Information Entropy Theory and Asset Valuation: A Literature Survey


  • Sana Gaied Chortane Institute of Higher Business Study of Sousse, University of Sousse, Tunisia, and Member of LA REMFiQ Laboratory, University of Sousse, Tunisia
  • Kamel Naoui University. Manouba, ESCT, LARIMRAF LR21ES29, Manouba University campus, 2010, Tunisia



Information entropy theory, asset valuation, Capital Asset Pricing Model(CAPM), Diversification, Gaussian Distribution


The purpose of this study is to review the empirical work applied to market efficiency, portfolio selection and asset valuation, focusing on the presentation of the comprehensive theoretical framework of Information Entropy Theory (IET). In addition, we examine how entropy addresses the shortcomings of traditional models for valuing financial assets, including the market efficiency hypothesis, the capital asset pricing model (CAPM), and the Black and Scholes option pricing model. We thoroughly reviewed the literature from 1948 to 2022 to achieve our objectives, including well-known asset pricing models and prominent research on information entropy theory. Our results show that portfolio managers are particularly attracted to valuations and strive to achieve maximum returns with minimal risk. The entropy-based portfolio selection model outperforms the standard model when return distributions are non-Gaussian, providing more comprehensive information about asset and distribution probabilities while emphasising the diversification principle. This distribution is then linked to the entropic interpretation of the no-arbitrage principle, especially when extreme fluctuations are considered, making it preferable to the Gaussian distribution for asset valuation. This study draws important conclusions from its extensive analysis. First, entropy better captures diversification effects than variance, as entropy measures diversification effects more generically than variance. Second, mutual information and conditional entropy provide reasonable estimates of systematic and specific risk in the linear equilibrium model. Third, entropy can be used to model non-linear dependencies in stock return time series, outperforming beta in predictability. Finally, information entropy theory is strengthened by empirical validation and alignment with financial views. Our findings enhance the understanding of market efficiency, portfolio selection and asset pricing for investors and decision-makers. Using Information Entropy Theory as a theoretical framework, this study sheds new light on its effectiveness in resolving some of the limitations in traditional asset valuation models, generating valuable insights into the theoretical framework of the theory.


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Ahn, K., Lee, D., Sohn, S., & Yang, B. (2019). Stock market uncertainty and economic fundamentals: an entropy-based approach. Quantitative Finance, 19(7), 1151–1163. DOI:

Aksaraylı, M., & Pala, O. (2018). A polynomial goal programming model for portfolio optimization based on entropy and higher moments. Expert Systems with Applications, 94, 185–192. DOI:

Assaf, A., Charif, H., & Demir, E. (2022). Information sharing among cryptocurrencies: Evidence from mutual information and approximate entropy during COVID-19. Finance Research Letters, 47, 102556. DOI:

Ausloos, M. (1998). The Money Games Physicists Play. Europhysics News, 29(2), 70–72. DOI:

BACKUS, D., CHERNOV, M., & ZIN, S. (2014). Sources of Entropy in Representative Agent Models. The Journal of Finance, 69(1), 51–99. DOI:

Barbi, A. Q., & Prataviera, G. A. (2019). Nonlinear dependencies on Brazilian equity network from mutual information minimum spanning trees. Physica A: Statistical Mechanics and Its Applications, 523, 876–885. DOI:

Becker, R., Clements, A. E., Doolan, M. B., & Hurn, A. S. (2015). Selecting volatility forecasting models for portfolio allocation purposes. International Journal of Forecasting, 31(3), 849–861. DOI:

Behr, P., Guettler, A., & Miebs, F. (2013). On portfolio optimization: Imposing the right constraints. Journal of Banking & Finance, 37(4), 1232–1242. DOI:

Best, M. J., & Grauer, R. R. (1992). The analytics of sensitivity analysis for mean-variance portfolio problems. International Review of Financial Analysis, 1(1), 17–37. DOI:

Bhaduri, S. N. (2014). Applying Approximate Entropy (ApEn) to Speculative Bubble in the Stock Market. Journal of Emerging Market Finance, 13(1), 43–68. DOI:

Bhandari, D., & Pal, N. R. (1993). Some new information measures for fuzzy sets. Information Sciences, 67(3), 209–228. DOI:

Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637–654. DOI:

Bodnar, T., Mazur, S., & Okhrin, Y. (2017). Bayesian estimation of the global minimum variance portfolio. European Journal of Operational Research, 256(1), 292–307. DOI:

Boltzmann, L. (1872). Boltzmann equation. Sitzungsber Akade Wissen, 66, 275–370.

