August 2007 Quant Equity Turbulence:

Presentation to Columbia University Industrial Engineering and Operations Research Seminar August 2007 Quant Equity Turbulence: An Unknown Unknown Becomes a Known Unknown September 15, 2008

Quant Equity Funds Use Computer Models to Trade Stocks Quant equity funds typically hold hundreds of stocks long and short Portfolios generally not concentrated: largest positions only 2-3% Usually neutral to equity market moves Some funds allow other systematic exposures Recent growth in long-biased, 130/30 funds Leverage of 2-4x per side is typical Some funds use price and trading volume only Statistical Arbitrage (Stat Arb) funds use mean reversion over days or weeks Black Box funds use pattern recognition over range of time scales Other funds use corporate accounting data Equity Market Neutral (EMN) funds typically hold stocks for several months 1

Quant Equity Funds Endured a Turbulent August 2007 Differences in discretionary timing of portfolio leverage drove August dispersion Monthly cross-sectional returns of EMN funds from Lehman Brothers data base Month-end returns understate August volatility, as some funds partially recovered Similar results for other quant equity strategies 4% Median and Quartile Returns of Quant Equity Market Neutral Funds, Feb 2003 - Jan 2008 2% 0% Monthly Fund Return -2% -4% -6% Median Return -8% -10% Bottom Quartile Return -12% Feb-03 Aug-03 Feb-04 Aug-04 Feb-05 Aug-05 Feb-06 Aug-06 Feb-07 Aug-07 Source: LBAIM Peer Group database, contains data from TASS, Altvest and EurekaHedge Past performance is not indicative of future results 2

Quant Equity Holdings Exhibit Large August Drawdowns We collected holdings data on 34 quant equity funds from public filings 13-F filings across 4,200 US equities No data on short positions; excludes prop desks and mixed quant/discretionary funds Holdings return distributions computed during August sub-periods Two proxies used for aggregate short exposure Market weights and aggregate short interest weights used for shorts Net holdings returns exhibit drawdowns similar to those seen in quant equity funds Performance of Holdings of 34 Quantitative Equity Hedge Funds in August 2007 Aggregate 4x Levered ( Holdings - Short Holdings Returns Market Short Interest 4x Levered ( Holdings - Market ) Interest ) Date Range 25%-ile Median 75%-ile Return Portfolio Return 25%-ile Median 75%-ile 25%-ile Median 75%-ile August 1-6 -2.2% -1.3% -0.8% 0.2% -0.8% -9.9% -6.2% -4.1% -5.8% -2.1% 0.0% August 7-9 -3.2% -1.8% -0.8% -0.5% 1.3% -10.8% -5.2% -1.2% -17.9% -12.3% -8.3% August 10-13 0.8% 1.9% 3.4% 0.1% -0.6% 2.8% 7.2% 13.3% 5.4% 9.8% 15.9% August 14-31 1.3% 1.5% 1.7% 1.5% 1.1% -0.9% 0.0% 0.9% 0.7% 1.6% 2.5% Source: FactSet and LBAIM Analysis Past performance is not indicative of future results 3

Large Losses Not Due to Standard Risk Factors Risk management at quant equity funds focused on controlling exposures Concentration in individual stocks Sector/industry exposure, market cap bias, value bias (multiple measures) Often weighted toward recent data We formed aggregate net holdings portfolio to analyze exposures Equal weight portfolio guards against omission/misclassification of funds Aggregate portfolio contains some factor exposures Industry over-/underweights Bias towards small-cap and mid-cap stocks Exposures did not contribute meaningfully to overall portfolio volatility Negligible factor contributions to Aug 7-9 losses (Aug 10-13 gains) Small-cap bias exerted indirect effect through reduced liquidity Such exposures exacerbated losses at some funds 4

