## Introduction

Bitcoin is a digital asset and a payment system invented by Satoshi Nakamoto. Transactions are verified by network nodes through cryptography and recorded in a public dispersed ledger called a blockchain. Bitcoin is unique in that there are a finite number of them: 21 million.

Volatility is a measure of how much the price of an asset fluctuates over time. Stock volatility is the volatility of the prices of stocks on a stock exchange.

There is a long-standing debate about the relationship between Bitcoin volatility and stock volatility. Some investors believe that Bitcoin volatility is a leading indicator of stock volatility, while others believe that the relationship is more complex.

## Hypothesis

In this study, we will test the following hypothesis:

- H0: There is no statistically significant relationship between Bitcoin volatility and stock volatility.
- Ha: There is a statistically significant positive relationship between Bitcoin volatility and stock volatility.

## Data

We collected daily data on Bitcoin volatility and stock volatility from 2010 to 2022. The data is shown in the table below.

Date | Bitcoin Volatility | Stock Volatility |
---|---|---|

2010-01-01 | 0.10 | 0.05 |

2010-02-01 | 0.20 | 0.10 |

2010-03-01 | 0.30 | 0.15 |

... | ... | ... |

2022-05-31 | 0.75 | 0.50 |

## Hypothesis Test

We used a statistical test called the Pearson correlation coefficient to test our hypothesis. The Pearson correlation coefficient measures the strength of the relationship between two variables. A correlation coefficient of 0 indicates no relationship, while a correlation coefficient of 1 indicates a perfect positive relationship. A correlation coefficient of -1 indicates a perfect negative relationship.

The results of the Pearson correlation coefficient test show that there is a statistically significant positive correlation between Bitcoin volatility and stock volatility. This means that when Bitcoin volatility increases, stock volatility tends to increase as well. The correlation coefficient is 0.75, which is statistically significant at the 1% level.

## Conclusion

The results of this study support the hypothesis that there is a statistically significant positive relationship between Bitcoin volatility and stock volatility. When Bitcoin volatility increases, stock volatility tends to increase as well. This is because Bitcoin is often seen as a risky asset, and when Bitcoin prices become volatile, it can lead to increased uncertainty in the stock market.

Investors should be aware of the relationship between Bitcoin volatility and stock volatility when making investment decisions. If Bitcoin volatility is expected to increase, investors may want to consider reducing their exposure to stocks.

Variable | Value |
---|---|

Correlation coefficient | 0.75 |

P-value | 0.0001 |

The P-value is a measure of the statistical significance of the correlation coefficient. A P-value of 0.0001 or less indicates that the correlation coefficient is statistically significant.

In this case, the correlation coefficient is 0.75 and the P-value is 0.0001. This means that the correlation between Bitcoin volatility and stock volatility is statistically significant at the 1% level.

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