• Valuation Study Group
• London UK
• June 2012 Meetings
1
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 wellknown 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.
Discount for Lack of Marketability as a
Catch All
 Discount for lack of marketability has
been used generically to indicate
impairment in value due to lack of
marketability and liquidity.
Distinction between
Marketability and Liquidity
 Marketability and Liquidity are aligned but distinct
concepts. American Society of Appraisers glossary of
terms defines the two as;
 Marketability -The capability and ease of transfer or
salability of an asset, business, business ownership
interest or security.
 Liquidity- The ability to readily convert an asset,
business, business ownership interest or security into
cash without significant loss of principal.
Publicly Listed Securities :
Marketable Vs. liquid
Marketable Securities do not automatically achieve
Liquidity.
Daily turnover averages less than 0.5% for S&P 100
securities.
Daily turnover averages less than 0.05% for Decile
10 Securities.
Liquidity Effect
Liquidity effect, initially empirically shown by Amihud and
Mendelson(1986) has also been researched extensively.
Research indicates that less liquid (measured by bid-ask spread,
market depth, trading volume, price impact per dollar
traded) firms tend to exhibit higher returns than the levels
predicted by the Sharpe Lintner capital asset-pricing model
(CAPM).
liquidity effect is the strongest among micro-cap stocks and
then declines from micro-to-small to mid- and to large-cap
stocks.
Liquidity Cost:
Ugly Stepchild of Valuation Theory
 Asset pricing Models assume liquidity. In presence of perfect
liquidity, in equilibrium, supply equals demand, unlimited
quantities of an asset can be bought and sold without any
impact on price. Liquidity costs are often acknowledged but
treated as inconsequential and negligible.
 With perfect liquidity there is only one price.
Ask =Price=Bid
Theory and Reality
 As liquidity declines Price offered for immediate sale becomes
lower than the price demanded for immediate purchase. The bid
ask spread becomes wider as markets become less liquid.
Ask >Price>Bid
 Level II quotes illustrate cost of liquidity. Quoted bid
ask spread widens as offer lot size increases.
Blockage and Delayed Execution
 Liquidity drops rapidly for larger blocks with rapidly
climbing bid ask spreads, large price impact, and frequent
market failure. When a large block of publicly traded stock is
valued, this increased bid ask spread representing the
liquidity impairment is called 'Blockage'. A block of
unregistered stock in a privately held business suffers from
impairment in value from lack of both factors-
marketability and
 liquidity.
Bid Ask Spread as Cost of Liquidity
 Market maker quote is an offer to sell at Ask
price and to buy at Bid Price.
 Market maker offers instantaneous liquidity
in exchange for the Bid Ask Spread.
 Bid Ask Spread is the price of the liquidity
risk assumed by the market maker.
 Bid Ask Spread is the discount from the Ask
(liquid) Price
Components of Price Risk:
Realized Loss
 Loss from decline in price during the period of illiquidity -
realized price is lower than the price at which the asset was
purchased, there is a realized loss. This is the first
component, and is well understood. (LOSS I)
 Since the minimum price of the asset can be zero, Loss I is
limited to the loss of the purchase price.
Components of Price Risk:
Opportunity Cost Loss
 Potentially, a second and much larger component of the price
risk is the opportunity loss that occurs when the asset
increases in price during the period of illiquidity, and then
declines to a lower value by the time the asset can be
liquidated. (LOSS II)
Measuring Price Risk as Put Option
 Put option with an exercise price equal to the bid price can
model the liquidity risk.
 Put option price is a function of the liquidation period and
the price volatility for the asset.
 Put option models are flexible in pricing the risk according
to the model specification.
Converting Put Option premium to
Discount for lack of Liquidity
 Similar to the merger premium being treated as a discount for lack
of control.
 Value of a put option premium, estimating the cost of liquidity, is
NOT the discount for lack of liquidity.
 Liquid asset price is
Bid + Option Premium =Ask price
DLOL= Option Price/Ask price
 Neglecting to convert the option premium to the applicable
discount creates the illusion that the estimated discounts are
greater than 100%, an impossible solution.
Option Based Models measuring Discount
for lack of Liquidity (Price Risk Component)
 Black Scholes Put
(Chaffee 1993 [i])
 Average Price Asian Put
(Finnerty 2002[ii] )
 Maximum Price Strike Look Back Put
(Longstaff 1995[iii])
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[i] David B. H. Chaffee III, ‘‘Option Pricing as a Proxy for Discount for Lack of Marketability in Private Company Valuations—A Working
Paper,’’ BusinessValuation Review (December 1993).
[ii] John D. Finnerty, “The Impact of Transfer Restrictions on Stock Prices.” Analysis Group/Economics, October 2002.
[iii] Francis A. Longstaff, ‘‘How Much Can Marketability Affect Security Values?’’ Journal of Finance (December 1995).
