https://www.tradingview.com/chart/4nFiKQrA/
The price of BTC fell when stock markets crashed recently.
But does this mean there is a linear relationship between BTC price and stock market performance?
When stock markets recently fell, there did indeed appear to be a linear relationship between BTC price and the stock market.
However, when stock markets picked up following essentially limitless QE, the price of BTC did not rocket, as one might have expected.
What might this mean?
It may mean that the value of the correlation coefficient as between BTC and the stock market varies depending upon whether the stock market is rising or falling.
Crudely put, the correlation coefficient (the closeness of the relationship between the price of BTC and stock market performance) may be linear (may have a value at or close to +1) when the stock market is crashing.
However, the correlation coefficient may be considerably lower than +1 when the stock market conditions are improving (ie BTC price does not rise linearly with improvements in stock market performance.
If this hypothesis is correct, it may be explained by reference to a corollary of the Cauchy-Swartz inequality such that the absolute value of a Pearson correlation coefficient is not bigger than 1. Accordingly, the value of the correlation coefficient ranges between -1 and +1.
The correlation coefficient is +1 in the case of a perfect linear relationship between the price of BTC and the stock market during the recent crash but appears to have a value of <1 when the stock market picks up.
Hence we have seen a large degree of correlation between BTC price and stock market performance during a major crash, but a significantly lower degree of correlation between the price of BTC and stock market performance as stock market performance improvs.
Accordingly, I hypothesise that there is correlation between BTC price and the stock market during a crash, and yet, there is non-trivial anticorrelation between BTC price and stock market performance when the stock market improves.
Simply put, BTC crashes when the stock market crashes, but BTC does not similarly rise in price when the stock market improves. Any perfect linear correlation is only during a crash, and not otherwise, even if the anticorrelation does not approach -1.
The price of BTC fell when stock markets crashed recently.
But does this mean there is a linear relationship between BTC price and stock market performance?
When stock markets recently fell, there did indeed appear to be a linear relationship between BTC price and the stock market.
However, when stock markets picked up following essentially limitless QE, the price of BTC did not rocket, as one might have expected.
What might this mean?
It may mean that the value of the correlation coefficient as between BTC and the stock market varies depending upon whether the stock market is rising or falling.
Crudely put, the correlation coefficient (the closeness of the relationship between the price of BTC and stock market performance) may be linear (may have a value at or close to +1) when the stock market is crashing.
However, the correlation coefficient may be considerably lower than +1 when the stock market conditions are improving (ie BTC price does not rise linearly with improvements in stock market performance.
If this hypothesis is correct, it may be explained by reference to a corollary of the Cauchy-Swartz inequality such that the absolute value of a Pearson correlation coefficient is not bigger than 1. Accordingly, the value of the correlation coefficient ranges between -1 and +1.
The correlation coefficient is +1 in the case of a perfect linear relationship between the price of BTC and the stock market during the recent crash but appears to have a value of <1 when the stock market picks up.
Hence we have seen a large degree of correlation between BTC price and stock market performance during a major crash, but a significantly lower degree of correlation between the price of BTC and stock market performance as stock market performance improvs.
Accordingly, I hypothesise that there is correlation between BTC price and the stock market during a crash, and yet, there is non-trivial anticorrelation between BTC price and stock market performance when the stock market improves.
Simply put, BTC crashes when the stock market crashes, but BTC does not similarly rise in price when the stock market improves. Any perfect linear correlation is only during a crash, and not otherwise, even if the anticorrelation does not approach -1.