Practical Portfolio Optimization Victor DeMiguel London Business School Based on joint research with Lorenzo Garlappi Alberto Martin-Utrera Xiaoling Mei U. of British Columbia U. Carlos III de Madrid U. Carlos III de Madrid Francisco J. Nogales Yuliya Plyakha Raman Uppal U. Carlos III de Madrid Goethe University Frankfurt EDHEC Business School Grigory Vilkov Goethe University Frankfurt Semi-plenary talk Fourth International Conference on Continuous Optimization Universidade Nova de Lisboa Lisbon, July 2013
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Practical Portfolio Optimization
Victor DeMiguelLondon Business School
Based on joint research with
Lorenzo Garlappi Alberto Martin-Utrera Xiaoling MeiU. of British Columbia U. Carlos III de Madrid U. Carlos III de Madrid
Francisco J. Nogales Yuliya Plyakha Raman UppalU. Carlos III de Madrid Goethe University Frankfurt EDHEC Business School
Grigory VilkovGoethe University Frankfurt
Semi-plenary talkFourth International Conference on Continuous Optimization
Universidade Nova de LisboaLisbon, July 2013
“The motivation behind my dissertation was to applymathematics to the stock market” Harry Markowitz
“This is not a dissertation in economics, and we cannotgive you a PhD in economics for this” Milton Friedman
Mean-variance efficient frontier
I Efficient frontier: Investor concerned only about mean andvariance of returns chooses portfolio on efficient frontier.
Improving Portfolio Selection UsingOption-Implied Volatility and Skewness
DeMiguel, Plyakha, Uppal, and Vilkov, JFQA
I Implied volatilities improvevolatility by 10-20%.
I Implied correlations do notimprove performance.
I Implied skewness andvolatility risk premiumproxy mean returns.
I Improve Sharpe ratioeven with moderatetransactions costs forweekly and monthlyrebalancing.
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II. Better mean
To obtain better estimates of mean:
1. Ignore means
2. Use Bayesian estimates
3. Use robust optimization
4. Use option-implied information
5. Use stock return serial dependence
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Stock Return Serial Dependence and Out Of SamplePerformance, DeMiguel, Nogales, Uppal (2013)
I Stock return serialdependence
I Contrarian: “buy losersand sell winners”.
I Momentum: “buywinners and sell losers”.
I Can this be exploitedsystematically with manyassets?
I Yes, for transaction costsbelow 10 basis points.
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II. Better mean
To obtain better estimates of mean:
1. Ignore historical means
2. Use Bayesian estimates
3. Use robust optimization
4. Use option-implied information
5. Use stock return serial dependence
6. Exploit anomalies
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Exploit anomalies
I size: small firmsoutperform largefirms,
I momentum: pastwinners outperformpast losers,
I book-to-market: highbook-to-market ratiofirms outperform lowbook-to-market ratiofirms.
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III. Better constraints
To improve performance impose:
1. Shortsale constraints
2. Parametric portfolios
3. Performance-based regularization
4. Norm constraints
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III. Better constraints
To improve performance impose:
1. Shortsale constraints
2. Parametric portfolios[Brandt et al., 2009] impose constraint
w1
w2
...wN
=
wM
1wM
2...
wMN
+
me1 btm1 mom1
me2 btm2 mom2
......
...meN btmN momN
θme
θbtmθmom
,
me = market equity,btm = book-to-market ratio,
mom = momentum or average return over past 12 months.
3. Performance-based regularization
4. Norm constraints
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III. Better constraints
To improve performance impose:
1. Shortsale constraints
2. Parametric portfolios
3. Performance-based regularization
I Constrain variance of estimators of portfolio mean and CVaR.
I “Performance-based regularization in mean-CVaR portfoliooptimization”, [Karoui et al., 2011](Thu.A.18, Optimization in Finance II).
4. Norm constraints
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III. Better constraints
To improve performance impose:
1. Shortsale constraints
2. Parametric portfolios
3. Performance-based regularization
4. Norm constraints
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A Generalized Approach to Portfolio Optimization:Improving Performance by Constraining Portfolio Norms
DGNU (MS, 2009)
minw
w>Σw
s.t. w>e = 1
‖w‖ ≤ δ
I Nests 1/N, shrinkage covariance matrix of[Ledoit and Wolf, 2004b], and shortsale constraints,
I Diversification: 2-norm,
I Leverage constraint: 1-norm.57 / 73
Help wanted
I Optimization can make a difference in portfolio selection.