Daily Equity Returns Indicate August Liquidation Event Returns of 4,200 US equities plotted as Aug 10-13 vs Aug 7-9 Strong diagonal pattern: Stocks down Aug 7-9 recovered Aug 10-13 and vice versa Rapid rebound consistent with liquidity-driven trades, not fundamentals Stocks retraced 44% of their Aug 7-9 move during Aug 10-13 on average US Equity Returns August 10-13 vs Aug 7-9 (4,193 Stocks) 50 40 30 Retu rn s o f Sto cks Au gu st 10,13 (% ) 20 10 0-100 -80-60 -40-20 0 20 40 60 80 100-10 -20-30 August 10-13 Return = -0.44*August 7-9 Return + 0.57bp R 2 = 0.38-40 -50 Returns of Stocks August 7-9 (%) Source: FactSet and Lehman Brothers Analysis Past performance is not indicative of future results 5

Stocks Popularity in Quant Equity Holdings Drove August Returns Daily cross-sectional model for 4,200 stock returns Two factors use number of funds holding stock, market cap and short interest Explanatory power (r-squared) peaks at 14% on Aug. 10 - typically below 1% Despite their low historical correlations, funds had substantial overlap in positions R-Squared of Model Based on Quant Fund Holdings 14% 12% 10% 8% 6% 4% 2% 0% Daily R-Squared of Two-Factor Model for Cross-Sectional Excess Stock Returns 1-Aug-07 3-Aug-07 7-Aug-07 9-Aug-07 13-Aug-07 15-Aug-07 17-Aug-07 21-Aug-07 23-Aug-07 27-Aug-07 29-Aug-07 31-Aug-07 5-Sep-07 7-Sep-07 11-Sep-07 13-Sep-07 17-Sep-07 19-Sep-07 21-Sep-07 25-Sep-07 27-Sep-07 Source: FactSet and Lehman Brothers Analysis Past performance is not indicative of future results 6

Factor Sensitivities of Stocks Consistent with Liquidation Stock returns consistent with rapid reduction in both long and short exposure Popular stocks in quant equity holdings lost then gained during August Unpopular stocks with high short interest gained then lost during August Trading volume also consistent with liquidation Betas of Daily Excess Returns to Positive Unexpected Counts in Quant Fund Holdings and Short Interest Ratios Times Negative Unexpected Counts 20 0.8 15 0.6 Positive Unexpected Coun 10 5 0-5 -10 0.4 0.2 0-0.2-15 -20 1-Aug -0 7 3-Aug -0 7 7-Aug -0 7 9-Aug -0 7 13 -Aug -0 7 15 -Aug -0 7 17 -Aug -0 7 21 -Aug -0 7 23 -Aug -0 7 27 -Aug -0 7 29 -Aug -0 7 31 -Aug -0 7 5-Sep -0 7 7-Sep -0 7 11-Sep-07 13-Sep-07 17-Sep-07 19-Sep-07 21-Sep-07 Short Interest 25-Sep-07 27-Sep-07 Beta to Short Interest * Neg Unexp Count Beta to Positive Unexpected Count -0.4-0.6 Source: FactSet and Lehman Brothers Analysis Past performance is not indicative of future results 7

What Triggered August De-levering? I. Value-Biased Quant Equity Funds Some EMN funds have value-biased portfolios Worked well for several years, but July 2007 was worst month for value in five years May have led value-oriented funds to cut exposure Risk models indicating higher value-at-risk post-july Need for cash to meet anticipated investor redemptions Prime broker-mandated leverage reductions 12% Monthly Relative Performance of Value Stocks vs Growth Stocks (Fama-French HML Factor) 10% 8% Rel. V alu e vs G ro w th R etu rn 6% 4% 2% 0% -2% -4% -4.4% in July 2007, worst in 5 years -6% Jul-02 Jan-03 Jul-03 Jan-04 Jul-04 Jan-05 Jul-05 Jan-06 Jul-06 Jan-07 Jul-07 Source: Kenneth R. French Data Library Past performance is not indicative of future results 8

