My son's statistics teacher claims that you need statistics to consistently make money from investing. She cites James Harris Simons and quants as examples. On my advice, I told my son to respond that many billionaire investors like Warren Buffett, Ray Dalio, Kenneth C. Griffin, Israel Englander, Stephen Schwarzmann, and David Tepper got rich from investing, but they never studied complicated math or statistics. By complicated, I mean the math and statistics at the level of James Simons.

Teacher agreed that these men in my response haven't studied complicated statistics THEMSELVES, but she argued that these billionaire investors don't need to because they have hired quants to work for them. Thus her point still stands.

Who's correct?

  • 7
    Lies, damn lies, then statistics.
    – quid
    Oct 19 at 22:54
  • 53
    You might ask what percentage of those taking advanced statistics courses actually get rich from investing, and whether their success rate is statistically different from those who got rich from investing without statistics. Might be a good research paper :-)
    – jamesqf
    Oct 20 at 3:56
  • 4
    As a statistics teacher she should be familiar with the concept that with enough people investing there will be people who get rich (whatever that means) based on pure luck alone. Here is a paper comparing common investing strategies against a random one. Oct 20 at 13:19
  • 2
    Nice "moving the goalposts" by the teacher in their response, by the way.
    – xLeitix
    Oct 20 at 16:15
  • 1
    There’s a distinction to be made between amateur investor and professional investor. These days, from my understanding, many of the very successful professional investors do use quantitative strategies. In contrast, Buffett uses the principles behind value investing to realize large gains. Those principles are statistically informed and value investing is one framework to build a good investing strategy that’s statistically sound, even if it doesn’t require statistical analysis itself — it nonetheless does require significant financial analysis of the balance sheet/investment characteristics.
    – Greenstick
    Oct 20 at 17:45

13 Answers 13


Invest in index funds inside retirement accounts. The fees are low, taxes are deferred or nonexistent. The number of hours you need to spend each year on analysis is minimal.

Over the decades the value of your investments will rise with the broad market. No advanced degrees required.

  • 4
    It really is very simple. Earn, put money in index funds, and leave it there.
    – Pete B.
    Oct 20 at 10:12
  • 34
    This doesn't answer the question. Oct 20 at 13:05
  • 8
    @elevendollar: Clearly the people who follow this strategy require no advanced math/statistics, and regularly become wealthy (becoming a "401(k) millionaire" basically means maxing out your 401(k) contributions, possibly Roth IRA contributions, for 20 years, give or take, investing moderately aggressive index funds; you need to earn enough to invest that much so it's mostly for those already somewhat above middle class, but it's possible without starting wealthy). Ergo, the implied answer is "Yes, it's possible." Oct 20 at 16:07
  • 4
    @user1721135: Pundits have been saying that for literally decades. Oct 20 at 19:04
  • 4
    @user1721135 index funds just mirror the market. If they're a bubble waiting to pop, then so is the market as a whole. Do you really think the average person, especially without the proper background, is really able to separate the wheat from the chaff?
    – swineone
    Oct 20 at 20:56

Your son's statistics teacher should be familiar with survivorship bias. For every famous billionaire who got rich by trading on the stock market, there are thousands who never got rich (or lost a fortune). Therefore, without considering this (very large) control group, one cannot make statistical inferences from the characteristics of individuals who became billionaires on the stock market.

survivorship bias
Source: XKCD


Never stop buying lottery tickets, no matter what anyone tells you. I failed again and again, but I never gave up. I took extra jobs and poured the money into tickets. And here I am, proof that if you put in the time, it pays off!

Every inspirational speech by someone successful should have to start with a disclaimer about survivorship bias.

  • 3
    This, I think, is the true argument against the teacher. One can easily see this effect on various investing forums on reddit. You have many people touting their amazing returns through their one neat trick, and then the many many more people trying to follow the same line and failing (and posting how they lost thousands of $$ in the process).
    – zephyr
    Oct 20 at 15:27
  • @zephyr it is the argument against both, but especially against “lucky” billionaires since they would likely play lottery rather than look for inefficiencies in the market. Traders who are familiar with statistics (formally or informally through practice) don’t make billions - they make for living as any other job. Although some quantitative traders become lucky too, but it is still useless for everyone else for the same reasons
    – dk14
    Oct 21 at 9:31
  • P.S. People posting on reddit so on are not representative group for quantitative traders. Conspirologist in me suspects that they’re likely hired to create hype around asset they promote. Also, inefficiencies that quantitative traders are looking for get closed as soon as they discovered (that’s the whole point - to discover them faster), so obviously no way to reproduce and make infinite cash - you have to find something new every time. So same job as any other in the same salary range.
    – dk14
    Oct 21 at 9:41

It's true that some people will consistently make money because they have advanced statistics ability. But it's also true that many will do quite well without a lick of statistics knowledge.

