Transcript Old Mutual UK Select Mid Cap Fund

CF963, Autumn Term 2010-11
Learning and Computational Intelligence in Economics and Finance
Portfolio Optimization
University of Essex
26th November June 2010
Dr Amadeo Alentorn
Head of Quantitative Research
[email protected]
Part 1: Introduction to quantitative investing in hedge funds
Part 2: The problem of portfolio optimisation
Part 3: Application of heuristic portfolio optimization
OMAM at a glance
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Dynamic investment firm, focused on high performance and absolute returns
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Independent investment teams – no house view or investment style
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Expertise in
– Discretionary equities
– Fixed income
– Quantitative strategies
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Range of long only and alternative products designed to meet the needs of retail and
institutional investors
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New product innovation
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Independent risk management team
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USD6.5 billion assets under management*
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Part of Old Mutual Group, a constituent of the FTSE 100 index.
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* Source: OMAM, as at 30/10/09
OMAM Quantitative Strategies Group
Academic
Advisory Board
Investment
research
Investment team
V-Lab: PhD
and post-doctoral
researchers
Portfolio
construction and
management
Systems development
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Equity investing styles: discretionary/systematic spectrum
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Discretionary investing
– Mostly driven by fundamental analysis
– Analysis of company’s accounts, business plans, competitors, etc
Discretionary
– Meeting management and understanding business model
– Usually focus in one country/ sector/ industry
– Longer holding horizon
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Quantitative investing
– Factor models based on both fundamental and technical analysis
– Able to analyse and evaluate 1000s of companies
– Highly diversified portfolios
– Medium term holding horizon
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Statistical arbitrage
– Usually based on technical analysis, price driven (i.e. pairs trading)
Systematic
– High frequency execution, usually intra-day trading
– Short holding horizon
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Across the industry, many different variations: “quantamentals”, quant overlays, etc.
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Types of equity funds: passive/active spectrum
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Index tracking
– Tracking error TE < 0.25%
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Enhanced long only
– TE between 0.50 to 1.50%
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Passive
Long only funds
Active long only
– TE greater than 2.00%
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Short extension (130/30)
– Equivalent to index plus 30/30 market neutral
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Market neutral hedge funds
– Dollar neutral, i.e. 100/100
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Long/short hedge funds
Hedge funds
Active
– Variable net exposure
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Trade-off between risk and expected return.
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Types of equity funds: long, short and net positions
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Given $100 of capital, the structure of the portfolio will be very different, for
different types of funds.
200
150
100
Long book
50
Short book
0
Net position
-50
-100
-150
Long only
Short
extension
Market
neutral
Long short
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Performance of a market neutral fund vs. market
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Market risk is the primary source of risk for a long only equity fund in absolute terms
– When equity markets fall by 30%, the best outcome for a LO fund is -30% + TE.
– Market neutral designed to deliver positive returns in all market environments
0
10
Jan94
Sep95
May97
Dec98
Aug00
Apr02
MSCI World Index
Market neutral hedge fund
Nov03
Return
3.1
11.0
Jul05
Risk
15.5
4.6
Feb07
Oct08
Sharpe Sortino
0.20
0.28
2.37
3.63
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Short-selling
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Traditionally investing (long only constraint) can create miss-pricings, because
only positive views about stocks can be fully reflected into prices
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Hedge funds are able to reflect “buy” and “sell” ideas into the portfolios, by buying
stocks with positive forecasts, and “shorting” stocks with negative forecasts
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How does it work?
– Broker/dealers on behalf of clients identify stock owners (i.e. pension funds)
– Hedge fund borrows stock, and sells it on the open market
– At a future date, hedge fund buys back the stock, and returns it to the lender
– Stock owner receives a lending fee for the service
– Note: “naked” short selling is banned!