Borup, D., Christensen, B. J., Mühlbach, N. S., & Nielsen, M. S. (2023). Targeting predictors in random forest regression. International Journal of Forecasting, 39(2), 841–868. DOI:

Breuer, T., & Csiszár, I. (2013). Systematic stress tests with entropic plausibility constraints. Journal of Banking & Finance, 37(5), 1552–1559. DOI:

Brissaud, J.-B. (2005). The meanings of entropy. Entropy, 7(1), 68–96. DOI:

Brody, D. C., Buckley, I. R. C., Constantinou, I. C., & Meister, B. K. (2005). Entropic calibration revisited. Physics Letters A, 337(4–6), 257–264. DOI:

Buchen, P. W., & Kelly, M. (1996). The Maximum Entropy Distribution of an Asset Inferred from Option Prices. The Journal of Financial and Quantitative Analysis, 31(1), 143. DOI:

Caferra, R. (2022). Sentiment spillover and price dynamics: Information flow in the cryptocurrency and stock market. Physica A: Statistical Mechanics and Its Applications, 593, 126983. DOI:

Campbell, J. Y., Lo, A. W., & MacKinlay, A. C. (1997). The Econometrics of Financial Markets. Princeton University Press. DOI:

Campbell, J. Y., & Thompson, S. B. (2008). Predicting Excess Stock Returns Out of Sample: Can Anything Beat the Historical Average? Review of Financial Studies, 21(4), 1509–1531. DOI:

Carhart, M. M. (1997). On Persistence in Mutual Fund Performance. The Journal of Finance, 52(1), 57–82. DOI:

Carroll, A., O’Brien, F., & Ryan, J. (2017). An Examination of European Firms’ Derivatives Usage: The Importance of Model Selection. European Financial Management, 23(4), 648–690. DOI:

Clausius, R. (1854). On the heat produced by an electric discharge: To the editors of the Philosophical Magazine and Journal. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 7(45), 297. DOI:

Cover, T. M., & Thomas, J. A. (2006). Elements of information theory second edition solutions to problems. Internet Access, 19–20.

Dacorogna, M. (1999). Econophysicists find a forum. Physics World, 12(9), 19–20. DOI:

Daniel, K. D., Hirshleifer, D., & Subrahmanyam, A. (2001). Overconfidence, Arbitrage, and Equilibrium Asset Pricing. The Journal of Finance, 56(3), 921–965. DOI:

Daniel, K., & Titman, S. (1999). Market Efficiency in an Irrational World. Financial Analysts Journal, 55(6), 28–40. DOI:

De Luca, A., & Termini, S. (1972). A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Information and Control, 20(4), 301–312. DOI:

Deng, Y. (2016). Deng entropy. Chaos, Solitons & Fractals, 91, 549–553. DOI:

Dhifaoui, Z., Khalfaoui, R., Abedin, M. Z., & Shi, B. (2022). Quantifying information transfer among clean energy, carbon, oil, and precious metals: A novel transfer entropy-based approach. Finance Research Letters, 49, 103138. DOI:

Dionisio, A., Menezes, R., & Mendes, D. A. (2006). An econophysics approach to analyse uncertainty in financial markets: an application to the Portuguese stock market. The European Physical Journal B - Condensed Matter and Complex Systems, 50(1–2), 161–164. DOI:

Dolfsma, W., & Leydesdorff, L. (2008). ‘Medium-tech’ industries may be of greater importance to a local economy than ‘High-tech’ firms: New methods for measuring the knowledge base of an economic system. Medical Hypotheses, 71(3), 330–334. DOI:

Fama, E. F. (1965). The Behavior of Stock-Market Prices. The Journal of Business, 38(1), 34. DOI:

Fama, E. F. (1970). Efficient Capital Markets: A Review of Theory and Empirical Work. The Journal of Finance, 25(2), 383. DOI:

Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3–56. DOI:

