- 1 - © 2006 lifecycle returns, inc. all rights reserved sources: financial statements and price...

- 1 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform

- 1 -© 2006 LifeCycle Returns, Inc. All Rights Reserved

AGENDAAGENDA History, Application, and Examples of Value Charts Including Analysts’ EPS to Produce Forecasted Valuations Tracking Errors as Measures of Model Accuracy Traditional Multi-Period and Capitalization DCF Valuations The Cash Economic Return (CER) Fade Concept – Regression toward the Mean

– Reflects empirical basis for competitive reaction and its likely impact on future cash flows of the firm

Option Pricing Functions to Describe Fade Capitalization DCF Valuations Value Charts and Summaries of Tracking Errors to Measure the Accuracy of Multiple Models Back Tests on Predictive Capability of Model as Price Migrates toward Intrinsic Value over

several Quarters – Consistent with contrarian strategies related to behavior finance psychological herd

tendencies Stable Paretian versus Gaussian Normal Distributions of Price Change and % Under (Over)

Valuation– Application of alpha peakedness parameter of the Stable Paretian Distribution as a risk

measure to assure proper diversification Provide the author your e-mail address to receive a link to the LCRT web site for this

presentation and other material or e-mail [email protected]



PRESENTATION CONCLUSIONSPRESENTATION CONCLUSIONS

Suggests two empirical research measurement methodologies to improve DCF models

– Value Charts with tracking errors for individual companies (based on capitalization methods using only historical information with minimal analyst intervention)

– Cumulative Tracking errors for large sample of companies Fading Cash Economic Returns provides a conceptual and

empirical basis for dealing effectively with competitive reaction and its likely impact on the future cash flows of the firm

Back tests suggest excess investment returns result from prices migrating toward intrinsic values over several quarters

– More accurate models are more predictive The Stable Paretian Alpha Peakedness parameter provides one

replacement risk measure for traditional mean variance CAPM beta, as it identifies regions of the universe where the tails of the distribution become so fat that the mean becomes indeterminate



HISTORY OF ‘VALUE CHARTS’HISTORY OF ‘VALUE CHARTS’

Value Line began employing “Value Charts” in the 1930’s to display its capitalization of cash flow (income + depreciation) as their valuation model

In 1984, the author suggested Callard employ this visual technique to show CMA valuation model results

Subsequently, CMA Offshoots - HOLT Planning, HOLT Value, The Boston Consulting Group, Applied Financial Group, CSFB HOLT, Ativo, Lafferty, and LCRT illustrated their models with “Value Charts”

In 2001, the author began illustrating results of multiple models with “Value Charts”

White Bars depict high / low trading range of fiscal year prices

Small hollow circle represent closing price at Fiscal Year + 3 Months

Red line connects single period estimates produced by the valuation model each year

Takeaway … The ‘Value Chart’ represents a powerful research tool for illustrating the historical tracking of valuation models against actual price data.

Robert Shiller (1981) compares prices for the market to an intrinsic value derived from a dividend discount model. He observes that prices are much more volatile than the intrinsic values, as we discern above for this individual firm.



INCLUDING ANALYSTS’ EPS ESTIMATES EXTENDS

THE ‘VALUE LINE’ INTO THE FUTURE INCLUDING ANALYSTS’ EPS ESTIMATES EXTENDS

THE ‘VALUE LINE’ INTO THE FUTURE

Assuming constant non-earnings margin and capital turnover extends the ‘Value Line’ into the Future

Decrease in EPS for current 2005 before rebounding in 2006 translates to a decline in intrinsic value in 2005

Takeaway … History provides a Baseline to judge a Valuation Model, before extending its results into the future. More accurate models help pick under valued stocks for investment.

Thanks to Tom Copeland for suggesting that this methodology effectively separates the migration of price toward intrinsic value based purely on history from the migration of price toward analysts’ forecasts.



THE LCRT RESEARCH MODEL TRACKS BIOTECH START-UPS THE LCRT RESEARCH MODEL TRACKS BIOTECH START-UPS WHEN NO OTHER MODELS CALCULATE A SENSIBLE VALUEWHEN NO OTHER MODELS CALCULATE A SENSIBLE VALUE

THE LCRT RESEARCH MODEL TRACKS BIOTECH START-UPS THE LCRT RESEARCH MODEL TRACKS BIOTECH START-UPS WHEN NO OTHER MODELS CALCULATE A SENSIBLE VALUEWHEN NO OTHER MODELS CALCULATE A SENSIBLE VALUE

Takeaway … Start-Ups represent one class of firms where traditional models require a multi-year forecast, but option pricing suggests an alternative approach, illustrated later.



DATA FROM VALUE CHARTS PROVIDE TRACKING ERRORS TO MEASURE ‘GOODNESS OF FIT’ OF

THE MODEL TO ACTUAL PRICES

DATA FROM VALUE CHARTS PROVIDE TRACKING ERRORS TO MEASURE ‘GOODNESS OF FIT’ OF

THE MODEL TO ACTUAL PRICES

Takeaway … Tracking Errors provide a quantitative way to compare the accuracy of several models and the accuracy of a model applied to one firm’s common stock.



TRADITIONAL DCF RESIDES AT THE VERY ‘HEART OF VALUATION’

TRADITIONAL DCF RESIDES AT THE VERY ‘HEART OF VALUATION’

Different analysts using DCF can honestly arrive at divergent company values using the same set of information

Most appraisers and analysts employ a multi-period model

Analysts employ a Capitalization Method as the terminal value when the company reaches stability in its growth of revenues, earnings, and cash flow at a consistent rate (Gordon Growth Model represents one single state DCF)

Theoretically, both capitalization and multi-period models should return the same value, but frequently do not

Net Free cash flow contains well publicized faults – greatest risk is reliance on subjective analyst input on 20 or more assumptions (sales growth, margins, capital turns, capital structure, etc.)

Author suggests a baseline model, formed from ‘Value Charts’ as one empirical way to evaluate DCF output for reasonableness

A baseline value model uses historical financial information to determine a company’s value with minimal analyst intervention

Net Income

204,104

+ Depreciation +22,772

+ Working Capital Decreases +51,587

- Capital Expenditures -34,809

= Net Free Cash Flow 243,654

Takeaway … Very wide acceptance of DCF by practitioners may have produced complacency in modeling applications, failing to ask how empirical research may test to improve the model.



