Fuqua Investment Analytics

Fuqua Investment Analytics Building Blocks for a Long/Short Strategy Driven by Quantitative Stock Selection Stefan D. Gertsch Brian Wachob

Purpose of Study • Build a quantitative stock selection model to guide portfolio management at a long/short hedge fund. • Adopted perspective of a fund with $100M in assets under management • This fund size estimate guided investable universe definition. • Assumed goal of maximizing returns with negligible correlation to other asset classes • In practice, we did consider variance as well, but it is of much lesser importance if correlations with other asset classes are indeed negligible. © Gertsch & Wachob

Overview • Definitions: Universe, Methodology, Conventions • Cross-Sectional (Time Invariant) Factor Research • Identification and Evaluation • Factor Refinement • Negative Factor Values and Counter-Intuitive Resultant Rankings • These concerns are often overlooked by others and arise among very common factor definitions (such as forward earnings yield) • Industry Normalization • Optimal Fractile Resolution and Clustering/Groupings/Aggregation • Integration of Factor Portfolios into a Multivariate Model • Based on Mean-Variance Portfolio Optimization with the Imposition of Custom Constraints • Multivariate Model’s Out-of-Sample Performance • Forecasting Factor Portfolio Returns • Demonstration of dynamic factor weightings based on factor performance forecasts © Gertsch & Wachob

Universe Definition • U.S. stocks only • Time-scaled min. market cap threshold • $54M in 1987, rises by 7% annually to $200M in 2005 • Time-scaled min. estimated mean daily dollar volume threshold • $84K in 1987, rises by 10.4% annually to $500K in 2005 • Excluded ETFs and other investment funds trading as stocks • Excluded 3 instances of likely erroneous Compustat returns data • Number of stocks in universe grows with time • 998 on 1/31/1987 • 2,649 on 11/31/2001 • ≈3,336 today (4/27/2005) © Gertsch & Wachob

Methodology / Conventions * specified in FactSet Alpha Testing as 1/31/1987-11/31/2001 • In-sample period: February 1987 – December 2001 • Out-of-sample period: January 2002 – March 2005* • FactSet Alpha Testing fractile sorts • Monthly rebalancing, 1 month holding period • Convention: High factor values are assigned to low-numbered fractiles** When historical data necessary to evaluate the univariate sorting factor for a given stock is unavailable, that stock is excluded from the universe for that backtest date. * specified in FactSet Alpha Testing as 12/31/2001-2/31/2005 * Note that using 31 as the last day of the month when specifying the date range in Factset’s Alpha Testing is necessary—even when there is no 31st day of the specified month. If not used in this way, lagged variables may not work properly in alpha tester. ** Note that sometimes our factor transformations have reversed the effective convention of associating high factor values with low-numbered fractiles. We will try to make explicit notations indicating when this phenomena is impacting our results to address any confusion this may cause with regard to interpretation of our results. © Gertsch & Wachob

Factor Identification • Factor Categories • Valuation • Accounting/Earnings Quality • Sentiment • Technical • Unclassified © Gertsch & Wachob

Factor Refinement • Address negative factor values and counter-intuitive resultant rankings • Empirically evaluate different technical factor definitions • Identify optimal evaluation window • Identify best source database (e.g. Compustat? I/B/E/S?) • Standardization? Absolute change? % change? • Address NAs in data set • Industry normalization • Factor portfolio returns: predictive forecasts • Isolate factor performance within sub-universes (e.g. small cap momentum versus large cap momentum) • Optimal fractile resolution and fractile groupings/partitioning towards multivariate integration © Gertsch & Wachob

Valuation Factors • Evaluated in a previous study http://faculty.fuqua.duke.edu/~charvey/Teaching/BA453_2005/DIA/DIA%20Final%20Project_007.ppt#1 • Dividend Yield • Book to Market • Historical (Trailing) Earnings Yield • (Crude) Implied Cost of Capital • Candidates for future studies • Cash Flow Yield (or FCF/TEV) • Reinvestment Rate • ROE • Sales to Market • Comprehensive Implied Cost of Capital • Chosen for implementation in this study • Forward Earnings Yield © Gertsch & Wachob

Accounting/Earnings Quality Factors • Change in Net Accruals scaled by Assets • There are many ways to isolate different elements of accounting accruals– experimentation with factors based on these different elements of accruals is a recommended area of future research • Other measures of earnings quality also constitute an area for recommended future research © Gertsch & Wachob

