Quantitative Stock Selection

James F. Page III, CFA

May 2005

Project Summary

1. Why Quant Selection is Attractive

2. Methodology

3. Historical Back Testing

4. Model Results

5. Dynamic Weights / Regime Change

6. Benchmarks

7. Next Generation Models

8. Concluding Thoughts

I. Quantitative Stock Selection

Quant Stock Selection

Premise

(1) In aggregate, certain fundamental, expectational, and macro variables may contain valuable information in predicting stock returns

(2) Not unlike traditional fundamental analysis, just more systematic

Quant Stock SelectionPros: Anecdotal evidence suggests ~80% of stock picking is done ‘by

hand’ (individuals making calls on fundamentals) Relies heavily on talent (or luck) of individual analyst Individuals can only process so much information (sector focus) Human nature suggests cognitive biases likely

Market structure may perpetuate mis-pricings (Street incentives, value weighted benchmarks, short sale restrictions)

Little academic research on subject (trade rather than publish) Evidence suggests that investors systematically over pay for

‘growth’ Quantitative selection is scaleable

Quant Stock SelectionCons: Black box nature of model

Explain approach without revealing too much information Attribution analysis – must be able to explain performance

Protecting against common modeling errors Credibility of simulated results Adapting to individual client restraints

Quant Stock Selection

Market Neutral

Generate returns from both undervalued and overvalued stocks At present, high market valuation = low future returns Market exposure is commodity but good stock selection is valued

(higher management fees) Low return expectations combined with geo-political environment

suggests absolute return approach prudent

II. Methodology

Methodology

1. Hypothesize Develop candidate list of potential factors that may assist in

predicting stock returns (valuation, growth, etc.) ‘Priors’ reduce data mining

2. Back Test Decide on “universe” for testing (capitalization, index, sector, etc) Use sorting or regressions to test individual candidate variables FactSet’s AlphaTester currently available to Duke students

3. Rebalance Periodically rebalance portfolios (monthly, annually, etc.)

Methodology

4. Analyze Results Consider factor performance and consistency (both long and

short candidates) in predicting returns balanced against turnover

Select most promising factors for inclusion in the model

5. Weight Once individual factors selected must decide on weights for

final model by either:a) ‘Eye balling’ best factors and assigning weights for a scoring

model

b) Pushing individual factor portfolios into a mean-variance optimizer

III. Historical Back Testing

Historical Back Testing

Access to reasonably accurate historical data is costly FactSet’s AlphaTester is currently available to Duke students Two approaches common in practice

Regression of factors on security returns (Panel, etc.) Sorting universe into fractiles based on factor characteristics (AlphaTester)

Must protect against common modeling errors Survivorship bias Information / reporting lags Data mining Inaccuracies in data

Credibility of simulated returns is critical

Historical Back TestingTerm 3 Model Discredited Errors in Historical Returns

Scrub Example.xls Survivorship Bias

Difficult to rule out unless you spend a lot of time examining results Fractile Misspecification

MSFT grouped in F1 Div Yield for 85-04 because of Special Dividend

Betas not believable Subject to similar errors as returns information Makes market neutral simulation difficult

Combing factors into comprehensive model increases complexity

Historical Back TestingTo Mitigate Potential Errors: Universe Selection is critical component

Market Cap weighted Adds to turnover (98-00) Unstable sector allocations Less undervalued firms to buy

Revenue weighted Sector bias Less overvalued firms to sell

Actual Indices (Preferred method) Limit universe to actual benchmark Limit survivorship bias Historical indices available (but option not turned on for Duke) Greatly enhance credibility – look to acquire for next year’s

class

Historical Back TestingTo Mitigate Potential Errors: Factor Syntax

If you do not get this right – data is worthless (lots of opportunities to get it wrong)

Consider consolidating our “approved” syntax for future students as starting point

Expectational (instead of accounting/fundamental) produced significantly fewer errors

Survivorship Bias Selecting “Research Companies” does not protect without:

Appropriate Syntax on Factors Correct specification of Universe

Sanity checks on early period companies # of NA companies can be signal

Errors You must clean historical data Consider median returns as back of envelope option

Historical Back TestingRecommendations: Use historical indices as universe

S&P 500 Barra 1000

Start with “approved” list of factor syntax Clean historical results (particularly returns) Do not rely on betas to construct market neutral portfolio Research ways to limit reliance on AlphaTester

Look for other data providers – ask managers what they use Interface with CompuStat/IBES directly?