COMPARISON OF TRADITIONAL VALUATION TO OFFSHOOTS OF CALLARD, MADDEN (CMA) (1)


Selecting and applying public information for private company and business unit valuation represents accepted practice

Traditional appraisal valuations usually employ industry as the primary screen for comparables

In contrast, Offshoots of CMA choose companies based on economics alone– Cash Flow Return on Investment (CFROI®) or Cash Economic Return (CER)– Sustainable Growth Rate– Size– Leverage– Asset Life and Age– Inflation Effects– Asset Mix between depreciating and non-depreciation assets

The CFROI and CER build on the work of Solomon, Salaman, Ijiri, and Madden to create an annual economic return measure for the whole company (explained later)

– Eliminates cash, accounting, and inflation distortions to traditional measures on depreciated book assets

– Reflects the cash investment into the company’s operations from the investor’s point of view, adjusted for units of common purchasing power

– Equals the real internal rate of return of all the projects in place CFROI® is a registered Trademark of CSFB

HOLT





Offshoots of CMA employ a capitalization model produced from company economic returns for only a single period instead of using several future periods, as traditionally done in multi period models

– Substitute ‘fade’ in place of discrete forecast periods to obtain normalized structure and cash flow over time

– Of great research significance, employing a single period model enables extensive empirical testing of several models applied to thousands of companies over a decade

– Fade represents the single most important tool that permits the analyst to utilize a single period model rather than a multi period forecasting model

– As a mathematical measure of competitive regression toward the mean, fade adjusts abnormal economic returns, positive or negative, to a normalized return over time



ADVANCED LCRT RESEARCH:REPRESENTATIVE CASH ECONOMIC RETURN

FADE PATTERNS

ADVANCED LCRT RESEARCH:REPRESENTATIVE CASH ECONOMIC RETURN

FADE PATTERNS

(80)

(60)

(40)

(20)

0

20

40

60

80

0 1 2 3 4 5 6 7 8 9 10

Year

Cas

h E

con

om

ic R

etu

rn

Small High

Large High

Small Low

Large Low

Takeaway … Fade based on proprietary uniform empirical adjustments to reflect market expectations so 50% of firms are under valued and 50% are over valued in every region of the universe.



NUMERIC EXAMPLE ILLUSTRATES THE FADE CONCEPT APPLIED TO ASSET GROWTH RATESNUMERIC EXAMPLE ILLUSTRATES THE FADE

CONCEPT APPLIED TO ASSET GROWTH RATES

In 2004, the company employs constant dollar gross investment of $21,779 Million

Its sustainable growth rate is 5.67%

Fading the 5.67% growth rate at an 80% rate toward the 3.0% economic growth rate produces a 3.54% growth rate

3.54 = 0.8 * (5.67 – 3.00) + 3.00 Applying the 3.54% to 21,770

investment produces a $22,549 2005 investment

Constant

Future Dollar

Growth Gross

Year Rate Investment

2004 5.67 21,779

2005 3.54 22,549

Takeaway … The fade pattern represents market expected growth rates from sustainable growth. It also represents the single most important procedure to explain how a capitalized intrinsic value model can replace an analyst multi-period model.



NUMERIC EXAMPLE ILLUSTRATES THE FADE CONCEPT APPLIED TO CASH ECONOMIC RETURN (CER)

NUMERIC EXAMPLE ILLUSTRATES THE FADE CONCEPT APPLIED TO CASH ECONOMIC RETURN (CER)

The company achieves a 20.17% Cash Economic Return in 2004

Fading the 20.17% CER at a 50% rate to an empirically derived 16.56% fade-to produces a 16.56% CER in 2005

16.56 = 0.5 * (20.17 – 12.57) + 12.57

Applying the 16.56% to the 22,549 2000 investment produces 5,977 in gross cash flow (net income + depreciation)

Constant Dollar Gross Cash Investment Increases 770

ConstantConstant

Dollar Cash Dollar

Gross Economic Gross

Cash Return Cash

Year Investment (CER) Flow

2004 21,779 20.17 6,462

2005 22,549 16.56 5,977

Increase 770

Takeaway … The fade pattern represents market expected Cash Economic Returns from competitive pressures. It also represents the single most important procedure to explain how a capitalized intrinsic value model can replace an analyst multi-period model.



CMA OFFSHOOTS EMPLOY DIFFERENT DRIVERS TO PRODUCE

VALUATION

CMA OFFSHOOTS EMPLOY DIFFERENT DRIVERS TO PRODUCE

VALUATION Instead of traditional Sales

growth rates, margins and capital turns as drivers, CMA Offshoots employ fading growth rates and CER to produce net free cash flows

Subtracting replacement and growth investments form $3,134 in net constant dollar cash flows

Gross Cash Flows+5,977

Replacement Investments -1,973

Growth Investments - 770

Constant Dollar Net

Free Cash Flow+3,134

Takeaway … CMA Offshoots ultimately produce Net Free Cash Flow, but unlike traditional DCF models it is constant dollar and derived from CFROI or CER and gross asset growth rates as value drivers instead of the traditional sales growth rates, margins, and capital turns.



INTRINSIC VALUES PER SHARE RESULT FROM TRADITIONAL

CALCULATIONS

INTRINSIC VALUES PER SHARE RESULT FROM TRADITIONAL

CALCULATIONS Present Value of

constant dollar net cash flows forms the 80,516 enterprise value

Adding non-operating cash, subtracting debt and dividing by 2,911 shares outstanding produces the 28.93 spot intrinsic value per share

Present Value of Cash Flows+80,516

Cash Less Debt + 3,687

Equity Intrinsic Value+84,203

Number of Shares Outstanding 2,911

Equity Intrinsic Value Per Share 28.93



CMA OFFSHOOTS EMPLOY CFROI® OR CER AND GROSS ASSET GROWTH RATES AS

PRIMARY VALUE DRIVERS

CMA OFFSHOOTS EMPLOY CFROI® OR CER AND GROSS ASSET GROWTH RATES AS

PRIMARY VALUE DRIVERS The top panel

compares CER to the discount rate for HPQ

The second panel compares gross asset growth rates to sustainable growth rates



Income $206

A: Eliminate Non-Operating Special Extraordinary Items After Tax 33

Items (-) Non-operating Expense After-Tax (16)

B: Translate to Cash Non-Cash Charges 333

C: Restate for Inflation Inflation Gain on Non-Fixed Assets 14

D: Eliminate Leverage After-Tax Interest (Debt and Operating Leases) 134 $781

$206 Rentals – Principal Payments 77 Current Dollar

Income E: Capitalize Expenses (-) Advertising and R & D After Tax (0) Gross Cash Flow

Assets Total Assets $5,825 Current Dollar

$5,825 A: Eliminate Non-Operating (-) Non-Operating Assets (137) Investor Gross

Items (-) Purchase Goodwill (1,531) Cash

Receivables Reserve 23 Investment

B: Translate to Cash Invest. LIFO Reserve 141 $5,704

Accumulated Depreciation 1,580

C: Restate for Inflation Inflation Adjustments to Land, Gross Plant and Deferred Taxes 249

D: Eliminate Leverage Gross Leased Property from Operating Leases 1,202

E: Capitalize Expenses Capitalized Advertising, R & D 0

F: Capital Owner Cash Invest. (-) Operating Non-Interest Bearing Liabilities (1,648)

CASH ECONOMIC RETURN EXAMPLE:ACCOUNTING TO CASH

SUPERVALU– 2001 ($Millions)

CASH ECONOMIC RETURN EXAMPLE:ACCOUNTING TO CASH

SUPERVALU– 2001 ($Millions)



CASH ECONOMIC RETURN EXAMPLE:CASH TO ECONOMICS SUPERVALU– 2001 ($ MILLIONS)

CASH ECONOMIC RETURN EXAMPLE:CASH TO ECONOMICS SUPERVALU– 2001 ($ MILLIONS)

Current Dollar Gross Cash Flow

$781Non-Depreciating

Asset Release

$727

($5,704)

