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The story so far: Pennyless joe gets a "groundhog potion" that supposedly allows to repeat one day once. He drinks it and proceeds to win the state lottery by memorizing the numbers. He then discovers that he is fated to repeat every day for 3 to 5 times (randomly). He also finds out that other "groundhoggers" are on the search for him.

(formerly pennyless) Joe took to his wandering lifestyle very well. In administering his finances earned through winning the state lottery, he took to day trading.

What a marvel. Since Joe repeats his days, he knows what stocks go up and what stocks go down. His day trading brings in more money than he needs to meet his travelling lifestyle.

And the more, he can trade through the web, from anywhere.

But Joe is really worried that his 99% success rate[note 1] in profits through stock trading will raise some red flags with the government and/or regulatory agencies.

His tinfoil hat is tingling, since he received an enthusiastic email from his broker congratulating him on his successful trading choices and asking him to answer a form and sign some papers about a "trader profile upgrade" to "unlock more profitable trading options". Something like this form but for already-customers (disclaimer: the link above is merely visually informative, no endorsement on either party assumed).

Joe is new to investing, but is afraid that someone might come knocking asking what his "secret formula" is.

So, there are several points I'd like to clear:

  • Would a 99% successful day trader really raise some red flags with the government? Assume he is filing all the taxes and papers lawfully.
  • Would he be sued for "insider trading"?
  • How could Joe change his trading behaviour to better avoid prosecution, if it indeed could happen?

[note 1]: The 1% loss rate is due to other groundhoggers (around 12 in the USA) also trading and the "butterfly effect"

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    $\begingroup$ So he doesn't always repeat the same day, but moves on after some cycles, and repeats another day? $\endgroup$ – JDługosz May 23 '16 at 17:13
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    $\begingroup$ He could make vast profits day trading, but is there any reason why he would need to make so much income? If he's taken a wandering, nomadic lifestyle then all he really needs is enough cash for the next week or so, and if he wants to stay under the radar then cash is the best way. Joe should place bets with local bookmakers; he can easily make a $1000 a day in cash while still flying under the radar. $\endgroup$ – Qwerky May 24 '16 at 8:45
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    $\begingroup$ @Qwerky I think I should've asked what is the best on-the-go moneymaking strategy for his wanderer phase before going with online stocks. $\endgroup$ – Mindwin May 24 '16 at 12:55
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    $\begingroup$ If you allow for the butterfly effect per your note 1, it would be almost impossible to draw the same lottery numbers on repeated days, even if Joe tries to do everything identically. Most are drawn using highly chaotic sources of entropy such as tumbling plastic balls. The mere difference of Joe's memory (and the resulting miniscule but nonzero changes in EM and gravitational fields caused by his brain) would be enough to completely alter the outcome of the drawing. $\endgroup$ – MooseBoys May 25 '16 at 5:42
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    $\begingroup$ Insider trading investigations usually need to uncover the source of the inside information and how the defendant got it, because you can't just charge someone for being right all the time, even if being right all the time usually involves doing something that is illegal. "He used time travel to break the law!" doesn't sound like a particularly strong or likely case to me, but maybe that's only because we can't time travel. $\endgroup$ – HopelessN00b May 25 '16 at 14:36

10 Answers 10

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He Would Be Okay

Joe will be fine. The government is likely to uncover his success eventually, but building a successful investigation will be next to impossible. Joe can lower his risk by not engaging in flashy purchases or suspicious transactions (such as transfers to off-shore accounts).

Tip off

Before anything else can happen, the government would have to become suspicious of him. In real world fraud examination, this typically happens a couple ways:

  1. Someone who knows Joe tips off the government that something fishy is going on. These people are typically coworkers, co-conspirators, or jealous neighbors.
  2. Joe files some tax paperwork with the government. It stands out because the automated system picks up on some irregularities.

Since Joe isn't doing anything illegal, there are no co-conspirators. He is self-employed, so no coworkers can tip the government off. He may have jealous neighbors or fellow traders who think he is suspiciously lucky. However, most people never report anyway.

Supposing that Joe is honest, he makes all the appropriate SEC/tax filings. He likely has a lawyer or accountant handle the details, because he can afford it and it is definitely worth the money to him.

Despite this, Joe will eventually be on someone's radar because he is able to earn insane amounts of cash. In my opinion, it's most likely to happen as he files yearly income tax statements which show huge gains year over year, most of which come from investments.

He could avoid detection by having an ordinary day job, significantly limiting the amount of money he earns, showing regular losses, and avoiding flashy purchases or funds transfers.

