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The return (on investment) is a percentage (%) in the Sharpe formula, not a dollar amount.
In this example it’s 100%.

500,000.25 to be exact.

Now we plug the data into the formula (100 - 1) divided by 500,000.25 and we get a sharpe ratio of 0 (very close to zero).

So you measure returns in %s, and standard deviation of the returns in \$s. That’s an interesting approach.

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.

Just make it percentage…

I will, right now I am watching the market.

Sorry. I thought that was a return.

Just use my example. Assume risk-free return is 0%.

Month 1: -1%
Month 2: +10%
Month 3: -1%
Month 4: +10%
Month 5: -1%
Month 6: +10%
Month 7: -1%
Month 8: +10%
Month 9: -1%
Month 10: +10%
Month 11: -1%
Month 12: +10%

Compounded Return% is 166.788951495
The standard deviation of monthly return%: 5.5

SR = 166/5.5 = 30

The sharpe formula does not use compounded return, remember?

I define the Sharpe ratio as the compounded return (CAR) divided by the standard deviation (sd) of returns.

In other words you are creating your own personal Sharpe ratio formula out of nowhere.

Most funds adopt CAR… Otherwise, which one are you using??? you just sum them up and divide them by 12 months??? Using CAR is the most appropriate way to calculate SR

Rx should not be the average of return… The guy is wrong

Right, so these guys are wrong too?

YES! Most people use annualized returns.

Avg return doesn’t work in the case that the strategy is not profitable, but the average return is still positive.

Month 1: -99%
Month 2: +100%

If you use avg return, the shape ratio is positive, but the SR should be negative because it is losing money.

We will talk some more about that subject tomorrow, very busy at the moment.

It seems that there are many ways to calculate the sharpe ratio (SR) of a trading system.
How this SR is calculated on C2 is still unclear, as far as I can tell from these two Sharpe ratio topics :

For this question, why don’t you just tag @MatthewKlein? Everyone should know the answer 