“Valuation and Financial Forensics – Educate, Communicate, Preserve” NACVA and IBA’s Annual Consultants’ Conference Discount for Lack of Marketability (Liquidity) Models: A Comparative Analysis Mainstream Track and Ashok Abbott, PhD present May 27-30, 2009 Boston, MA
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
“Valuation and Financial Forensics – Educate, Communicate, Preserve”
“Valuation and Financial Forensics – Educate, Communicate, Preserve”
NACVA and IBA’s Annual Consultants’ ConferenceNACVA and IBA’s Annual Consultants’ Conference
Discount for Lack of Marketability (Liquidity) Models: A Comparative Analysis
Discount for Lack of Marketability (Liquidity) Models: A Comparative Analysis
Mainstream Track
and
Ashok Abbott, PhD present
Mainstream Track
and
Ashok Abbott, PhD present
May 27-30, 2009Boston, MA
May 27-30, 2009Boston, MA
Please set pagers, cell phones, etc. on Please set pagers, cell phones, etc. on vibrate modevibrate mode or turn them off. or turn them off.
Please complete and hand in the Please complete and hand in the Presenter EvaluationPresenter Evaluation forms. forms.
Don’t forget to complete your CPE Don’t forget to complete your CPE Attestation Form.Attestation Form. Add your NACVA# Add your NACVA# (located on your name badge) and sign it. (located on your name badge) and sign it. Keep the white copy for your records. Turn Keep the white copy for your records. Turn in the yellow copy at the NACVA in the yellow copy at the NACVA Registration Desk.Registration Desk.
Please set pagers, cell phones, etc. on Please set pagers, cell phones, etc. on vibrate modevibrate mode or turn them off. or turn them off.
Please complete and hand in the Please complete and hand in the Presenter EvaluationPresenter Evaluation forms. forms.
Don’t forget to complete your CPE Don’t forget to complete your CPE Attestation Form.Attestation Form. Add your NACVA# Add your NACVA# (located on your name badge) and sign it. (located on your name badge) and sign it. Keep the white copy for your records. Turn Keep the white copy for your records. Turn in the yellow copy at the NACVA in the yellow copy at the NACVA Registration Desk.Registration Desk.
Discount for Lack of Marketability (Liquidity) Models: A Comparative Analysis
Discount for Lack of Marketability (Liquidity) Models: A Comparative Analysis
LN (RPRS) is natural logarithm of the relative price of restricted stock expressed in percentage terms [(p*/p) • 100].
LN (REV), the natural logarithm of the firm's revenues (in millions);
LN (RBRT), the natural logarithm of the restricted block relative to total common stock (in per cent);
DERN, a dummy variable equal to one if the firm's earnings are positive and equal to zero otherwise; and
DCUST, a dummy variable equal to one if there is a customer relationship between the investor and the firm issuing the restricted stock and zero otherwise.
12
Bajaj ( 2001)
Discount = a + 0.40 x Fraction of Shares Issued -0.08 x Z-Score + 3.13 x Standard Deviation of Returns + b 4 x Registration Indicator.
Models Considering lack of diversification but assuming Marketability and Liquidity
Tabak Meulbroek
15
Tabak
DLOM= 1-exponent ( σs2 / σm
2)XRPXT Discount for lack of diversification RP is the equity risk premium T is the time to liquidation
16
Meulbroek DLOM= 1-(1/(1+R)n)
Where R is the product of the market risk premium multiplied by the difference between the asset’s beta and the ratio of standard deviation of returns for the asset and the market, a measure of incremental risk.
((σs / σm)- β)XRP
17
Models considering Delayed Liquidation as lack of Marketability
QMDM Stockdale
18
DCF Models QMDM /Stockdale
QMDM Framework The Expected Holding Period (HP) Expected Distribution Yield (D%) Expected Growth in Distributions (GD
%) Projected Terminal Value Stockdale Enhancements
19
Stockdale explicitly accommodates inherent
uncertainty in the estimated liquidation period.
Assumes a linear liquidation probability, the model is flexible enough to accommodate any selected probability distribution.
Allows for the starting point for the period of liquidation to be any time in future rather than the present time period
20
Time Volatility (Option) Models
Black Scholes Put (BSP) (Chaffee 1993) Average Price Asian Put (AAP) (Finnerty 2002) Look Back Put (LBP) (Longstaff 1995) (Abbott 2007)
21
BSP
Black Scholes Put (BSP) is a simple contract. It provides protection against any realized loss in value at maturity of the contract. (LOSS I) The minimum value any asset can reach is zero. Therefore, the maximum value payable under a BSP contract is the exercise price for the put.