Blanket statements like the one made by your son's teacher are generalizations that may apply to some and not to others.

Many successful traders have been good bridge players. However, if you play bridge, that doesn't mean that you have a shot at trading successfully.

  • 5
    If you're good in statistics, then you invest in ways that uses it. If you're not good at it, then invest in ways that don't need it (Index Funds). "Good" in this sense is actually extremely good. Most money managers are not in this category and actually do worse than index funds. Even Warren Buffet vouches for index funds, and he's considered good. You should listen to him instead.
    – Nelson
    Oct 20 at 2:52
  • If one's statistics knowledge could consistently beat the market by even a small margin, wouldn't they make more money selling their secret (or software) than investing? It seems like one of those many things that would work at first but be quickly factored in.
    – HorseHair
    Oct 21 at 2:22
  • 2
    The quants at Goldman Sachs and other firms with trading desks make money fairly consistently. The guys selling their software are the guys who don't have an edge. Oct 21 at 2:32
  • 2
    @HorseHair The act of having more people use that specific "secret" actually dilutes its effect and makes it perform worse. If you figured out an edge, the last thing you want to do is for everyone in the world to know about it, because that immediately destroys your advantage and it just becomes the norm.
    – Nelson
    Oct 21 at 2:38

In my opinion, your son's teacher is incorrect. There are definitely counter-examples, but I don't think you are going to be able to prove this either way without a TON of research.

I think it is a dubious claim at best that advanced statistics are even useful when selecting investments, much less getting rich at it. Also, overall I'd venture to say that MOST investors consistently make money that invest and aren't taking crazy risks. I know I have and I am terrible at statistics.

I'd also be shocked if Warren Buffet relied heavily on "quants" or any type of advanced financial analysis beyond the fundamental soundness of the company and the competency of its management team.

  • 2
    On the other hand Buffet made a lot of his money by investing in insurance companies all of whom rely on teams of actuaries and statisticians to price their insurance offerings. Oct 20 at 0:03
  • 14
    Right, but that's different from OPs point. Investing in companies that hire statisticians is not the same as using them to pick companies.
    – JohnFx
    Oct 20 at 1:16
  • 2
    @CharlesE.Grant So what? You don't need to be a mechanical engineer to invest in a car manufacturer or a software developer to invest in a tech company.
    – Philipp
    Oct 20 at 14:10

You don't need to know a ton of statistics to do well in investing. Many economists have already done this statistical work in the past, and they've published their results. This allows people to take advantage of it without having to study all the data themselves. Your teacher's statement is analogous to saying that you need to be an engineer in order to drive a car.

One of the easiest ways to do this is by buying mutual funds instead of investing in individual stocks yourself. The fund managers research companies and/or use statistical tools for you. Or you can invest in index funds, which require no research at all (which makes the management fees lower).

Some basic statistical understanding can be helpful, though. I work with a financial advisor, and in our discussions he will show me the statistical analysis of my portfolio's performance over time, compared with the market. Understanding things like "beta" and "standard deviation" can help you to understand how well you're doing.

If you want to get into the business of investing, either as a financial planner, analyst, software developer for financial companies, quant, etc., then you should have a thorough understanding of statistics. But it's not needed for personal investing.


Large Starting Value

To turn this a little on its head...

The way to make money in the stock market is to have money already. If everyone makes roughly 10% growth, the person with 1,000,000 in the market makes much more than the person with 100,000 in the market.

In fact, someone with 100k and a consistent return of 15% would need to sustain that high rate of return for nearly 50 years to end up with more money than someone who started with 1M and only made 10% return.

And that assumes no additional contributions. If the millionaire is a high earner, and can make larger contributions throughout there life, they will remain ahead for far longer.

Math Correlates with Money

So, understanding that the amount invested is key, and knowing that people who work in finance are high earners, the way to get rich investing is clear: Work in finance. This gives you a larger salary than average, which enables you to turn that constant 10% growth into more money over time.