FAMA, E. F., & FRENCH, K. R. (1996). Multifactor Explanations of Asset Pricing Anomalies. The Journal of Finance, 51(1), 55–84. DOI:

Fama, E. F., & French, K. R. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1–22. DOI:

Fard, F. A., Tchatoka, F. D., & Sriananthakumar, S. (2021). Maximum Entropy Evaluation of Asymptotic Hedging Error under a Generalised Jump-Diffusion Model. Journal of Risk and Financial Management, 14(3), 97. DOI:

George, G., Merrill, R. K., & Schillebeeckx, S. J. D. (2021). Digital Sustainability and Entrepreneurship: How Digital Innovations Are Helping Tackle Climate Change and Sustainable Development. Entrepreneurship Theory and Practice, 45(5), 999–1027. DOI:

Goldstein, S., Lebowitz, J. L., Tumulka, R., & Zanghì, N. (2020). Gibbs and Boltzmann Entropy in Classical and Quantum Mechanics. In Statistical Mechanics and Scientific Explanation (pp. 519–581). WORLD SCIENTIFIC. DOI:

Gonçalves-Bradley, D. C., Lannin, N. A., Clemson, L., Cameron, I. D., & Shepperd, S. (2022). Discharge planning from hospital. Cochrane Database of Systematic Reviews, 2022(2). DOI:

Gong, X., Min, L., & Yu, C. (2022). Multi-period portfolio selection under the coherent fuzzy environment with dynamic risk-tolerance and expected-return levels. Applied Soft Computing, 114, 108104. DOI:

Grossman, S. J., & Stiglitz, J. E. (1980). On the Impossibility of Informationally Efficient Markets. The American Economic Review, 70(3), 393–408.

Gu, R., Chen, Q., & Zhang, Q. (2021). Portfolio Selection with respect to the Probabilistic Preference in Variable Risk Appetites: A Double-Hierarchy Analysis Method. Complexity, 2021, 1–14. DOI:

Gulko, L. (1999). The entropy theory of stock option pricing. International Journal of Theoretical and Applied Finance, 02(03), 331–355. DOI:

Gulko, L. (2002). The entropy theory of bond option pricing. International Journal of Theoretical and Applied Finance, 05(04), 355–383. DOI:

Gupta, P. (2022). Portfolio optimization using elliptic entropy and semi-entropy of coherent fuzzy numbers. Information Sciences, 614, 240–262. DOI:

Hancock, P. A., Billings, D. R., Schaefer, K. E., Chen, J. Y. C., de Visser, E. J., & Parasuraman, R. (2011). A Meta-Analysis of Factors Affecting Trust in Human-Robot Interaction. Human Factors: The Journal of the Human Factors and Ergonomics Society, 53(5), 517–527. DOI:

Hartley, R. V. L. (1928). Transmission of Information 1. Bell System Technical Journal, 7(3), 535–563. DOI:

Havrda, J., & Chárvat, F. (1967). Quantification method of classification processes. The concept of structural α-entropy, Kybernetika 3, 30.

Horta, P., Lagoa, S., & Martins, L. (2014). The impact of the 2008 and 2010 financial crises on the Hurst exponents of international stock markets: Implications for efficiency and contagion. International Review of Financial Analysis, 35, 140–153. DOI:

Hübner, G., Lambert, M., & Papageorgiou, N. (2015). Higher-moment Risk Exposures in Hedge Funds. European Financial Management, 21(2), 236–264. DOI:

Hunt, J., & Devolder, P. (2011). Semi-Markov regime switching interest rate models and minimal entropy measure. Physica A: Statistical Mechanics and Its Applications, 390(21–22), 3767–3781. DOI:

Jaynes, E. T. (1957). Information theory and statistical mechanics. Physical Review, 106(4), 620. DOI:

Jensen, M. C. (1978). Some anomalous evidence regarding market efficiency. Journal of Financial Economics, 6(2–3), 95–101. DOI:

Jizba, P., & Arimitsu, T. (2004). Observability of Rényi’s entropy. Physical Review E, 69(2), 026128. DOI:

Knez, P. J., & Ready, M. J. (1997). On The Robustness of Size and Book‐to‐Market in Cross‐Sectional Regressions. The Journal of Finance, 52(4), 1355–1382. DOI:

