Is it accurate to say that if I was to trade something, my probability of success can't be worse than random?
"The stock market is not a zero-sum game.  Some parts are (forex, some option trading), but plain old stock trading is not zero sum. That is to say, if you were to invest ""at random"", you would on average make money.  That's because the market as a whole makes money - it goes up over time (6-10% annually, averaged over time).  That's because you're not just gambling when you buy a stock; you're actually contributing money to a company (directly or indirectly), which it uses to fund activities that (on average) make money.  When you buy Caterpillar stock, you're indirectly funding Caterpillar building tractors, which they then sell for a profit, and thus your stock appreciates in value.  While not every company makes a profit, and thus not every stock appreciates in true value, the average one does. To some extent, buying index funds is pretty close to ""investing at random"".  It has a far lower risk quotient, of course, since you're not buying a few stocks at random but instead are buying all stocks in an index; but buying stocks from the S&P 500 at random would on average give the same return as VOO (with way more volatility). So for one, you definitely could do worse than 50/50; if you simply sold the market short (sold random stocks short), you would lose money over time on average, above and beyond the transaction cost, since the market will go up over time on average. Secondly, there is the consideration of limited and unlimited gains or losses. Some trades, specifically some option trades, have limited potential gains, and unlimited potential losses. Take for example, a simple call option.  If you sell a naked call option - meaning you sell a call option but don't own the stock - for $100, at a strike price of $20, for 100 shares, you make money as long as the price of that stock is under $21.  You have a potential to make $100, because that's what you sold it for; if the price is under $20, it's not exercised, and you just get that $100, free.   But, on the other hand, if the stock goes up, you could potentially be out any amount of money.  If the stock trades at $24, you're out $400-100 = $300, right?  (Plus transaction costs.)   But what if it trades at $60?  Or $100?  Or $10000?  You're still out 100 * that amount, so in the latter case, $1 million.  It's not likely to trade at that point, but it could. If you were to trade ""at random"", you'd probably run into one of those types of situations.  That's because there are lots of potential trades out there that nobody expects anyone to take - but that doesn't mean that people wouldn't be happy to take your money if you offered it to them.   That's the reason your 16.66 vs 83.33 argument is faulty:  you're absolutely right that if there were a consistently losing line, that the consistently winning line would exist, but that requires someone that is willing to take the losing line.  Trades require two actors, one on each side; if you're willing to be the patsy, there's always someone happy to take advantage of you, but you might not get a patsy." One key piece missing from your theory is the bid/ask spread. If you buy a stock for $10, you usually can't immediately turn around and sell it for $10. You can only sell it for whatever someone is willing to pay for it.  So virtually any random investment (stocks, bonds, forex, whatever) immediately loses a small amount of value, and over the long run you will almost certainly lose money if you buy/sell at random. "I'm just trying to visualize the costs of trading. Say I set up an account to trade something (forex, stock, even bitcoin) and I was going to let a random generator determine when I should buy or sell it. If I do this, I would assume I have an equal probability to make a profit or a loss. Your question is what a mathematician would call an ""ill-posed problem.""  It makes it a challenge to answer.  The short answer is ""no.""  We will have to consider three broad cases for types of assets and two time intervals. Let us start with a very short time interval.  The bid-ask spread covers the anticipated cost to the market maker of holding an asset bought in the market equal to the opportunity costs over the half-life of the holding period.  A consequence of this is that you are nearly guaranteed to lose money if your time interval between trades is less than the half-life of the actual portfolio of the market maker.  To use a dice analogy, imagine having to pay a fee per roll before you can gamble.  You can win, but it will be biased toward losing. Now let us go to the extreme opposite time period, which is that you will buy now and sell one minute before you die.  For stocks, you would have received the dividends plus any stocks you sold from mergers.  Conversely, you would have had to pay the dividends on your short sales and received a gain on every short stock that went bankrupt.  Because you have to pay interest on short sales and dividends passed, you will lose money on a net basis to the market maker.  Maybe you are seeing a pattern here.  