Current Dollar Investor Gross

Cash Investment

Economic Life: 11.55 Years

Cash Economic Return - IRR: 9.09% Years IRR

11 8.62

12 9.48

11.55 9.09



CASH ECONOMIC RETURN REFLECTS THE AVERAGE INTERNAL RATE OF RETURN OF ALL

THE PROJECTS IN PLACE

CASH ECONOMIC RETURN REFLECTS THE AVERAGE INTERNAL RATE OF RETURN OF ALL

THE PROJECTS IN PLACE

Cash Economic Return

Existing Projects

Operating Net Income + Depreciation - Inflation Adjustments

Working Capital + Land

Net

Op

erat

ing

Ass

ets

+

Acc

um

ula

ted

Dep

reci

atio

n +

In

flat

ion

Ad

just

men

t



ADVANCED LCRT RESEARCH:CASH ECONOMIC RETURN FADE TO’S RELY ON

SMALL FIRM PUTAND MEDIUM SIZE STRADDLE FUNCTIONS

ADVANCED LCRT RESEARCH:CASH ECONOMIC RETURN FADE TO’S RELY ON

SMALL FIRM PUTAND MEDIUM SIZE STRADDLE FUNCTIONS

0

5

10

15

20

25

30

35

40

-100 -50 0 50 100 150 200

Beginning Cash Economic Return (CER)

Cas

h E

con

om

ic R

etu

rnF

ade-

To Largest

Medium

Smallest

Smallest Start-Up

Firms

Smallest Start-Up

Firms

Largest and Smallest FirmsLargest and Smallest Firms



ADVANCED LCRT RESEARCH:CASH ECONOMIC RETURN FADE RATES

RELY ON PUT FUNCTIONS

ADVANCED LCRT RESEARCH:CASH ECONOMIC RETURN FADE RATES

RELY ON PUT FUNCTIONS

0

20

40

60

80

100

-100 -50 0 50 100 150 200

Beginning Cash Economic Return (CER)

Cas

h E

con

om

ic R

etu

rnF

ade

Rat

es Smallest

Medium

Largest



LCRT ADVANCED RESEARCH:LCRT PLACES LEVERAGE RELATED RISK IN THE CASH FLOWS

INSTEAD OF THE DISCOUNT RATE IN ORDER TO EMPLOY A UNIFORM DISCOUNT RATE FOR ALL FIRMS IN THE SUPER SECTOR EACH YEAR

LCRT ADVANCED RESEARCH:LCRT PLACES LEVERAGE RELATED RISK IN THE CASH FLOWS

INSTEAD OF THE DISCOUNT RATE IN ORDER TO EMPLOY A UNIFORM DISCOUNT RATE FOR ALL FIRMS IN THE SUPER SECTOR EACH YEAR

01020304050607080

0 25 50 75 100 125 150

% Debt to Debt Capacity (PV of Cash Flows from Existing Assets)

% L

oss

of

Intr

insi

c V

alu

e

Smallest

Medium

Largest

Deadweight Financial Distress Costs of Higher Leverage

Deadweight Financial Distress Costs of Higher Leverage

[0,1] Function of Equity Put for ANY Debt

[0,1] Function of Equity Put for ANY Debt

Call FunctionsCall Functions



PRESENTATION WOULD NOT BE COMPLETE WITHOUT COMPARING THREE MODELS

PRESENTATION WOULD NOT BE COMPLETE WITHOUT COMPARING THREE MODELS

Net Free Cash Flow based on specifications by Dan Van Vleet (while at Willamette)

– Growing net free cash flows for ‘T’ years

– Net Free Cash Flow = income after taxes + depreciation & amortization – non-operating items after tax – normalized capital expenditures – working capital additions

– Terminal year’s cash flow capitalized by median industry CAPM nominal discount rate less nominal growth rate

LCRT Model

(18.0%)

8 X EBITDA

(30.7%)Net Free Cash Flow

(37.4%)

(Absolute Tracking Error)

Takeaways … A single company by no means represents a sufficient sample for empirical testing, but remains useful for portfolio investment decisions. Comparisons represent an objective empirical research process for testing models and improving DCF valuations for individual firms.



A CUMULATIVE TRACKING ERROR CHART SUMMARIZES

5,500 FIRMS FOR ABOUT 30,000 COMPANY-YEARS

A CUMULATIVE TRACKING ERROR CHART SUMMARIZES

5,500 FIRMS FOR ABOUT 30,000 COMPANY-YEARS

Median Absolute Tracking Errors

Net Free Cash Flow 166%

8 X EBITDA 86%

LCRT Model 51%

Results may help to explain why security analysts and portfolio managers prefer simple multiples over DCF net free cash flow valuation models

More accurate models may be more predictive

Cumulative % of Universe

LOG2 of % Absolute Model Tracking Error versus Actual Price –

Fiscal Year +3 Months to reflect Disclosure Lag

1994-2004 5,500 Industrials

LCRT Model

8 X EBITDA

Net Free Cash Flow

Takeaways … Comparisons represent an objective empirical research process for testing models and improving DCF valuations for large samples of firms.

More accurate models are up and to the left. Less accurate models are down and to the right.

- 24 -- 24 -© 2006 LifeCycle Returns, Inc. All Rights Reserved

LCRT BACKTESTSLCRT BACKTESTSLCRT BACKTESTSLCRT BACKTESTS

Annual

Quantile

Quarterly



THE LCRT RESEARCH DCF MODEL THE LCRT RESEARCH DCF MODEL SEPARATES “WINNERS” AND “LOSERS” SEPARATES “WINNERS” AND “LOSERS” CONSISTENTLY THROUGH MOST YEARSCONSISTENTLY THROUGH MOST YEARS

THE LCRT RESEARCH DCF MODEL THE LCRT RESEARCH DCF MODEL SEPARATES “WINNERS” AND “LOSERS” SEPARATES “WINNERS” AND “LOSERS” CONSISTENTLY THROUGH MOST YEARSCONSISTENTLY THROUGH MOST YEARS

Performance of Top and Bottom 20% Under (Over) Valued Firms

10

100

1000

10000

1995 1997 1999 2001 2003 2005

Total Shareholder Return Ending Year

Wea

lth

In

dex

Top 20%

Universe

Bottom 20%

Source: Industrial Firms 1994-2003, % Debt to Debt Capacity <

62%; Hemscott Data, LCRT Platform Calculations

Annual Rebalancing

Purchase at Fiscal Year + 3 Months

Sale at Fiscal Year + 15 Months

No Transaction or Price Pressure Costs Included

Equal Weighted

Past performance of a back test is no guarantee

of future performance.



LCRT’S RESEARCH DCF MODEL LCRT’S RESEARCH DCF MODEL SEPARATES THE UNIVERSE INTO SEPARATES THE UNIVERSE INTO

“WINNERS” & “LOSERS”“WINNERS” & “LOSERS”

LCRT’S RESEARCH DCF MODEL LCRT’S RESEARCH DCF MODEL SEPARATES THE UNIVERSE INTO SEPARATES THE UNIVERSE INTO

“WINNERS” & “LOSERS”“WINNERS” & “LOSERS”

-20

0

20

40

60

Total Shareholder

Return Relative to S&P 500 FY +3 to +15 Mos.

