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."
Firstly, I highly doubt anyone on this site will be able to provide you with accurate input on this matter regarding what TO DO.  It's the what not to do that may be possible. That said, if you want to offer equipment for rent, which in a developing country is probably a decent idea, I'd start by asking around and doing some research on what people really need and are wanting to rent.  I would suggest studying other developing/developed countries histories to see what companies were successful around a similar stage as well. I'd start small: pressure washers, generators, concrete mixers, fork lifts, hydraulic ladders, etc.  Getting things that are just a bit too expensive for someone to own and something they don't need all the time.  These can be great revenue generators because they're cheap to purchase, but can be rented at a premium. As someone who works on the sell side, I can tell you you're partially right.  Yes, we do make money off of trades (so just getting people to trade gets the company money) but we do try to be right.  We like to look at overall trends with growth projections and earnings estimates, and (as long as the analyst isn't a bad one) will try to get the right answer.  Often, we try to present different angles to the research and aren't afraid to go out on a limb--so that you'll read it. We like being right though.  The reason we like to be right and make people understand that we know what is going on is simple: a company won't respect research if it's bullshit.  And that goes for trading and buy side firms, but also from the companies involved in the research.  For an investment bank, a large chunk (often over 50%) of revenue comes from M&amp;A deals, and often a company will choose to do a deal with companies they know will give a good value-that come's from their first experience with the company-equity research.  So yes, we don't like to beat up on companies, but we do want to be right.    If the analyst has that bad a rate of success, he's probably pretty bad or you're looking at an industry where nobody saw some huge shift coming.  Edit: Oh, and analysts can't buy or sell any company in their sector (I think this is industry-wide, not just my firm) "The question is: how do you quantify investment risk? As Michael S says, one approach is to treat investment returns as a random variable. Bill Goetzmann (Yale finance professor) told me that if you accept that markets are efficient or that the price of an asset reflects it's underlying value, then changes in price represent changes in value, so standard deviation naturally becomes the appropriate measure for riskiness of an asset. Essentially, the more volatile an asset, the riskier it is. There is another school of thought that comes from Ben Graham and Warren Buffett, which says that volatility is not inherently risky. Rather, risk should be defined as the permanent loss of capital, so the riskiness of an asset is the probability of a permanent loss of capital invested.  This is easy to do in casino games, based on basic probability such as   roulette or slots. But what has been done with the various kinds of   investment risks? My point is saying that certain bonds are ""low risk""   isn't good enough; I'd like some numbers--or at least a range of   numbers--and therefore one could calculate expected payoff (in the   statistics sense). Or can it not be done--and if not, why not? Investing is more art than science. In theory, a Triple-A bond rating means the asset is riskless or nearly riskless, but we saw that this was obviously wrong since several of the AAA mortgage backed securities (MBS) went under prior to the recent US recession. More recently, the current threat of default suggests that bond ratings are not entirely accurate, since US Treasuries are considered riskless assets.  Investors often use bond ratings to evaluate investments - a bond is considered investment grade if it's BBB- or higher. To adequately price bonds and evaluate risk, there are too many factors to simply refer to a chart because things like the issuer, credit quality, liquidity risk, systematic risk, and unsystematic risk all play a factor.  Another factor you have to consider is the overall portfolio. Markowitz showed that adding a riskier asset can actually lower the overall risk of a portfolio because of diversification. This is all under the assumption that risk = variance, which I think is bunk.  I'm aware that Wall Street is nothing like roulette, but then again   there must be some math and heavy economics behind calculating risk   for individual investors. This is, after all, what ""quants"" are paid   to do, in part. Is it all voodoo? I suspect some of it is, but not all   of it. Quants are often involved in high frequency trading as well, but that's another note. There are complicated risk management products, such as the Aladdin system by BlackRock, which incorporate modern portfolio theory (Markowitz, Fama, Sharpe, Samuelson, etc) and financial formulas to manage risk.  Crouhy's Risk Management covers some of the concepts applied.  I also tend to think that when people point to the last x number of   years of stock market performance, that is of less value than they   expect. Even going back to 1900 provides ""only"" 110 years of data, and   in my view, complex systems need more data than those 40,500 data   points. 10,000 years' worth of data, ok, but not 110. Any books or articles that address these issues, or your own informed   views, would be helfpul. I fully agree with you here. A lot of work is done in the Santa Fe Institute to study ""complex adaptive systems,"" and we don't have any big, clear theory as of yet. Conventional risk management is based on the ideas of modern portfolio theory, but a lot of that is seen to be wrong. Behavioral finance is introducing new ideas on how investors behave and why the old models are wrong, which is why I cannot suggest you study risk management and risk models because I and many skilled investors consider them to be largely wrong. There are many good books on investing, the best of which is Benjamin Graham's The Intelligent Investor. Although not a book on risk solely, it provides a different viewpoint on how to invest and covers how to protect investments via a ""Margin of Safety."" Lastly, I'd recommend Against the Gods by Peter Bernstein, which covers the history of risk and risk analysis. It's not solely a finance book but rather a fascinating historical view of risk, and it helps but many things in context. Hope it helps!" Assuming you were immersed in math with your CS degree, the book **'A Non-Random Walk Down Wall Street' by Andrew Lo** is a very interesting book about the random walk hypothesis and it's application to financial markets and how efficient markets might not necessarily imply complete randomness.    