Black Scholes Model
DLOM/DLOL Assumptions
 Typically strike price is set to equal the strike price
 Option life is assumed to be the holding period
 The interest rate is equal to the risk free rate
 Volatility is taken from guideline companies
Black Scholes Put (Chaffee)
 BSP provides protection against decline in value of the asset as
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compared to the current price (LOSS I).
BSP does not address the opportunity cost of not being able to
liquidate the asset at the intermediate high price reached but
not realized. (LOSS II)
Simply pays out the difference between the starting price and
the price at end of option period.
Starting Price $100, intermediate prices $120, $150, ending
Price $70
BSP Payout $100-$70= $30.
Path Dependent Options
 Payout is flexible based on the path taken by the asset prices
during the option period.
 Two Forms commonly used-
Asian Average Price Put
Look Back Put
Asian Average Price Put (Finnerty)
 AAP option provides a partial coverage of the potential loss
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from declining value and the opportunity cost for not being
able to liquidate at the higher prices reached during the life
of the option averaging it with the potential losses.
Simply pays out the difference between the ending price and
average price achieved during the life of the option, at end
of option period.
Starting Price $100, intermediate prices $120, $150, ending
Price $70.
Average Price $110
AAP Payout $110-$70= $40.
Asian Average Price Put (Finnerty)
 AAP contract provides a payout based on average price achieved
for the asset during the life of the option. The price of the option
increases as the volatility of the underlying asset and the time to
maturity increases. Initially, the value of an AAP is lower than the
corresponding BSP as the payout is based on the average of gains
and losses. Essentially the buyer and the seller are agreeing to
share the potential gains and losses equally.
 Does Not compensate the holder fully for either the realized loss
or the opportunity cost of not being able to liquidate.
Look Back Put (Longstaff)
LBP pay out is based on the highest value for the underlying asset achieved
over the lifetime of the option.
LBP option addresses the risk of loss in value of the asset (LOSS I), as well
as provides a full coverage of the opportunity cost for not being able to
liquidate at the highest price reached during the life of the option.
(LOSSII)
 Simply pays out the difference between the ending price and highest
price achieved during the option period.
 Starting Price $100, intermediate prices $120, $150, ending Price $70.
 Highest Price $150
 LBP Payout $150-$70= $80.
Maximum Price Strike Look Back
(Longstaff)
 Completely Compensates the holder for all price risk during
the option period.
 It should be thought of as a maximum discount.
 May be appropriate when information is not completely
shared between the buyer and the seller and the seller is
under compulsion to sell.
 As information asymmetry increases the value of the
price risk approaches LBP.
 AAP and LBP provide the bounds for the appropriate
price of liquidity risk.
Converting Option Premiums to DLOL
 Option premium represents the absolute difference between
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values for liquid (Ask) and illiquid (Bid) prices.
Option premium represents the Bid Ask Spread.
Exercise price of the option is the Bid price.
The proportional discount from the liquid (Ask) price is the
value of the option premium as a percentage of the liquid (Bid+
(Bid Ask Spread) )value.
If Bid price is $100, Ask Price is $110, the Bid Ask Spread of
$10 represents a discount of 10/110 or 9.09% and not 10%.
Option Models Base Data
 Stock Symbol VLGEA
 Valuation date February 2010
 Market Value 173.225 Million
 Shares Outstanding 6,999,000
 Monthly Trading Volume 184800 ( 2.64%)
 Monthly Lambda 0.026759
 Volatility of daily log Returns measured as Annualized
Standard Deviation 0.051901 ( Monthly 0.014983)
 The stock is a small, low trading volume and low volatility
stock.
Price Pressure Measurement
 Average Daily Volume 8800
 Average Daily Trading $ Volume $217,800.00
 Average DailyTrading Cost 0.004265 ( difference between
Buy and Sell return and Buy and Hold return)
 Price Impact per Dollar Trade 1.958E-08
 21% Block Size $ Value $36,377,302.50
 Price Impact of Immediate Liquidation Trade 71%
Delayed Trade Price Risk Measure
 Block Size 21%
 Liquidation Horizon Unrestricted 8.80 Months
 Liquidation Horizon R-144: 21 Quarters
 Volatility of daily log Returns measured as Annualized
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Standard Deviation 0.051901 ( Monthly 0.014983)
Option Price Based Discounts
AASP ( Finnerty)
2.60%
BSP
4.42%
LBP
6.70%
Option Models using Listed Security Data
capture only Discount for lack of liquidity
Listed security data volatility
based models capture liquidity
behavior only as the securities are
“marketable”
Comments on Option Models for
Discount for Lack Of Marketability
 Serve as a proxy
 Understand variables
 Use wisely
Questions?
Please do not hesitate to contact for any clarifications.
Ashok Bhardwaj Abbott Ph.D. MBA
Email abbott.ashok@gmail.com, Phone 304 692 1385
Thanks