Universe Large Small

Company Size

Stock Performance Relative to Under (Over) Valuation at FY + 3 Mos.

Top 5%

Top 10%

Top 20%

2nd 20%

3rd 20%

4th 20%

Bottom 20%

Bottom 10%

Bottom 5%Source: Industrial Firms 1994-2003, % Debt to Debt Capacity <



Equal Weighted



Performance of Top and Bottom 20% Under (Over) Valued Firms @ FY + 3 Months

90

100110

120

130140

150

1 2 3 4 5

Total Shareholder Return Ending Quarter

Wealt

h I

nd

ex

Top 20%, N = 3,426

Universe, N = 17,095

Bottom 20%, N = 3,407

THE LCRT DCF RESEARCH MODEL SEPARATES “WINNERS” THE LCRT DCF RESEARCH MODEL SEPARATES “WINNERS” AND “LOSERS” CONSISTENTLY THROUGH QUARTERSAND “LOSERS” CONSISTENTLY THROUGH QUARTERS

FROM ANNUAL DATAFROM ANNUAL DATA

THE LCRT DCF RESEARCH MODEL SEPARATES “WINNERS” THE LCRT DCF RESEARCH MODEL SEPARATES “WINNERS” AND “LOSERS” CONSISTENTLY THROUGH QUARTERSAND “LOSERS” CONSISTENTLY THROUGH QUARTERS

FROM ANNUAL DATAFROM ANNUAL DATA

Source: Industrial Firms 1994-2003, % Debt to Debt Capacity <



Equal Weighted


Risk Metrics in Portfolio Risk Metrics in Portfolio ConstructionConstruction

Implications of Intrinsic Valuation ResearchImplications of Intrinsic Valuation Research

Risk Metrics in Portfolio Risk Metrics in Portfolio ConstructionConstruction

Implications of Intrinsic Valuation ResearchImplications of Intrinsic Valuation Research

By

Rawley Thomas

President

LifeCycle Returns, Inc.

January 6, 2006



INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION Our research into intrinsic equity valuations reveals the

existence of fat tailed distributions in % under/over valuations and therefore suggests that the use of traditional risk measures may need to be reassessed

Based on this empirical evidence, portfolio managers may wish to reconsider the use of CAPM Beta as a primary risk metric

The research suggests a possible replacement risk measure, displayed in the empirical research contained in the next slides



TWO TRADITIONAL PORTFOLIO CONSTRUCTION AND TWO TRADITIONAL PORTFOLIO CONSTRUCTION AND DIVERSIFICATION APPROACHES (PORTFOLIO RISK BELIEFS)DIVERSIFICATION APPROACHES (PORTFOLIO RISK BELIEFS)

TWO TRADITIONAL PORTFOLIO CONSTRUCTION AND TWO TRADITIONAL PORTFOLIO CONSTRUCTION AND DIVERSIFICATION APPROACHES (PORTFOLIO RISK BELIEFS)DIVERSIFICATION APPROACHES (PORTFOLIO RISK BELIEFS)

Sector Neutral

– Pick stocks so each sector is represented proportional to its market cap

– May overweight or underweight within constraints

Mean Variance (Markowitz)

– Pick stocks to target an average CAPM Beta for the portfolio

Takeaway … Are these approaches to portfolio risk adequate and appropriate when faced with fat tailed distributions?



ADVANCED PORTFOLIO CONSTRUCTION AND ADVANCED PORTFOLIO CONSTRUCTION AND DIVERSIFICATIONDIVERSIFICATION

ADVANCED PORTFOLIO CONSTRUCTION AND ADVANCED PORTFOLIO CONSTRUCTION AND DIVERSIFICATIONDIVERSIFICATION

Our observations are based on combining the Stable Paretian fat tailed distribution insights from Benoit Mandelbrot and J. Huston McCulloch with our research on the distributions of under/over valuation

– Benoit Mandelbrot, “The Variation of Certain Speculative Prices,” in Paul Cootner, The Random Character of Stock Market Prices, MIT Press, 1964, pp. 307-332.

– Benoit Mandelbrot and Richard L. Hudson, The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward, Basic Books, 2004.

– J. Huston McCulloch, “Simple Consistent Estimators of Stable Distribution Parameters,” Commun. Statist. – Simula., 15(4), 1986, pp. 1109-1136. (Programmed with the help of Paul Kettler and Terry Heiland)

– A literature search will produce articles and books by other authors in the field – Frank Fabozzi, Aleksander Janiski, Hartmut Jurgens, Christian Menn, Edward Ott, Heinz-Otto Peitgen, Edgar Peters, Svetlozar Rachev, Gennady Samorodnitsky, Dietmar Saupe, Tim Sauer, Jacky So, Dietrich Stoyan, Helga Stoyan, Murad Taqqu, Aleksander Weron, and James Yorke



STABLE PARETIAN DISTRIBUTION PROPERTIES (1)STABLE PARETIAN DISTRIBUTION PROPERTIES (1)STABLE PARETIAN DISTRIBUTION PROPERTIES (1)STABLE PARETIAN DISTRIBUTION PROPERTIES (1)

The Gaussian Normal Distribution (the “Bell Shaped Curve) is a special case of Stable Paretian where the alpha peakedness parameter = 2.00

The variance of distributions with alpha peakedness parameters < 2.00 is infinite

Most all value-performance data we analyzed showed fat tailed distributions with alpha peakedness parameters significantly less than 2.00 with infinite variances

Therefore, risk measures relying on variance, covariance, and standard deviation are indeterminate

– This includes CAPM Beta

Consequently, portfolio managers should consider replacement measures of portfolio risk and diversification



A FAT TAILED STABLE PARETIAN DISTRIBUTION DISPLAYS A FAT TAILED STABLE PARETIAN DISTRIBUTION DISPLAYS A BETTER VISUAL FIT TO TOTAL SHAREHOLDER RETURN A BETTER VISUAL FIT TO TOTAL SHAREHOLDER RETURN

DATA THAN DOES GAUSSIAN NORMALDATA THAN DOES GAUSSIAN NORMAL

A FAT TAILED STABLE PARETIAN DISTRIBUTION DISPLAYS A FAT TAILED STABLE PARETIAN DISTRIBUTION DISPLAYS A BETTER VISUAL FIT TO TOTAL SHAREHOLDER RETURN A BETTER VISUAL FIT TO TOTAL SHAREHOLDER RETURN

DATA THAN DOES GAUSSIAN NORMALDATA THAN DOES GAUSSIAN NORMAL

0

500

1000

1500

2000

2500

3000

-100 -4

0 20 80 140

200

260

320

380

Total Shareholder Returns

Nu

mb

er o

f C

om

pan

y -

Yea

rs

Actual

Normal

0

500

1000

1500

2000

2500

3000

-100 -4

0 20 80 140

200

260

320

380


Nu

mb

er o

f C

om

pan

y -

Yea

rs

Actual

Stable

Sources: 5.500 Industrial Firms 1994-2003, Total Shareholder Return (TSR) from FY+3 to +15 Months Relative to S&P 500, Hemscott Data, LCRT Platform Calculations, J. Huston McCulloch, “Simple Consistent Estimators of Stable Distribution Parameters,” Commun. Statist. – Simula., 15(4), 1986, pp. 1109-1136.

