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Bitcoin versus S&P 500 Index: Return and Risk Analysis (2310.02436v1)

Published 3 Oct 2023 in q-fin.ST

Abstract: The S&P 500 index is considered the most popular trading instrument in financial markets. With the rise of cryptocurrencies over the past years, Bitcoin has also grown in popularity and adoption. The paper aims to analyze the daily return distribution of the Bitcoin and S&P 500 index and assess their tail probabilities through two financial risk measures. As a methodology, We use Bitcoin and S&P 500 Index daily return data to fit The seven-parameter General Tempered Stable (GTS) distribution using the advanced Fast Fractional Fourier transform (FRFT) scheme developed by combining the Fast Fractional Fourier (FRFT) algorithm and the 12-point rule Composite Newton-Cotes Quadrature. The findings show that peakedness is the main characteristic of the S&P 500 return distribution, whereas heavy-tailedness is the main characteristic of the Bitcoin return distribution. The GTS distribution shows that $80.05\%$ of S&P 500 returns are within $-1.06\%$ and $1.23\%$ against only $40.32\%$ of Bitcoin returns. At a risk level ($\alpha$), the severity of the loss ($AVaR_{\alpha}(X)$) on the left side of the distribution is larger than the severity of the profit ($AVaR_{1-\alpha}(X)$) on the right side of the distribution. Compared to the S&P 500 index, Bitcoin has $39.73\%$ more prevalence to produce high daily returns (more than $1.23\%$ or less than $-1.06\%$). The severity analysis shows that at a risk level ($\alpha$) the average value-at-risk ($AVaR(X)$) of the bitcoin returns at one significant figure is four times larger than that of the S&P 500 index returns at the same risk.

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References (36)
  1. Antony Lewis. The basics of bitcoins and blockchains: an introduction to cryptocurrencies and the technology that powers them. Mango Media Inc., 2018.
  2. Satoshi Nakamoto. Bitcoin: A peer-to-peer electronic cash system. Decentralized business review, 2008.
  3. The volatility of bitcoin and its role as a medium of exchange and a store of value. Empirical Economics, 61(5):2663–2683, 2021.
  4. Bitcoin–currency or asset? Melbourne Business School, 2016.
  5. Ole Bjerg. How is bitcoin money? Theory, culture & society, 33(1):53–72, 2016.
  6. David Yermack. Is bitcoin a real currency? an economic appraisal. In Handbook of digital currency, pages 31–43. Elsevier, 2015.
  7. Lo Stephanie and Wang J Christina. Bitcoin as money. Current Policy Perspectives, (14-4), 2014.
  8. Bitcoin: Medium of exchange or speculative assets? Journal of International Financial Markets, Institutions and Money, 54:177–189, 2018.
  9. The economics of bitcoin price formation. Applied economics, 48(19):1799–1815, 2016.
  10. Dimitrios Koutmos. Investor sentiment and bitcoin prices. Review of Quantitative Finance and Accounting, 60(1):1–29, 2023.
  11. Fear sentiment, uncertainty, and bitcoin price dynamics: The case of covid-19. Emerging Markets Finance and Trade, 56(10):2298–2309, 2020.
  12. Rodrigo Hakim das Neves. Bitcoin pricing: impact of attractiveness variables. Financial Innovation, 6(1):21, 2020.
  13. The variance gamma process and option pricing. Review of Finance, 2(1):79–105, 1998.
  14. A. H. Nzokem. Pricing european options under stochastic volatility models: Case of five-parameter variance-gamma process. Journal of Risk and Financial Management, 16(1), 2023.
  15. A. H. Nzokem. Gamma variance model: Fractional fourier transform (FRFT). Journal of Physics: Conference Series, 2090(1):012094, nov 2021.
  16. The ornstein–uhlenbeck process and variance gamma process: Parameter estimation and simulations. Thai Journal of Mathematics, 21(3):160–168, Sep. 2023.
  17. Tempered stable distributions and processes. Stochastic Processes and their Applications, 123(12):4256–4293, 2013.
  18. A. H. Nzokem. European option pricing under generalized tempered stable process: Empirical analysis. arXiv.2304.06060[q-fin.PR], 2023.
  19. Stochastic volatility for lévy processes. Mathematical finance, 13(3):345–382, 2003.
  20. Stable distributions. In Statistical tools for finance and insurance, pages 21–44. Springer, 2005.
  21. Non-Gaussian Merton-Black-Scholes Theory, volume 9. World scientific, 2002.
  22. Financial models with Lévy processes and volatility clustering, volume 187. John Wiley & Sons, 2011.
  23. Handbook of heavy-tailed distributions in asset management and risk management. World Scientific, 2019.
  24. Fitting generalized tempered stable distribution: Fractional fourier transform (frft) approach. ARXIV.2205.00586[q-fin.ST], 2022.
  25. The fractional fourier transform and applications. SIAM review, 33(3):389–404, 1991.
  26. A. H. Nzokem. Fitting infinitely divisible distribution: Case of gamma-variance model. arXiv.2104.07580[stat.ME], 2021.
  27. A. H. Nzokem. Stochastic and Renewal Methods Applied to Epidemic Models. PhD thesis, York University , YorkSpace institutional repository, 2020.
  28. A. H. Nzokem. Numerical solution of a gamma - integral equation using a higher order composite newton-cotes formulas. Journal of Physics: Conference Series, 2084(1):012019, nov 2021.
  29. A. H. Nzokem. Sis epidemic model: Birth-and-death markov chain approach. International Journal of Statistics and Probability, 10(4):10–20, July 2021.
  30. Wiley series in computational statistics, volume 596. Wiley Online Library, 2013.
  31. Paul S Horn. A measure for peakedness. The American Statistician, 37(1):55–56, 1983.
  32. Błażej Kochański. Does kurtosis measure the peakedness of a distribution? Wiadomości Statystyczne. The Polish Statistician, 67(11):43–61, 2022.
  33. Peter H Westfall. Kurtosis as peakedness, 1905–2014. rip. The American Statistician, 68(3):191–195, 2014.
  34. Computing var and avar in infinitely divisible distributions. 2009.
  35. Advanced stochastic models, risk assessment, and portfolio optimization: The ideal risk, uncertainty, and performance measures. Wiley, 2008.
  36. Hasan Fallahgoul. Quantile-based inference for tempered sta-ble distributions monash cqfis working paper 2017–9. 2017.
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