What Triggered August De-levering? II. Multi-Strategy Hedge Funds Some funds have both credit and quant equity portfolios Seizing of credit markets in July caused mark-to-market losses Sowood lost 50% ($1.5bn) in July and sold its portfolio to Citadel Multi-strategy funds may have cut equity leverage due to credit losses Either across-the-board cut or cash to meet credit margin calls Evidence that multi-strategy funds preceded EMN funds in Aug. 7-9 liquidation 14% Daily R-Squared of Excess Holdings Returns for Three Categories of Quant Equity Funds 6% R-squared of Daily Excess Returns for EMN Funds 12% 10% 8% 6% 4% 2% Earlier relative increase in R-squared for types of Multi-strat funds (dashed lines), compared with EMN funds (solid line) 5% 4% 3% 2% 1% 0% 1-Aug-07 4-Aug-07 7-Aug-07 10-Aug-07 13-Aug-07 16-Aug-07 19-Aug-07 22-Aug-07 25-Aug-07 28-Aug-07 31-Aug-07 3-Sep-07 6-Sep-07 9-Sep-07 12-Sep-07 15-Sep-07 18-Sep-07 21-Sep-07 24-Sep-07 27-Sep-07 Multi-Strat Funds 0% Source: FactSet, Lehman Brothers Analysis Past performance is not indicative of future results 9

Growth in Strategy Assets Created Potential for Liquidity Event Market value of quant equity sample quadrupled, Dec 2004 Jun 2007 At June 2007 peak, these funds had $205 bn in US equity market value 23% of total hedge fund holdings (all styles) and 1% of equity market capitalization June 2008 total is $121 bn, due to lower leverage and redemptions (60% of max) Mkt value stabilized in June 2008, but potential end-of-year redemptions loom Evolution of Total Market Value of Quant Equity Holdings, 2004-2008 1,000.0 $912 bn $800 bn $363 bn TMV in $ billion 100.0 $205 bn $121 bn $49 bn Quant Equity Holdings Aggregate Hedge Fund Equity Holdings August 2007 10.0 Dec-04 Jun-05 Dec-05 Jun-06 Dec-06 Jun-07 Dec-07 Jun-08 Sources: FactSet and LBAIM analysis 10

EMN Returns More Volatile Post-August 2007 Median EMN fund volatility returned to levels last seen in internet bubble/collapse August 2007 still worst month, but Jan 2008 perhaps 2 nd worst since 2000 Increased factor volatility and sector dispersion only partially explain increased vol HML (value/growth) factor vol doubled since 2007, but far below 2002 level 6% Median and Quartile Monthly Returns of Equity Market Neutral Funds, August 1999 - June 2008 4% 2% Monthly Fund Return 0% -2% -4% -6% -8% -10% Aug-99 Aug-00 Aug-01 Aug-02 Aug-03 Aug-04 Aug-05 Aug-06 Aug-07 Sources: TASS, Altvest and LBAIM analysis 11

EMN Suffered in Bad Months for Hedge Funds Overall Strategy has provided little diversification to hedge fund portfolios in down months In four worst months for HFR composite, median EMN fund lost an average of 1% Somewhat surprising, given the lack of equity or credit market exposure in EMN Performance of Equity Market Neutral (EMN) Funds in Difficult Months for Hedge Funds, 2007-8 HFR Composite LBAIM EMN Peer Group Month Hedge Fund Index 1 Median Fund Return 2 Aug-07-1.53% -1.77% Nov-07-2.20% -0.55% Jan-08-2.69% -1.26% Mar-08-2.24% -0.46% 1 Data for HFR Composite hedge fund index available from w w w.hedgefundresearch.com 2 Monthly median return among a set of 25-40 equity market neutral (EMN) hedge funds, as collected by LBAIM Sources: HFR, TASS, Altvest and LBAIM analysis 12

Headline Events Mark Sharp Declines in Large-Cap Correlations Bear Stearns collapse and Fannie/Freddie concerns dominate recent landscape Aug 2007 quant equity turbulence a non-event for large cap portfolios Also observe a drop on January 22, 2008, date of emergency Fed rate cut Sharp drops in correlations of long and short portfolios signal higher EMN volatility 1 Large-Cap Stocks: Correlation of Market Portfolio and Aggregate Short Interest Portfolio (Rolling 60 Day) 0.995 "Ghost" of Bear Stearns Collapse Jan 22 Fed Rate Cut 0.99 Quant Fund Meltdown 0.985 0.98 Bear Stearns Collapse Feb 26, 2007 Crash 0.975 Fannie/Freddie Concerns 0.97 27-Nov-06 30-Jan-07 30-Mar-07 31-May-07 31-Jul-07 28-Sep-07 28-Nov-07 30-Jan-08 01-Apr-08 30-May-08 30-Jul-08 Sources: FactSet and LBAIM analysis 13

