The Use of Optimisation in Portfolio Construction and Trading Michael Steliaros Mar 2012 Market Environment: • • • • • Lower Liquidity Longer Transactional Duration Increased Factor Exposure Higher Implementation Cost Lower Returns Key Areas of Focus: • Optimised Portfolio Construction • Optimised Execution • Reducing tracking error & costs 2 Outline Optimised Portfolio Construction • Portfolio creation alternatives. • Medium/short horizon strategies. • For and against examples. Optimised Execution • Optimised hedging. • Optimised liquidation. • Reducing tracking error & costs. 3 Portfolio Construction Alternatives Equally Weighted Signal Weighted Optimised + Lower turnover. Lower performance volatility. High transfer coefficient. Targeted portfolio. Controlled exposure to risk factors. - Agnostic regarding marginal contributions. Can result in higher turnover. Higher chance of extreme hits. ‘Undesirable’ positioning from a signal point of view. 4 Example 1: Trade Ideas Set-up: • Data from Apr. ‘07 to Nov. ’10 on all eligible European trade ideas scored +1 for Buys and -1 for Sells. • End of day returns and positions. • Index future returns are included for SX5E, FTSE100, DAX and CAC. • Currency exposures are hedged out by currency assets. • A full daily optimization run from 2007-2010, where: – Objective is to maximize portfolio alphas (using +/-1 alphas) minus (riskAversion)* total risk. – Constraints for the Optimised portfolios are: • Dollar neutral • Trade/position limits <= 10% ADV • Sector/Country exposure within +/-5%, with quadratic penalty • MT Momentum, ST Momentum, Volatility, Size within +/-10%, with quadratic penalty • Position limits +/- 1.5% of total AUM 5 Risk Attribution OPT RAW 6 Performance Attribution R A W O P T 7 Performance Comparisons Realized Returns Realized Risk Average Turnover: Av. no. of Assets per Period: Sharpe Ratio: EqWt 4.52% ScaledShort 6.08% EqWt+Index 5.19% Fundamental Opt 6.36% Statistical Opt 6.35% 14.91% 13.8% 368 0.30 6.31% 20.7% 369 0.96 5.57% 17.9% 371 0.93 3.62% 23.7% 366 1.76 3.75% 26.8% 360 1.69 8 Example 2: Analyst Forecasts Set-up: • Data from 2000 to 2010 on all individual analyst forecasts globally for all ‘investable’ equities. Approximately 8000 analysts forecasting various accounting items for 3000 European companies, updated daily. • Overnight (continuous) signal creation, trade the following day. Optimization : – Objective is to maximize portfolio alphas minus (riskAversion)* total risk. – Constraints for the Optimised portfolios are: • Dollar neutral • Trade <= 5% ADV • Sector/Country exposure within +/-3%, with quadratic penalty • ST Momentum, Volatility, Size within +/-5%, with quadratic penalty • Position limits +/- 1.2% of total aum 9 EW OPT 1.43 max DD -9% -14% Aug-10 1.88 Jun-10 IR Apr-10 EW Feb-10 OPT Dec-09 Oct-09 Aug-09 Jun-09 9% Apr-09 6% Feb-09 13% Dec-08 11% Oct-08 EW Aug-08 OPT Jun-08 Apr-08 Feb-08 ann stdev Dec-07 ann ret Oct-07 Aug-07 Jun-07 Apr-07 Feb-07 Dec-06 Oct-06 Aug-06 Jun-06 Apr-06 Performance Comparisons (2006-10) 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1 0.9 0.8 10 Focus on 2008 / 2009 11 TRADING Shortcomings of (most) current practices • Trading optimisation –when employed- not accounting for market microstructure endogenously. • Single period estimation window. • One-size-fits-all parameterisation. • Disjoint portfolio construction and trading process (alpha neglect). • Volume and volatility estimation based on historical data fitted models only. 12 TRADING Execution Framework • Multi-period, intraday liquidation optimisation framework with dual risk horizon targeting with EU, US and Global portfolio coverage. • Choice between: (i) Liquidation only, (ii) Liquidation subject to risk constraints, (iii) Liquidation with risk constraints and hedging (index futures, etfs and/or a customisable liquid stock universe can be used as hedging instruments). Hedging Framework • Flexibility to add own assets/calculations: – Estimate optimal hedge depending on order size, time of day and trading cost subject to: • Max ADV trading and holding limits. 13 Motivation 1 Intraday Correlation: 14 Single Stock Trading Hedge Realised TE Gain ENEL IM ELE SM EDP PL GAS SM EDPR PL GSZ FP IBR SM VIE FP IPR LN FUM1V FH SEV FP EDF FP NG/ LN SVT LN EOAN GY SSE LN UU/ LN CNA LN RWE GY -0.20% Telco -0.15% -0.10% Utilities -0.05% 0.00% TEF SM TIT IM NOK1V FH ALU FP TEL NO BT/A LN 0.05% ERICB SS FTE FP CWC LN TLSN SS TKA AV BELG BB DTE GY KPN NA VOD LN SCMN VX -0.35% -0.30% -0.25% -0.20% -0.15% -0.10% -0.05% 0.00% 15 0.05% 0.10% Motivation 2 Intraday portfolio P&L in event time: 16 Dual-Horizon Optimised Portfolio Execution Base Case HARD CONSTR+NO RISK 1 Period 2-pd HARD CONSTR 2-pd SOFT CONSTR + SECTOR NEUT Initial Risk 3.15% 3.15% 3.15% 3.15% Final Risk 1.58% 1.13% 0.91% 0.79% Market Impact ST 0.07% 0.08% 0.11% 0.12% Market Impact LT 0.07% 0.08% 0.04% 0.03% Initial Holding (% of ADV) 8.6% 8.6% 8.6% 8.6% Tradeout (% of ADV) 4.2% 3.4% 5.2% 4.6% Liquidation rate 49% 40% 61% 54% 17 Multi-Horizon Optimised Portfolio Execution • Day split in accordance to volume, volatility and correlation waves. • Market impact and covariance matrices estimated within each day segment. Multiple risk model benchmarking (intraday empirical + daily factor). • Simultaneous multi-period estimation of optimal liquidation schedule to minimise aggregate eod risk and market impact. • Ability to apply combinatorial constraints. • Option to incorporate alpha parameter during liquidation. 18 Multi-Horizon Optimised Execution (cont.) Objective function: • Maximise [Alpha – (Daily Risk + Intraday Risk + Market Impact)] (Alpha is an optional input) • Risk = Combination of daily risk model forecast + intraday, empirical, minute by minute return based volatility adjustment. • MI = Exchange specific, intraday MI forecasts based on minutely volume, b-a spread and volatility estimates. • Customisable relative weights between alpha, risk and MI and within the hybrid specification between daily and intraday risk. 19 Multi-Horizon Optimised Execution (cont.) Constraints: • Max % of volume. • Min holding limits. • Min trading limits. • Max Country, Sector and Style exposure both as an absolute limit and/or dynamic decay with respect to underlying portfolio exposures (continuously evolving throughout the day). • Max hedging $ limit both as an absolute value at start up and/or intraday dynamic constraint with respect to residual portfolio value. • All constraints can be applied in ‘hard’ or ‘soft’ format (linear and quadratic penalty functions available) with violation statistics. 