Once comfortable with model, begin sorting real time ASAP

IV. Model Results

Model Results

Desired Universe: S&P 500

Why: ‘Considered’ to be highly efficient Value weighted index suggests low hanging fruit Historical data for testing is plentiful and reasonably accurate Highly liquid (market impact costs and borrow) Very scaleable because of market capitalizations

Actual Universe: First choose US Companies with highest sales (~ 500) Had to switch to Market Cap because of data limitations

Model ResultsUniverse Comments: Unstable during bubble period (1998-2000) Less undervalued firms to buy (but more overvalued firms to sell) Sector allocations float with market sentiment

Other: Rebalanced “official” results annually due to time consuming nature

of “cleaning returns” Equal number of companies in each bucket Equal weight returns Did not impose sector constraints Included two groups of Factors – Fundamental and Expectational Actively looking for “Quality” factor to add to the model Assume “beta” exposure is equal is both portfolios – probably

conservative

Results seem “too good” – further ‘cleaning’ necessary

Model ResultsIndividual Factor Performance

Monthly Statistics 1989 – 2004

Long Factors correlated with Value and visa versa

View Portfolios

Date F1 F2 E1 E2 F1 F2 E1 E2Mean 1.31% 1.14% 1.47% 1.47% 1.09% 0.95% 0.85% 0.77%Median 1.65% 1.13% 1.76% 1.87% 1.29% 1.08% 1.26% 1.34%High 20.50% 11.78% 14.15% 13.84% 27.40% 16.35% 28.57% 23.83%Low -14.59% -12.73% -15.00% -19.03% -19.64% -17.20% -25.75% -19.91%St Dev 4.87% 3.74% 4.96% 5.40% 6.30% 5.30% 7.35% 5.74%

CorrelationsS&P 500 82% 81% 83% 89% 75% 85% 73% 75%500 / Growth 70% 66% 69% 78% 81% 85% 78% 78%500 / Value 89% 89% 91% 93% 59% 75% 60% 63%

Long Factors Short Factors

Model ResultsFixed Weighting Scheme

Views Scoring OptimizedF1 18% 10%F2 18% 10%E1 27% 30%E2 36% 50%

F1 -10% -10%F2 -20% -16%E1 -30% -24%E2 -40% -50%

Returns 7.8% 7.8%Volatility 20.3% 17.6%

Long Weights

Short Weights

Model ResultsScoring Model Heat Map

Long Short Portfolio1989 29.3% 27.8% 1.5%1990 -11.4% -5.0% -6.4%1991 48.0% 39.4% 8.6%1992 16.3% 7.6% 8.7%1993 23.0% 12.8% 10.2%1994 1.0% 2.9% -1.9%1995 38.2% 23.4% 14.8%1996 25.7% 13.7% 12.0%1997 30.1% 18.6% 11.5%1998 8.0% 36.7% -28.8%1999 10.0% 37.6% -27.5%2000 20.3% -26.2% 46.5%2001 4.9% -37.1% 42.1%2002 -11.7% -28.2% 16.5%2003 68.2% 39.1% 29.1%2004 22.6% 12.5% 10.1%

Model Results

Summary Statistics

Long Short PortfolioMean 20.2% 11.0% 9.2%Geometric 19.8% 8.6% 7.8%Median 21.5% 13.2% 10.1%High 68.2% 39.4% 46.5%Low -11.7% -37.1% -28.8%St Dev 20.8% 24.6% 20.3%Turnover 83.2% 89.9%

V. Dynamic Weights / Regime Change

Dynamic Weights / Regime Change A factor’s effectiveness may vary in different states of

nature (PE ratios impacted by inflation) Certain market / macro conditions may favor growth or

value (value was dog in late 1990s) Dynamic factor weights allow model to capitalize on

conditional information Few managers currently employ dynamic weighting

schemes This area “is the Holy Grail” of Quant Strategies

Dynamic Weights / Regime ChangeForecasting Regime Change Inflection point for style (growth or value) relative performance Used S&P 500 Barra Value and Growth Indices as Proxies Examined macro economic variables that might assist in

forecasting these inflection points Two variables demonstrated “promise” in forecasting style relative

performances over the following year

Dynamic Weights / Regime ChangeRegime Change – Factor 1

Correlation Matrix Variable RegimeChange

Variable 1.000

RegimeChange 0.436 1.000

Regression Statistics

R R Square Adj.RSqr Std.Err. # Cases

0.436 0.191 0.187 0.446 240

Summary Table

Variable Coeff. Std.Err. t Stat. P-value

Intercept 0.421 0.029 14.616 0.000

Variable 0.216 0.029 7.484 0.000

Dynamic Weights / Regime ChangeRegime Change – Factor 2

Correlation Matrix RegimeChange Variable

RegimeChange 1.000

Variable 0.411 1.000

Regression Statistics

R R Square Adj.RSqr Std.Err. # Cases

0.411 0.169 0.165 0.452 240

Summary Table

Variable Coeff. Std.Err. t Stat. P-value

Intercept 0.421 0.029 14.424 0.000

Variable 0.203 0.029 6.952 0.000

Dynamic Weights / Regime ChangeThe Same Can Be Applied to View Portfolios

Expectational Factor #2 and Regime Change Factor #1:Prediction of Long outperforming Short

