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I'm from a mathematics background and I'm curious to understand the skill of profiting off the stock market as an individual. Is it ones ability to predict successful businesses? Is quantitative trading viable anymore for individuals? Is it a lot of luck?

I'm interested in getting into the stock market, but I'm not sure what I should research into (e.g. quantitative trading, business, economics, etc) which is why I'm asking these questions. I'd like to hear your thoughts, cheers!

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I am kind of a math guy myself, probably not as much as you, but decent. Enough of a math guy that it was very hard to learn the lesson presented in the next paragraph.

What I have come to realize is that long term stock market success is far more about behavior than math. It is far simpler than most realize. Decide on a broker, an asset allocation, and pick some low cost mutual funds. I do have some actively managed funds, but the majority is in index funds. Then invest regularly and re-balance occasionally.

As a math guy your time is valuable, and you can probably earn a lot of money at your chosen profession. Focusing on your career, and improving your service to others will yield far better results then efforts in stock market trading. Strangely, you will then have even more money to invest. This would hold true, as well, for someone making close to minimum wage.

So yes, I would encourage you to get "into the stock market" but with a long term perspective. Cooking a meal in a crock pot is a decent analogy. Active trading for yourself is a great way to "bend over dollars to pick up pennies".

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    Yes, by default, passive investing works for most. And yet, a knowledge of trading is quite useful for making good money in turbulent markets as well as protecting one's crock pot. It's rather unpleasant to "bend over" and find that your dollars are now measured in pennies (see 2000, 2008 and the past month). – Bob Baerker Apr 1 at 10:41
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    the part about earning a lot of money reminds me of all the jokes about Math PhDs and how much they earn. sorry! (ironically, it's probably the financial jobs like quants that actually do pay the best for a math major, so maybe... go into that sector professionally?) – Michael Apr 1 at 20:17
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    I would go one step further, ditch the broker, and buy ETFs instead. Ultimately, fees are a bigger impact on your profits than which fund you choose. – Lawnmower Man Apr 1 at 20:55
  • @LawnmowerMan There's really no fees any more. Maybe with some less mainstream brokers. – MCMastery Apr 2 at 1:30
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    @MCMastery I don't mean broker commissions. I mean mutual fund management fees. But if you are buying ETFs or mutual funds, why do you even need to involve a human broker? They're just going to sell you on products which are good for them. – Lawnmower Man Apr 2 at 3:29
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Quantitative investing is a tricky, but potentially very lucrative business. Personally I would be wary of doing this as an individual. Even as some who is a professional quant I would hesitate to do this myself. In fact most professional quants I know don't do this with their personal portfolios. The main reason is the difficulty and number of problems encountered can be hard for one individual to address. Typically most quant shops have a team of PhDs in math, physics, and engineering to tackle these problems. The background required becomes quite extensive. Here are some of the areas you need a high level understanding in to develop these kinds of systems

Mathematics: functional analysis, measure theory and probability, multivariate statistics, matrix analysis, experimental design, and convex optimization.

Computer Science and Engineering: adaptive signal processing, parallel computing, analysis of algorithm, database design and management, and scientific computing.

As you may have gleaned the development of the mathematical theory behind techniques, along with the ability to build and maintain the high performance computing systems to execute them is not really a one man job. You also need to have a good understanding of finance and economics in order to aid in rational model development.

A final point to consider is money. 95% of quant strategies rely on large diversified portfolios (this is essentially to exploit the Law of Large Numbers). What you typically see is portfolios with 1000 stock positions or more. This means at a minimum it would take a few million dollars to put together such a portfolio.

Having said all of this I do see people who start up their own quant strategies and try to get them funded by people in the hedge fund industry. Once in a while you do see a gem. If you are interested to learn more about this I suggest looking into the top quantitative finance programs in the US. The majority of PhDs getting hired by hedge funds and big banks come from Princeton, Stanford, Stony Brook, Berkeley, and Carnegie Mellon.

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  • This means at a minimum it would take a few million dollars to put together such a portfolio. => Furthermore, there are also specific certifications and qualifications that are required to perform some actions such as short selling: trading certification, agreement with the exchange, minimum funds parked at a guarantor, etc... to enable the whole thing. So certain trading strategies are simply out of reach of individual laymen. – Matthieu M. Apr 3 at 17:40
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    Thinking that you can use "math" as an individual investor to beat the market is definitely misguided. "Once in a while you do see a gem." And with an infinite number of monkeys on typewriters... – ahaas Apr 3 at 23:24
  • In addition to the on site technical requirements you do a good job of mentioning, there's also the infrastructure requirements: how good (and consistent) is the latency from wherever you're at to New York and London.... – Jared Smith Apr 4 at 10:57
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Trading is all about supply & demand. Period.