Sentiment Factors • Revision Ratio • We experimented with various ways of defining this metric • Ultimately chose to use a three-month trailing window and aggregate the number of up versus down earnings revisions, scaling by the total number of estimates • Candidates for future studies • Aggregated consensus analyst buy/sell recommendations (or changes) • Debt or equity ratings (or changes) • Change in mean or median consensus earnings estimate © Gertsch & Wachob

Technical Factors • Price Momentum • We only looked at the classic momentum definition: percentage price change over the month -13 to month -2 window • Reversal (Last month’s return) • Candidates for future studies • Other known quant. models separately consider 6-month price momentum and 20-month price momentum • We examined reversals (1-month price change), but found no significant signal; perhaps more study is warranted • Perhaps momentum should be considered on a beta-adjusted basis (i.e. rank stocks on estimated alphas rather than on raw % return). As presently constructed, this factor may effectively sort on beta during periods of strong market directional moves. • MACD • On-balance volume • Gap-related technical factors • Myriad other quantifiable technical factors © Gertsch & Wachob

Unclassified Factors • Percentage Change in Shares Outstanding • Standardized Unexpected Earnings • Abnormal Dollar Volume or Abnormal Turnover • Size • Incorporated only with regard to potential for forecasting periods of small cap outperformance versus periods of large cap outperformance • Candidates for future studies • Institutional ownership: % level or accumulation/distribution • Insider purchases/sales © Gertsch & Wachob

Factor Evaluation • Required painstaking data inspection in FactSet • Parameter codes and syntax must be very carefully selected • Avoid or work around data sets with erroneous or misaligned data (can impose look-ahead bias or present stale data) • Avoid survivorship bias that can easily taint a universe via certain parameter specifications • Universe definition must also be very carefully specified and coded to avoid biases © Gertsch & Wachob

Factor Evaluation • All analysis pertains to Equal-Weighting fractile constituents. • As a small hedge fund (per our assumed perspective), our universe definition is considered sufficient to limit our strategies to tradable (sufficiently liquid) stocks. • Our method of combining independently evaluated factors into an ultimate multivariate strategy is congruous with this equal-weighting • S&P500 Index is used throughout as a benchmark • A future analysis should consider a different benchmark (perhaps the equal-weighted mean return of all stocks entering our universe in any given month) • The S&P500 represents performance of very large capitalization companies– our universe equally weights a broad cross-section of large cap and small cap firms (more like an equal-weighted Russell 3000) © Gertsch & Wachob

Forward Earnings YieldFactor Refinement– Technical Definition • Examined various measures of forward earnings • Mean and median forecasts • Weighted and unweighted forecasts • Next Twelve Months, Second Twelve Months, FY1, FY2, and FY3 forecasts • Various combinations and substitution schemes for NAs among these earnings forecast parameters • Selected FactSet code AVAIL(IH_MED_EPS_NTMA(0), IH_MEDIAN_NTM(0), G_IBES_FY1_MED_USD(0))/MP(0) We suspect that further experimentation can identify an even better FactSet-based definition for Forward Earnings Yield. © Gertsch & Wachob

Forward Earnings YieldFactor Refinement– Data Cleaning • Excluded firms with forward earnings yield estimates of dubious accuracy from dataset (i.e. forward earnings yield universe). • Forward earnings yield estimates consistently exceeded 1 for a few firms early in the in-sample data set. One firm (SEIBELS BRUCE GROUP INC) even surpassed 100. • Set criteria for exclusion to FEY>1. © Gertsch & Wachob

Forward Earnings YieldFactor Refinement– Negative Values • For negative earnings forecasts, consistent value-based sorting on forward earnings yield is unclear. • Example • Company A: E = 1, P = 10 E/P = .10 • Company B: E = 1, P = 100 E/P = .01 • Company C: E = -1, P = 100 E/P = -.01 • Company D: E = -10, P = 100 E/P = -.10 • Company Y: E = -10, P = 1000 E/P = -.01 • Company Z: E = -100, P = 1000 E/P = -.10 • Problem: Sort on Forward Earnings Yield gives A, B, C/Y (tie), D/Z (tie) • Desired result: A, B, C, D, Y, Z • All else being equal, we prefer earnings that are less negative and we prefer lesser prices, but a rational tradeoff assessing a preferred price paid per unit of negative earnings is unclear © Gertsch & Wachob

