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

1. Hedge Funds Strategies
Statistical arbitrage

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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