The Use of Optimisation in Portfolio Construction and Trading

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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

EqWt

ScaledShort

EqWt+Index

Fundamental Opt


Statistical Opt

Realized Returns

4.52%

6.08%

5.19%

6.36%

6.35%

Realized Risk

14.91%

6.31%

5.57%

3.62%

3.75%

Average Turnover:

13.8%

20.7%

17.9%

23.7%

26.8%

Av. no. of Assets per Period:

368

369

371

366

360

Sharpe Ratio:

0.30

0.96

0.93

1.76

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

Performance Comparisons (2006
-
10)

0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Apr-06
Jun-06
Aug-06
Oct-06
Dec-06
Feb-07
Apr-07
Jun-07
Aug-07
Oct-07
Dec-07
Feb-08
Apr-08
Jun-08
Aug-08
Oct-08
Dec-08
Feb-09
Apr-09
Jun-09
Aug-09
Oct-09
Dec-09
Feb-10
Apr-10
Jun-10
Aug-10
EW
OPT


OPT

EW



OPT

EW

ann

ret

11%

13%


IR

1.88

1.43

ann

stdev

6%

9%


max DD

-
9%

-
14%

10

Focus on 2008 / 2009

11

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.

TRADING

12

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.


TRADING

13

Motivation 1

Intraday Correlation
:

14

Single Stock Trading Hedge Realised TE Gain

-0.20%
-0.15%
-0.10%
-0.05%
0.00%
0.05%
RWE GY
CNA LN
UU/ LN
SSE LN
EOAN GY
SVT LN
NG/ LN
EDF FP
SEV FP
FUM1V FH
IPR LN
VIE FP
IBR SM
GSZ FP
EDPR PL
GAS SM
EDP PL
ELE SM
ENEL IM
-0.35%
-0.30%
-0.25%
-0.20%
-0.15%
-0.10%
-0.05%
0.00%
0.05%
0.10%
SCMN VX
VOD LN
KPN NA
DTE GY
BELG BB
TKA AV
TLSN SS
CWC LN
FTE FP
ERICB SS
BT/A LN
TEL NO
ALU FP
NOK1V FH
TIT IM
TEF SM
Telco

Utilities

15

Intraday portfolio P&L in event time
:

Motivation 2

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

IMMEDIATE

Initial

Period1

Period2

Period3

Period4


$2,250,148

Risk(USD)

4,637,713

0

0

0

0

0

Risk(%)

0.78%

0

0

0

0

MarketImpact
(USD)

2,250,148

0

0

0

2,250,148

MarketImpact(%)

0.38%

0

0

0

Long (USD)

416,067,925

0

0

0

0

Short (USD)

178,595,279

0

0

0

0

Turnover (%)

100%

0

0

0

EQUALLY DISTRIBUTED

Initial

Period1

Period2

Period3

Period4

$8,411,869

Risk(USD)


4,637,713

3,478,285

2,318,856

1,159,428

0

6,956,569

Risk(%)

0.78%

0.58%

0.39%

0.19%

0

MarketImpact(USD)


281,269

515,972


376,791


281,269

1,455,300

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

Turnover (%)

25%

25%

25%

25%

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:

21

OPTIMIZED 2

Initial

Period1

Period2

Period3

Period4

$ 2,100,152

Risk(USD)

4,637,713

306,578

217,412

127,118

0

651,109

Risk(%)

0.78%

0.05%

0.04%

0.02%

0

MarketImpact
(USD)

824,477

142,295

196,863

285,408

1,449,043

MarketImpact
(%)

0.14%

0.02%

0.03%

0.05%

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

Turnover (%)

52.77%

9.69%

14.66%

22.89%

DISTRIBUTED
wrt

Opt2

Initial

Period1

Period2

Period3

Period4

$ 6,395,029

Risk(USD)

4,637,713

2,190,392

1,740,997

1,061,109


0

4,992,498

Risk(%)

0.78%

0.37%

0.29%

0.18%

0.00%

MarketImpact
(USD)

862,565

124,509

169,197


246,261


1,402,532

MarketImpact(%)

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

Turnover (%)

52.77%

9.69%

14.66%

22.88%

1% EXPOSURE CONSTRAINTS ON SECTOR/COUNTRY/STYLE

OPTIMIZED 3

Initial

Period1

Period2

Period3

Period4

$ 2,073,767

Risk(USD)

4,637,713

283,721

199,506

119,030

0


602,257

Risk(%)

0.78%

0.05%

0.03%

0.02%

0.00%

MarketImpact
(USD)

875,955

142,503

184,870

268,183


1,471,510

MarketImpact
(%)

0.15%

0.02%

0.03%

0.05%

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

Turnover (%)

54.20%

9.77%

14.09%

21.94%

Trading Schedule Comparisons (cont.)

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

26



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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