By Hoi, Steven C. H.; Li, Bin
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Additional info for Online portfolio selection : principles and algorithms
To test whether simple luck can generate the return achieved by a strategy, portfolio management practitioners (Grinold and Kahn 1999) can conduct statistical tests. Since all test datasets are just samples of the market population, such tests can validate a strategy for future. We conduct a Student’s t-test to determine the likelihood that the observed profitability is due to chance alone (under the assumption that a strategy is not profitable in the population). Since the sample profitability is being compared with no profitability, 0 is subtracted from the sample mean profit/loss.
With the mean reversion nature, it is difficult to obtain a useful regret bound for Anticor. Although heuristic and without theoretical guarantee, Anticor empirically outperforms all other strategies at the time. On the other hand, though Anticor obtains good performance, its heuristic nature cannot fully exploit mean reversion. Thus, exploiting the property via systematic learning algorithms is highly desired, which motivates one part of our research. 3 Summary Although counterintuitive, the follow the loser principle is quite useful in obtaining a high cumulative return in the empirical studies.
Finally, the probability of the t-statistic can be calculated with a degree of freedom equal to the number of periods minus 1. Note that the Student’s t-test assumes that the underlying distribution of data is normal. According to the central limit theorem, as the sample size increases, the distribution of the sample mean approaches normal. If a sample ∗ Here, 252 denotes the average number of annual trading days. For other frequencies, we can choose their corresponding numbers. 000159 per day.