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Say you get a million dollars on your account through a mistake by the bank and they don't realise it for a month: how much could you make from clever investing the money before they charge it back a month later?

Edit: to address an issue brought up in one answer we are assuming the current market situation.

closed as too broad by NL - Apologize to Monica, Chris W. Rea, Rupert Morrish, MD-Tech, Dheer May 22 at 17:16

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    The real issue is getting the money out of the account without the bank looking more closely at where it came from in the first place. Withdrawing $1,000,000 is very different from withdrawing, say, $100. – chepner May 21 at 13:31
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    Are you expecting that the specific situation you've described (the money was deposited into your account by mistake and removed a month later) would result in a different answer than just asking "how much could I make after a month if I invest a million dollars?" (Which, I guess pretty obviously, is not a question that can be answered accurately unless you own a time machine). – dwizum May 21 at 15:46
  • @dwizum I expect it to be different, at least because of how to mitigate potential losses. – plocks May 22 at 2:52
  • How to mitigate losses (from any risk) seems like a pretty different question from "what is the maximum theoretical gain?" - Maybe it's just me, but I'm still confused about what you're actually trying to ask. – dwizum May 22 at 16:54
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You could safely make 0.2%, by putting the money in an FDIC-insured savings account paying 2.5% APY (there are several in the 2.4-2.5% range with no upper limit on investment). Actually you'll need 4 accounts if you want to stay fully insured, because the FDIC limit per beneficiary per bank is 250k.

That would be a safe and easy $2000.

Higher returns would involve risk.

  • This sounds reasonable. – plocks May 22 at 3:02
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The issue is how much could you lose.

If you lost 1% of the value in one month, you would have to make up the $10,000 lost when the bank demanded their money.

Based on the stipulation that you are talking about current market conditions and that in the last 30 days the S&P 500 is down 2.33% that would mean that you would have lost $23,300 of the banks money. Which they will expect you to replace.

  • Fair point, but I'd belive there are more risk averse methods to invest. – plocks May 22 at 3:00
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Infinity. There is no theoretical ceiling just the same way there is no theoretical ceiling to investment growth in any other contrived situation.

Edit to address the edit added to the question: In this current market the answer is still infinity.

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    Infinity is not a number. And the numbers practically “close” to infinity are a LOT bigger than the current value of the S&P500. – RonJohn May 21 at 22:51
  • You know there are other ways to participate in markets that offer exponentially more leverage than simply buying SPY and holding, right? The limit of theoretical gain (which there isn't one) that can be realized in a month has nothing to do with the current level of the S&P500. – quid May 21 at 22:53
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    Please elaborate, how this should work. Since you claim infinity, I claim impossibility. – plocks May 22 at 3:01
  • The question asked does not specify risk tolerance or probability of outcome, just "theoretical gain" from "clever investing", there is not a limit to the theoretical gain. You are free to believe that the only possible investment is SPY (even SPY COULD increase 9,999,999,999,999,999,999% tonight, it's just not likely; and if you were in a 3x levered fund it'd be that x3 and if you were margined on top of that it would be higher and if you were only holding options directly it'd be higher yet again). There is no theoretical limit, there's a probable range, but that's a different question. – quid May 22 at 7:59
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    "Infinity" is the correct answer. @quid is not claiming that he knows how to get a billion percent gain. If he did know how to do that, he'd be out working the market rather than chatting on this forum. But there is no fixed upper bound to the "theoretical" maximum. If someone say 1000%, I could always say, what if I did just a little better than that? Couldn't I manage 1001%? Etc. That's pretty much the definition of infinity: whatever number you give me, I could always say "add one to that". – Jay May 22 at 15:38
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As @quid says, there's no absolute upper bound. If you are smart or lucky enough to make just the right investments, you could make 1000% profit every day or more. Well, I suppose someone could come up with "real world" upper bounds. If after 10 days you own all the wealth in the world, you're pretty much done, unless you can figure out ways to dramatically increase the world's total wealth.

But two things to bear in mind:

(a) Every investment has potential for gain, but also risk of loss. What if you invested this million dollars and lost money, and then the bank comes asking for their money back? You'd presumably have to make up the difference.

(b) Even if you did make money, I'd question if you would be allowed to keep it.

I read a story in the news years ago that the IRS made a mistake and sent a taxpayer a refund check for, I forget the numbers, but he was supposed to get a few hundred dollars and instead they sent him tens of millions. He got the clever idea that he would deposit the check in an interest-bearing account, then promptly contact the IRS so there was no question that he was trying to keep the money. He hoped that it would take a long time for the bureaucratic wheels to grind and for the IRS to tell him to pay the money back and to tell him what mechanics to go through to do that, who to write the check to and where to send it or whatever. In the mean time he'd collect the interest on tens of millions of dollars.

Nice try, but the IRS demanded he pay back the money with interest. He didn't get to keep any of it.

  • How did they know how much interest they could charge back? – plocks Jun 2 at 8:45
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    @plocks I don't know, I read about it in a news story and they didn't say. I'd guess they demanded he give them a bank statement showing how much interest he'd collected. – Jay Jun 3 at 16:51
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The answer really is nearly infinite.

If you can front run Trump's tweets and Xi's statements, even by a few minutes... and then you use that to buy options.. on the most affected stocks...

You could in theory be the richest person on the planet in inside a month starting with a million.

On the right options with the right tweets and statements, you can easily get 10x returns in a day (at least in the beginning)...

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