I am not really sure where I have said anything wrong...Two wrongs. Let's see if we can make it right.
First, "return/risk//day" seeks what all of your economics classes tried to turn you towards: marginal return -- and even better, marginal risk-adjusted return -- and even better-better,
PV(marginal risk-adjusted return)
That is the understanding that each of us should have, for each and every trade, *before* we put it on, *and* after.
Capital efficiency -- like capital preservation -- is the shit.
And to put money AT RISK before you even know how that trade will affect your portfolio (on its own, and as compared to all *alternative* uses of your capital) -- is NOT what you want your money manager to do -- even if YOU are your money manager.
{stepping off soapbox now....}
Second big thought: To the OP: don't confuse position reward/risk, with portfolio reward/risk -- these terms are conflated all over the place, and they are starkly different. But you'll still hear people raving/comparing numbers that are completely and truly, apples to oranges.
If I pursue 50¢ on a $5 spread, I can claim a 10% reward-to-risk on that trade. But what will be my annual return on portfolio capital? We have no idea until we disclose how much total capital was available.
Algebraically, there are many different ways to get to the same result: time-weighted risk-adjusted marginal returns. End of story.
Far be it from me to suggest that the basic measure I have suggested is the "right one". Ultimately, there is no right answer to these questions, since everyone has different constraints and different targets.
Broadly, this rabbit hole can be as deep or as shallow as you want to make it. Lots of clever people have lots of clever ways of doing this. As I said, you can do the basic thing, as long as you're aware of all the caveats, limitations and flaws.
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