Takeaway … This suggests potential for the use of non-traditional measures of risk based on fat tailed Stable instead of Gaussian distributions



THE 1.39 ALPHA PEAKEDNESS STATISTICAL RESULTS THE 1.39 ALPHA PEAKEDNESS STATISTICAL RESULTS CONFIRM THE TSR DISTRIBUTION IS 41.4 STANDARD CONFIRM THE TSR DISTRIBUTION IS 41.4 STANDARD

ERRORS AWAY FROM GAUSSIAN NORMAL ERRORS AWAY FROM GAUSSIAN NORMAL (Where Alpha Peakedness = 2.00)(Where Alpha Peakedness = 2.00)

THE 1.39 ALPHA PEAKEDNESS STATISTICAL RESULTS THE 1.39 ALPHA PEAKEDNESS STATISTICAL RESULTS CONFIRM THE TSR DISTRIBUTION IS 41.4 STANDARD CONFIRM THE TSR DISTRIBUTION IS 41.4 STANDARD

ERRORS AWAY FROM GAUSSIAN NORMAL ERRORS AWAY FROM GAUSSIAN NORMAL (Where Alpha Peakedness = 2.00)(Where Alpha Peakedness = 2.00)

Results Value Std. Error t-Statistic

alpha ("peakedness") 1.39 0.01 41.41 Difference from 2.00

beta ("skewness") 0.83 0.03 32.27 Difference from 0.00

c ("dispersion") 33.02 0.01 4,205.23 Difference from 0.00

delta ("location" or "average") 24.12 0.05 449.93 Difference from 0.00

Sources: 5,500 Industrial Firms 1994-2003, Total Shareholder Return (TSR) from FY+3 to +15 Months Relative to S&P 500, Hemscott Data, LCRT Platform Calculations, J. Huston McCulloch, “Simple Consistent Estimators of

Stable Distribution Parameters,” Commun. Statist. – Simula., 15(4), 1986, pp. 1109-1136.

Takeaway … This suggests limitations in the appropriate use of CAPM Beta as a risk measure, since CAPM Beta relies on the existence of the indeterminate covariance statistic



A FAT TAILED STABLE PARETIAN DISTRIBUTION DISPLAYS A FAT TAILED STABLE PARETIAN DISTRIBUTION DISPLAYS A BETTER VISUAL FIT TO LN OF TOTAL SHAREHOLDER A BETTER VISUAL FIT TO LN OF TOTAL SHAREHOLDER

RETURN DATA THAN 2.00 FOR GAUSSIAN NORMALRETURN DATA THAN 2.00 FOR GAUSSIAN NORMAL

A FAT TAILED STABLE PARETIAN DISTRIBUTION DISPLAYS A FAT TAILED STABLE PARETIAN DISTRIBUTION DISPLAYS A BETTER VISUAL FIT TO LN OF TOTAL SHAREHOLDER A BETTER VISUAL FIT TO LN OF TOTAL SHAREHOLDER

RETURN DATA THAN 2.00 FOR GAUSSIAN NORMALRETURN DATA THAN 2.00 FOR GAUSSIAN NORMAL

0

500

1000

1500

2000

2500

3000

-4

-3.3

-2.6

-1.9

-1.2

-0.5 0.2

0.9

1.6

LN of Wealth Index from Total Shareholder Return Relative to S&P 500

Nu

mb

er o

f C

om

pan

y -

Yea

rs

Actual

Normal

0

500

1000

1500

2000

2500

3000

-4

-3.3

-2.6

-1.9

-1.2

-0.5 0.2

0.9

1.6

LN of Wealth Index from Total Shareholder Return Relative to S&P 500

Nu

mb

er o

f C

om

pan

y -

Yea

rs

Actual

Stable

Sources: 5,500 Industrial Firms 1994-2003, Total Shareholder Return (TSR) from FY+3 to +15 Months Relative to S&P 500, Hemscott Data, LCRT Platform Calculations, J. Huston McCulloch, “Simple Consistent Estimators of Stable Distribution Parameters,” Commun. Statist. – Simula., 15(4), 1986, pp. 1109-1136.

Takeaway … This suggests the LN transform or assuming a log normal distribution is inadequate to fix the fit problem.



THE 1.48 ALPHA PEAKEDNESS STATISTICAL RESULTS THE 1.48 ALPHA PEAKEDNESS STATISTICAL RESULTS CONFIRM THE LN OF TSR DISTRIBUTION IS 43.4 STANDARD CONFIRM THE LN OF TSR DISTRIBUTION IS 43.4 STANDARD

ERRORS AWAY FROM 2.00 FORERRORS AWAY FROM 2.00 FORGAUSSIAN NORMALGAUSSIAN NORMAL

THE 1.48 ALPHA PEAKEDNESS STATISTICAL RESULTS THE 1.48 ALPHA PEAKEDNESS STATISTICAL RESULTS CONFIRM THE LN OF TSR DISTRIBUTION IS 43.4 STANDARD CONFIRM THE LN OF TSR DISTRIBUTION IS 43.4 STANDARD

ERRORS AWAY FROM 2.00 FORERRORS AWAY FROM 2.00 FORGAUSSIAN NORMALGAUSSIAN NORMAL

Sources: 5,500 Industrial Firms 1994-2003, Total Shareholder Return (TSR) from FY+3 to +15 Months Relative to S&P 500, Hemscott Data, LCRT Platform Calculations, J. Huston McCulloch, “Simple Consistent Estimators of Stable Distribution Parameters,” Commun. Statist. – Simula.,

15(4), 1986, pp. 1109-1136.

Results Value Std. Error t-Statistic


beta ("skewness") -0.31 0.02 -17.55 Difference from 0.00

c ("dispersion") 0.39 0.01 50.60 Difference from 0.00

delta ("location" or "average") -0.16 0.02 -7.32 Difference from 0.00

Takeaway … again suggesting the limitations in the use of CAPM Beta as a risk measure



THE % UNDER/OVER VALUATION OF OUR DCF “RESEARCH THE % UNDER/OVER VALUATION OF OUR DCF “RESEARCH MODEL” ALSO DISPLAYS STABLE PARETIAN DISTRIBUTION MODEL” ALSO DISPLAYS STABLE PARETIAN DISTRIBUTION

CHARACTERISTICSCHARACTERISTICS

THE % UNDER/OVER VALUATION OF OUR DCF “RESEARCH THE % UNDER/OVER VALUATION OF OUR DCF “RESEARCH MODEL” ALSO DISPLAYS STABLE PARETIAN DISTRIBUTION MODEL” ALSO DISPLAYS STABLE PARETIAN DISTRIBUTION

CHARACTERISTICSCHARACTERISTICS

0

200

400

600

800

1000

1200

1400

1600

-100 -30 40 110

180

250

320

390

460

LCRT Research Model % Under (Over) Valuation

Nu

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Yea

rs

Actual

Stable

The 1.33 alpha peakedness parameter is 36.9 standard errors away from the 2.00 value for a Gaussian Normal distribution

The distribution displayed covers industrial firms with % debt to debt capacity (PV cash flows from existing assets) < 75%


Results ValueStd.