To work in finance, you need a math background, especially statistics.

Note that this works with many white collar jobs - engineers, computer programmers, accountants, etc. all require higher math, and pay more money than the average job.

You may not need to be a quant to get rich, but most quants are richer than average, because their pay is higher than average.

I'm pretty confident that this is not what your son's teacher meant, but I still think its worthwhile advice. ;-)

  • But it seems like you might as well become a doctor, lawyer, or professional football player... Oct 20 at 18:12
  • @user3067860 - If you are interested in stocks, taking statistics and working in finance allows you to get rich and explore your interest. Otherwise - sure, advanced degrees (MD / JD) or just getting lucky (pro sports) are also good ways to get rich.
    – codeMonkey
    Oct 20 at 18:27

It all depends on how you want to make your money!

Because to say there's only one way to make money in the financial sector is crazily silly.

Let me use a few wildly different examples, taken from Michael Lewis' writings:

Jamie Mai and Charlie Ledley (before the housing crisis) made their money with a rather unique theory: people underestimated the odds of drastic change - they modeled the world 1 year from now being very similar to the world right now. So they made a killing betting the opposite way - buying stock options that would only pay off on drastic swings in stock prices. Company XYZ is in legal limbo? Their stock being at $30 doesn't mean the shares are actually worth $30. The actual worth is likely either worthless (legal case crushes them) or $70 (legal issues get resolved without much fuss.) The $30 is just the risk baked in. So if you can get really cheap options to buy the stock for $50, why wouldn't you? It might not pay off - and if it doesn't, you lose a small amount of money (simply the amount to purchase the option; you don't have to actually buy the stock.) But if it does pay off, you'll make a killing. These two used some math, but it wasn't Quantitative Finance or such - you could say it was at the level of basic algebra. The novel thing they had wasn't the math, but the theory/idea behind why they were investing.

High Frequency Traders. These are probably the people the teacher is thinking of. Where they take advanced, super-duper-secret algorithms and faster-than-regular-people connections to the various exchanges, and use that information to conceive elaborate algorithms to shave small fractions of a profit in a riskless way from the money other people invest. But to do this, they need to be able to accurately model not only the connections between all the exchanges, but also the various approaches brokers might use to hide their large order for a particular stock. Absolutely crazy amounts of math and engineering are required for this.

Dan Spivey. This guy made a killing in finance... by building a private fiberoptic cable from Chicago to New Jersey. Those High Frequency Traders? They needed to be faster than their competition, and having a 12 millisecond pathway from the Chicago Stock Exchange to the main exchange in New Jersey (instead of the ~17 ms average connection over the various telecoms) was worth billions per year. About the extent of the math knowledge he needed was basic trig and algebra.

Lew Ranieri. This guy made money by a simple concept (which he refined further): instead of underwriting a single house and having someone underwrite that specific mortgage, bundle a lot of morgages together into a 'Mortgage Backed Security' - basically, a Bond that covered a wide swath of houses. So instead of someone investing in a specific home mortgage (which might be defaulted upon or paid out early), they get to invest in a pool of those morgages, which gives a much more stable platform. The math here definitely doesn't rise to 'Quant' levels (especially back at the beginning before Tranches came into play, when they were relatively simple.)

The Short Story: Basically, the most important thing is: The Idea. Some ideas will require a metric butt-ton of math. Some ideas will require very little math. Having all the math in the world won't help you if you don't have an idea how you want to apply it.

The Even Shorter Story: ... but you should probably learn the math, because what happens if your idea requires knowing it?


Your son's statistics teacher is incorrect.

The statement "you need statistics to consistently make money from investing" is false based on my interpretation of the statement. If someone were to have invested in the S&P500 50 years ago at 95.65, their investment would have made a compounded 8.1% across 50 years at Oct 19's close of 4519.63. 8.1% every year for 50 years seems like pretty consistently making money to me. I imagine the same is true for bonds as well with a lower positive return and less volatility. All that took was a basic investment thesis of "I think the 500 biggest companies in the US will continue to grow". That does not take statistics, just intuition. If you broaden the horizon of the word "invest" beyond public equity/debt markets, then you could look at any successful business owner that risked their own capital, some of which surely have been successful over long periods without utilizing statistics.