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Risks
– Stock recall
– Short squeezes: when prices go up, rush to cover positions
– Potential of infinite loss
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Short-selling: Northern Rock case study
Northern Rock Plc
100
1200
90
1000
80
70
800
60
50
600
40
400
30
20
200
10
0
Utilisation
Price
Source: Data Explorers www.dataexplorers.com
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Jun10
Apr10
Feb10
Dec09
Oct09
Aug09
Jun09
Apr09
Feb09
Dec08
Oct08
Aug08
Jun08
Apr08
Feb08
Dec07
Oct07
Aug07
Jun07
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Types of equity hedge funds
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Hedge fund indices have become a useful tool for monitoring the performance of
the different hedge fund strategies
– But issues with survivorship bias, self-selection bias (voluntary reporting), etc
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Useful indication of risk associated with each strategy
Source: Hedge Fund Research www.hedgefundresearch.com
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Our investment approach and philosophy
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Market inefficiencies result from behavioural biases and structural anomalies
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Investment insights, not statistics, drive research
– Many of the investment strategies are not different than those used by fundamental fund
managers (i.e. valuation, earnings quality, etc)
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Rigorous backtesting of data to validate investment criteria
– One of the key advantages over fundamental managers, we are able to test the historic
performance of an investment strategy
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Continuous research to maintain and enhance information ratio
– To mitigate risk of imitation and of crowded trades
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Multi factor models designed to perform throughout the business cycle
– Factor modelling lends itself to market neutral investing, generating both buys and sells
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Investment strategies based on behavioural finance
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Financial markets are complex systems
– Prices are the result of complex interactions between market participants
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Academic literature on behavioural finance aims to provide an understanding of how human
behaviour influence prices, and helps to explain some of the observed miss-pricings and
anomalies:
– Overconfidence: “all traders are above average”, over-trading
– Prospect theory: people value gains and losses differently
– Anchoring
– Under-reaction/ overreaction / herding
– Naïve extrapolation
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A solid understanding of the rationale for an observed market “anomaly” from a behavioural
finance point of view, when researching investment strategies, helps to avoid falling into “data
mining” traps.
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Quantitative investment allows to remove emotion from the investment process
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Academic research vs. industry research
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Liquidity
– Many academic studies use the CRSP database as the universe of stocks on
which to test a hypothesis, up to 26,000 stocks.
– In practice, only around 3,500 stocks worldwide with enough liquidity to invest
with negligible market impact.
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Survivorship bias
– Important to include companies that are no longer in the universe (impact of
bankruptcies/corporate actions)
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Reporting lags
– Point in time databases.
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Backfilling
– See “Rewriting history”
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Transaction costs
– Specially for high frequency strategies
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Factors: academic debate alpha vs. risk? (Fama French)
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Market
Size
Value
RF
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Rtrn Rsk
5.6 18.9
2.3 11.5
4.2 12.4
3.6
IR
Sortino
0.30 0.45
0.20 0.34
0.34 0.59
1
10
0
10
1930
1940
1950
1960
1970
1980
1990
2000
Source: Kenneth French website
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2010
Quantitative investment process
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Fully systematic investment process.
Universe: top
95% of market
capitalisation in
each country:
around 3,500
stocks1
Multi factor
stock
selection
criteria
Stocks ranked
by
attractiveness
Optimise risk
and return
profile of
portfolio
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Final
portfolio
Portfolio optimisation process
Trade
cost
model
Relative
return
model
Continuous research on all
three proprietary models
and process
Optimisation
and portfolio
construction
Risk
model
Trade list
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Part 1: Introduction to quantitative investing in hedge funds
Part 2: The problem of portfolio optimisation
Part 3: Application of heuristic portfolio optimization
What’s portfolio optimisation?
> Given a universe of stocks, and a set of expectations about the future
performance of these stocks, the problem is how to construct a portfolio
by selecting how to allocate the capital.
> The classic model for portfolio construction is the mean-variance
optimisation introduced by Markowitz in 1952.
> A portfolio optimization problem typically consists in maximising return,
minimising risk or maximising utility by finding the optimal set of stock
weights (i.e., percentages of invested capital) that satisfies a set of
constraints.
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The mean-variance frontier
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The traditional optimisation problem
> The traditional portfolio optimisation problem with no shorting allows only
positive (long) stock positions:
> The mean-variance objective function represents a trade-off between
expected return and expected risk, weighted by a risk aversion
parameter λ:
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Long vs short stock positions
> Long: a long position means the investor has gone to the market and
bought some shares in a company. The proportion of the value of these
shares of the total portfolio is the portfolio weight of that company in the
investor’s portfolio, represented by a positive portfolio weight.
> Short: a short position is achieved when an investor “sells” shares that
does not own, and this is represented by a negative portfolio weight.
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The optimisation problem for a market neutral hedge fund
> For a market neutral hedge fund, we remove the no-shorting constraint
to allow negative weights:
> Objective functions:
> Mean Variance
> Mean Value-At-Risk
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Why heuristic optimisation?
> Stock returns exhibit non-normal characteristics, including skewness
and fat tails, and most investors are loss averse
> These invalidate the assumptions in the traditional approach.
> Heuristic optimisation methods provide a more flexible toolset where no
simplifying assumptions are needed.
> Some of the applications have successfully achieved:
> The use of non-quadratic risk measures such as Value at Risk
> Incorporation of integer constraints, such as cardinality constraints.
