Migration Tracking and Dynamic Weighting February 28, 2005 Team Members Dae Jin Choi Nicolas Paleokrassas Juliet Xu John Duval Wei King Ng Global Blue Devil Partners

- 1 - Global Blue Devil Partners CONTEXT AND PURPOSE Context Global Blue Devil Partners wanted to explore: mechanics of factor selection and evaluation migration tracking static and dynamic weighting Purpose of this document Explain methodology employed Summarize key results Evaluate migration tracking, static and dynamic weighting

- 2 - Global Blue Devil Partners Analysis Road Map: The Different Returns Analyzed Long-Short Migration Tracking Static Weights Optimization Dynamic Weights Optimization Optimized score Long-Short Complexity X XX X X X XX X X X X XX XX XX X XXX X X X X X X

- 3 - Global Blue Devil Partners Started By Examining a Large Number of Factors Retained Earnings Growth/ΔMarket Cap Current Price / 52 Week High Price CFO/Price EPS Growth-Price Growth EPS Growth* Price Growth* (E/P) / (Book/Price) *Also Examined by Industry Only Looked at Largest 500 Compustat Companies, Best Factors: Retained Earnings Growth/ Δ Mkt Cap CFO/Price Price Growth Examined Heat Maps and chose based on consistency of returns, average return, Sharpe Return, Maximum Drawdown Kept Fractiles 1 and 5 for each Factor Factors ExaminedResults Chosen Factors a combination of Price Momentum and Value strategies

- 4 - Global Blue Devil Partners Value Weighted Individual Screen Results Returns (%) Measures Sharpe Ratio Maximum Negative Excess Return (LS) Max No. Consecutive Down Periods Retained Earning Growth/Market Cap CFO/PricePrice Growth Fractile 1Fractile 5Fractile 1Fractile 5Fractile 1Fractile % Period Negative Returns (LS) (17.7%) 4 (12%) 9 (8.7%) 5

- 5 - Global Blue Devil Partners But can Migration Tracking Improve the Results? Rank T Rank T-1 Rank T-2 Rank T-3 Created New Factors based on lagged variables Computationally intensive to do for all time periods, so chose a few discrete intervals Combined new factors with subjective score giving more weight to more recent ranks Not possible if variables hard to lag Important to remember difference in rank of average factor versus average factor rank! Methodology

- 6 - Global Blue Devil Partners Value Weighted Migration Tracking Individual Screen Results Returns (%) Measures Sharpe Ratio Maximum Negative Excess Return (LS) Max No. Consecutive Down Periods Price Growth Earnings/Price & Book/Price CFO/Price % Period Negative Returns (LS) Retained Earnings Growth/ Market Cap 0.02 Fractile 1,Fractile (18%) Fractile 1,Fractile (10%) Fractile 1,Fractile (24%) Fractile 1,Fractile (24%) 4

- 7 - Global Blue Devil Partners Summary of Migration Tracking CFO / Price: Worse Price Growth: Better Earnings/Price / Book/Price: Mixed Results Retained Earnings Growth / Market Cap: Better Unclear whether or not should expect better results Expected Migration Tracking to work better for some factors than others: Persistent effects modeled better with migration tracking Long-lived rankings may already be priced into market CFO / Price: Worse Price Growth: Better Earnings/Price / Book/Price: Mixed Results Retained Earnings Growth / Market Cap: Better Unclear whether or not should expect better results Expected Migration Tracking to work better for some factors than others: Persistent effects modeled better with migration tracking Long-lived rankings may already be priced into market

- 8 - Global Blue Devil Partners After Migration, Optimization Looked at Simple Long-Short Portfolios & Long-Short Migration Tracking Portfolios Result: Optimized 3-factor Migration tracking portfolio beats 3-factor No-Migration Tracking portfolio. Expected Return: 25.33%, Sharpe Ratio: 1.24 Optimizing with multiple fractile always creates a portfolio with a higher Sharpe Ratio and Expected Return, and beats any single factor. The weights from the optimization are static portfolio weights that we can apply to the fractiles Max(w 1 r 1 + w 2 r 2 + w 3 r 3 + w x r x ) Var<= Variance of S&P 500 Total Returns w 1 + w 2 + w 3 + w 4 = 0 Still use fractiles 1 and 5 Fractile returns assumed to equal mean historical- no re-sampling Results