The phrase ""market maker"" will come up a lot. Now let us look at currencies.  In the long run, if the current fiat money policy regime holds, you will lose a lot of money.  Deflation is not a big deal under a commodity money regime, but it is a problem under fiat money, so central banks avoid it.  So your long currency holdings will depreciate.  Your short would appreciate, except you have to pay interest on them at a rate greater than the rate of inflation to the market maker. Finally, for commodities, no one will allow perpetual holding of short positions in commodities because people want them delivered.  Because insider knowledge is presumed under the commodities trading laws, a random investor would be at a giant disadvantage similar to what a chess player who played randomly would face against a grand master chess player.  There is a very strong information asymmetry in commodity contracts.  There are people who actually do know how much cotton there is in the world, how much is planted in the ground, and what the demand will be and that knowledge is not shared with the world at large.  You would be fleeced. Can I also assume that probabilistically speaking, a trader cannot do   worst than random? Say, if I had to guess the roll of a dice, my   chance of being correct can't be less than 16.667%. A physicist, a con man, a magician and a statistician would tell you that dice rolls and coin tosses are not random.  While we teach ""fair"" coins and ""fair"" dice in introductory college classes to simplify many complex ideas, they also do not exist.  If you want to see a funny version of the dice roll game, watch the 1962 Japanese movie Zatoichi.  It is an action movie, but it begins with a dice game.   Consider adopting a Bayesian perspective on probability as it would be a healthier perspective based on how you are thinking about this problem.  A ""frequency"" approach always assumes the null model is true, which is what you are doing.  Had you tried this will real money, your model would have been falsified, but you still wouldn't know the true model. Yes, you can do much worse than 1/6th of the time.  Even if you are trying to be ""fair,"" you have not accounted for the variance. Extending that logic, then for an inexperienced trader, is it right to   say then that it's equally difficult to purposely make a loss then it   is to purposely make a profit? Because if I can purposely make a loss,   I would purposely just do the opposite of what I'm doing to make a   profit. So in the dice example, if I can somehow lower my chances of   winning below 16.6667%, it means I would simply need to bet on the   other 5 numbers to give myself a better than 83% chance of winning. If the game were ""fair,"" but for things like forex the rules of the game are purposefully changed by the market maker to maximize long-run profitability.  Under US law, forex is not regulated by anything other than common law.  As a result, the market maker can state any price, including prices far from the market, with the intent to make a system used by actors losing systems, such as to trigger margin calls.  The prices quoted by forex dealers in the US move loosely with the global rates, but vary enough that only the dealer should make money systematically.  A fixed strategy would promote loss. You are assuming that only you know the odds and they would let you profit from your 83.33 percentage chance of winning. So then, is the costs of trading from a purely probabilistic point of   view simply the transaction costs? No matter what, my chances cannot   be worse than random and if my trading system has an edge that is   greater than the percentage of the transaction that is transaction   cost, then I am probabilistically likely to make a profit? No, the cost of trading is the opportunity cost of the money.  The transaction costs are explicit costs, but you have ignored the implicit costs of foregone interest and foregone happiness using the money for other things. You will want to be careful here in understanding probability because the distribution of returns for all of these assets lack a first moment and so there cannot be a ""mean return.""  A modal return would be an intellectually more consistent perspective, implying you should use an ""all-or-nothing"" cost function to evaluate your methodology." "If i do this, I would assume I have an equal probability to make a profit or a loss. The ""random walk""/EMH theory that you are assuming is debatable. Among many arguments against EMH, one of the more relevant ones is that there are actually winning trading strategies (e.g. momentum models in trending markets) which invalidates EMH.  Can I also assume that probabilistically speaking, a trader cannot do worst than random? Say, if I had to guess the roll of a dice, my chance of being correct can't be less than 16.667%. It's only true if the market is truly an independent stochastic process. As mentioned above, there are empirical evidences suggesting that it's not.  is it right to say then that it's equally difficult to purposely make a loss then it is to purposely make a profit?  