> Heuristic algorithms already used to tackle this problem:
– Genetic Algorithms, and
– Threshold Accepting algorithms
> In the last part of the lecture, we will look at a new heuristic algorithm:
the GNMA
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Part 1: Introduction to quantitative investing in hedge funds
Part 2: The problem of portfolio optimisation
Part 3: Application of heuristic portfolio optimization
Introduction
> This work is based on a recent paper presented at UKCI
– “Heuristic Portfolio Optimisation for a Hedge Fund Strategy using the
Geometric Nelder-Mead Algorithm”
> We present a framework for implementing a heuristic portfolio
optimisation framework for a market neutral hedge fund investment
strategy.
> We also illustrates the application of the recently developed Geometric
Nelder-Mead Algorithm (GNMA) in solving this real world optimization
problem, and compare it with a Genetic Algorithm (GA) approach.
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Nelder-Mead Algorithm (NMA)
> Numerical optimization method published in 1965 by Nelder and Mead!
> Heavily used by practitioners in optimisation
> Cousin of Particle Swarm Optimization (PSO) and Differential Evolution (DE):
- it does not use derivative information
- it can be seen as a population based evolutionary algorithms with special operators
> Its search is explicitly geometric and attempts to adapt to the fitness landscape
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Operations in geometric transformation
> NMA applies these 4 operations until convergence:
> Worst solution reflected about the centre
> If R is the best, expand in this direction
> If R is the worst, we may have “overshoot”
> If nothing has worked, shrink towards best
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Geometric Generalization & Specification
> Recently, Moraglio and Johnson (2010) generalised the NMA from continuous to
combinatorial spaces.
> Reflection, expansion, contraction, shrinking operations can be naturally defined in
terms of distance relations among points and generalized to spaces equipped with a
formal notion of distance
> By plugging a new distance in their definitions, we can derive the same operators for a
new space: by using the Hamming distance on binary strings, we can derive these
operators for binary strings
A. Moraglio and C. Johnson. Geometric generalization of the nelder mead algorithm. In Proceedings of the 10th
European Conference on Evolutionary Computation in Combinatorial Optimization, 2010.
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Binary Encoding of Portfolio
> Fixed set of reference stocks
> The composition of the portfolio is represented by a binary string
> Each stock is associated with two bits:
> Presence bit: stock included or not
> Sign bit: long (0) or short (1) position
> Quantity of stock: budget equally partitioned on shorts and longs to have
a neutral portfolio
0
0
1
0
0
0
0
0
1
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1
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Data
> Daily stock returns for the 100 names of the FTSE100 index between
Jan 2007 and Dec 2009
> Covariance matrix based on full covariance with a rolling window of 250
days
> VaR based on the historical method, the 99% VaR is the third worst point
over the last 250 days
> Stock return forecasts are such that by construction reflect some level of
predictive power (5%), with 95% pure noise.
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Experiments
> Two optimisation algorithms:
> GA vs GNMA
> Interested in fitness and execution time
> Two objective functions (strategies):
> Mean-variance vs mean-VaR
> Risk aversion parameters were calibrated so that the risk levels of
the two strategies were similar
> Interested in differences in investment performance
> A total of 4 strategies
> Portfolios optimised over 250 days, average 10 runs.
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Results: quality of solutions
> Similar fitness levels achieved by both algorithms
> Similar execution time taken to achieve best fitness by both algorithms
> The new GNMA algorithm is comparable with the established GA
approach.
> Realised risks across strategies is comparable.
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Results: investment performance
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Findings of the paper
> Portfolios optimised for VaR deliver higher returns, as they take advantage of the
asymmetry in the risk penalty function
> Better reflects investor preferences about loss aversion and downside risk
> The results validate the models chosen:
> Return: we have shown that a low level of information content in return forecasts
(95% of noise) delivers realistic positive returns
> Risk: forecasted vs. realised risks are in line
> We have shown for the first time how the recently developed GNMA method is
suitable for tacking a real world problem, delivering a performance in line with the GA
approach.
> Optimising using VaR instead of variance as the risk measure for a market neutral
portfolio limits downside risk and is able to deliver higher returns, while variance
limits both downside and upside potential and therefore results in lower returns.
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Conclusion of the lecture
> Overview of the world of quantitative investing in practice
> Issues encountered in portfolio optimization:
– Size of problems: hard to move away from traditional frameworks
– Number and types of constraints
– Inputs are estimates: how to incorporate errors?
> Companies doing interesting work in portfolio optimisation:
– Market leader in portfolio optimisation software: www.axioma.com
– Robust portfolio optimisation software: http://bitarisk.cor-fs.com/
– Heuristic methods for random portfolio analysis: www.portfolioprobe.com
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Thank you! Questions?