I Research opportunities
I Integer variables:
I VaR:
I fixed costs and cardinality constraints:
I Multistage optimization:
I return predictability,
I transaction costs,
I Calibration, calibration, calibration:
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Help wanted
I Optimization can make a difference in portfolio selection.
I Research opportunities
I Integer variables:
I VaR:
[Gaivoronski and Pflug, 2005], [Benati and Rizzi, 2007],Vera and Zuluaga (2013).
I fixed costs and cardinality constraints:
I [Brito and Vicente, 2012], “Efficient cardinality/mean-varianceportfolios”, Optimization in Finance III, Thu.B.18, derivativefree algorithm based on direct multisearch.
I [Roman et al., 2013], “Enhanced indexation based onsecond-order stochastic dominance”,Optimization in Finance I, Wed.D.18.
I Multistage optimization:
I return predictability,
I transaction costs,
I Calibration, calibration, calibration:
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Help wanted
I Optimization can make a difference in portfolio selection.
I Research opportunities
I Integer variables:
I VaR:
I fixed costs and cardinality constraints:
I Multistage optimization:
I return predictability,
I transaction costs,
I Mei, D., Nogales, (2013), “Multiperiod Portfolio Optimizationwith General Transaction Costs”,Optimization in Finance II, Thu.A.18.
I Calibration, calibration, calibration:
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Help wanted
I Optimization can make a difference in portfolio selection.
I Research opportunities
I Integer variables:
I VaR:
I fixed costs and cardinality constraints:
I Multistage optimization:
I return predictability,
I transaction costs,
I Calibration, calibration, calibration:
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Same dog, different collar?Devil Is in One Detail: Calibration
Constraints Robust
optimization
Bayesian
portfolios
Shrinkage
estimators
Gotoh &
Takeda CMS 2011
DGNU MS 2009
Goldfarb
Iyengar MOR 2003
Caramanis
Mannor
Xu (2011)
Jorion JFQA 1986
Jaganathan
Ma JoF, 2003
DGNU MS 2009
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Help wanted
I Optimization can make a difference in portfolio selection.
I Research opportunities
I Integer variables:
I value at Risk.I fixed costs and cardinality constraints,
I Multistage optimization:
I return predictability,I transaction costs.
I Calibration, calibration, calibration:
I “Size Matters: Optimal Calibration of Shrinkage Estimatorsfor Portfolio Selection”, [Martin-Utrera, D., Nogales, 2013],
I choose criterion carefully, get nonparametric.I Martin-Utrera, D., Nogales, (2013), “Parameter Uncertainty in
Multiperiod Portfolio Optimization with Transaction Costs”,Optimization in Finance II, Thu.A.18.
I Statistics/big data/real-time estimation and optimization:
I high-frequency trading.
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Help wanted
I Optimization can make a difference in portfolio selection.
I Research opportunities
I Integer variables:
I value at Risk.I fixed costs and cardinality constraints,
I Multistage optimization:
I return predictability,I transaction costs.
I Calibration, calibration, calibration:
I “Size Matters: Optimal Calibration of Shrinkage Estimatorsfor Portfolio Selection”, [Martin-Utrera, D., Nogales, 2013],
I choose criterion carefully, get nonparametric.I Martin-Utrera, D., Nogales, (2013), “Parameter Uncertainty in
Multiperiod Portfolio Optimization with Transaction Costs”,Optimization in Finance II, Thu.A.18.
I Statistics/big data/real-time estimation and optimization:
I high-frequency trading.
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High frequency trading
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High frequency trading
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Thank you
Victor DeMiguelhttp://www.london.edu/avmiguel/
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A Generalized Approach to Portfolio Optimization: Improving Performance By Constraining PortfolioNorms.
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Parameter uncertainty in multiperiod portfolio optimization with transaction costs.
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Size matters: Optimal calibration of shrinkage estimators for portfolio selection.
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Multiperiod portfolio optimization with general transaction costs.
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Portfolio selection with robust estimation.
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Stock return serial dependence and out-of-sample portfolio performance.
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London Business School working paper.
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Improving portfolio selection using option-implied volatility and skewness.
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