Kosko, B. (1986). Fuzzy entropy and conditioning. Information Sciences, 40(2), 165–174. DOI:

Kothari, S. P., & Warner, J. B. (2001). Evaluating Mutual Fund Performance. The Journal of Finance, 56(5), 1985–2010. DOI:

Kullback, S., & Leibler, R. A. (1951). On Information and Sufficiency. The Annals of Mathematical Statistics, 22(1), 79–86. DOI:

Lo, A. W. (2004). The Adaptive Markets Hypothesis. The Journal of Portfolio Management, 30(5), 15–29. DOI:

MacKay, D. J. C. (2003). Information theory, inference and learning algorithms. Cambridge university press.

MacLean, L., Yu, L., & Zhao, Y. (2022). A Generalized Entropy Approach to Portfolio Selection under a Hidden Markov Model. Journal of Risk and Financial Management, 15(8), 337. DOI:

Mahmoud, I., & Naoui, K. (2017). Measuring systematic and specific risk: Approach mean-entropy. Asian Journal of Empirical Research, 7(3), 42–60. DOI:

Mandelbrot, B. (1967). The Variation of Some Other Speculative Prices. The Journal of Business, 40(4), 393. DOI:

Mandelbrot, B. B. (1971). When Can Price be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models. The Review of Economics and Statistics, 53(3), 225. DOI:

Mandelbrot, B. B., & Hudson, R. L. (2004). The (Mis) Behaviour of Markets: A Fractal View of Risk, Ruin and Reward, paperback. Profile Books, London, originally published by Basic Books, United States.

Markovitz, H. M. (1959). Portfolio selection: Efficient diversification of investments. John Wiley.

Markowitz, H. (1952). The Utility of Wealth. Journal of Political Economy, 60(2), 151–158. DOI:

Mossin, J. (1966). Equilibrium in a Capital Asset Market. Econometrica, 34(4), 768. DOI:

Neri, C., & Schneider, L. (2012). Maximum entropy distributions inferred from option portfolios on an asset. Finance and Stochastics, 16(2), 293–318. DOI:

Oh, G., Kim, H., Ahn, S.-W., & Kwak, W. (2015). Analyzing the financial crisis using the entropy density function. Physica A: Statistical Mechanics and Its Applications, 419, 464–469. DOI:

Oh, G., Kim, S., & Eom, C. (2007). Market efficiency in foreign exchange markets. Physica A: Statistical Mechanics and Its Applications, 382(1), 209–212. DOI:

Ormos, M., & Zibriczky, D. (2014). Entropy-Based Financial Asset Pricing. PLoS ONE, 9(12), e115742. DOI:

Owusu Junior, P., Frimpong, S., Adam, A. M., Agyei, S. K., Gyamfi, E. N., Agyapong, D., & Tweneboah, G. (2021). COVID-19 as Information Transmitter to Global Equity Markets: Evidence from CEEMDAN-Based Transfer Entropy Approach. Mathematical Problems in Engineering, 2021, 1–19. DOI:

Patil, G. P., & Taillie, C. (1982). Diversity as a Concept and its Measurement. Journal of the American Statistical Association, 77(379), 548–561. DOI:

Pincus, S., & Kalman, R. E. (2004). Irregularity, volatility, risk, and financial market time series. Proceedings of the National Academy of Sciences, 101(38), 13709–13714. DOI:

Pincus, S. M. (1991). Approximate entropy as a measure of system complexity. Proceedings of the National Academy of Sciences, 88(6), 2297–2301. DOI:

Pincus, S., & Singer, B. H. (1996). Randomness and degrees of irregularity. Proceedings of the National Academy of Sciences, 93(5), 2083–2088. DOI:

Li, P., & Liu, B. (2008). Entropy of Credibility Distributions for Fuzzy Variables. IEEE Transactions on Fuzzy Systems, 16(1), 123–129. DOI:

