Finding Alphas, 2nd Edition

9Backtest – Signal or Overfitting?

By Zhuangxi Fang and and Peng Yan

INTRODUCTION

Over the past decade, quite a few quant funds have gained tremendous success in the financial markets through their alpha portfolios. But does that mean an alpha can effectively predict stock prices? More specifically, can quants predict the price of a given stock on a given date in the future? Unfortunately, we probably cannot make single predictions with any reasonable confidence. It is the nature of statistical arbitrage that prediction is possible only in a “statistical” sense: only over a large number of predictions do random errors average out to a usable level of accuracy in the aggregate. More interestingly, there are many ways of making such statistical price predictions.

STATISTICAL ARBITRAGE

The key underlying assumption of statistical arbitrage is that the prices of financial instruments are driven by consistent rules, which can be discovered from their historical behavior and applied to the future. The prices of financial instruments are influenced by multiple factors, including trading microstructures, fundamental valuation, and investor psychology. Therefore, it is to be expected that various kinds of price-driving rules can be discovered and used to create alphas. As the prices of securities are determined by multiple rules, or factors, not every rule will apply to any particular instrument at any given moment.

A real price-driving rule – and a good alpha based on this rule ...