Bitcoin versus S&P 500 Index: Return and Risk Analysis

Abstract

The S&P 500 Index is considered the most popular trading instrument in financial markets. With the rise of cryptocurrencies over the past few years, Bitcoin has grown in popularity and adoption. This study analyzes the daily return distribution of Bitcoin and the S&P 500 Index and assesses their tail probabilities using 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 transform algorithm and the 12-point composite Newton–Cotes rule. The findings show that peakedness is the main characteristic of the S&P 500 Index return distribution, whereas heavy-tailedness is the main characteristic of Bitcoin return distribution. The GTS distribution shows that (Formula presented.) of S&P 500 returns are within (Formula presented.) and (Formula presented.) against only (Formula presented.) of Bitcoin returns. At a risk level ( (Formula presented.) ), the severity of the loss ( (Formula presented.) ) on the left side of the distribution is larger than the severity of the profit ( (Formula presented.) ) on the right side of the distribution. Compared to the S&P 500 Index, Bitcoin has (Formula presented.) more prevalence to produce high daily returns (more than (Formula presented.) or less than (Formula presented.) ). The severity analysis shows that, at (Formula presented.) risk level, the average value-at-risk ( (Formula presented.) ) of Bitcoin returns at one significant figure is four times larger than that of the S&P 500 Index returns at the same risk.