The ability to profit is more than just being able to make a right call on which direction the market will be going. Even beginners can have a >50% chance of getting on the right side of the trades. It's the position management that kills most of the PnL." It seems to be that your main point is this: No matter what, my chances cannot be worse than random and if my trading system has an edge that is greater than the percentage of the transaction that is transaction cost, then I am probabilistically likely to make a profit? In general, yes, that is true, but... Consider this very bad strategy: Buy one share of stock and sell it one minute later, and repeat this every minute of the day. Obviously you would bleed your account dry with fees. However, even this horrible strategy still meets your criteria because: if this bad strategy had an edge beyond the transaction fees you would likely still make a profit. In other words, your conclusion reduces to an uninteresting statement: If there were no transactions fees, then if your trading system has an edge then you will likely make a profit. Sorry to be the bearer of bad news, but IMHO, that statement, and others made in the question are just obvious things stated in convoluted ways. I don't want to discourage you from thinking about these things though. I personally really enjoy these type of thought experiments. I just feel you missed the mark on this one... "The previous answers make valid points regarding the risks, and why you can't reasonably compare trading for profit/loss to a roll of the die. This answer looks at the math instead. Your assumption: I have an equal probability to make a profit or a loss. Is incorrect, for the reasons stated in other answers. However, the answer to your question: Can I also assume that probabilistically speaking, a trader cannot do worst than random? Is ""yes"". But only because the question is flawed. Consequently it's throwing people in all directions with their answers. But quite simply, in a truly random environment the worst case scenario, no matter how improbable, is that you lose over and over again until you have nothing left. This can happen in sequential rolls of the dice AND in trading securities/bonds/whatever. You could guess wrong for every roll of the die AND all of your stock picks could become worthless. Both outcomes result in $0 (assuming you do not gamble with credit). Tell me, which $0 is ""worse""? Given the infinite number of plays that ""random"" implies, the chance of losing your entire bankroll exists in both scenarios, and that is enough by itself to make neither option ""worse"" than the other. Of course, the opposite is also true. You could only pick winners, with an unlimited upside potential, but again that could happen with either dice rolls or stock picks. It's just highly improbable. my chances cannot be worse than random and if my trading system has an edge that is greater than the percentage of the transaction that is transaction cost, then I am probabilistically likely to make a profit? Nope. This is where it all falls apart. Just because your chances of losing it all are similarly improbable, does not make you more likely to win with one method or the other. Regression to the mean, when given infinite, truly random outcomes, makes it impossible to ""have an edge"". Also, ""probabilistically"" isn't a word, but ""probably"" is." In theory, in a perfect world, what you state is almost true. Apart from transaction fees, if you assume that the market is perfectly efficient (ie: public information is immediately reflected in a perfect reflection of future share value, in all share prices when the information becomes available), then in theory any transaction you would choose to take is opposed by a reasonable person who is not taking advantage of you, just moving their position around. This would make any and all transactions completely reasonable from a cost-benefit perspective.  ie: if the future value of all dividends to be paid by Apple [ie: the value of holding a share in Apple] exactly matches Apple's share price of $1,000, then buying a share for $1,000 is an even trade. Selling a share for $1,000 is also an even trade. Now in a perfectly efficient market, which we have assumed, then there is no edge to valuing a company using your own methods. If you take Apple's financial statements / press releases / reported information, and if you apply modern financial theory to evaluate the future dividends from Apple, you should get the same $1,000 share price that the market has already arrived at. So in this example, why wouldn't you just throw darts at a printout of the S&P 500 and invest in whatever it lands on? Because, even if the 'perfectly efficient market' agrees on the true value of something, different investments have different characteristics. As an example, consider a simple comparison of corporate bonds: Corporations make bond offerings to the public, allowing individual investors to effectively lend money to the corporation, for a future benefit. For simplicity, assume a bond with a 'face value' (the amount to be repaid to the investor on maturity) of $1,000 has these 3 defining characteristics: (1) The price [What the investor pays to acquire it]; (2) Interest payments [how much, if any, the corporation will pay to the investor before maturity, and when those payments will be made]; and (3) a bond rating [which is a third party assessment of how risky the bond is, based on the 'health' of the corporation]. Now if the bond rating agency is perfect in its risk assessment, and if the price of all bond's is fair, then why does it matter who you loan your money to? It matters because different people want different things out of their investments. If you are waiting to make a down payment on a house next year, then you don't want risk - you want to be certain that you will get your cash back, even if it means lower returns. So, even though a high-risk bond may be perfectly priced, it should only be bought by someone willing to bear that risk. If you are retired, and you need your bonds to pay you interest regularly as your sole source of income, then of course a zero-coupon bond [one that pays no interest] is not helpful to you. If you are young, and have a long time to invest, then you may want risk, because you have time to overcome losses and you want to get the most return possible. In addition, taxes are not universal between all investors. Some people benefit from things that would be tax-heavy to their neighbors. For example in Canada, there is a 'dividend tax credit' which reduces the taxes owing on dividends received by a corporation. This credit exists to prevent 'double-taxation', because otherwise the corporation would pay its ~30% of tax, and then a wealthy investor would pay another ~45% of tax. Due to the mechanics of how the credit is calculated, however, someone who makes less money, gets an even lower tax bill than they normally would. This means that someone making under the top tax bracket in Canada, has a tax benefit by receiving dividends. This means that while 2 stocks may be both fairly priced, if one pays dividends and the other doesn't [ie: if the other company instead reinvests more heavily in future projects, creating even more value for shareholders down the road], then someone in the bottom tax brackets may want the dividend paying stock more than the other. In conclusion: Picking investments yourself does require some knowledge to prevent yourself from making a 'bad buy'; this is because the market is not perfectly efficient. As well, specific market mechanics make some trades more costly than they should be in theory; consider for example transaction fees and tax mechanics. Finally, even if you assume that all of the above is irrelevant as a theoretical idea, different investors still have different needs. Just because $1,000,000 is the 'fair' price for a factory in your home town, doesn't mean you might as well convert your retirement savings to buy it as your sole asset. "Don't compare investing with a roll of the dice, compare it with blackjack and the decision to stand or hit, or put more money on the table (double down or increase bet size) , based on an assessment of the state of the table and history.  A naive strategy of say ""always hitting to 16"" isn't as awful as randomly hitting and standing (which, from time to to time will draw to 21 fair and square) , but there's a basic strategy that gets close to 50% and by increasing or decreasing bet based on counting face cards can get into positive expectations. Randomly buying and selling stock is randomly hitting.  Buying a market index fund is like always hitting to 16.  Determining an asset allocation strategy and periodically rebalancing is basic strategy.  Adjusting allocations based on business cycle and economic indicators is turning skill into advantage."
I've worked at a bank, and even the best prop traders have low Sharpe ratios and large swings.  I would advise that the average person without access to flow information does not a chance, and will end up losing eventually. "Is playing the lottery a wise investment? --Probably not.  Is playing the lottery an investment at all? --Probably not though I'll make a remark on that further below.  Does it make any sense to play the lottery in order to improve your total asset allocation? --If you follow the theory of the Black Swan, it actually might.  Let me elaborate. The Black Swan theory says that events that we consider extremely improbable can have an extreme impact. So extreme, in fact, that its value would massively outweigh the combined value of all impacts of all probable events together. In statistical terms, we are speaking about events on the outer limits of the common probablity distribution, so called outliers that have a high impact.  Example: If you invest $2000 on the stock market today, stay invested for 20 years, and reinvest all earnings, it is probable within a 66% confidence interval that you will have an 8 % expected return (ER) per year on average, giving you a total of roughly $9300. That's very much simplified, of course, the actual number can be very different depending on the deviations from the ER and when they happen. Now let's take the same $2000 and buy weekly lottery tickets for 20 years. For the sake of simplicity I will forgo an NPV calculation and assume one ticket costs roughly $2. If you should win, which would be an entirely improbable event, your winnings would by far outweigh your ER from investing the same amount.  