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Migration Tracking and Dynamic Weighting

This document explores the mechanics of factor selection and evaluation, migration tracking, and static and dynamic weighting. Methodology, key results, and evaluation of migration tracking and weighting are discussed.

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Migration Tracking and Dynamic Weighting

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

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

  3. Analysis Road Map: The Different Returns Analyzed Complexity Long-Short Migration Tracking Static Weights Optimization Dynamic Weights Optimization Optimized score Long-Short X X X X X X X X X X X X X X X X X X X X X X X X X X X X

  4. Started By Examining a Large Number of Factors Factors Examined Results • 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, 1995-2004 • Best Factors: • Retained Earnings Growth/ ΔMkt 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 Chosen Factors a combination of Price Momentum and Value strategies

  5. Value Weighted Individual Screen Results % Period Negative Returns (LS) Returns (%) Retained Earning Growth/Market Cap CFO/Price Price Growth Measures Fractile 1 Fractile 5 Fractile 1 Fractile 5 Fractile 1 Fractile 5 • 0.56 • (12%) • 9 • 0.20 • 0.67 • (8.7%) • 5 • 0.20 • 0.64 • (17.7%) • 4 • 0.18 • Sharpe Ratio • Maximum Negative Excess Return (LS) • Max No. Consecutive Down Periods

  6. But can Migration Tracking Improve the Results? RankT RankT-1 RankT-2 RankT-3 Methodology • 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!

  7. Value Weighted Migration Tracking Individual Screen Results % Period Negative Returns (LS) Returns (%) Price Growth Earnings/Price & Book/Price CFO/Price Retained Earnings Growth/ Market Cap Measures Fractile 1, Fractile 5 Fractile 1, Fractile 5 Fractile 1, Fractile 5 Fractile 1, Fractile 5 • 0.61 • 0.22 • 0.74 • 0.02 • 0.60 • 0.28 • (18%) • 4 • 0.81 • (24%) • 7 • 0.30 • (10%) • 4 • (24%) • 4 • Sharpe Ratio • Maximum Negative Excess Return (LS) • Max No. Consecutive Down Periods

  8. 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

  9. After Migration, Optimization Max(w1r1 + w2r2 + w3r3 + wxrx) Var<= Variance of S&P 500 Total Returns w1 + w2 + w3 + w4 = 0 Still use fractiles 1 and 5 Fractile returns assumed to equal mean historical- no re-sampling Results • 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

  10. Putting Optimization Weights into a Scoring Model: 1. Apply weights to Companies… Factor 1 Fractile 1 Factor 1 Fractile 5 Factor 2 Fractile 1 Factor X Fractile 1 c1 c2 . . . . cn c1 c2 . . . . cn c1 c2 . . . . cn c1 c2 . . . . cn …Wx W1 W2 W3 2. Add weights together to create a score for each company across fractiles… For company 1, ∑ (W1c1+ W2c1+ W3c1+ Wx,c1 ) = ScoreC1

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

  12. Optimized weights scoring model are not necessarily better! % Period Negative Returns (LS) Returns (%) MT Price Growth & E/P with B/P Price Growth & E/P with B/P MT Price Growth & CFO/Price Price Growth & CFO/Price Measures Fractile 1, Fractile 5 Fractile 1, Fractile 5 Fractile 1, Fractile 5 Fractile 1, Fractile 5 • 0.61 • 0.29 • 0.78 • 0.16 • 0.69 • 0.39 • (11%) • 4 • 0.68 • (12%) • 6 • 0.23 • (14%) • 5 • (14%) • 7 • Sharpe Ratio • Maximum Negative Excess Return (LS) • Max No. Consecutive Down Periods

  13. Dynamic Weighting Optimized weights were fixed over time: Fractile X Fractile 1 Fractile 2 Fractile 3 r1 r2 . . . . rt r1 r2 . . . . rt r1 r2 . . . . rt r1 r2 . . . . rt Portfolio Return …+Wx = W1 +W2 +W3 Not optimal if correlations or expected returns differ by period Creates need to find a way to dynamically change weights

  14. Dynamic Weighting • Insight: Changing the returns dynamically effectively changes the weights dynamically: Fractile X (Dynamically Weighted) ΔTerm Structure Slope Fractile X r1 r2 r2 . . . rt - + + . . . . 0 r2 r2 . . . . = x • Interacting Fractile Returns with Change in Slope of Term Structure Created Dynamic Weights • The new fractilereturns: • Underperformed other portfolios • Lost ability to invest when down market predicted • Next Step: Only Interact Fractile 1

  15. Dynamic Weighting with Logit and Probit Models 2. Regress Binary Variable on Predictive Variable: Lagged Yield Spread 1. Create a dependent variable that is equal to 1 if fractile 1 beats 5, 0 otherwise Υ = α + β1Χ1 + ε Υ = 0 or 1 Factor 1 Fractile 5 Factor 1 Fractile 1 r1 r2 r2 . . . rt r1 r2 r2 . . . rt • 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 -

  16. 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

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