Piquet, V., Luczak, C., Seiler, F., Monaury, J., Martini, A., Ward, A. B., Gracies, J.-M., Motavasseli, D., Piquet, V., Luczak, C., Seiler, F., Monaury, J., Lépine, E., Chambard, L., Baude, M., Hutin, E., Martini, A., Samaniego, A., Bayle, N., … Motavasseli, D. (2021). Do Patients With COVID-19 Benefit from Rehabilitation? Functional Outcomes of the First 100 Patients in a COVID-19 Rehabilitation Unit. Archives of Physical Medicine and Rehabilitation, 102(6), 1067–1074. DOI:

Rosenberg, B., Reid, K., & Lanstein, R. (1985). Persuasive evidence of market inefficiency. The Journal of Portfolio Management, 11(3), 9–16. DOI:

Ross, S. A. (1976). Options and Efficiency. The Quarterly Journal of Economics, 90(1), 75. DOI:

Ross, S. A. (1989). Information and Volatility: The No‐Arbitrage Martingale Approach to Timing and Resolution Irrelevancy. The Journal of Finance, 44(1), 1–17. DOI:

RUBINSTEIN, M. (1994). Implied Binomial Trees. The Journal of Finance, 49(3), 771–818. DOI:

Samuelson, P. A. (1973). Proof That Properly Discounted Present Values of Assets Vibrate Randomly. The Bell Journal of Economics and Management Science, 4(2), 369–374. DOI:

Shannon, C. E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal, 27(3), 379–423. DOI:

Sharpe, W. F. (1963). A Simplified Model for Portfolio Analysis. Management Science, 9(2), 277–293. DOI:

Sharpe, W. F. (1964). Capital asset prices: a theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3), 425–442. DOI:

Sharpe, W. F. (1966). Security prices, risk, and maximal gains from diversification: reply. The Journal of Finance, 21(4), 743–744. DOI:

Smimou, K., Bector, C. R., & Jacoby, G. (2007). A subjective assessment of approximate probabilities with a portfolio application. Research in International Business and Finance, 21(2), 134–160. DOI:

Sukpitak, J., & Hengpunya, V. (2016). Efficiency of Thai stock markets: Detrended fluctuation analysis. Physica A: Statistical Mechanics and Its Applications, 458, 204–209. DOI:

Tabakis, E. (2000). Information and entropy in incomplete markets. International Journal of Theoretical and Applied Finance, 03(03), 561–561. DOI:

Treynor, J. (1965). How to rate management of investment funds. Harvard Business Review, 63–75.

Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics, 52, 479–487. DOI:

Ünal, B. (2022). Causality Analysis for COVID-19 among Countries Using Effective Transfer Entropy. Entropy, 24(8), 1115. DOI:

Usta, I., & Kantar, Y. M. (2011). Mean-Variance-Skewness-Entropy Measures: A Multi-Objective Approach for Portfolio Selection. Entropy, 13(1), 117–133. DOI:

Wang, Z., & Shang, P. (2021). Generalized entropy plane based on multiscale weighted multivariate dispersion entropy for financial time series. Chaos, Solitons & Fractals, 142, 110473. DOI:

Xiao, F. (2020). Generalization of Dempster–Shafer theory: A complex mass function. Applied Intelligence, 50(10), 3266–3275. DOI:

Xu, H., Dinev, T., Smith, J., & Hart, P. (2011). Information Privacy Concerns: Linking Individual Perceptions with Institutional Privacy Assurances. Journal of the Association for Information Systems, 12(12), 798–824. DOI:

Yager, R. R. (2000). On the entropy of fuzzy measures. IEEE Transactions on Fuzzy Systems, 8(4), 453–461. DOI:

Yu, J.-R., Lee, W.-Y., & Chiou, W.-J. P. (2014). Diversified portfolios with different entropy measures. Applied Mathematics and Computation, 241, 47–63. DOI:

Zhao, S., Lin, Q., Ran, J., Musa, S. S., Yang, G., Wang, W., Lou, Y., Gao, D., Yang, L., He, D., & Wang, M. H. (2020). Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early phase of the outbreak. International Journal of Infectious Diseases, 92, 214–217. DOI:

Zhou, R., Cai, R., & Tong, G. (2013). Applications of Entropy in Finance: A Review. Entropy, 15(12), 4909–4931. DOI:




How to Cite

Chortane, S. G., & Naoui, K. . (2024). Information Entropy Theory and Asset Valuation: A Literature Survey. International Journal of Accounting, Business and Finance, 2(1), 42–60.



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