The above is a tremendously, deceptively simple answer that truly does encompass everything in the markets. The trick is learning to interpret supply & demand effectively enough to make a consistent profit. Note that consistent does not equal "never losing". Losses are inevitable in trading, and you have to become completely comfortable with not "knowing" what's going to happen, or indeed with not even attempting to forecast or predict. That can work for a while, but it's as much to do with luck as anything.

"Math guys" tend to get eaten for lunch in the markets if they hold rigidly to that identity, because they assume and expect that the markets are in fact all about math. Here is the obligatory XKCD:

enter image description here

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People often think that if they're smart enough, they can beat the market. However, the math of trading is the easy part. Making the model line up with reality has always been the hard part. Even assuming you're the smartest guy in the room, getting the information and capital necessary to be able to exploit your smartness in the first place is the limiting factor.

The vast majority of active traders lose money compared to the market (basically the SP500). These are not amateurs - they are people who spend 9-5 (often much longer) trying to come up with intelligent trading strategies. So if you want to outsmart the vast majority of active traders, you'll say "I know math, the odds are drastically stacked against me," and you'll simply buy something like VOO, which tracks the SP500.

The traditional economic explanation for this is the Efficient Market Hypothesis - market prices already reflect all the available information out there, since people who know something will trade on it for an easy profit, so you can't beat it. In fact, this necessarily implies that any short term fluctuations outside the true value are random noise (so good luck "beating" that!). Couple this with Hayek's explanation for the failure of central planning - all of the information necessary for organizing society is scattered about the economy in individuals' behaviors and plans and reactions to changing incentives, and it is always changing; by the time you gather a big data set for the central planners, it's already out of date! Lenin ran into this exact problem and eventually stopped trying to plan. Guess who the central planner is in our situation? You!

However, the traditional explanation isn't entirely accurate. If markets are perfectly efficient, what incentive is there to gather and trade on information in the first place such that it is reflected in the market prices? Likewise, we have empirical evidence of a number of people and funds who have consistently beaten the market over time.

You might want to read Efficiently Inefficient by Lasse Pedersen, a prominent hedge fund academic. He argues that markets are efficiently inefficient. They're efficient only until it's no longer worth the investment to make them more efficient by exploiting pricing inefficiencies. For example, at the announcement of a corporate buyout, the stock price will not rise to the full level offered by the buyers, and the spread reflects the risk that the buyout will not go through. Event-driven specialists can trade on this "inefficiency" and make a profit over many such events. The cost of making potentially even more efficient trades will not be worth any additional profit.

The book also indirectly shows the requirements for being able to implement a smart money trading strategy in the first place. Quant strategies require lots of computing power and data. Event-driven funds have their own internal databases of how mergers and acquisitions panned out. Sometimes it's just about having a strong enough rolodex to be able to find shares you want to short in the first place, since you can't always just short a security because your model says you should.

Purely mathematical smarts are not the limiting factor for individual investors. Think about this question in any other field. "I'm good at chemistry, do you think I can make a new wonder drug?" Well, perhaps, but with what lab, what data sets, what funding for FDA trials? "I'm good at circuits, do you think I can make an improved GPU?" Well, perhaps, but with what what lab, software, analysis tools, and fab?

tl;dr: The Efficient Market Hypothesis is functionally true for individual investors, although funds with access to exceptional amounts of information, technical skill, and capital can beat the market (and even then most don't!).

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There's no one size fits all answer because there are a multitude of ways to invest and trade. They may involve mathematical, fundamental, or technical analysis. You occasionally read a story about an investment banker whose trading pulled down a multi million dollar payoff. But these are the exceptions rather than the rule. Most Average Joe traders lose money.

I'm a math kinda guy. For me, what's useful is basic math skills (not the number theory, statistics or numerous calculus courses that I studied 40 years ago and promptly forgot not long after graduating). It sounds a bit elliptical but AFAIC, sound math skills are useful for math skill trading. I could (not will) show you a mechanical system based on no more than arithmetic and whose yield would make any Average Joe trader happy. The problem is that it's useless most of the time and only thrives in periods of high volatility (see 2008, the market correction when China tariffs were announced, the winter 2018 correction, this past month's whacking, etc.). The rest of the time it's pretty useless.

