Devi, Sandhya
(2018):
*Financial Portfolios based on Tsallis Relative Entropy as the Risk Measure.*

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## Abstract

Tsallis relative entropy, which is the generalization of Kullback-Leibler relative entropy to non-extensive systems, is investigated as a possible risk measure in constructing risk optimal portfolios whose returns beat market returns. The results are compared with those from three other risk measures: 1) the commonly used ‘beta’ of the Capital Asset Pricing Model (CAPM), 2) Kullback-Leibler relative entropy, and 3) the relative standard deviation. Portfolios are constructed by binning the securities according to their risk values. The mean risk value and the mean return in excess of market returns for each bin is calculated to get the risk-return patterns of the portfolios. The investigations have been carried out for both long (~18 years) and shorter (~9 years) terms that include the dot-com bubble and the 2008 crash periods. In all cases, a linear fit can be obtained for the risk and excess return profiles, both for long and shorter periods. For longer periods, the linear fits have a positive slope, with Tsallis relative entropy giving the best goodness of fit. For shorter periods, the risk-return profiles from Tsallis relative entropy show a more consistent behavior in terms of goodness of fit than the other three risk measures.

Item Type: | MPRA Paper |
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Original Title: | Financial Portfolios based on Tsallis Relative Entropy as the Risk Measure |

English Title: | Financial Portfolios based on Tsallis Relative Entropy as the Risk Measure |

Language: | English |

Keywords: | Non-extensive statistics, Tsallis relative entropy, Kullback-Leibler relative entropy, q-Gaussian distribution, Capital Asset Pricing Model, Beta, Risk optimal portfolio, Econophysics |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General |

Item ID: | 91614 |

Depositing User: | Dr. Sandhya Devi |

Date Deposited: | 22 Jan 2019 10:56 |

Last Modified: | 27 Sep 2019 12:22 |

References: | [1] Sharpe W F, 1964 Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk, The Journal of Finance, 19, 425 [2] Fama E F, 1968 Risk, Return and Equilibrium, Report No. 6831 (Chicago; Center for Mathematical Studies in Business and Economics, University of Chicago) [3] Fama E F, 1968 Risk, Return, and Equilibrium: Some Clarifying Comments, The Journal of Finance, 23, 29 [4] Markowitz H M, 1959 Portfolio Selection: Efficient Diversification of Investments (New York; Wiley) [5] Jensen M C, 1969 Risk, The Pricing of Capital Assets, and The Evaluation of Investment Portfolios, The Journal of Business, 42, 167 [6] Sharpe W F, 1966 Mutual Fund Performance, The Journal of Business, 39, 119 [7] Fama E F, 1965 The Behavior of Stock-Market Prices, The Journal of Business, 38, 34 [8] Bachelier L, 1964, Theory of Speculation, The Random Character of Stock Market Prices (Cambridge, MA; MIT Press, ed. Cootner P) [9] Miller M H and Scholes M, 1972 Rates of return in relation to risk: a re-examination of some recent findings, Studies in the Theory of Capital Markets (New York; Praeger, ed. Jensen M C) [10] Black F, Jensen M C and Scholes M, 1972 The Capital Asset Pricing Model: Some Empirical Tests, Studies in the Theory of Capital Markets (New York; Praeger, ed. Jensen M C) [11] Clausius R, 1870 On a mechanical theorem applicable to heat, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 40, 122 [12] Boltzmann L, 2012 Weitere Studien über das Wärmegleichgewicht unter Gas-molekülen, Wissenschaftliche Abhandlungen Volume 1 (Cambridge: Cambridge University Press, ed. Hasenöhrl, F) [13] Shannon C E, 1948 A Mathematical Theory of Communication, The Bell System Technical Journal, 27, 379 [14] Philippatos G C and Wilson C J, 1972 Entropy, market risk, and the selection of efficient portfolios. Applied Economics 4, 209 [15] Dionisio A, Menezes R and 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, 50, 161 [16] Maasoumi E and Racine J, 2001 Entropy and predictability of stock market returns, Journal of Econometrics 107, 291 [17] Zhou R, Cai R and Tong G, 2013, Applications of Entropy in Finance: A Review, Entropy, 15, 4909 [18] Lassance N and Vrins F, 2018 Minimum Rényi Entropy Portfolios, arXiv:1705.05666v4 [19] Ormos M and Zibriczky D, 2002 Entropy-Based Financial Asset Pricing, PLoS ONE 9, 1 [20] Tsallis C, 1998 Generalized entropy-based criterion for consistent testing, Physical Review E 58, 1442 [21] Kullback S, 1959 Information Theory and Statistics (New York, Wiley) [22] Tsallis C, Anteneodo C, Borland L and Osorio R, 2003 Nonextensive statistical mechanics and economics, Physica A, 324, 89 [23] Osorio R, Borland L and Tsallis C, 2004 Distributions of High-Frequency Stock-Market Observables, Nonextensive Entropy: Interdisciplinary Applications (New York; Oxford University Press, eds. Tsallis C and Gell-Mann M) [24] Tsallis C, 2000 Introduction to Nonextensive Statistical Mechanics (New York; Springer) [25] Mantegna R N and Stanley H E, 2000 An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge; Cambridge University Press) [26] Devi S, 2017 Financial market dynamics: superdiffusive or not? Journal of Statistical Mechanics: Theory and Experiment, 2017, 083207 [27] Shalizi C R, 2007 Maximum Likelihood Estimation for q-Exponential (Tsallis) Distributions, arXiv:math/0701854 [28] Furuichi S, Yanagi K and Kuriyama K, 2004 Fundamental properties of Tsallis relative entropy, Journal of Mathematical Physics, 45, 4868 [29] Massey F J, 1951 The Kolmogorov-Smirnov Test for Goodness of Fit, Journal of the American Statistical Association, 46, 68 [30] Iliopoulos A C, Pavlos G P, Magafas L, Karakatsanis L, Xenakis M and Pavlos E, 2015 Tsallis q-triplet and stock market indices: the cases of S&P 500 and TVIX, Journal of Engineering Science and Technology Review, 8, 34 |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/91614 |