20 Long-Short, Institutional Trade Value ($) # Names Est MI Risl ($) Risk (%) 95% VaR Net 237,472,646 287 1,529,619 4,637,580 0.78 7,626,909 Long 416,067,925 198 1,081,236 7,729,275 1.86 12,711,473 Short 178,595,279 89 448,383 3,141,124 1.76 5,165,855 Gross 594,663,204 Trading Schedule Comparisons: IMMEDIATE Initial Risk(USD) Period1 4,637,713 Risk(%) 0.78% MarketImpact(USD) 416,067,925 Short (USD) 178,595,279 Risk(USD) Risk(%) Initial Period4 $2,250,148 0 0 0 0 0 0 0 0 0 0 0 0.38% 0 0 0 0 0 0 0 0 0 0 0 100% 0 0 0 Turnover (%) EQUALLY DISTRIBUTED Period3 2,250,148 MarketImpact(%) Long (USD) Period2 Period1 Period2 Period3 Period4 3,478,285 2,318,856 1,159,428 0 0.78% 0.58% 0.39% 0.19% 0 281,269 515,972 376,791 281,269 MarketImpact(%) 0.05% 0.09% 0.06% 0.05% Long (USD) 416,067,925 312,050,944 208,033,963 104,016,981 0 Short (USD) 178,595,279 133,946,459 89,297,639 44,648,820 0 25% 25% 25% 25% Turnover (%) 2,250,148 $8,411,869 4,637,713 MarketImpact(USD) 0 6,956,569 1,455,300 21 Trading Schedule Comparisons (cont.) OPTIMIZED 2 Initial Risk(USD) Period1 Period2 Period3 Period4 $ 2,100,152 4,637,713 306,578 217,412 127,118 0 0.78% 0.05% 0.04% 0.02% 0 824,477 142,295 196,863 285,408 0.14% 0.02% 0.03% 0.05% Risk(%) MarketImpact(USD) MarketImpact(%) Long (USD) 416,067,925 141,560,980 110,943,182 67,614,480 0 Short (USD) 178,595,279 139,317,839 112,311,693 68,489,723 0 52.77% 9.69% 14.66% 22.89% Turnover (%) DISTRIBUTED wrt Opt2 Risk(USD) Initial Period1 Period2 Period3 Period4 2,190,392 1,740,997 1,061,109 0 0.78% 0.37% 0.29% 0.18% 0.00% 862,565 124,509 MarketImpact(USD) MarketImpact(%) 169,197 246,261 0.15% 0.02% 0.03% 0.04% Long (USD) 416,067,925 196,508,881 156,191,899 95,196,341 0 Short (USD) 178,595,279 84,350,550 67,044,668 40,862,600 0 52.77% 9.69% 14.66% 22.88% Turnover (%) 1,449,043 $ 6,395,029 4,637,713 Risk(%) 651,109 4,992,498 1,402,532 1% EXPOSURE CONSTRAINTS ON SECTOR/COUNTRY/STYLE OPTIMIZED 3 Initial Risk(USD) Risk(%) Period1 Period2 Period3 Period4 $ 2,073,767 4,637,713 283,721 199,506 119,030 0 0.78% 0.05% 0.03% 0.02% 0.00% 875,955 142,503 184,870 268,183 0.15% 0.02% 0.03% 0.05% MarketImpact(USD) MarketImpact(%) Long (USD) 416,067,925 139,504,009 108,311,829 65,357,158 0 Short (USD) 178,595,279 132,833,602 105,937,618 65,107,040 0 54.20% 9.77% 14.09% 21.94% Turnover (%) 602,257 1,471,510 22 Market Neutral, Hedge Fund Trade 20min rolling stdev of optimised (red) vs inline 10% of adv (green) unwind. Minute by minute optimised portfolio returns in blue ‘Realised’ risk: Optimised= 46bps, Inline= 58bps (scaled with respect to the residual gross notional at each point in time for illustration purposes) 23 Market Neutral, Hedge Fund Trade (cont.) 20min rolling stdev of optimised (red) vs inline 10% of adv (green) vs vwap (blue) unwind. (realised risk scaled with respect to initial portfolio size) 24 Market Neutral, Hedge Fund Trade (cont.) 20min rolling stdev of intraday risk overweight (blue) vs daily risk overweight (red) unwind. (realised risk scaled with respect to initial portfolio size) 25 Conclusion • Using the granularity offered by higher frequency measurements alongside a state-of-the-art optimisation process, we can fit the volume, volatility and correlation characteristics of the trading day to a high degree of accuracy thus achieving superior results. • The flexibility to allow (i) combinatorial and risk constraints with (ii) dual periodicity in the objective function, (iii) up-to-the-minute fit of volume and volatility profiles and (iv) alpha, coupled with full configurability of all parameters to backtest and tailor to varying portfolio characteristics, we believe satisfies the widest possible array of execution needs. • Currently in development: incorporation of newsflow for real-time, forward looking adjustments to volume and risk estimates. Michael.steliaros@baml.com 26 Disclaimer / Notice to Recipient In certain regions or jurisdictions this disclaimer may not apply. 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