- 9 - Global Blue Devil Partners Putting Optimization Weights into a Scoring Model: c1c2....cnc1c2....cn Factor 1 Fractile 1 W1W1 c1c2....cnc1c2....cn W2W2 c1c2....cnc1c2....cn W3W3 c1c2....cnc1c2....cn …W x 1. Apply weights to Companies… 2. Add weights together to create a score for each company across fractiles… For company 1, ∑ (W 1c1 + W 2c1 + W 3c1 + W x,c1 ) = Score C1 Factor 1 Fractile 5 Factor 2 Fractile 1 Factor X Fractile 1

Global Blue Devil Partners Putting Optimization Weights into a Scoring Model: (2) Fractile 1 Score Factor 3. Use score as a new factor to sort and rank: Fractile 2 Fractile 3 Fractile 4 Fractile 5 4. Go long fractile 1, short fractile 5

Global Blue Devil Partners Optimized weights scoring model are not necessarily better! Returns (%) Measures Sharpe Ratio Maximum Negative Excess Return (LS) Max No. Consecutive Down Periods MT Price Growth & E/P with B/P Price Growth & E/P with B/P MT Price Growth & CFO/Price % Period Negative Returns (LS) Price Growth & CFO/Price 0.16 Fractile 1,Fractile (11%) Fractile 1,Fractile (14%) Fractile 1,Fractile (12%) Fractile 1,Fractile (14%) 7

Global Blue Devil Partners Dynamic Weighting r1r2....rtr1r2....rt Fractile 1 = W 1 r1r2....rtr1r2....rt Fractile 2 +W 2 r1r2....rtr1r2....rt Fractile 3 +W 3 r1r2....rtr1r2....rt Fractile X …+W x Optimized weights were fixed over time: Portfolio Return Not optimal if correlations or expected returns differ by period Creates need to find a way to dynamically change weights

Global Blue Devil Partners Dynamic Weighting r1r2r2...rtr1r2r2...rt Fractile X ΔTerm Structure Slope 0r2r2....0r2r2.... Fractile X (Dynamically Weighted) x Interacting Fractile Returns with Change in Slope of Term Structure Created Dynamic Weights The new fractile returns: Underperformed other portfolios Lost ability to invest when down market predicted Next Step: Only Interact Fractile 1 = Insight: Changing the returns dynamically effectively changes the weights dynamically:

Global Blue Devil Partners Dynamic Weighting with Logit and Probit Models r1r2r2...rtr1r2r2...rt Factor 1 Fractile 1 - r1r2r2...rtr1r2r2...rt Factor 1 Fractile 5 1. Create a dependent variable that is equal to 1 if fractile 1 beats 5, 0 otherwise 2. Regress Binary Variable on Predictive Variable: Lagged Yield Spread Υ = α + β 1 Χ 1 + ε Υ = 0 or 1 Must use logistic or probabilistic distribution: bounded by 1 and zero Interpretation of result as probability of a positive long- short, dynamically weight based on probability Best if done by company, not fractile

Global Blue Devil Partners SUMMARY AND KEY LEARNINGS Migration tracking allows fine-tuning of factors, and may be especially valuable for use with persistent factors. Scoring model results in inconsistent improvements, but appears to work better for factors that incorporate migration tracking. Value of dynamic weights are highly dependent on power of predictive variables, and may be less valuable with long-short models that consistently provide returns in both up and down markets. Further Areas of Potential Study: -Incorporate trading costs into optimization by penalizing returns -Put dynamic returns into scoring model -Analyze longer time periods -Calculate Migration Tracking variables over different time periods or with different subjective weights