Both the teacher and yourself are citing the top 0.1% of successful investors, which I think is irrelevant for the statement to be refuted. But even so, the thought that successful private equity investors like Warren Buffet and Stephen Schwarzman rely on advanced math or statistics is unlikely (I really really doubt that Warren Buffet has ever hired a quant, and I doubt there's a quant at Blackstone on the private equity/real estate side of the business). I have experience in private equity and project finance investing, and I'm struggling to remember when advanced math or statistics has ever been used. There are a lot of complicated financial models, but it always involves arithmetic.

In my private investing in public markets, I often use Modern Portfolio Theory (which you and the teacher probably consider statistics based), which I consider extremely useful in determining asset allocation. It never dictates my decision though.

How would I alter the statement to be correct while maintaining as much of the spirit as possible:

  • An investment thesis can be solely based on advanced math and statistics and be successful over long periods of time. (Renaissance is the obvious proof of this statement. Side note: you really can't define math and statistics at that level though. That's cutting edge math and statistics that the teacher likely doesn't understand.)
  • A working knowledge of statistics is beneficial to public equity and debt investing. (this probably the least controversial)
  • A knowledge of statistics is critical to consistently successful investing in a portfolio of individual public debt or derivative instruments (This is probably true. The nature and relationship of debt and/or derivative instruments to a portfolio can get highly mathematical very quickly. It's unlikely anyone has consistent success without the comprehensive understanding of the financial instruments that advanced math can give)

Surprised no one has mentioned this, but there's a difference between investing and trading.

My understanding is that being consistently successful at trading on an institutional level requires a lot of statistical and mathematical knowledge, paired with some impressive technology to leverage that knowledge in the form of algorithms. The strategies that quants come up with won't necessarily work for more than a few weeks, so proprietary trading firms need to constantly cook up new strategies.

Investing on the other hand is (almost by definition according to Benjamin Graham) long-term and non-speculative. People invest in a company on the basis of a valuation narrative for it business and the attractiveness of its stock price at the moment in comparison to that narrative. The math that goes into a company's valuation is very basic, and Benjamin Graham in fact includes a section in his venerated book "The Intelligent Investor" warning the amateur investor not to buy into complicated mathematical models predicting long-term stock performance (emphasis on long-term).

The most successful investors all have their personal investment philosophies, but they all share the common feature of being formulated in easy-spoken English which don't appeal to much more math than that needed to understand cash flows.

I would say the teacher is partially right, and partially wrong--but definitely confused and very smug.


There's a fundamental problem with using any particular logic to invest: if it is true, then other people will discover it, and their purchases and sales will shift the price, in way that makes the technique stop working. The stock market is a machine for making prices unpredictable.

Unless you are really, really good at maths, there are better mathematicians than you already working for banks. So a maths based approach suffers this problem more than most.

To do as well as the market trend, invest in a tracker fund. To do better, you must be right about something that most investors are wrong about. For example, if you think that most people continue to underestimate climate change, then invest in the few stocks that will do better in a changing climate.


The largest factor in determining whether someone makes money over the long-term, is simply the act of investing the money. Yes, you want to do a bit of due diligence to check on your investments, but extensive analysis is not necessary to receive a decent rate of return.

If you are considering making money over the short-term, the teacher's point becomes a bit more relevant, but even then there are multiple studies which had an animal randomly picking stocks which then beat the rate of return of managed funds. I think there was a similar study of someone throwing darts at a wall with individual stocks scattered across it, which was also able to beat many actively managed funds.

So I would be more inclined to believe the teacher's absolute position that "investing productively requires statistics" is incorrect.


Most economists believe that the Efficient Markets Hypothesis is correct. It posits that all the big markets where it’s possible to make a lot of money already take into account all the public information. Or, in other words, that it’s not possible to beat the market by being good at analyzing it. You might, though, need to be good just to keep up. This leads to the common advice that you, an ordinary investor, should not attempt to pick stocks, or even try to pick a fund that’s performed well, but instead should invest in an index fund with low fees.

Since “The interesting part of any theory is its ceteris paribus clause,” the people who say that of course have to explain how some people did beat the markets.

First, if someone’s beating the markets, but only by hiring quants or spending twelve hours a day doing the job of a quant, they’re not really coming out ahead unless they’re making more money than they have to spend hiring quants, or than they could make by hiring themselves out as a quant. And both of those things cannot be true at once. If quants are underpaid, you’d expect them to quit and use their skills to run their own fund. If quants are overpaid, you’d expect them to make more as a quant than they would by picking stocks for themselves. And if they’re truly that good at financial analysis, you’d think they’d realize which it is. The equilibrium here is that quants capture all the premium they make for their employers (or that Big Finance overvalues them and the supply of candidates is limited).

