

9

1030

Amivest ratio

amivest_Mean

Market Returns Volatility (1926-2010)

0

0.001

0.002

0.003

0.004

0.005

0.006

1 21 41

61

81

101

121

141

161

181

201

221

241

261

281

301

321

341

361

381

40

14

214

41

46

14

81

501

521

541

561

581

60

16

216

41

66

16

81

701

721

741

761

781

80

18

218

41

86

18

81

90

19

219

41

96

19

81

100

1

Market Volatility

lpretw_Var_Mean

Liquidity and Returns ( 1926-2010)

Liquidity Annual

returns Compares

95%

Confidence

Mean equal to Interval

Liquid 0.1193 None ( 0.118: 0.120)

Illiquid 0.1455 None ( 0.145: 0.146)

Liquidity

Premium 0.0262

Size and Returns(1926-2010)

Size Annual returns Compares

95%

Confidence

Mean equal to Interval

Large 0.1222 None ( 0.121: 0.123)

Small 0.1433 None ( 0.142: 0.144)

Size

Premium 0.0211

Liquidity and Size Impact ( 1926-2010)

Liquidity sorted

by size

Annual

Return Compares 95% Confidence

Mean equal to Interval

Liquid and Large 0.1179 None ( 0.117: 0.119)

Liquid and Small 0.1208 None ( 0.119: 0.122)

Illiquid and

Large 0.1241 None ( 0.123: 0.125)

Illiquid and

Small 0.1669 None ( 0.166: 0.168)

Aggregate

Difference

0.049

Size premium Adjusted for Liquidity 0.02285

Size and Liquidity Impact (1926-2010)

Size sorted by

Liquidity

Annual

returns Compares 95% Confidence

Mean equal to Interval

Large and Liquid 0.1191 None ( 0.118: 0.120)

Large and

Illiquid 0.1254 None ( 0.124: 0.127)

Small and Liquid 0.1281 None ( 0.127: 0.129)

Small and

Illiquid 0.1586 None ( 0.157: 0.160)

Aggregate

Difference

0.0395

Liquidity premium Adjusted for Size 0.0184

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%

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%

Liquidity and Trading Cost

Group

Mean Winsorized Difference Proportion Trading Cost

Illiquid

and Small 7.79%

Liquid

and Small 2.31% 5.48% 89.66%

Liquid

and large 1.68% 0.63% 10.34% 6.11%

Decomposing Cost of Liquidity

Group Gret 12 Month

after Trading Costs

Illiquid and Small 8.90%

Liquid and Small 9.77%

Liquid and large 10.11%

Liquidity Costs are not trivial Liquidity Costs significantly reduce any gains

associated with small stock premium and need to be accounted for.

Small stock premium may be a statistical artifact for annual holding periods in view of the substantial illiquidity observed.

Conclusion: Size and Liquidity are both important in explaining asset returns.

We have illustrated the role of liquidity in explaining the returns on assets across time.

Liquidity differences can explain a very substantial part of the differences in returns between small and large as well as liquid and illiquid assets.

Size and liquidity premiums are not mutually exclusive.

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