Error t-Statistic





Takeaway … you should consider employing different risk measures if you are using over/under intrinsic value as an investment decision tool



STABLE PARETIAN DISTRIBUTION PROPERTIES (2)STABLE PARETIAN DISTRIBUTION PROPERTIES (2)STABLE PARETIAN DISTRIBUTION PROPERTIES (2)STABLE PARETIAN DISTRIBUTION PROPERTIES (2)

For alpha peakedness parameters < 2.00, the variance is infinite As the alpha peakedness parameter approaches 1.00 (A Cauchy Distribution,

pronounced Kōō – Shēē), the mean becomes infinite Consequently, we have no confidence in calculating the mean as the alpha

peakedness parameter approaches 1.00 We hypothesize that distributions with tails so fat that the mean becomes

indeterminate are very risky, where effective diversification becomes impossible

The Stable Paretian alpha peakedness parameter may become a replacement measure for portfolio risk and effective diversification to replace traditional measures

– A new measure of portfolio risk is also necessary to replace traditional CAPM cost of capital estimates as our research model places all the “risk” in the certainty equivalent cash flows and therefore employs a single real discount rate for the entire super sector each year



FOR HIGH DEBT FIRMS, THE DISTRIBUTION BECOMES CLOSE TO FOR HIGH DEBT FIRMS, THE DISTRIBUTION BECOMES CLOSE TO CAUCHY, WHERE THE MEAN BECOMES INDETERMINATE AND CAUCHY, WHERE THE MEAN BECOMES INDETERMINATE AND

DIVERSIFICATION BECOMES PROBLEMATIC DIVERSIFICATION BECOMES PROBLEMATIC – INVEST IN THE DEBT OR THE EQUITY(?)– INVEST IN THE DEBT OR THE EQUITY(?)

FOR HIGH DEBT FIRMS, THE DISTRIBUTION BECOMES CLOSE TO FOR HIGH DEBT FIRMS, THE DISTRIBUTION BECOMES CLOSE TO CAUCHY, WHERE THE MEAN BECOMES INDETERMINATE AND CAUCHY, WHERE THE MEAN BECOMES INDETERMINATE AND

DIVERSIFICATION BECOMES PROBLEMATIC DIVERSIFICATION BECOMES PROBLEMATIC – INVEST IN THE DEBT OR THE EQUITY(?)– INVEST IN THE DEBT OR THE EQUITY(?)

0

50

100

150

200

250

-300

-200

-100 0

100

200

300

400

500

LCRT Research Model % Under (Over) Valuation

Nu

mb

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pan

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Yea

rs

Actual

Stable

The distribution displayed covers industrial firms with % debt to debt capacity (PV cash flows from existing assets) > 75%

The 1.07 alpha peakedness parameter is only 1.91 standard errors away from the 1.00 value for a Cauchy distribution with infinite mean

Sources: From 5,500 Industrial Firms 1994-2003, Total Shareholder Return (TSR) from FY+3 to +15 Months Relative to S&P 500, Hemscott Data, LCRT Platform Calculations, J. Huston McCulloch, “Simple Consistent Estimators of Stable Distribution Parameters,” Commun. Statist. – Simula., 15(4), 1986, pp. 1109-1136.

Results ValueStd.

Error t-Statistic

alpha ("peakedness") 1.07 0.03 -1.91 Difference from 1.00



delta ("location" or "average") 538.21 #N/A #N/A Difference from 0.00

To assure calculation in all regions of the universe, the % under (over) valuation statistic is normalized by the stock price, which, unlike the intrinsic value, is always greater than zero.

% under (over) valuation = 100% * (intrinsic value – price) / price.

Regions < -100% probably represent firms where debt trades at a discount from par.



THE TOP QUINTILE (20%) OF UNDER VALUED FIRMS SHOW THE TOP QUINTILE (20%) OF UNDER VALUED FIRMS SHOW A 34.3% MEAN RELATIVE SHAREHOLDER RETURN AND A 34.3% MEAN RELATIVE SHAREHOLDER RETURN AND

A DETERMINATE 1.38 ALPHA PEAKEDNESSA DETERMINATE 1.38 ALPHA PEAKEDNESS

THE TOP QUINTILE (20%) OF UNDER VALUED FIRMS SHOW THE TOP QUINTILE (20%) OF UNDER VALUED FIRMS SHOW A 34.3% MEAN RELATIVE SHAREHOLDER RETURN AND A 34.3% MEAN RELATIVE SHAREHOLDER RETURN AND

A DETERMINATE 1.38 ALPHA PEAKEDNESSA DETERMINATE 1.38 ALPHA PEAKEDNESS

0

50

100

150

200

250

300

350

-100 0 100 200 300 400 500


Nu

mb

er o

f C

om

pan

y -

Yea

rs

Actual

Stable

The distribution displayed covers industrial firms with % debt to debt capacity (PV cash flows from existing assets) < 75%

The 1.38 alpha peakedness parameter is 8.73 standard errors away from the 1.00 value for a Cauchy distribution

Sources: From 5,500 Industrial Firms 1994-2003, Total Shareholder Return (TSR) from FY+3 to +15 Months Relative to S&P 500, Hemscott Data, LCRT Platform Calculations, J. Huston McCulloch, “Simple Consistent Estimators of Stable Distribution Parameters,” Commun. Statist. – Simula., 15(4), 1986, pp. 1109-1136.

Mean = 34.3

Results ValueStd.

Error t-Statistic





Takeaway… This suggests that in this area of the universe, diversification can be used to achieve mean performance



0

10

20

30

40

50

60

70

80

90

100

-100 150 400 650 900


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pan

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Yea

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Actual

Stable

THE TOP 5% OF UNDER VALUED SMALL FIRMS SHOW A THE TOP 5% OF UNDER VALUED SMALL FIRMS SHOW A 61.8% MEAN RELATIVE SHAREHOLDER RETURN BUT AN 61.8% MEAN RELATIVE SHAREHOLDER RETURN BUT AN

INDETERMINATE 1.20 ALPHA PEAKEDNESS, NOT INDETERMINATE 1.20 ALPHA PEAKEDNESS, NOT SIGNIFICANTLY DIFFERENT FROM CAUCHY 1.00SIGNIFICANTLY DIFFERENT FROM CAUCHY 1.00

THE TOP 5% OF UNDER VALUED SMALL FIRMS SHOW A THE TOP 5% OF UNDER VALUED SMALL FIRMS SHOW A 61.8% MEAN RELATIVE SHAREHOLDER RETURN BUT AN 61.8% MEAN RELATIVE SHAREHOLDER RETURN BUT AN

INDETERMINATE 1.20 ALPHA PEAKEDNESS, NOT INDETERMINATE 1.20 ALPHA PEAKEDNESS, NOT SIGNIFICANTLY DIFFERENT FROM CAUCHY 1.00SIGNIFICANTLY DIFFERENT FROM CAUCHY 1.00

The “risk” of one or more torpedo stocks is too great compared to large gains of a few stocks

Sources: 529 Small Industrial Firms 1994-2003, C$GI < 100, Total Shareholder Return (TSR) from FY+3 to +15 Months Relative to S&P 500, Hemscott Data, LCRT Platform Calculations, J. Huston McCulloch, “Simple Consistent Estimators of Stable Distribution Parameters,” Commun. Statist. – Simula., 15(4), 1986, pp. 1109-1136.

