I have two assets which seem not correlated (correlation coefficient = 6.3% using monthly frequency and 48 data points).
I want to test the significance of the correlation. Null hypothesis is that correlation is nil, and if the p-value is lower than 0.05 then we can reject the null hypothesis (ie correlation is significantly different than 0, ie there is correlation).
Keeping the correlation constant (at 6.3%) I notice that as I increase $N$ (and so I increase $N-2$ degrees of freedom) the p-value reduces and will eventually be lower than 0.05.
I am confused, why having more $N$ make the correlation becoming statistically significant, if the actual correlation of returns is still low?