Forward Earnings YieldFactor Refinement– Negative Values • Proposed solution: Use EFY2/P, EFY3/P, and/or Sales/P ratios to perform a secondary sort among subset of negative forecast NTM earnings firms • “Best” methodology assigned percentile score to each firm based on these three attributes evaluated only against other negative NTM earnings firms. • Weighted average of these scores (with greater weights on EFY2/P and EFY3/P) was used to sort this subset of firms • Special scoring methodology was applied to NAs and to score firms with negative EFY2/P or EFY3/P © Gertsch & Wachob

Forward Earnings YieldFactor Refinement– Negative Values Disappointing results If anything, we observe lesser separation among lowest fractiles with our negative value adjustment scheme. © Gertsch & Wachob

Forward Earnings YieldFactor Refinement– Negative Values • Abandoned effort to improve negative value treatment in forward earnings yield factor. • Our proposed methods were not found to be empirically superior. • We still believe that better treatment of these negative values (by some other method) can improve factor performance. • We leave such efforts to future research. • With proper assumptions applied, an implied cost of capital metric seems like a potentially far superior valuation factor. © Gertsch & Wachob

Industry Normalization • Perhaps relative assessments of factors against only a firm’s industry peers lends additional information that is obscured by universal sorts. • Proposed methods of industry-normalization • Industry-specific factor standardization (by demeaning or z-scores) • How to handle negative industry means? • How to handle outlier firms that might disproportionately affect estimated industry factor means and standard deviations? How to treat non-normal intra-industry factor distributions? • Industry-specific factor sorts and percentile binning © Gertsch & Wachob

Industry Normalization • Firms change industries over time. • Most FactSet industry classification codes only retrieve present-day industry classification data. Using these might introduce biases into our backtests. • Solution: Historically updating Industry Codes • Compustat’s historically updated SIC Codes • How to define and partition firms into industries? • Group firms with similar risk of underlying assets (cost of capital) • Group firms with similar overall risk profiles– such as sensitivities to macroeconomic environment • Group firms for which our factors have similar predictive power • E/P, leverage, and forecast growth rates are some specific metrics we examined to evaluate appropriate grouping schemes • To enable historically accurate industry classifications in FactSet, we must define our industries based on SIC Codes © Gertsch & Wachob

Industry NormalizationDefining Industries Initial Grouping Sanity Check / Regrouping Industries Sic Codes 0100 Group 1 • Number of companies binning to each group through time (’87, ’94, ’05, etc.) • E/P ratios • D/E • Growth • forecasts • Market cap Industry 1 0101 ... 1000 … ... … 9000 … Industry 60 9900 Group X … 9999 © Gertsch & Wachob

Industry NormalizationDefining Industries • What is the optimal number of Industry groupings? • More industries will more closely match firms • Greater similarities among risk exposures and sensitivities • Greater similarities among factor characteristics and sensitivities • Fewer firms per industry • Fewer industries allows more dispersion among intra-industry factor values • This may yield better distinction between attractive and unattractive stocks • More firms per industry • Our approach: 60 Industries © Gertsch & Wachob

Industry Normalization • Intra-industry factor sorts and percentile binning • Final universe-wide sort is performed on these intra-industry percentile scores • Final fractiles that result are industry-neutral (i.e. same number of firms from each industry are binned to each of the final fractiles) • Intra-industry factor information is isolated; Inter-industry factor information is discarded © Gertsch & Wachob

Industry NormalizationIntra-industry factor sorts and percentile binning Rank within Industry Group By Industry Factor Percentile Fractiles Industry 1 high F1 … F2 low … high … F3 … … … low F4 Industry 60 high … F5 low © Gertsch & Wachob

Industry Normalization#1 Control: Forward Earnings Yield, Non-Industry Normalized *Note: Here, high fractile numbers are associated with high factor values © Gertsch & Wachob

Industry Normalization#2 Forward Earnings Yield, Industry Normalized *Note: Here, high fractile numbers are associated with high factor values © Gertsch & Wachob

Industry Normalization • Fractile alphas look very similar between industry-normalized forward earnings yield and non-industry normalized forward earnings yield • Next investigation: Does a secondary sequential sort on industry-normalized forward earnings yield within standard FEY quintiles add any informational benefit over merely sorting again (with finer fractile resolution) on standard FEY? © Gertsch & Wachob