Mean = 61.8

Results ValueStd.

Error t-Statistic





Takeaway … suggesting that in this area of the universe, diversification can’t be used to achieve mean performance

Traditional dispersion

risk measures

of standard deviation

and CAPM Beta don’t

pick up this effect



THE CASH ECONOMIC RETURN FUNDAMENTAL DRIVER OF THESE DCF THE CASH ECONOMIC RETURN FUNDAMENTAL DRIVER OF THESE DCF INTRINSIC VALUATIONS ALSO FOLLOWS A STABLE PARETIAN INTRINSIC VALUATIONS ALSO FOLLOWS A STABLE PARETIAN

DISTRIBUTION WITH TAILS FATTER THAN CAUCHY OF 1.00 ALPHA DISTRIBUTION WITH TAILS FATTER THAN CAUCHY OF 1.00 ALPHA PEAKEDNESS PARAMETERPEAKEDNESS PARAMETER

THE CASH ECONOMIC RETURN FUNDAMENTAL DRIVER OF THESE DCF THE CASH ECONOMIC RETURN FUNDAMENTAL DRIVER OF THESE DCF INTRINSIC VALUATIONS ALSO FOLLOWS A STABLE PARETIAN INTRINSIC VALUATIONS ALSO FOLLOWS A STABLE PARETIAN

DISTRIBUTION WITH TAILS FATTER THAN CAUCHY OF 1.00 ALPHA DISTRIBUTION WITH TAILS FATTER THAN CAUCHY OF 1.00 ALPHA PEAKEDNESS PARAMETERPEAKEDNESS PARAMETER

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

-100 -7

5-5

0-2

5 0 25 50 75 100

Cash Economic Return

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Actual

Normal

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

-100 -7

5-5

0-2

5 0 25 50 75 100

Cash Economic Returns

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Stable


Results ValueStd.

Error t-Statistic


beta ("skewness") -0.37 0.01 -25.81 Difference from 0.00



The LCRT approximation procedure divides the Stable Paretian intervals

into 128 pieces (limited by Excel’s 256 columns), which is not sufficient

enough to model the tails accurately for distributions fatter than Cauchy.

Takeaway …A lot of “risk” exists in estimating future changes in the Cash Economic Return of selected stocks.



CONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONS

Our research into intrinsic valuation reveals the existence of fat tailed distributions in % under/over valuations and therefore suggests that traditional measures of risk may need re-evaluation

Based on this empirical evidence, portfolio managers may wish to reconsider the use of CAPM Beta as a primary risk measure

The research suggests the alpha peakedness parameter of the Stable Paretian distribution as a valid replacement risk measure– Assures effective portfolio diversification with fat tailed

distributions– Our valuation platform includes the data necessary to

measure this form of risk and % under/over valuation


LCRT BACKTESTS ON FIRMS LCRT BACKTESTS ON FIRMS ABOVE $5 PER SHAREABOVE $5 PER SHARE

LCRT BACKTESTS ON FIRMS LCRT BACKTESTS ON FIRMS ABOVE $5 PER SHAREABOVE $5 PER SHARE

By

Rawley Thomas

President of LifeCycle Returns (LCRT)

January 31, 2006



INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION

A sophisticated portfolio manager client asked LCRT to extend our back tests to include only companies with stock prices greater than $5 per share at Fiscal Year + 3 Months– Excludes firms where borrowing stock to short is

restricted

– Excludes firms where some institutions decline to trade

LCRT extends the tests to include effects of– Longer holding periods for quarters 5-13

– Screening on signed model tracking error



THE LCRT RESEARCH DCF MODEL SEPARATES “WINNERS” AND THE LCRT RESEARCH DCF MODEL SEPARATES “WINNERS” AND “LOSERS” CONSISTENTLY THROUGH MOST YEARS BY A FACTOR “LOSERS” CONSISTENTLY THROUGH MOST YEARS BY A FACTOR

OF 4 (= 200 / 50) OVER 9 YEARSOF 4 (= 200 / 50) OVER 9 YEARS

THE LCRT RESEARCH DCF MODEL SEPARATES “WINNERS” AND THE LCRT RESEARCH DCF MODEL SEPARATES “WINNERS” AND “LOSERS” CONSISTENTLY THROUGH MOST YEARS BY A FACTOR “LOSERS” CONSISTENTLY THROUGH MOST YEARS BY A FACTOR

OF 4 (= 200 / 50) OVER 9 YEARSOF 4 (= 200 / 50) OVER 9 YEARS

Performance of Top and Bottom 10% Under (Over) Valued Firms

0

50

100

150

200

250

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Total Shareholder Return Ending Year

Wea

lth

In

dex

Top 10%

Universe

Bottom 10%

Source: Industrial Firms 1994-2003, % Debt to Debt Capacity < 83%; Prices > $5 Per Share; Hemscott Data, LCRT Platform Calculations; Annual Rebalancing; Purchase at Fiscal Year + 3 Months; Sale at Fiscal Year + 15 Months; No Transaction or Price Pressure Costs Included; Equal Weighted

Takeaway … suggests purchasing under valued stocks outperforms the universe.

Past performance of a back test is no guarantee

of future performance.



THE SPREAD BETWEEN THE TOP AND BOTTOM DECILES OF THE SPREAD BETWEEN THE TOP AND BOTTOM DECILES OF LCRT’S UNDER (OVER) VALUATION IS ABOUT 15% (9%+6%)LCRT’S UNDER (OVER) VALUATION IS ABOUT 15% (9%+6%)

THE SPREAD BETWEEN THE TOP AND BOTTOM DECILES OF THE SPREAD BETWEEN THE TOP AND BOTTOM DECILES OF LCRT’S UNDER (OVER) VALUATION IS ABOUT 15% (9%+6%)LCRT’S UNDER (OVER) VALUATION IS ABOUT 15% (9%+6%)

-10

-5

0

5

10

Total Shareholder

Return Relative to S&P 500 FY +3 to +15 Mos.

Firms with Stock Prices Over $5Per share

Stock Performance Relative to Under (Over) Valuation at FY + 3 Mos.

Top 5%

Top 10%

Top 20%

2nd 20%

3rd 20%

4th 20%

Bottom 20%

Bottom 10%

Bottom 5%Source: Industrial Firms 1994-2003, % Debt to Debt Capacity < 83%; N=16,026 Company-Years; Prices > $5 Per Share; Hemscott Data, LCRT Platform Calculations; Annual Rebalancing; Purchase at Fiscal Year + 3 Months; Sale at Fiscal Year + 15 Months; No Transaction or Price Pressure Costs Included; Equal Weighted

Takeaway … suggests the LCRT Research DCF Model under (over) valuation effectively separates performance as price migrates toward intrinsic value.



