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## Tsallis Relative Entropy

# In an earlier post (Entropy), we discussed Information Entropy and how it can be used to define risk in financial markets. We also briefly touched upon Tsallis Entropy which unlike Shannon Entropy, defines entropy for systems with long range interations. Since the performance of financial markets is the result of many interacting agents, an appropriate entropy used to define risk is the Tsallis Entropy.

Relative Entropy is the risk associated with an equity, compared to a standard index such as S&P 500 , Nasdaq ---. This is important in portfolio management, where one is interested in constructing and managing portfolios that beat market returns in the long run (> 5-6 yrs).

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# Tsallis Relative Entropy(TRE) shows how much the risk (defined by Tsallis entropy) of an individual equity differs from that of a standard index. Our back studies show that over a period of 6 years or longer, portfolios constructed/managed using 'Tsallis Relative Entropy' as the risk measure, outperform both the markets and those managed using the risk measure 'beta', usually used by investment managers.

# For definitions and details of Tsallis Entropy and Tsallis Relative Entropy , see publications below. Also see A New Risk Measure for details.

Financial Portfolios based on Tsallis relative entropy as the Risk Measure, Sandhya Devi, 2019, Journal of Statistical Mechanics 093207

https://doi.org/10.1088/1742-5468/ab3bc5

This article can also be found in

https://arxiv.org/abs/1901.04945v3

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