Another example might be the skill of hedging. It's not much more than basic math skills and enables one to avoid the portfolio carnage of 2000, 2008 and the past month. But you have to have amass the assets first and that's not likely to come from trading alone.

I guess what I'm trying to say, albeit ineloquently is that trading skills are useful and can be additive but they're not likely to be the main course.

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People with math backgrounds that work in business, industry, or in engineering, they first acquire the fundamentals of the project that they are working-on and then apply math to detailed situations.

Investing will be in the same way. Something must define the investing endeavor and then math can be applied to make it more systematic.

However, I would suggest a few simple situations such as hedged income, curve fit of stock or commodity prices, accumulation strategies in a falling market, use of leverage to balance core holdings, and position correlations.

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I worked for many years building systems that run several of the exchanges in Chicago. The body of knowledge related to investing and capital markets is very large. There are three main ways civilians participate: investor, trader, or sucker. Investors buy and sell positions based on an estimate of business and economic fundamentals, ultimately the sustainable profitability of the underlying. This is the long game and comes with cyclical gains and losses. You can either educate yourself in these matters or pay someone to do that and act on your behalf. The evidence shows can't beat the market in the long run. I have another full time job, so personally, I rely on Vanguard to do this for me and I don't mind paying them about 0.25% of my portfolio to do so. You make money by being patient and adjusting your risk exposure according to your time horizon.

Traders don't pay much attention to fundamentals and seek arbitrage opportunities. This is mostly automated these days, seeking arbitrage of a few pennies that may exist for a few milliseconds, often less. The traders I knew who lasted generally followed an insurance business model: they assumed eventual catastrophic payouts and structured the rest of their trading business to generate a reasonable profit in spite of that. Some mastered the art of getting market moving information a few seconds in advance and trading on it, often at the edge of legality. It is not a game for amateurs.

Suckers think they know better than both and break even if they are lucky, which they usually aren't.

Paraphrasing an old cliche, investors make a little, traders make a little, and the suckers get slaughtered.

If you like quantitative analysis, you'll probably find option trading models interesting. They're useful for investors or traders if you know what you're doing. If you don't, you'll be helping someone else get rich. Some brokerages offer simulated trading in options and underlyings, where you can experiment with strategies without actually taking a real position. This is a good way to learn.

In the last few weeks, I've been reminded of another cliche and how much wisdom it encapsulates: "Trade when you can, not when you have to."

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I'm also kind of a a math guy too, even though my university education was not pure math but rather kind of applied physics of electricity. I would heavily suggest you to learn fundamental analysis.

My kind of fundamental analysis begins by analyzing what the company produces and how much of it produces. I divide the total production by the shares outstanding to obtain a per-share production.

For example, I calculated that after completion of Olkiluoto 3 and Hanhikivi 1 nuclear power plants, Fortum produces 78.423 kWh/a of electricity.

I estimated that my use of electricity (direct and indirect) is:

  • 2500 kWh/a used in my home
  • 4500 kWh/a to be used by the future electric car I yet don't have
  • 1500 kWh/a to be used by my steel usage that will use hydrogen reduction in the future (and hydrogen produced from electricity by electrolysis)
  • 3500 kWh/a per capita used by the industry and services sectors in EU-28 countries on the average
  • 4600 kWh/a used in the future to produce district heating for my home (currently the district heating is produced by coal but that will soon change to be based on electricity)

Thus, I use 16600 kWh/a. I double this figure to 33200 kWh/a due to taxation effects (on the average, of every extra dollar Fortum gets, half are taxes and half flow back to me as dividends).

Thus, I need 423.35 = approximately 423 shares of Fortum.

Then, I check the financials.

423 shares of Fortum costs 5532.84 EUR currently. Does that pass the intuition test? (Intuitively, am I paying too much for this? Electricity will be a crucial asset in the future, so I find it not too expensive.) The answer to this is yes, I'm not paying too much.

Then I check what kind of return I can obtain. The P/E ratio is around 8 (based on past earnings) and dividend yield is 8.41%. For a company as safe as Fortum, I find it extraordinarily cheap. So, I made the decision to purchase the full amount of shares of Fortum, i.e. 423 shares. If the P/E ratio was above 20, or the diviend yield below 3%, I probably would not have invested.

In companies very early in the supply chain (such as Fortum that produces electricity), it also makes sense to check if the company is the most cost-efficient producer of the raw material / raw goods produced. In case of Fortum, the answer is yes, as it produces electricity by hydropower and existing nuclear power. They have the lowest per-unit costs.

There are other kinds of fundamental analysis strategies, too. For example, not everyone agrees with my strategy.

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