August 2007 and January 2008 Dominate Mid-Cap Correlation Plot Quant equity turbulence had dramatic effect on $2-10 bn stocks Sharp declines in long/short portfolio correlations indicate higher EMN fund vol 60-day correlation measurement interval creates ghost increases in correlations Nonlinear relation between change in correlation and change in volatility Aug 2007 volatility increased by 130%, while Jan 2008 volatility rose by only 30% 1 Mid-Cap Stocks: Correlation of Market Portfolio and Aggregate Short Interest Portfolio (Rolling 60 Day) 0.998 0.996 "Ghost" of Quant Turbulence 0.994 0.992 0.99 Feb 26, 2007 Crash "Ghost" of Sell-off / Jan 22 cut 0.988 0.986 0.984 Quant Fund Turbulence Sell-off / Jan 22 Fed Rate Cut 0.982 0.98 27-Nov-06 30-Jan-07 30-Mar-07 31-May-07 31-Jul-07 28-Sep-07 28-Nov-07 30-Jan-08 01-Apr-08 30-May-08 30-Jul-08 Sources: FactSet and LBAIM analysis 14

Holdings Factors Give Mixed Picture on Jan 2008 Quant Deleveraging Short-interest factor correlation rises sharply on Jan 22 Consistent with short-covering by quant hedge funds driving up prices Long holdings factor falls slightly, but remains positive on Jan 22 Inconsistent with selling by quant funds driving down prices 15% Correlations Between Daily Cross-Sectional Residual Returns and Factors Related to Popularity Among Quant Funds 10% Correlation to PUC Correlation to I_nuc * SI Short positions suffer 5% Correlation 0% -5% -10% Short positions working Emergency Fed Rate Cut -15% 02-Jan-08 07-Jan-08 10-Jan-08 15-Jan-08 18-Jan-08 24-Jan-08 29-Jan-08 Sources: FactSet and LBAIM analysis 15

Quant Sell-Off Likely Did Not Drive Markets in Jan 2008 R-squared of two-factor holdings model peaks at 2.5% in Jan 2008 Compared with 14% at August 2007 peak R-squared of 2.5% reached at other times in August 2007 and Jan 2008 not uncommon Quant funds suffered in Jan 2008 and may have exacerbated event by deleveraging 3.0% Explanatory Power of Two Factors Based on Quant Fund Holdings for Daily Cross-Sectional Stock Residuals 2.5% R-squared of Two Factor Model 2.0% 1.5% 1.0% Emergency Fed Rate Cut 0.5% 0.0% 2-Jan-08 7-Jan-08 10-Jan-08 15-Jan-08 18-Jan-08 24-Jan-08 29-Jan-08 Sources: FactSet and LBAIM analysis 16

Most Quant Fund Portfolios Smaller than Pre-August 2007 25 of 31 funds have lower total market value of equity holdings than in June 2007 Only 3 funds have substantially higher TMV 8 funds have 0-20% of June 2007 TMV; another 6 funds have 20-40% of June 2007 TMV Funds with steepest declines in TMV at risk of liquidation 2 Ratio of Long US Equity Market Value to June 2007 Long US Equity Market Value for 31 Quant Equity Funds 1.8 1.6 TMV / June 2007 TMV 1.4 1.2 1 0.8 0.6 0.4 0.2 3 funds 3 funds 2 funds 6 funds 3 funds 6 funds 8 funds 0 30-Jun-07 30-Sep-07 31-Dec-07 31-Mar-08 30-Jun-08 Sources: FactSet and LBAIM analysis 17

Conclusions and Open Questions Conclusions Aug 2007 quant equity turbulence due to simultaneous fund de-levering Growth of strategy assets created potential for liquidation risk Multi-strategy funds likely played role in triggering de-levering event Unanticipated new risk, rather than previously-known risks led to losses Open Questions What is risk of repeat scenario at current aggregate market value? Will investors (and leverage!) return to these strategies? Can quant equity funds reduce overlap without sacrificing performance? What is proper role of human discretion in a systematic equity fund? 18

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