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Transcript of - 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]
- 2 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 2 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 3 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 3 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
- 4 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 4 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
- 5 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 5 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
- 6 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 6 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
- 7 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 7 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
- 8 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 8 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
COMPARISON OF TRADITIONAL VALUATION TO OFFSHOOTS OF CALLARD, MADDEN (CMA) (1)
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
- 9 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 9 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
COMPARISON OF TRADITIONAL VALUATION TO OFFSHOOTS OF CALLARD, MADDEN (CMA) (2)
COMPARISON OF TRADITIONAL VALUATION TO OFFSHOOTS OF CALLARD, MADDEN (CMA) (2)
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
- 10 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 10 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
- 11 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 11 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
- 12 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 12 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
- 13 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 13 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
- 14 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 14 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 15 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 15 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 16 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 16 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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 ($Millions)
- 17 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 17 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
CASH ECONOMIC RETURN EXAMPLE:CASH TO ECONOMICS SUPERVALU– 2001 ($ 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
- 18 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 18 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 19 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 19 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 20 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 20 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 21 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 21 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 22 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 22 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
- 23 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 23 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 25 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 25 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
- 26 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 26 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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 <
62%; Hemscott Data, LCRT Platform Calculations
No Transaction or Price Pressure Costs Included
Equal Weighted
- 27 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 27 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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 <
62%; Hemscott Data, LCRT Platform Calculations
No Transaction or Price Pressure Costs Included
Equal Weighted
- 28 -- 28 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 29 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 29 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 30 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 30 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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?
- 31 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 31 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 32 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 32 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 33 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 33 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
Total Shareholder Returns
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
- 34 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 34 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 35 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 35 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
- 36 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 36 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
alpha ("peakedness") 1.48 0.01 43.41 Difference from 2.00
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
- 37 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 37 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
mb
er o
f C
om
pan
y -
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%
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 ValueStd.
Error t-Statistic
alpha ("peakedness") 1.33 0.02 36.90 Difference from 2.00
beta ("skewness") 1.00 0.03 31.37 Difference from 0.00
c ("dispersion") 44.03 0.01 4,264.60 Difference from 0.00
delta ("location" or "average") 65.68 0.10 668.51 Difference from 0.00
Takeaway … you should consider employing different risk measures if you are using over/under intrinsic value as an investment decision tool
- 38 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 38 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 39 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 39 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
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 1.07 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
beta ("skewness") 0.82 0.04 20.59 Difference from 0.00
c ("dispersion") 71.91 0.04 1,827.43 Difference from 0.00
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.
- 40 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 40 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
Total Shareholder Returns
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
alpha ("peakedness") 1.38 0.04 -8.73 Difference from 1.00
beta ("skewness") 0.99 0.08 12.07 Difference from 0.00
c ("dispersion") 36.29 0.02 1,548.21 Difference from 0.00
delta ("location" or "average") 48.37 0.18 269.51 Difference from 0.00
Takeaway… This suggests that in this area of the universe, diversification can be used to achieve mean performance
- 41 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 41 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
0
10
20
30
40
50
60
70
80
90
100
-100 150 400 650 900
Total Shareholder Returns
Nu
mb
er o
f C
om
pan
y -
Yea
rs
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
alpha ("peakedness") 1.20 0.11 -1.86 Difference from 1.00
beta ("skewness") 1.00 0.16 6.27 Difference from 0.00
c ("dispersion") 48.41 0.07 669.22 Difference from 0.00
delta ("location" or "average") 131.59 #N/A #N/A Difference from 0.00
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
- 42 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 42 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
Nu
mb
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pan
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Yea
rs
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
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.
Results ValueStd.
Error t-Statistic
alpha ("peakedness") 0.92 0.01 8.08 Difference from 1.00
beta ("skewness") -0.37 0.01 -25.81 Difference from 0.00
c ("dispersion") 4.02 0.02 258.78 Difference from 0.00
delta ("location" or "average") 18.58 #N/A #N/A 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.
- 43 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 43 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 44 -- 44 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 45 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 45 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 46 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 46 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
- 47 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 47 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
- 48 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 48 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
- 49 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 49 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
Source: Industrial Firms 1998-2003, % 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
Alpha Peakedness rises from 1.5 to 1.8 approaching Gaussian Normal (less risk)
- 50 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 50 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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.
Source: Industrial Firms 1998-2003, % 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
Year N1998 171999 202000 202001 352002 352003 63
190
Alpha Peakedness rises from 1.5 to 1.9
approaching Gaussian Normal (less risk)
- 51 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 51 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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
- 52 -Sources: Financial Statements and Price Data – CapitalIQ & CoreData - Calculations – LCRT Platform
- 52 -© 2006 LifeCycle Returns, Inc. All Rights Reserved
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