"Percentage gain in PL" and "percentage gain in the account" are not the same thing. I doubt that you really want to know the percentage gain in PL, but I'll never say never. If I change the example to PL at t1 = $0 and PL at t2 = $100, then your percentage gain in PL is undefined (or infinite if you want to define it that way) but I doubt this is of much value to you. You need to think through your use case carefully and then you'll know how to define percent change for your application. Most (all?) traders care about their PL relative to their account size, the amount at risk, the notional contract size, and/or the amount of margin they put up, etc., not relative to some other PL in dollar units. I think it's likely that you are solving the wrong problem. That said, the generally accepted formula for percent change uses the starting point as the denominator. In the case of negative PLs, you are discussing losses, not profits, and so you can change the sign and change the unit to "loss": A "profit" of -$200 is equivalent to a loss of +$200 and a "profit" of -$100 is equivalent to a loss of +$100. So, moving from a "profit" of -$200 to a "profit" of -$100 is equivalent to moving from a loss of $200 to a loss of $100 which is a 50% reduction in loss (as many have already pointed out). (100 - 200) / 200 * 100 % = -100/200*100 % = -50% = reduction of loss by 50%. I would argue that it does not make sense in this context to discuss the change in profit since there never was a profit. That is, personally, I would not define a formula for "percentage change in PL" across negative and positive values and would instead treat profits and losses as separate situations. It is meaningless to talk about the "percent change in PL" from -$200 to +$100, for instance. You COULD come up with a definition, but I don't think it would provide CLARITY, which is the ultimate objective of applying mathematics. Applied math is meant to make sense of real world situations; you can create formulas and define terms however you like, but real world utility should be the guiding principle, not the "official" formula. To quote the late, great George Box, "All models are wrong, but some are useful." Use mathematics, but don't be a slave to it. Good luck with the startup!!
Account yesterday was $-200, today it's $-100. So obviously it rose by $+100 in that time period. Now the interesting question is: how much percent has the account changed in that time period? My math says the account changed by +100%. Other people say it changed by only +50%. So, who is right?
I think you answer the question here. If the account rose by 100 how can it be 2x (100% gain) of 200? 200 to 100 is always 50%. If you went the other way, started with -100 and moved to -200, now your loss has doubled — the change between the two can be described as “100%”. But whether you start with -200 and get to -100 or start with 200 and get to 100, you always end up with 50%.
@Statistical Trader, thx, but just imagine a drop of more than 100% as is very well possible with short positions (esp. options as well stocks). It's about percent change from period x to period x+1 (ie. day x to day x+1 etc.), not relative to the initial account or position value.
Thx for the effort, but definitely wrong when negative numbers are involved And: it was not supposed to be any social experiment, but the answers are indeed very interesting Reminds me of the saying "One million flies can't be wrong"
Ignorance, like faith, is invincible ... 1 million traders, can't be wrong, but 999000 will lose $$$ with their "knowledge"
Maths doesn't lie No need to exaggerate. Make that 50:50, ie. on average 50% will win, 50% will lose in a fair 0-sum game.
LOL sure! (not sure what 50% has to do with a 0-sum game) Math wouldn't lie if one knew it Relative variation is a basic "definition" covered in elementary schools over here (f-o)/ |o|. I could understand some initial "confusion" in a mathematically unprepared person when the 2 numbers are of different signs, but this is not even the case. Anyway, I know you are just trolling and laughing ... the experiment continues