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# Statistical Arbitrage - Hedge Fund Strategies

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A brief over view of a hedge fund strategy used in alternative investment markets.

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### Statistical Arbitrage - Hedge Fund Strategies

1. 1. Hedge Funds Strategies Statistical arbitrage
2. 2. Statistical arbitrage Index: 1. Definition 2. Limits of Arbitrage 3. Statistical arbitrage trading strategies 3.1. Pairs trade 3.2. Multi-factor models 3.3. Mean-reverting strategies 3.4. Cointegration 3.4.1. Index tracking 3.4.2. Enhanced index tracking and statistical arbitrag
3. 3. 1. Definition Arbitrage is the simultaneous purchase and sale of the same securities, for advantageously different prices, in two different markets (Sharpe and Alexander, 1990)
4. 4. 1. Definition According Getmansky & Lo (2005): Statistical abritrage: using two securities with similar payoffs and act essentially the same except that at some time, one security is overpriced and another is underpriced. The hedge fund manager will buy an underpriced security and short sell the overpriced one, hoping that the prices will converge in the future, making the profit.
5. 5. 2. Limits of Arbitrage According to the efficient market hypothesis (Samuelson, 1965) and the Law of One Price, the profitable arbitrage cannot exist: - Law of One Price: any two assets (or positions) with the same payoff must have the same price or value; - Efficient market hypothesis: no one can predict the market’s future direction, thus, must be “random”. Prices have to be set by well informed and rational investors.
6. 6. 3. Statistical arbitrage trading strategies 3.1. Pairs trade Pairs trade: stocks are put into pairs by market-based similarities or fundamental (HedgeFund-index (n.d.)): One stock in a pair outperforms the other: The poorer performing stock is bought long with the expectation that it will climb, the other is sold short. This hedges risk from whole-market movements.
7. 7. 3.2. Multi-factor models Arbitrage Pricing Theory: define factors which influence stock returns, picking the stocks for portfolio on the basis of their respective correlations, through multiple regressions on those factors (Sudak & Suslova, n.d.)
8. 8. 3.3. Mean-reverting strategies Contrarian trading: The stock prices are mean-reverting, where it’s expected to move in the future in the opposite direction, if the stock price deviates from its supposed average value. (Sudak & Suslova, n.d.) The underperforming stock (expected to increase) should be bought while the outperforming stock should be sold short.
9. 9. 3.4. Cointegration According Sudak & Suslova, n.d., mean reverting tracking error, better use of the information comprised in the stock prices and enhanced weights stability, allow a flexible design of various funded and self-financing trading strategies, from index and enhanced index tracking, to long-short market neutral and alpha transfer techniques.
10. 10. 3.4. Cointegration 3.4.1. Index tracking: Two stages: - select the stocks to be included in the tracking portfolio; - determin the portfolio holdings in each stock based on a cointegration optimization technique. (Sudak & Suslova, n.d.)
11. 11. 3.4. Cointegration 3.4.2. Enhanced index tracking and statistical arbitrag - Replicate artificial indexes, 'plus' or 'minus', constructed as to linearly underperform or over-perform the market index by a given amount per annum. - Short on a portfolio tracking the 'minus' benchmark; long on a portfolio tracking the 'plus' benchmark. This type of statistical arbitrage strategy should generate returns according: . the 'plus'/'minus' spread (i.e. double alpha) with no significant correlation with the market returns and low volatility (Sudak & Suslova, n.d.)
12. 12. References M. Getmansky, 2005, ‘Limits of arbitrage: Understanding how hedge funds fail’, Proceedings of the 23rd International Conference of the System Dynamic Society Sharpe, William & Gordon A., 1990, ‘Investments’, 4th edition. Prentice Hall, Englewood Cliffs, N.J. Sudak, D. & Suslova, O., n.d., ‘Behavioral Statistical Arbitrage’, Thesis, Master of Science in Banking and Finance Program at HEC, University of Lausanne