F1 F2 F1 F1 F1 F1 F3 F2 F2 F2 F2 F4 F3 F3 F3 F3 F5 F4 F4 F4 F4 F5 F5 F5 F5 Industry NormalizationCombining intra-industry signals with meta-signal Industry Normalized Sub-Fractiles 25 Fractiles Derived from Sequential Sorting Universal Standard Factor Fractiles F1 F1 … F2 F3 F4 F5 F25 © Gertsch & Wachob

Industry Normalization#3 Combination Approach: Sequentially Sorted *Note: Here, high fractile numbers are associated with high factor values © Gertsch & Wachob

Industry NormalizationComparing Approaches: #1 (Blue) and #3 (Purple) *Note: Here, high fractile numbers are associated with high factor values © Gertsch & Wachob

Industry Normalization • Conclusion • The steeper intra-quintile alpha slopes in the sequentially sorted plot indicate that intra-industry normalization does add informational benefit– at least in the lower FEY quintiles. © Gertsch & Wachob

Industry NormalizationNext Steps in a Future Analysis • At this point, we cut off our investigation of industry normalization, but we believe that further study would reveal substantial opportunities to improve our overall model. • Areas of Future Study • Further study and experimentation with industry groupings– seeking optimal partitioning strategy for a given universe • Examine impact of industry normalization for all factors (not just FEY as studied here) • For any factor, identify the industries in which the factor works well– only model that factor in those industries. • Explore other ways to combine inter-industry and intra-industry signals • Perhaps isolate industry-to-market signal and consider separately from firm-to-industry signal • Integrate industry-normalized signals into final comprehensive stock selection model © Gertsch & Wachob

Univariate Factor Diagnostics • We sought to identify factors that distinguished most dramatically between high and low alpha stocks. • Among the many factors that we studied, we present only those for which the strongest apparent signals were observed along with the lowest inter-factor correlations between factor returns. • Aggregated factor portfolios are defined that group multiple fractiles (25-tiles) together based on similarity in alphas across adjacent 25-tiles. • We have defined between 3 and 6 aggregated factor portfolios for each significant factor. • Returns series from these aggregated factor portfolios will be input to a portfolio optimization algorithm to determine desired weightings in an integrated multivariate stock selection model. © Gertsch & Wachob

Forward Earnings Yield (FEY)Selected Definition and FactSet Code Excerpt • I/B/E/S weighted median analyst EPS forecast for next twelve months (div. by price) • If NA, revert to I/B/E/S unweighted median analyst EPS forecast for next twelve months (div. by price) • If both are NA, revert to “G_” I/B/E/S median analyst forecast for the current fiscal year (div. by price) • Selected FactSet code AVAIL(IH_MED_EPS_NTMA(0), IH_MEDIAN_NTM(0), G_IBES_FY1_MED_USD(0))/MP(0) • Note that we experimented with many definitions of forward earnings yield. Refer to previous slides for further commentary. © Gertsch & Wachob

Momentum (MOM)Selected Definition and FactSet Code Excerpt • % Return over the 12-month period leading up to the previous month (i.e. months -13 through -2) • Selected FactSet code (CM_P(-1)-CM_P(-13))/CM_P(-13) • Note that there are many other ways to quantify “momentum” • For example, 6-month or 20-month trailing returns • There are many other ways (besides simple trailing returns) to measure price trends or other relevant price patterns (generally considered to fall within the realm of “technical analysis”) © Gertsch & Wachob

Abnormal Dollar Volume in Biggest 30% of Universe (ADB)Selected Definition • Estimate daily dollar volume over each month going 65 months into the past (any stocks without sufficient historical data are excluded from the universe) • Exclude the lowest 70% of market caps (among remaining firms) from the universe • For each of the past 6 months, compute the arithmetic average of estimated dollar volumes over a trailing 60-month window • For each of the past 6 months, compute the log difference in dollar volume relative to the 60-month trailing average • Sum these log differences of the past 6 months • Note that we examined many definitions for this metric along with measures of abnormal turnover– we believe there may be more signal available to be harnessed with regard to a stock’s variation in trading volume. © Gertsch & Wachob

Fuqua Investment Analytics