Performance of Top and Bottom 10% Under (Over) Valued Firms @ FY + 3 Months

8090

100110120130140150

Total Shareholder Return Ending Quarter Relative to S&P 500

Wealt

h I

nd

ex

Top 10%, N = 1,508

Universe, N = 15,166

Bottom 10%, N = 1,478

THE LCRT DCF RESEARCH MODEL SEPARATES “WINNERS” AND “LOSERS” THE LCRT DCF RESEARCH MODEL SEPARATES “WINNERS” AND “LOSERS” CONSISTENTLY THROUGH QUARTERSCONSISTENTLY THROUGH QUARTERS

FROM ANNUAL DATA WITH A PERSISTENCY BEYOND ONE YEARFROM ANNUAL DATA WITH A PERSISTENCY BEYOND ONE YEAR

THE LCRT DCF RESEARCH MODEL SEPARATES “WINNERS” AND “LOSERS” THE LCRT DCF RESEARCH MODEL SEPARATES “WINNERS” AND “LOSERS” CONSISTENTLY THROUGH QUARTERSCONSISTENTLY THROUGH QUARTERS

FROM ANNUAL DATA WITH A PERSISTENCY BEYOND ONE YEARFROM ANNUAL DATA WITH A PERSISTENCY BEYOND ONE YEAR

Source: Industrial Firms 1994-2003, % Debt to Debt Capacity < 83%; Prices > $5 Per Share; Hemscott Data, LCRT Platform Calculations; Annual Rebalancing; Purchase at Fiscal Year + 3 Months; Sale through Quarter indicated ; No Transaction or Price Pressure Costs Included; Equal Weighted

Note the run down and run up of prices just prior to financial statement release, indicating Inflection Points.

Takeaway … suggests the migration of price toward intrinsic value may take several quarters to 2-3 years.



FOR THE TOP DECILE OF UNDER-VALUED FIRMS, SCREENING FOR THE TOP DECILE OF UNDER-VALUED FIRMS, SCREENING ON TRACKING ERROR INCREASES RETURN FROM 20 TO 34 ON TRACKING ERROR INCREASES RETURN FROM 20 TO 34

AND REDUCES ALPHA PEAKEDNESS RISKAND REDUCES ALPHA PEAKEDNESS RISK

FOR THE TOP DECILE OF UNDER-VALUED FIRMS, SCREENING FOR THE TOP DECILE OF UNDER-VALUED FIRMS, SCREENING ON TRACKING ERROR INCREASES RETURN FROM 20 TO 34 ON TRACKING ERROR INCREASES RETURN FROM 20 TO 34

AND REDUCES ALPHA PEAKEDNESS RISKAND REDUCES ALPHA PEAKEDNESS RISK

0

5

10

15

20

25

30

35

40

45

Unlimite

d

128 (

95th

)

80 (9

0th)

53 (8

5th)

39 (8

0th)

27 (7

5th)

18 (7

0th)

11 (6

5th)

4 (6

0th)

-2 (5

5th)

-8 (5

0th)

-14 (

45th

)

-19 (

40th

)

-25 (

35th

)

Signed Model Tracking Error (Percentile)

To

tal

Sh

areh

old

er R

etu

rn R

elat

ive

to S

&P

50

0 F

Y +

3 to

+15

Mo

s.

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

Alp

ha

Pea

ked

nes

s R

isk

Par

amet

er o

f S

tab

le P

aret

ian

Dis

trib

uti

on

Mean TSR

Peakedness

Region of Max Return and Min

Peakedness Risk

N=1,050

N=130

Takeaway … suggests that a more accurate model enhances return and reduces risk, but due care must also be given to the smaller number of stocks in the portfolio and the related potential torpedo risk of a few large losers.

Year N1998 81999 142000 192001 352002 312003 23

130


Alpha Peakedness rises from 1.5 to 1.8 approaching Gaussian Normal (less risk)



FOR THE BOTTOM DECILE OF OVER-VALUED FIRMS, FOR THE BOTTOM DECILE OF OVER-VALUED FIRMS, SCREENING ON TRACKING ERROR REDUCES RETURN FROM SCREENING ON TRACKING ERROR REDUCES RETURN FROM

-2 TO -4 AND REDUCES ALPHA PEAKEDNESS RISK-2 TO -4 AND REDUCES ALPHA PEAKEDNESS RISK

FOR THE BOTTOM DECILE OF OVER-VALUED FIRMS, FOR THE BOTTOM DECILE OF OVER-VALUED FIRMS, SCREENING ON TRACKING ERROR REDUCES RETURN FROM SCREENING ON TRACKING ERROR REDUCES RETURN FROM

-2 TO -4 AND REDUCES ALPHA PEAKEDNESS RISK-2 TO -4 AND REDUCES ALPHA PEAKEDNESS RISK

-10

-8

-6

-4

-2

0

2Unlim

ited

-69 (

5th)

-56 (

10th

)

-49 (

15th

)

-42 (

20th

)

-36 (

25th

)

-30 (

30th

)

-25 (

35th

)

-19 (

40th

)

-14 (

45th

)

-8 (5

0th)

-2 (5

5th)

4 (6

0th)

11 (6

5th)

18 (7

0th)

Signed Model Tracking Error (Percentile)

To

tal

Sh

areh

old

er R

etu

rn R

elat

ive

to S

&P

50

0 F

Y +

3 to

+15

Mo

s.

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

Alp

ha

Pea

ked

nes

s R

isk

Par

amet

er o

f S

tab

le P

aret

ian

Dis

trib

uti

on

Mean TSR

Peakedness

Region of Min Return and Min

Peakedness Risk

N=1,044

N=190

Takeaway … suggests that a more accurate model enhances return and reduces risk for shorts, but due care must also be given to the smaller number of stocks in the portfolio and the related potential torpedo risk of a few large losers.


Year N1998 171999 202000 202001 352002 352003 63

190

Alpha Peakedness rises from 1.5 to 1.9

approaching Gaussian Normal (less risk)



CONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONS These results extend our back test research to those firms with

prices greater than $5 per share at Fiscal Year + 3 Months Over nine years, the top decile of under valued firms double in

relative wealth, while the bottom decile of over valued firms loses half its value

The spread between top and bottom deciles approximate 15% per year as price migrates toward intrinsic value

The migration toward intrinsic value takes several quarters to 2-3 years

– The run down and run up of prices during the quarter prior to the release of financial statements at Fiscal Year + 3 months suggest inflection points for under and (over) valued firms arising from the change in intrinsic valuations derived from Cash Economic Returns

A more accurate model measured by tracking error significantly enhances return and reduces risk



PRESENTATION CONCLUSIONSPRESENTATION CONCLUSIONS

Suggests two empirical research measurement methodologies to improve DCF models

– Value Charts with tracking errors for individual companies (based on capitalization methods using only historical information with minimal analyst intervention)

– Cumulative Tracking errors for large sample of companies Fading Cash Economic Returns provides a conceptual and

empirical basis for dealing effectively with competitive reaction and its likely impact on the future cash flows of the firm

Back tests suggest significant excess investment returns result from prices migrating toward intrinsic values over several quarters

The Stable Paretian Alpha Peakedness parameter provides one replacement risk measure for traditional mean variance CAPM beta, as it identifies regions of the universe where the tails of the distribution become so fat that the mean becomes indeterminate

- 1 - © 2006 lifecycle returns, inc. all rights reserved sources: financial statements and price...

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