Some of the people you name are actually fund managers who collect fees for investing other people’s money. It turns out that they don’t really beat the market. They have good years and bad years that average out. When someone’s had a run of good years, investors pay them a lot of fees to invest their money. So they do well for themselves. Let’s suppose all investors were equally good and whether any of them beats the others is a coin toss, and see what happens. If a million people annually bet money on a coin toss, you’d expect at least one of them to guess right twenty years in a row, by random chance (with 61.5% probability), but that doesn’t mean they’re better at predicting coin tosses. They might think they are, since whatever they’re doing worked for them twenty times in a row, but they’re fooling themselves.

But that’s not the interesting part of the interesting part of the theory, because some people really do beat the market and it’s not just luck. For example, Warren Buffett doesn’t passively invest in stocks that he predicts people will decide are more valuable in the future. Buying a company’s voting shares means you own the company and get to choose its management. So, Buffett buys companies that he thinks would be worth more if they were better-managed, takes them over, and makes the changes he thinks will improve the value of the company. He’s built such a reputation for being great at this, he typically doesn’t have to do hostile takeovers (unlike one of your other examples, Stephen Schwarzmann). Companies are proud to have Warren Buffet think they’re worth investing in (There’s a best-selling book titled How to Build a Business Warren Buffett Would Buy.) and want his advice on what they should be doing better. He also does a lot of investigation into how strong a company’s fundamentals are that other investors don’t have (but this costs him money that should really be counted against his returns). None of this violates the Efficient Markets Hypothesis, because he isn’t reading Bloomberg News and noticing something nobody else does about which companies are underpriced.

Or, since the other names in the list started in the ’70s or the ’80s, someone might say, the market was not as efficient back then. A smart teenager could beat the market in the 1970s by being good at math. A rich kid like David Tepper could get a real advantage in the ’80s by owning a personal computer and a satellite dish to get up-to-the-minute stock quotes. And maybe someone out there is training an amazing AI to pick stocks, and buying a supercomputer to run it right next door to the exchange so it can trade faster than anyone else’s algorithm can trade. That would make someone a lot of money by exploiting an inefficiency in the market, namely that information valuable to quants currently becomes obsolete in milliseconds, not microseconds. But, I can’t pull that off.

A good analogy for some of this is poker. Nobody plays poker without knowing the rules, and it's possible to calculate the expected value of any move. But nobody has any more information about the risks and rewards of a hypothetical move than any other player. Anybody who didn’t understand the rules and their mathematical implications would certainly not be a successful poker player, and there are other skills than statistics involved in playing poker, but the winner of a given poker tournament will be luckier than the other players who are also good at both those things.


There's a bit of oversimplification here, but I disagree with the general consensus that the statistics teacher is 100% wrong.

To get rich via investing, that implies you have an equation:

W = w*rt

W (wealth) equals initial wealth times return to the power of time. (Yes, this is very simplified, but bear with me).

You can get to "Rich" (some particular value of W) by increasing any of the terms. Higher w (start with most of what you want), higher r (rate of return), or higher t (wait longer).

So, it's certainly wrong to say "in order to get rich you need to use advanced statistics", even assuming nobody in the flow of money needs one - if I just buy every stock in the S&P 500, with enough input wealth, or buy and hold for long enough, I'll end up "rich".

But, it's not wrong to say that the only consistent way to increase r is through advanced statistics. It's more than that, of course; order flow, latency, things like that affect the ability to make use of statistics. But, for people doing the kind of work that reliably beats the market - they're using advanced statistics to discover inefficiencies. All of them. Old style investing strategies are inconsistent at best, and usually just lose over time; the folks truly making "extra" money are the people using advanced statistics to find market inefficiencies and using arbitrage to make money.

So, I would say that a more true statement is that "if you want to get rich, given a defined starting pool of money, more quickly, using the general stock market, you need to use advanced statistics."

This also ignores a bunch of other things only really available to high net work investors - the VC "market", pre-IPO stuff, that sort of thing. If you can meaningfully play in the VC market (beyond handing your money to someone else to pool with a bunch of other people), you're already "rich" for the most part.

Not the answer you're looking for? Browse other questions tagged or ask your own question.