Investigation

After finding out about Joe, the government has to put together a case. Even "open and shut" financial crimes cases can take years to accumulate enough evidence to bring to trial. Actual fraud cases involving insider trading can take a decade. Basically - it's really hard to build a case for financial crimes. Succesful cases often involve getting a conspirator to admit to the crime, showing a long history of suspicious transactions, and uncovering what exactly the trading scheme is.

Joe will be able to deftly evade all of these tactics. He has no conspirators or accomplices to rat him out, there is no scheme to uncover. Ideally he trades in a large number of different financial instruments (and different funds/companies/currencies), which will styme investigators. How could he have insider knowledge on all of these things?

Even after being tipped off, investigators will find it very difficult to build a case against Joe. Additionally, his accountant or tax lawyer should have adequate documentation that shows his income is legitimate.


Appeal to authority: I am IRL an auditor for the government.

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    $\begingroup$ I agree the audit would be obfuscated to the point where the government will give up or back-burner it. I'm more concerned with civil lawsuits where the burden of proof is 51%. A disgruntled shareholder in a company he happens to trade a lot in... and his only defense is "I'm impossibly lucky with every other company too?" That'll come out either way. And the publicity kills him. $\endgroup$ – Harper May 24 '16 at 1:56
  • $\begingroup$ He couldn't find a telecommuting day job, and since he thinks he is being hunted, he is on the go, traveling to a different city each couple days. $\endgroup$ – Mindwin May 24 '16 at 12:56
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    $\begingroup$ In fact, when he is inevitably audited, he could just tell them he lives every 4th day over again (or whatever). Who would believe him? $\endgroup$ – Tony Ennis May 24 '16 at 22:21
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    $\begingroup$ @TonyEnnis: it's unwise to tell your tax auditor something you know they won't believe, because from the auditor's POV you appear to be a liar. So it's bad if they don't believe you and (I assume the story is set up such that) it's differently bad if they do! $\endgroup$ – Steve Jessop May 24 '16 at 23:24
  • $\begingroup$ He should get into directing stock purchases, say a mutual fund. What's less suspicious than a dude who's remarkably good at his job? A dude whose success makes you money, that's who. $\endgroup$ – The Nate May 25 '16 at 1:51
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He's in the wrong game.

People need to misattribute his success to other factors.

A daytrader would be too easy to catch. He's doing a lot of trades so he couldn't afford the sheer labor of setting up daytrading accounts under different aliases and all over the place. That means he's concentrating trades at one or a few brokers, and somebody (quite probably internal to the daytrading firm) is going to notice his success. Nevermind Federal prosecution; he could get sued by the trading house, and as that gets attention, it could snowball on him.

One way to go is the insider: be involved closely enough with the outcomes that his success would be attributed to an insider's ability to influence them. What would you say to someone who insisted they could prove, statistically, that Apple must surely have a crystal ball and can look 10 years into the future? Given a 24 hour window, this is harder: especially in the stock market because of insider trading rules. He might be able to do it, say, if he was a well-read pundit: but then he faces butterfly effect.

So I'll talk about another option: bury the advantage in the noise and appear successful for other reasons.

Consider the sportsbook game - Don't gamble, be the house. Tune your offered odds and handicaps slightly in favor of the known win. This gets rid of the butterfly effect and cross-groundhogger effects (teams don't do better or worse based on a half point in a sportsbook). He wins, he loses, just like any sportsbook, he just does it a little bit better.

And this whole area is already illegal, underground and/or generally pretty dodgy, with low expectations of reliability. They won't prosecute anyone for cheating by giving slightly better odds, when they're too busy prosecuting everyone else for really bad stuff. So be a responsible operator who plays fair and deals square. Be good at what you do, get a reputation for that. Which the "groundhog" will help with.

This will make people misattribute his success to actually being pretty good. Those who criticize him will sound spiteful. Deep-math spreadsheet theories about how he's doing the impossible in very tiny amounts, will seem like a conspiracy theory from the tinfoil hat types.

  • Work in an area in which dodginess is expected.
  • Don't dig for gold - sell shovels.
  • Bury your advantage in the noise.
  • Be actually pretty good.
  • Let that be a plausible explanation for your success.
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There's a simple way to protect himself--he's got a decent amount of money, he should quit going for 99%. Settle for 60%--deliberately make bad trades. His objective should be to turn in very good performance, not a performance that's way outside the curve.

If you're an extreme outlier somewhere, sometime it's going to come to notice. One day the company he's trading with decides to make some sort of offer to their most skilled clients--and a human double-checks it. Oops--this isn't right, they tell the SEC.

If you have something like this to hide you do not want to be at the end of a range anywhere. Stay at the edge of the pack, not beyond it.

Note: For a real-world example of this some card counters would deliberately make very large odds bets on craps if they were playing at a casino that permitted this. The bets have an average payback of 100% so it only cost them the small loss on the bet they had to make to get in a position to make the big ones. The objective was to introduce more variability into their win/loss record so they wouldn't stand out so much.

