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
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