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• Valuation Study Group• London UK• June 2012 Meetings

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.

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 LiquidityMarketability 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 EffectLiquidity 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 RealityAs 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>BidLevel II quotes illustrate cost of liquidity.

Quoted bid ask spread widens as offer lot size increases.

Blockage and Delayed ExecutionLiquidity 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 LossLoss 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 LossPotentially, 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 LiquiditySimilar 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 priceDLOL= 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])

[i] David B. H. Chaffee III, ‘‘Option Pricing as a Proxy for Discount for Lack of Marketability in Private Company Valuations—A 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).

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 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 OptionsPayout is flexible based on the path taken

by the asset prices during the option period.

Two Forms commonly used-

Asian Average Price PutLook Back Put

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 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 DLOLOption 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%.

Option Models Base Data Stock Symbol VLGEAValuation date February 2010Market Value 173.225 MillionShares Outstanding 6,999,000Monthly 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 8800Average 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 QuartersVolatility of daily log Returns measured as

Annualized Standard Deviation 0.051901 ( Monthly 0.014983)

Option Price Based DiscountsAASP ( 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 volatilitybased models capture liquidity behavior only as the securities are “marketable”

Comments on Option Models for Discount for Lack Of MarketabilityServe as a proxyUnderstand variables Use wisely

Questions?Please do not hesitate to contact for any

clarifications.Ashok Bhardwaj Abbott Ph.D. MBAEmail abbott.ashok@gmail.com, Phone

304 692 1385

Thanks