So how exactly would you calculate the Sharpe ratio in my example?

Again here are the numbers:

On January 1st (2020) I have exactly $5,999,997 in my trading account. The risk-free rate in the US is 1% (for example).

Here are my trading results for 2020:

##
Month 1: -$0.50

Month 2: +$1,000,000

Month 3: -$0.50

Month 4: +$1,000,000

Month 5: -$0.50

Month 6: +$1,000,000

Month 7: -$0.50

Month 8: +$1,000,000

Month 9: -$0.50

Month 10: +$1,000,000

Month 11: -$0.50

Month 12: +$1,000,000

Also note that a standard deviation is just a number, for example here are 4 measurements :

15, 20, 25, 30

The standard deviation is simply 5.5901 (a number), regardless of what you are measuring.

And finally we can also express the monthly returns in percentage, it won’t matter, in both cases the sharpe ratio will be close to zero.