Liquidity Discounts: Option Based Methods 1 Online Learning
Lecture Series Featured Presenters: Ashok Bhardwaj Abbott Michael
A. Gregory
Slide 2
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Slide 3
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Slide 4
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.
www.be.wvu.edu/faculty_staff/cv/ashok_abbott_cv.pdf
Slide 5
Michael A. Gregory is the Chief Manager of Michael Gregory
Consulting, LLC. This firm focuses on business valuation
consulting, issue resolution, and value added services related to
risk management. He is headquartered in Roseville, Minnesota. He
retired from the IRS in July 2011 as a Territory Manager who had
responsibilities for up to 23 states and was the Champion at the
IRS on issues such as the Discount for Lack of Marketability,
Reasonable Compensation, 409A, and Penalties on Appraisers. He is
publishing a book coming out in May entitled How to Work with the
IRS: Strategies for Attorneys, Accountants and Appraisers. He had
spoken extensively to the public while at the IRS. Now he offers
his services as a speaker on the topics from his new book to
professional organizations His focus area today in business
valuation is on the review of business valuation reports for
federal tax purposes, and consulting on issues related to conflict
management with the IRS on valuation and other related areas.
Having led various teams at the IRS on these topics he brings these
skills to assist the private sector. Michael Gregory is an AVA with
NACVA, an ASA with the American Society of Appraisers, and a
Qualified Neutral with the Minnesota Supreme Court. He also holds a
BS from Valparaiso University, a MS from the University of
Wisconsin Madison, and a MBA in Finance from DePaul University. You
can see more information about Michael Gregory and Michael Gregory
Consulting at www.mikegreg.com. www.mikegreg.com
Slide 6
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.
Slide 7
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.
Slide 8
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.
Slide 9
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.
Slide 10
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
Slide 11
Theory and Reality As liquidity declines Price offered for
immediate sale becomes lower than the price offered 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.
Slide 12
Level II Quotes Illustration of Cost of Liquidity SPDR S&P
500 ETF TR UNIT Asks Bids SHARESPRICESHARESPRICE 300137.15100136.95
600137.14100136.92 500137.11100136.90 100137.05500136.86
200137.04100136.85
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.
Slide 15
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.
Slide 16
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.
Slide 17
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)
Slide 18
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.
Slide 19
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.
Slide 20
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]) [i] David B. H. Chaffee III, Option
Pricing as a Proxy for Discount for Lack of Marketability in
Private Company ValuationsA Working Paper, Business Valuation
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).
Slide 21
Black Scholes Model History Application Six key variables Stock
price Strike price Risk free interest rate Expected option life
Interest rate Expected volatility
Slide 22
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
Slide 23
Black Scholes Put (Chaffee) BSP provides protection against
decline in value of the asset as 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.
Slide 24
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
Slide 25
Asian Average Price Put (Finnerty) AAP option provides a
partial coverage of the potential loss 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 at end of option
period. Starting Price $100, intermediate prices $120, $150, ending
Price $70. Average Price $110 AAP Payout $110-$70= $40.
Slide 26
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. May be appropriate when information is completely
shared between the buyer and the seller and neither is under any
compulsion to sell.
Slide 27
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.
Slide 28
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.
Slide 29
Converting Option Premiums to DLOL Option premium represents
the absolute difference between 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%.
Slide 30
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
Slide 31
Comments on Option Models for Discount for Lack Of
Marketability Serve as a proxy Understand variables Use wisely An
indicator of DLOM but does not consider quality factors See the
Discount for Lack of Marketability Job Aid for IRS Professionals at
www.irs.gov
Slide 32
Questions? Please do not hesitate to contact for any
clarifications. Ashok Bhardwaj Abbott Ph.D. MBA Email
[email protected], Phone 304 692 [email protected]
Michael A. Gregory AVA, ASA, MBA, Qualified Neutral with Minnesota
Supreme Court Email [email protected], Phone
[email protected] Thanks
Slide 33
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Sponsors. State boards of accountancy have final authority on the
acceptance of individual courses for CPE credit. Complaints
regarding registered sponsors may be submitted through its web
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