When making models that should be mathematically solvable, these outliers are usually not taken into consideration. Standard portfolio management (PM) theory is only working within so called confidence intervals up to 99% - everything else just wouldn't be practical. In other words, if there is not at least a 1% probability a certain outcome will happen, we'll ignore it. In practice, most analysts take even smaller confidence intervals, so they ignore even more.  That's the reason, though, why no object that would fall within the realms of this outer limit is an investment in terms of the PM theory. Or at least not a recommendable one. Having said all that, it still might improve your position if you add a lottery ticket to the mix. The Black Swan theory specifically does not only apply to the risk side of things, but also on the chance side. So, while standard PM theory would not consider the lottery ticket an investment, thus not accept it into the asset allocation, the Black Swan theory would appreciate the fact that there is minimal chance of huge success.  Still, in terms of valuation, it follows the PM theory. The lottery ticket, while it could be part of some ""investment balance sheet"", would have to be written off to 0 immediately and no expected value would be attached to it. Consequently, such an investment or gamble only makes sense if your other, safe investments give you so much income that you can easily afford it really without having to give up anything else in your life. In other words, you have to consider it money thrown out of the window.  So, while from a psychological perspective it makes sense that especially poorer people will buy a lottery ticket, as Eric very well explained, it is actually the wealthier who should consider doing so. If anyone. :)" Someone entering a casino with $15 could employ a very simple strategy and have a better-than-90% chance of walking out with $16.  Unfortunately, the person would have a non-trivial chance (about one in 14) of walking out with $0. If after losing $15 the person withdrew $240 from the bank and tried to win $16, the person would have a better-than-90% chance of succeeding and ending up ahead (holding the original $15, plus the additional $240, plus $1) but would have at that point about a one in 14 chance from that point of losing the $240 along with the original $15.  Measured from the starting point, you'd have about a 199 out of 200 chance of gaining $1, and a one out of 200 chance of losing $240. Market-timing bets are like that.  You can arrange things so you have a significant chance of making a small profit, but at the risk of a large downside.  If you haven't firmly decided exactly how much downside you are willing to accept, it's very easy to simultaneously believe you don't have much money at risk, but that you'll be able to win back anything you lose.  The only way you can hope to win back anything you lose is by bringing a lot more money to the table, which will of course greatly increase your downside risk. The probability of making money for the person willing to accept $15 of downside risk to earn $1 is about 93%.  The probability of making money for the person willing to accept $255 worth of risk is about 99.5%.  It's easy to see that there are ways of playing which have a 99.5% chance of winning, and that there are ways of playing that only have a 15:1 downside risk.  Unfortunately, the ways of playing that have the smaller risk don't have anything near a 99.9% chance of winning, and those that have a better chance of winning have a much larger downside risk. Think about Wall Street. It's the most highly paid occupation in the world and it's nothing but a casino. I don't think the article is saying that success is only luck, or that there aren't successes built far more on genius than luck, but that luck is the main factor in the majority of cases of great wealth. "Yes. The definition of unreasonable shows as ""not guided by or based on good sense."" 100% years require a high risk. Can your one stock double, or even go up three fold? Sure, but that would likely be a small part of your portfolio. Overall, long term, you are not likely to beat the market by such high numbers.  That said, I had 2 years of returns well over 100%. 1998, and 1999. The S&P was up 26.7% and 19.5%, and I was very leverage in high tech stock options. As others mentioned, leverage was key. (Mark used the term 'gearing' which I think is leverage). When 2000 started crashing, I had taken enough off the table to end the year down 12% vs the S&P -10%, but this was down from a near 50% gain in Q1 of that year. As the crash continued, I was no longer leveraged and haven't been since. The last 12 years or so, I've happily lagged the S&P by a few basis points (.04-.02%).  Also note, Buffet has returned an amazing 15.9%/yr on average for the last 30 years (vs the S&P 11.4%). 