22
BSP
P(T) = e-rT N(-d2)- N (-d1) Where d1= [(r+σ2/ 2) T]/ σT And d2 = d1- σT
The estimated BSP discount for lack of liquidity then becomes
P(T)/[1+P(T)]
23
BSP Basics
σ is the standard deviation for the returns computed for the same
d1= [Lognormal(S/K) + (r+σ2/ 2) T]/ σT
d2 = d1- σT And N(-d1) and N(-d2) are the Normal
cumulative distribution probabilities Setting S=K=1
24
Finnerty model :Asian Average Put
D(T) = V[ e rt N(r/ T +T / 2) –N (r/ T -T / 2)]
and 2 = σ2 T + Ln[2( e σ2 T - σ2 T -1)]
-2 Ln [e σ2 T -1]
25
Finnerty Model Discount
Once again setting V to 1, D(T) becomes
[ e rt N(r/ T +T / 2) –N (r/ T -T / 2)] and the corresponding discount for
lack of liquidity becomes D(T)/ 1+ D(T)
26
Look Back Put
F ( V,T) = V(2+ σ2 T/ 2) N(σ2T /2)
+ V ( σ2 T/2) e (-σ2T
/8) -V
27
Look back Put DISCOUNT
set V to 1, the LBP option premium becomes
F(T) = (2+ σ2 T/ 2) N( σ2 T /2) + (σ2 T/2) e (- σ2 T /8) -1
the corresponding LBP discount for lack of liquidity becomes
F(T)/ (2+ σ2 T/ 2) N( σ2 T /2) + (σ2 T/2) e (- σ2 T /8)
28
Estimated DLOL
Low Volatility (Annual σ 0.10-0.30),
Low Risk free rate (3%),
short duration (1 year)
29
Discounts ComparisonAnnual Standard Deviation BSP LBP AAP
0.1 2.56% 7.61% 4.00%
0.11 2.92% 8.33% 4.19%
0.12 3.27% 9.04% 4.38%
0.13 3.63% 9.75% 4.58%
0.14 3.98% 10.45% 4.77%
0.15 4.33% 11.14% 4.97%
0.16 4.68% 11.83% 5.17%
0.17 5.03% 12.51% 5.37%
0.18 5.38% 13.19% 5.56%
0.19 5.72% 13.86% 5.76%
0.2 6.07% 14.52% 5.96%
0.21 6.41% 15.17% 6.16%
0.22 6.74% 15.82% 6.35%
0.23 7.08% 16.47% 6.55%
0.24 7.41% 17.10% 6.75%
0.25 7.74% 17.74% 6.94%
0.26 8.07% 18.36% 7.14%
0.27 8.40% 18.98% 7.33%
0.28 8.72% 19.60% 7.52%
0.29 9.04% 20.20% 7.71%
0.3 9.36% 20.81% 7.90%
30
Estimated DLOL
Mid range Volatility (Annual σ . 0.40-0.60),
Medium Risk free rate (6%), Medium duration (5 year)
31
Annual Standard Deviation BSP LBP AAP
0.4 15.72% 48.38% 33.79%
0.41 16.18% 49.16% 34.22%
0.42 16.64% 49.92% 34.64%
0.43 17.09% 50.68% 35.06%
0.44 17.53% 51.41% 35.46%
0.45 17.97% 52.14% 35.86%
0.46 18.40% 52.85% 36.25%
0.47 18.83% 53.55% 36.63%
0.48 19.25% 54.23% 37.00%
0.49 19.66% 54.90% 37.36%
0.5 20.07% 55.56% 37.70%
0.51 20.47% 56.21% 38.04%
0.52 20.87% 56.84% 38.37%
0.53 21.26% 57.47% 38.69%
0.54 21.64% 58.08% 39.00%
0.55 22.02% 58.68% 39.30%
0.56 22.39% 59.27% 39.58%
0.57 22.76% 59.85% 39.86%
0.58 23.12% 60.42% 40.13%
0.59 23.47% 60.97% 40.39%
0.6 23.82% 61.52% 40.64%
32
Estimated DLOL
for High Volatility (Annual σ . 0.70-0.90),
High Risk free rate (9%), Long duration (10 year)
33
Annual Standard Deviation BSP LBP AAP
0.7 19.56% 76.91% 59.57%
0.71 19.81% 77.30% 59.57%
0.72 20.07% 77.69% 59.58%
0.73 20.31% 78.06% 59.59%
0.74 20.55% 78.43% 59.59%
0.75 20.79% 78.79% 59.60%
0.76 21.02% 79.14% 59.60%
0.77 21.24% 79.48% 59.60%
0.78 21.46% 79.81% 59.61%
0.79 21.68% 80.14% 59.61%
0.8 21.89% 80.46% 59.61%
0.81 22.09% 80.78% 59.62%
0.82 22.29% 81.08% 59.62%
0.83 22.49% 81.38% 59.62%
0.84 22.68% 81.68% 59.62%
0.85 22.86% 81.97% 59.62%
0.86 23.04% 82.25% 59.63%
0.87 23.22% 82.52% 59.63%
0.88 23.39% 82.79% 59.63%
0.89 23.56% 83.06% 59.63%
0.9 23.72% 83.32% 59.63%
Thank you for joining us.Thank you for joining us.
Please remember to turn in your Please remember to turn in your evaluation forms.evaluation forms.
Plan to join us next year for our Plan to join us next year for our Seventeenth Annual Conference.Seventeenth Annual Conference.