System and method for analyzing data associated with statistical arbitrage
Providing computer-based systems and methods for analyzing historical performance of financial securities and identifying trades in those securities based on the securities' current position as compared to this historical performance. These computer-based systems and computer-implemented methods include identifying stock pairs to include in a trading portfolio, based on a measure of the pair's relative performance, such as a modified Sharpe Ratio. The value of the stocks in each stock pair in the portfolio is assessed and deviations determined. This assessment can occur daily or at a longer or shorter time step. Stocks are bought or sold based on the current price of the stock as compared to historical performance. The present invention preferably employs a large number of stock pairs in the trading portfolio. This use of a large number of pairs results in a plurality of stocks being in more than one stock pair.
1. A system for statistical arbitrage, comprising:
a calibration module comprising instructions stored in a machine-readable medium for analyzing a set of stocks and selecting a plurality of stock pairs from within the set of stocks, wherein each of the selected stock pairs comprises a value greater than a performance measure and wherein fifty percent or more of the individual stocks in the plurality of stock pairs are included in more than one stock pair; and
an operations module comprising instructions stored in a machine-readable medium for automatically determining whether to buy or sell the stocks in the selected stock pairs based on the stocks' current performance as compared to the stocks' historical performance; and
a processor that executes the instructions of the calibration module and the operations module.
2. The system of claim 1 , further comprising a database module comprising historical price data for the stocks within the set of stocks.
3. A computerized method for identifying stock pairs for statistical arbitrage, comprising the steps of:
identifying a group of stock pairs from a set of stocks;
calculating, by a calibration module, a performance measure for each stock pair in the group of stock pairs;
comparing, by the calibration module, the calculated performance measure for each stock pair to a reference value for the performance measure; and
selecting, by the calibration module, the stock pairs for inclusion in a portfolio based on the comparison of the calculated performance measure to a reference value for the performance measure, wherein fifty percent or more of the individual stocks in the selected stock pairs are included in more than one stock pair,
wherein the calibration module is implemented in at least one computer system that comprises instructions stored in a machine-readable medium and a processor that executes the instructions.
4. The method of claim 3 , wherein the identified group comprises all possible stock pair combinations from the set of stocks.
5. The method of claim 3 , wherein the performance measure comprises a modified Sharpe Ratio.
6. The method of claim 3 , further comprising the step of calculating a weighting factor for the stock pair.
7. The method of claim 3 , wherein the number of pairs comprising the same stock comprises a maximum number greater than two pairs.
8. The system of claim 1 ,
wherein the operations module further comprises instructions stored in a machine-readable medium for, for each stock pair:
determining a first relative performance of the stock pair at a current time;
determining a second relative performance of the stock pair for a historical time; and
calculating a deviation in the first relative performance and the second relative performance, and
wherein the operations module further comprises instructions stored in a machine-readable medium for initiating one or more trades of a stock comprising one of the stocks of the plurality of stock pairs based on the calculated deviation regardless of the magnitude of the deviation.
9. The system, of claim 8 , wherein the magnitude of the trade of stock is proportional to the magnitude of the calculated deviation.
10. The system of claim 8 , wherein the historical time comprises a fixed time in the past.
11. The system of claim 10 , wherein the fixed time in the past comprises a reversion time for the stock pair.
12. The system of claim 8 , wherein the historical time comprises a range of time in the past.
13. A computerized method for statistical arbitrage comprising the steps of:
a) identifying a plurality of stock pairs from a set of stocks;
b) calculating a performance measure for a stock pair in the plurality of stock pairs;
c) comparing, by a calibration module, the calculated performance measure to a reference value for the performance measure;
d) selecting, by the calibration module, the stock pair for inclusion in a portfolio based on the comparison of the calculated performance measure to a reference value for the performance measure;
e) repeating steps b) through d) for each of the stock pairs in the identified plurality of stock pairs, wherein fifty percent or more of the individual stocks in the selected stock pairs are included in more than one stock pair;
f) determining a first relative performance of a stock pair in the portfolio at a current time;
g) determining a second relative performance of the stock pair for a historical time;
h) calculating, by an operations module, a deviation in the first relative performance and the second relative performance;
i) repeating steps f) through h) for each stock pair in the portfolio; and
j) initiating, by the operations module, one or more trades of a stock comprising one of the stocks of the portfolio based on the calculated deviation regardless of the magnitude of the deviation,
wherein the calibration module and operations module are implemented in at least one computer system that comprises instructions stored in a machine-readable medium and a processor that executes the instructions.
14. The method of claim 13 , wherein the step of determining a first relative performance of a stock pair in the portfolio at a current time comprises k) calculating, by the operations module, the natural logarithm of the price ratio of a first stock of the stock pair to a second stock of the stock pair at the current time;
the step of determining a second relative performance of the stock pair for a historical time comprises l) determining, by the operations module, the average of the natural logarithm of the price ratio of the first stock of the stock pair to the second stock of the stock pair for each day in a time period prior to the current time;
the step of calculating a deviation in the first relative performance and the second relative performance comprises m) determining, by the operations module, the difference in the value calculated at step (k) and the value determined at step (l); and
the step of initiating one or more trades of a stock comprising one of the stocks of the portfolio based on the calculated deviation regardless of the magnitude of the deviation comprises j) designating, by the operations module, one of the stocks in the stock pair as a stock to buy and the other stock in the stock pair as a stock to sell based on the difference.
15. The method of claim 14 , wherein, for step j) the first stock of the stock pair comprises the stock to sell and the second stock of the stock pair comprises the stock to buy if the value of step c) comprises a positive value.
16. The method of claim 14 , wherein, for step i) the second stock of the stock pair comprises the stock to sell and the first stock of the stock pair comprises the stock to buy if the value of step c) comprises a non-positive value.
17. The method of claim 13 , wherein the performance measure comprises a modified Shame Ratio.
18. The method of claim 13 , further comprising the step of calculating a weighting factor for the stock pair in the portfolio.
19. The method of claim 13 , wherein the magnitude of the trade of stock is proportional to the magnitude of the calculated deviation.
20. The method of claim 13 , wherein step j) comprises calculating a net trade for a stock comprising more than one stock pair.
21. The method of claim 13 , wherein the historical time comprises a fixed time in the past.
22. The method of claim 21 , wherein the fixed time in the past comprises a reversion time for the stock pair.
23. The method of claim 13 , wherein the historical time comprises a range of time in the past.
24. The method of claim 13 , wherein step d) further comprises the step of screening the selected stock pairs based on a characteristic of the stock pairs.