16% is far from 100%. The last 10 year, however, his return was a modest 8.6%, just .1% above the S&P." Well, yes.  Lewis (and anybody) is presuming that you accept take advantage of good fortune.  In his own example, though, he wasn't in any way prepared to go into finance.  Having gotten there, and established himself even, he pitched it in favor of writing a book.  Neither of those examples supports everyone calling luck the result of work plus brains. No. You're lucky, maybe, but not really a successful investor. Warren Buffet is, you're not him. Sometimes it is easier to pick stocks to bid on, sometimes its harder. I got my successes too. It is easier on a raising market, especially when it is recovering after a deep fall, like now. But generally it is very hard to beat the market. You need to remember that an individual investor, not backed by deep pockets, algo-trading and an army of analysts, is in a disadvantage on the market by definition. So what can you do? Get the deep pockets, algo-trading and an army of analysts. How? By pooling with others - investing through funds. I remember like 20 years ago someone did an experiment where Peter Lynch, elementary school kids, and an ape, all picked stocks in a situation similar to this. The result was almost the same, with the elementary school kids coming out slightly better  Picking correct stocks is a craps shoot, as the market is an emotional entity, and in the short run, even educated guesses don't give an edge. People like Peter Lynch eventually win of course because of discipline, long term goals, and knowledge of tools like derivatives "Sorry no. I don't like to hear that the difference between me and the bum on the street is ""luck."" Luck certainly makes a difference of one or two notches on the pay scale, or a few years here or there in your career. But hard work and good choices make the most of the luck we're given. Far too many piss that luck away with poor choices or no work and then look on with envy at those ""lucky bastards"" who made it big." No, I felt that's what aweraw was trying to say, but they were not doing a good job of it so I took a crack at it from my point of view. I see where you are coming from too. Really, I suspect if we all sat down and had to write a unified view of the role luck plays in our lives we would be surprised how much we agree. :) "Of course, which is why you need to have a scoring function / utility function for the ""filters"", i.e. Are you going to value it by rate of accuracy hor by a metric where wins = +2, losses = -1, such that it uses a criteria like that to decide whether or not a filter adds value, (some even use a compound effect i.e. wins = 2+e^(1+w) where w is the consecutive wins).  A metric like the above would capture the trade off between predictive power and profit. Also some traders watch their Max DD very carefully so they may be very risk averse." Yes under certain circumstances! Educate yourself first. Consider algorithmic trading when you code your strategies and implement your ideas - a bit easier for psychology. And let the computer to trade for you. Start with demo account without taking personal risk. Only after a year of experience try small amount of cash like you said 100$. Avoid trade when big news events are released. Stick to strategy, use money management, stop loss, write results in the journal... learn & improve... be careful it is very hard journey. I don't understand why these things are always either/or. It's not just lucky circumstances and it's not just hard work that makes someone successful. Example abound of rich kids who don't pan out and poor kids who make it.   Personally, I had access to a good education growing up and I pushed myself hard to capitalize on it. Luck is the access, but hard work was necessary to convert. I've had success in my career. Part of it is that I had opportunities to tackle tough challenges, but I also pushed to convert on those opportunities. "This article is written by an idiot!!  Risk ≠ failure, risk = possibility of failure  Reward (return) should be commensurate with risk and this is why long-shot propositions should be worthwhile. An example of this could be something like the following; an investment with a 95% chance of success should return about 5% on the investment (1 in 20 risk of loss, 1/20th return on investment for taking the risk) while a long-shot investment with a 5% chance of success should be paying a 2000% return (1 in 20 will succeed but they will pay 20 times the investment if they do).  An investment with a 0% chance of return (that you are suckered into due to ""opacity"") is not an investment, it is being robbed and it should be illegal. WTF is opacity? Lying?" What secular religious wannabe non-sense. Sure some things are random and you have the same chance as the next guy all other things considered equal, but the chances of all other things being equal is nil to zero. Luck is an illusion of probability, and it's better to shape those odds in your own favor than not. You say as much in your post, so why even argue with me about it?