Correlation Matrix Variable E2 Long / Short

Variable 1.000

E2 Long / Short 0.435 1.000

Regression Statistics

R R Square Adj.RSqr Std.Err. # Cases

0.435 0.189 0.184 0.388 169

Summary Table

Variable Coeff. Std.Err. t Stat. P-value

Intercept 0.776 0.030 25.848 0.000

Variable 0.176 0.028 6.240 0.000

Dynamic Weights / Regime ChangeThe Same Can Be Applied to View Portfolios

Expectational Factor #2 and Regime Change Factor #2:Prediction of Long Outperforming Short

Correlation Matrix E2 Long / Short Variable

E2 Long / Short 1.000

Variable 0.427 1.000

Regression Statistics

R R Square Adj.RSqr Std.Err. # Cases

0.427 0.183 0.178 0.390 169

Summary Table

Variable Coeff. Std.Err. t Stat. P-value

Intercept 0.788 0.030 25.922 0.000

Variable 0.171 0.028 6.110 0.000

VI. Benchmarks

BenchmarksValue or Equal Weight? Since 1990, EWI has outperformed by 177 basis points Turnover for EWI is 6x which begs the question …

Can we separate turnover between model signals and weighting scheme?

Metric S&P 500 S&P 500 EWIAnnual Total Return ('90-'04) 10.94% 12.71%Volatility ('90-'02) 15.27% 16.04%Annual Turnover ('92-'02) 4.97% 29.13%

BenchmarksValue or Equal Weight? Significant Implications for Sector Weights / Tracking Error

RelativeSector S&P 500 EWI WeightingConsumer Discretionary 11.9% 17.6% 47.8%Consumer Staples 10.5% 7.2% -31.5%Energy 7.2% 5.5% -23.2%Financials 20.6% 16.4% -20.6%Health Care 12.7% 10.9% -13.8%Industrials 11.8% 11.3% -3.8%Information Technology 16.1% 16.1% 0.4%Materials 3.1% 6.4% 107.1%Telecommunications Services 3.3% 2.0% -39.1%Utilities 2.9% 6.6% 123.8%

BenchmarksValue or Equal Weight? Correlations drift through time – implications for tracking error

BenchmarksValue or Equal Weight? EWI had positive loading on the size premium EWI has significant exposure to the value premium

Fama-French Risk Factor Exposures

500 EWIIntercept 0.413 0.385Market 1.009 1.060SMB Premium (0.181) 0.060HML Premium 0.050 0.370R-squared 99% 93%

Source: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

BenchmarksValue or Equal Weight? EWI has 82% correlation with 500 / Barra Growth EWI has 96% correlation with 500 / Barra Value Further proof of value tilt

500 / 500 /500 EWI Barra Growth Barra Value

500 100%EWI 93% 100%500 / Barra Growth 96% 82% 100%500 / Barra Value 94% 96% 81% 100%

BenchmarksValue or Equal Weight? Obvious Pros and Cons to both EWI benchmark will make returns look less impressive, but

help explain turnover EWI may be a better match for style Provide more stable weighting for sector allocations Equal weight is newer idea – historical data is limited If possible, choice should match weighting scheme of

portfolio

VII. Next Generation Models

Next Generation Models Refining Dynamic Factor Weights

Preferably done outside of FactSet Migration Tracking

May contain information to enhance returns or limit turnover

♥ ♥ ♥ ♥ ♥ ♥ ♥♣

♥ ♥ ♥♣ ♣

♣ ♣

♣ ♣ ♣

♣ ♣1 2 3 4 5 6 7 8 9 10

Fractile 5

Periods

♥ Score of Stock X ♣ Score of Stock Y

Fractile 1

Fractile 2

Fractile 3

Fractile 4

Next Generation ModelsModified Versions of S&P 500 Model Separate Models for Sector and Stock Selection More Conservative

More positions Limited tracking error

More Aggressive Directional Less positions Leverage

Other Domestic Models S&P Mid-Cap 400 / Russell 2000

International Models Developed / Emerging markets

VIII. Concluding Thoughts

Concluding ThoughtsTheoretical How long will excess returns exist How to stay ‘ahead of the curve’

Implementation Cost of data Credibility of simulation Returns during first 12 – 24 months Balance between turnover and model signals

Concluding Thoughts

Overall Quantitative Stock Selection Appealing Outperformance Seems Possible Long/Short Consistent with Absolute Return Approach

Bio

James F. Page III

Jimmy became interested in quantitative stock selection during Campbell Harvey’s Global Asset Allocation and Stock Selection class and a follow-up course dedicated to quantitative stock selection. He received his Bachelor of Science degree from the University of Florida and will receive his MBA from Duke University’s Fuqua School of Business in May 2005. Prior to enrolling at Duke, he spent four years in the Equity Research Department of Raymond James & Associates in St. Petersburg, FL. He is also a CFA charter holder.