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Depends on how greedy he is about it

Nobody cares if some dude makes \$10k in a day trade, especially if each \$10k gain is spread over a few dozen accounts with a half dozen banks, perhaps even under different aliases.

But when Joe makes a billion dollars by shorting BP on the day before a terror attack takes out their refinery in Nigeria, people tend to notice. You did not make it clear if getting shot ends the repeating cycle (I'll assume not), so perhaps this is a recoverable mistake, but if he ends up in Guantanamo on the non-repeating day, that would make for a very, very long sentence.

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    $\begingroup$ In this scenario though, there would be no evidence against him. $\endgroup$ – AmiralPatate May 23 '16 at 17:07
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    $\begingroup$ There is evidence against him: he showed clear foreknowledge of the event. He made a multimillion dollar gamble that only turned out successful because of a terror attack. He might not be convictable in a civilian court of law, but he may not get a chance to present his case, instead getting whisked away to Guantanamo Bay, or assassinated, or get tried in a kangaroo court. $\endgroup$ – prosfilaes May 23 '16 at 22:09
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    $\begingroup$ Believing a crime can be made legal by an innovative method is the geek's conceit. Bank robbery is not legal even if you find a way to do it with gummy bears. Some laws ban particular methods, but other laws ban the action regardless of method. They don't need to prove method, only that no other reasonable explanation exists. No mutual-fund manager has ever been able to outperform the S&P 500 index for long. $\endgroup$ – Harper May 24 '16 at 0:05
  • $\begingroup$ He probably needs a few million, not billions. Greed kills the best of men. $\endgroup$ – Tony Ennis May 24 '16 at 22:22
  • $\begingroup$ @Harper: It's not that simple. Jury instructions are frankly rather poorly written (defining "reasonable doubt" in terms of "reason and common sense", which is entirely circular) and don't squarely address this issue. There have been a number of controversial not-guilty verdicts in recent history in which the government (arguably) failed to prove a specific timeline of events. Now, you may argue all you like about the philosophical intent of the reasonable doubt standard, but juries are the ones actually implementing it. $\endgroup$ – Kevin May 25 '16 at 4:39
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Not if he makes an arrangement with sufficiently powerful people.

Our groundhogger doesn't merely have the ability to make himself obscenely wealthy, he has the ability to make other people obscenely wealthy. Other people could include powerful organizations, individuals, or even entire countries. He can absolutely guarantee his safety if he uses a connection with such an organization to do so.

The US government, for example, would love to know what both the US and the global economy is going to do at the start of every day, as well as the details of any terrorist attacks that are going to happen, and the outcome of any military maneuvers or expensive tests scheduled to happen. In exchange for that kind of knowledge about world events, the government would likely happily allow the groundhogger to quietly become obscenely wealthy without targeting him for crimes against statistics.

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  • $\begingroup$ Frankly, you could probably convince the government to just pay you obscene amounts of money directly by working as an informant/consultant/whatever-title. Although there is a risk of becoming a target by terrorists or the like. $\endgroup$ – jpmc26 May 25 '16 at 4:39
  • $\begingroup$ This gets you a special role as advisor-in-chains-for-national-security-reasons for the next 50 years if they do believe you, and scrutiny/doubt if they don't. Lose-lose. $\endgroup$ – Stilez Jun 1 '16 at 23:24
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Be greedy

Now, Serban's answer is nice (+1), but an alternative solution would be resorting to what usually (without future knowledge) would be very risky operations; v.g. operating with penny stocks.

If you bet for and against a well stablished business (Microsoft, BP, Apple), your only chances at winning a considerable amount is that such day a very big event happens to change their value (a oil spill happens, a software flaw is detected, a new almost magical material is announced). Being able to continuously benefit from those very unexpected events is bound to bring some unwanted attention.

But, on the other side of the spectrum, there are lots of investment options that can be very profitable at the cost of being very risky (v.g. the penny stocks). A big gain with those is not that unusual, since those values are more volatile; a succession of big gains with these may be just interpreted as that you are bold (or silly) but lucky. Add to this the spread of the values being inverted in (to avoid suspicion of market manipulation) and the occasional loss due to the butterfly effect (or just to draw away attention) and you get it.

Yes, you may get some attention, but it will be easier to conceal. After all, if there are thousands of people playing lotteries with penny stock someone has to win, and that could be you (just by coincidence, of course).