Lots of higher level concepts in the book but it's an interesting topic if you are trying to branch out into the quant world.  The book isn't very specific towards algorithmic trading but it's good for concept and ideas.  Especially for general finance, that will give you a good run down about markets and the way we tackle modern finance.    **A Random Walk Down Wall Street** (which the book above is named after) by **Burton Malkiel** is also supposed to be a good read and many have suggested reading it before the one I listed above, but there really isn't a need to do so.    For investing specifically, many mention **'The Intelligent Investor' by Benjamin Graham** who is the role model for the infamous Warren Buffet.  It's an older book and really dry and I think kind of out dated but mostly still relevant.  It's more specifically about individual trading rather than markets as a whole or general markets.  It sounds like you want to learn more about markets and finance rather than simply trading or buying stocks.  So I'd stick to the Andrew Lo book first.    ---  Also, since you might not know, it would be a good idea to understand the capital asset pricing model, free cash flow models, and maybe some dividend discount models, the last of which isn't so much relevant but good foundations for your finance knowledge.  They are models using various financial concepts (TVM is almost used in every case) and utilizing them in various ways to model certain concepts.  You'd most likely be immersed in many of these topics by reading a math-oriented Finance book.  Try to stay away from those penny stock trading books, I don't think I need to tell a math major (who is probably much smarter than I am) that you don't need to be engaging in penny stocks, but do your DD and come to a conclusion yourself if you'd like.  I'm not sure what career path you're trying to go down (personal trading, quant firm analyst, regular analyst, etc etc) but it sounds like you have the credentials to be doing quant trading.    ---  Check out www.quantopian.com.  It's a website with a python engine that has all the necessary libraries installed into the website which means you don't have to go through the trouble yourself (and yes, it is fucking trouble--you need a very outdated OS to run one of the libraries).  It has a lot of resources to get into algorithmic trading and you can begin coding immediately.  You'd need to learn a little bit of python to get into this but most of it will be using matplotlib, pandas, or some other library and its own personal syntax. Learning about alpha factors and the Pipeline API is also moderately difficult to get down but entirely possible within a short amount of dedicated time.     Also, if you want to get into algorithmic trading, check out Sentdex on youtube.  He's a python programmer who does a lot of videos on this very topic and has his own tool on quantopian called 'Sentiment Analyzer' (or something like that) which basically quantifies sentiment around any given security using web scrapers to scrape various news and media outlets.  Crazy cool stuff being developed over there and if you're good, you can even be partnered with investors at quantopian and share in profits.    You can also deploy your algorithms through the website onto various trading platforms such as Robinhood and another broker and run your algorithms yourself.    Lots of cool stuff being developed in the finance sector right now.  Modern corporate finance and investment knowledge is built on quite old theorems and insights so expect a lot of things to change in today's world.  ---  With a math degree, finance should be like algebra I back in the day.  You just gotta get familiar with all of the different rules and ideas and concepts.  There isn't that much difficult math until you begin getting into higher level finance and theory, which mostly deals with statistics anyways like covariance and regression and other statistic-related concepts.  Any other math is simple arithmetic. That makes sense.  So it's sort of a thoughtless process on a short time scale, but if you add up all that noise over time you could (potentially) end up with a more meaningful position than if you had valued and bet on each stock individually.  And I could see how these things could spread along a chain to unrelated stocks as well... "What determines your profitability is not your time, but your TRADES. It is probably a mistake to go into the market and say, I hope to make X% today/this month/this year. As a practical matter, you can make a lot of money in a short period of time, or lose a lot over a long period of time (the latter is more likely). You're better off looking at potential trades and saying ""I like this trade"" (be sure to know why) and ""I dislike that trade."" If you're right about your chosen trade, you'll make money. Probably not on your original timetable, because markets react more slowly than individual people do. Then make ONLY those trades that you genuinely like and understand. IF you get into a ""rhythm,"" (rather few people do), your experience might tell you that you are likely to make, say, X% per month or year. But that's ONLY if the market continues to accommodate YOUR style of trading. If the markets change, YOU must change (or get lost in the shuffle). Trading is a risky, if sometimes rewarding business. The operative motto here is: ""You pay your money and you take your chances,"" NOT ""You put in your time and eventually rewards will come.""" "I commend you for your desire to be a smart and engaged investor. Regarding the other comments, yes the market is unpredictable and dangerous, but such is everything that leads to profit.  I am currently reading, ""Advanced Options Pricing Models"" (Katz and McCormick) - mighy be at your local library. The book is helpful because in explaining the options market, it covers basic stock methodologies and then builds on them as it pursues a quant's math/computation based view of the market. The book is highly math oriented and discusses authors' custom design scripts/alogrithms to analyze market behavior. See similar post about technical analysis (since it often directs short term trading decisisions)." "&gt;Opportunities are not equal  But the OP and most of the ""it's all about luck"" folks here *are* saying opportunities are equal - if it's only about luck, then *anyone* can find that lucky penny.   Remember - that's the assertion here - that there are tons of people who could be billionaires; the ones who are only got there because *they* were the ones that someone whispered ""plastics"" to at a party.   Total egalitarianism; no meritocracy or plutocracy whatsoever. It's all about the spin of the wheel, man. Anyone can win the lottery."