# A Genetic Algorithm Tutorial [jnl article] by Whitley D.

By Whitley D.

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Obviously, other market factors may be included in the objective function to ensure zero portfolio exposure thereto. For q market factors, the objective function is: p f − kp p − λp l − λ1 p l1 − · · · − λq p lq Determining the portfolio that maximizes the objective function is a straightforward application of the Lagrange multiplier method. 2 Market Impact We forecast IBM stock to yield annualized return of 10 percent over the next week. The forecast is more certain than any forecast we have ever made.

As the analysis techniques used became more sophisticated and the models deployed more technical, so the sobriquet by which the discipline became known was elaborated. The term ‘‘statistical arbitrage’’ was first used in the early 1990s. Statistical arbitrage approaches range from the vanilla pairs trading scheme of old to sophisticated, dynamic, nonlinear models employing techniques including neural networks, wavelets, fractals— just about any pattern matching technology from statistics, physics, and mathematics has been tried, tested, and in a lot of cases, abandoned.

3 Rule Calibration Immediately when one extends the analysis beyond a single pair, or examines a longer history of a single pair, the problem of calibration is encountered. 3 Daily closing spread, CAL–AMR now for the single year 2000. 1 Wow! We should have shown that example earlier. The spread varies over a \$20 range, three times the opportunity of the CAL–AMR 1 The price series for AMR is adjusted for the spinoff of Sabre, the company’s reservations business, on March 16, 2000. Without proper adjustment, the close price series would drop from \$60 to \$30 overnight—an unrealistically dramatic spread change!