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  • $\begingroup$ Disagree. Regular stocks like Apple can and do easily lose even 10% in one day. You only need a few months of such compound asset growth to become filthy, obscenely rich. Starting with $1000, you're a billionaire in less than 5 months. $\endgroup$ – Serban Tanasa May 23 '16 at 17:01
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    $\begingroup$ @SerbanTanasa Apple can and do easily lose even 10% in one day But not each day, and not even most of days. The fact that you consistently know which day to invert and in which direction is what will attract attention to you. Now with stocks that easily double or triple their value (or sink to 0), you do not need an optimal investment to make lots of money, that someone wins a lot and someone else loses a lot is part of the nature of such risky investments. $\endgroup$ – SJuan76 May 23 '16 at 17:07
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    $\begingroup$ Well, there's literally thousands of stocks to pick each "day". Doesn't need to be Apple every day. At least one will have a large vol day in any day. $\endgroup$ – Serban Tanasa May 23 '16 at 17:11
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    $\begingroup$ In fact one of the advantages is that you do not need an optimal investment strategy... Stock X is going to raise tenfold? Sell it when it has rose fivefold; you get lots of money and the "lose" of the additional profit makes your profile more average (instead of buying exactly at the lower price and selling at the maximum to get that 10% margin). $\endgroup$ – SJuan76 May 23 '16 at 17:13
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    $\begingroup$ In English we use "e.g." which happens to match the pronunciation of example (egg zample). Most people don't know that stands for exempli gratia, as it's expanded as "for example". I guess that's why this synonym dominated in the end. $\endgroup$ – JDługosz May 23 '16 at 17:28
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He would almost certainly be investigated, but I don't think he could get convicted on statistical evidence alone. Trading well isn't a crime, insider trading and certain kinds of market manipulation are. Assuming the groundhogger has no insider connections, there's no real possibility than an investigation could turn anything up.

Also, unless the other groundhoggers have an independent reason for existing apart from explaining the first one's imperfect trading record, they're not necessary. Electronic trading is very susceptible to chaos propagation: the trader's own trades disrupt everything that occurs after. After enough groundhog days, the trader could definitely hit 100% trade success if he were the only groundhogger, but it may not be desireable for him to do so. His first goal would be to maximize his capital gains, not have every trade be a success. Most likely at the end of his groundhogging he will settle on a strategy that involves some intentional losses: trades that lose money when considered individually but set him up for a larger gain on a subsequent trade.

Edit: Whoa, did not see the discussion in the comments that 3-5 repetitions of each day was all he gets. 3-5 repetitions per day is not going to be enough to get to 100% or even 99% effective trading without a great measure of luck. If there are other groundhoggers engaged in day-trading that may not even be enough time to allow them all to break even or better every (final version of a) day.

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Gambling would be easier, and less traceable.

There are sporting events with betable outcomes almost everyday and moreover most bookies accept cash bets without any traceability. All he needs to do is pick a few winners on longish odds, drop some cash down before the event, collect later in the day. So long as he continues to move around, there's not much chance of anyone picking up on his bets.

Also, he doesn't actually need that much money: since he knows every day will repeat 3 to 5 times, he can blow as much money as he likes on the first two repeats to get his fix of fine dining, movies, hookers, blow - whatever his vice of choice is - and then live more sensibly on the other days. By keeping his expenses low, he can reduce the amount of cash he actually needs to get buy and thus reduce his chances of ever getting caught.

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    $\begingroup$ This is a really nice idea. Though he probably checks the situation on the first day, have a party at the second day and bet/trade on the 3-5 day. Also beware cross-groundhog interaction. $\endgroup$ – J_F_B_M May 26 '16 at 15:54
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I'd go a different route. Go for modest cash but excessive influence first, money (in excess) later. Here's how and why:

Money by itself gets attention. But powerful influential people are expected to gain money, which will shield him considerably.

I would look not for stock rises/market shocks, but for people who make sudden blunders, and gradually build a reputation as someone insanely perceptive about what people will do, and the decisions they will make. Become a journalist, pollster, or renowned economic/political voice. Call some major decisions right. Notice illegal actions, raids, major successful speeches, resignations after a crisis, action that will be taken in major geopolitical situations, just a day or so before anyone else publishes, and get them right rather often.

Nobody will litigate or arrest anyone for this, and it builds a reputation as a person to go-to for insight in the face of big gambles - will X win an election, will Y back down on some matter, will the head of oil company Z resign, will charges stick, or whatever.

With that reputation you can then start to offer consulting services to businesses who want to get a huge decision right, and your own success will then have a context to it which is a lot harder to challenge than just making freakishly lucky investment decisions all the time.

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The market will not be changing in a certain way during this period of time, and over time penniless Joe will be able to observe the change of the market and invest his money well. But ultimately he would not be able to make more money than this using the same means because there is a certain amount of money one can make over this given time. Therefore, he will need to do this again and again to gain money at the same rate. All in all he will not be in trouble if he loves what he is doing

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