Portfolio Optimization

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CF963, Autumn Term 2010-11 Learning and Computational Intelligence in Economics and Finance. Portfolio Optimization. University of Essex 26 th November June 2010 Dr Amadeo Alentorn Head of Quantitative Research amadeo.alentorn@omam.co.uk. - PowerPoint PPT Presentation

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  • Portfolio OptimizationUniversity of Essex26th November June 2010

    Dr Amadeo AlentornHead of Quantitative Researchamadeo.alentorn@omam.co.ukCF963, Autumn Term 2010-11Learning and Computational Intelligence in Economics and Finance

  • 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 glanceDynamic investment firm, focused on high performance and absolute returnsIndependent investment teams no house view or investment styleExpertise in Discretionary equitiesFixed incomeQuantitative strategies Range of long only and alternative products designed to meet the needs of retail and institutional investorsNew product innovationIndependent risk management teamUSD6.5 billion assets under management*Part of Old Mutual Group, a constituent of the FTSE 100 index.

    * Source: OMAM, as at 30/10/09

  • OMAM Quantitative Strategies GroupInvestment teamInvestment researchPortfolio construction and managementV-Lab: PhD and post-doctoral researchers Systems developmentAcademic Advisory Board

  • Equity investing styles: discretionary/systematic spectrumDiscretionary investingMostly driven by fundamental analysisAnalysis of companys accounts, business plans, competitors, etcMeeting management and understanding business modelUsually focus in one country/ sector/ industryLonger holding horizonQuantitative investingFactor models based on both fundamental and technical analysisAble to analyse and evaluate 1000s of companiesHighly diversified portfoliosMedium term holding horizonStatistical arbitrageUsually based on technical analysis, price driven (i.e. pairs trading) High frequency execution, usually intra-day tradingShort holding horizonAcross the industry, many different variations: quantamentals, quant overlays, etc.Discretionary

    Systematic

  • Types of equity funds: passive/active spectrumIndex trackingTracking error TE < 0.25%Enhanced long onlyTE between 0.50 to 1.50%Active long onlyTE greater than 2.00%Short extension (130/30)Equivalent to index plus 30/30 market neutralMarket neutral hedge fundsDollar neutral, i.e. 100/100Long/short hedge fundsVariable net exposure

    Trade-off between risk and expected return.Passive

    Active Long only funds Hedge funds

  • Types of equity funds: long, short and net positionsGiven $100 of capital, the structure of the portfolio will be very different, for different types of funds.

  • Performance of a market neutral fund vs. marketMarket risk is the primary source of risk for a long only equity fund in absolute termsWhen 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

  • Short-sellingTraditionally investing (long only constraint) can create miss-pricings, because only positive views about stocks can be fully reflected into pricesHedge funds are able to reflect buy and sell ideas into the portfolios, by buying stocks with positive forecasts, and shorting stocks with negative forecastsHow 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 marketAt a future date, hedge fund buys back the stock, and returns it to the lenderStock owner receives a lending fee for the serviceNote: naked short selling is banned!RisksStock recallShort squeezes: when prices go up, rush to cover positionsPotential of infinite loss

  • Short-selling: Northern Rock case studySource: Data Explorers www.dataexplorers.com

  • Types of equity hedge fundsHedge fund indices have become a useful tool for monitoring the performance of the different hedge fund strategiesBut issues with survivorship bias, self-selection bias (voluntary reporting), etcUseful indication of risk associated with each strategySource: Hedge Fund Research www.hedgefundresearch.com

  • Our investment approach and philosophyMarket inefficiencies result from behavioural biases and structural anomaliesInvestment insights, not statistics, drive researchMany of the investment strategies are not different than those used by fundamental fund managers (i.e. valuation, earnings quality, etc)Rigorous backtesting of data to validate investment criteriaOne of the key advantages over fundamental managers, we are able to test the historic performance of an investment strategyContinuous research to maintain and enhance information ratioTo mitigate risk of imitation and of crowded tradesMulti factor models designed to perform throughout the business cycleFactor modelling lends itself to market neutral investing, generating both buys and sells

  • Investment strategies based on behavioural finance Financial markets are complex systemsPrices are the result of complex interactions between market participantsAcademic 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-tradingProspect theory: people value gains and losses differentlyAnchoringUnder-reaction/ overreaction / herdingNave extrapolationA 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.

    Quantitative investment allows to remove emotion from the investment process

  • Academic research vs. industry researchLiquidityMany 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.Survivorship biasImportant to include companies that are no longer in the universe (impact of bankruptcies/corporate actions) Reporting lagsPoint in time databases. BackfillingSee Rewriting historyTransaction costsSpecially for high frequency strategies

  • Factors: academic debate alpha vs. risk? (Fama French)Source: Kenneth French website

  • Quantitative investment processFully systematic investment process.Universe: top 95% of market capitalisation in each country: around 3,500 stocks1Stocks ranked by attractivenessOptimise risk and return profile of portfolioFinal portfolioMulti factor stock selection criteria

  • Portfolio optimisation processTrade listTrade cost modelRelative return modelRisk modelOptimisation and portfolio constructionContinuous research on all three proprietary models and process

  • Part 1: Introduction to quantitative investing in hedge funds

    Part 2: The problem of portfolio optimisation

    Part 3: Application of heuristic portfolio optimization

  • *Whats 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.

  • The mean-variance frontier

  • *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 :

  • *Long vs short stock positionsLong: 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 investors 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.

  • *The optimisation problem for a market neutral hedge fundFor a market neutral hedge fund, we remove the no-shorting constraint to allow negative weights:

    Objective functions:Mean Variance

    Mean Value-At-Risk

  • *Why heuristic optimisation?Stock returns exhibit non-normal characteristics, including skewness and fat tails, and most investors are loss averseThese 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 RiskIncorporation of integer constraints, such as cardinality constraints.Heuristic algorithms already used to tackle this problem: Genetic Algorithms, and Threshold Accepting algorithmsIn the last part of the lecture, we will look at a new heuristic algorithm: the GNMA

  • Part 1: Introduction to quantitative investing in hedge funds

    Part 2: The problem of portfolio optimisation

    Part 3: Application of heuristic portfolio optimization

  • *IntroductionThis work is based on a recent paper presented at UKCIHeuristic 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 Algorit