How to Use Math to Trade Stocks

You can use math to trade stocks, and in this video I give one example of how to do that. This is also how casinos make money. This is a fictitious example and it does not consider all possible variables. This video is for entertainment only. You should always make your own trading decisions.
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Thank you:)

[@Nchinnam]

I graduated with a physics and math degree and just started interviewing for jr "quant" roles in banking. Literally got asked questions related to these. The actual job is just computational work but the interviewer asks tons of brain teasers with expected value questions.

[@TheMathSorcerer]

Oh wow how interesting!

[@Nchinnam]

@@TheMathSorcerer I was told the full work is taking the VaR and TVaR of portfolios at different weights using past performances or Monte Carlo modeling using geometric Brownian motion.

[@_SeaH0rse]

So you did a whole four years of mind bending physics just to do computational work that barely covers a fraction of all that? Wow lol...well, I guess as long as they’re paying you it’s all good.

[@Nchinnam]

@@_SeaH0rse physics wasn't fun anymore. It also ended up being just computational work that didn't pay as much. Hoping I get through the interviews tho

[@_SeaH0rse]

@@Nchinnam I’ve heard that from a couple of physics majors. Physics was a high school girlfriend that was just too pretty for my brain, so I envy any physics person I run into 😊. If I had a handful, and given the startup ideas I have, I don’t see why we couldn’t hit the big time (I like to think of myself as an aspiring marketing engineer).

[@daniellindner355]

Interesting. We did that a lot at school but never applied it in a hypothetical trade. Brings back memories to see this !!

[@TheMathSorcerer]

awesome!

[@NeutrinoParty]

Don't forget to subtract the cost of each trade when calculating E(x). You pay a transaction fee when you buy the stock and again when you sell. Also, "when 5 day SMA crosses 20 day SMA" should be "when 5 day SMA drops below the 20 day SMA" (unless you're shorting).

[@avilash2546]

No, it's the other way around. Why would you want to buy when the 5 day SMA (which gives greater weight to recent prices) drops below the 20 day SMA? If recent prices are strong, the 5 day SMA should be above the 20 day.

[@NeutrinoParty]

@@avilash2546 this is a simple moving average so the trend would "pull" the average back up toward the 20 day.

[@avilash2546]

@@NeutrinoParty Yes, that is what I said. The 5 day SMA crossing above the 20 day SMA would yield a buy signal, which is what he said in the video.

[@AceOfHearts001]

Nice to see how Discrete Random Variables can be used in trading! Thanks Math Sorcerer...

[@TheMathSorcerer]

👍

[@Tabu11211]

I have an idea: calculate a mean (preferably a low ripple, low phase method) and then center the price around this mean. Next you filter the the signal with a multi band compressor expander. What do you think about filtering centered price data like this?

[@_SeaH0rse]

Thank you very much for this. I wonder how optimization techniques, or Shannon entropy or information gain fit into this...

[@remlatzargonix1329]

Good luck with that....there a many huge corporations who would have already used various similar techniques if they worked....given the vast sums of money involved!

[@PlumThiefOW783]

I'd love to see more math and trading/finance videos

[@douglasstrother6584]

Look up his video titled "Mathematical Finance Wizardry".

[@dosgos]

The caveats are most interesting. Assume history applies forward, how far back do we look, what are the key factors driving the results. . .

[@TheMathSorcerer]

👍

[@douglasstrother6584]

That's pretty slick! I first came across the concept of expectation value in the context of Quantum and Statistical Mechanics.

[@TheMathSorcerer]

awesome!

[@remlatzargonix1329]

Be careful using ANY formula for trading securities.....profitably. Investments, finance, and economics are not hard sciences where you can use strategies such that if you do X, then it will result in Y profits. Anyone who tells you differently is either a fool or a liar or both! This is especially true with "technical analysis", which uses techniques such as moving averages and so on. Also, relying on the "long-run"....we are reminded of Keynes famous quote that "markets can remain irrational longer than we can remain solvent".... Caveat emptor!

[@TheMathSorcerer]

👍👍👍👍👍

[@accountname1047]

I'll add to this: for every additional variable your financial strategy has, the probability of a false positive from a backtest dramatically increases. The same holds if your dataset used in training a model doesn't account for survivorship bias, has too few data points, or the model goes beyond the optimal stopping point in selection processes

[@TepsiMorphic]

Can you recommend resources for learning finance/stocks for someone with a passion for math? I tried to learn some on my own time but it's hard to find resources where they emphasize the maths.

[@josephtraverso2700]

Thank you! Very cool 😊

[@MrVipron]

The problem is that if you backtest, first you typically backtest only a part of the history and so you don't have the full probability distribution, but also often, a specific strategy like the one you did will only work in certain type of market (like this one will certainly give good result in a bull market), but not in other market

[@TheMathSorcerer]

👍

[@maxpower677]

i think you can run a software with massive amounts of data (like all markets along all history) and backtest multiple strategies millions of times each to pickup just the best of them. i think it will not be perfect, but its very likely that you'll make some money in the long run. also, you can develop a portfolio distribution strategy with the same technique, that, even if your strategy didnt work on a prolonged bear market, you can rebalance it to buy low.

[@JLKeener77]

I think it would be fun to study financial mathematics/ financial engineering. Maybe the Math Sorcerer could do a book review for a good book on financial mathematics.

[@TheMathSorcerer]

👍

[@douglasstrother6584]

Look up his video titled "Mathematical Finance Wizardry".

[@jeffjuhre1494]

Heraclitus told us 2500 years ago that you can't step into the same river twice. There is no proof that the past valuations of a stock will resemble future ones. The factors that caused the prices in the past are "water under the bridge" and the river ahead is not seen with perfect clarity. Stock prices fluctuate for many reasons and a stock could be a good or bad investment until it isn't usually because of some new or changing condition.

[@keithphw]

You'll actually make the geometric average of -63.188% (=(1+−0.9)^0.6*(1+1.6)^0.4−1) per time period assuming that you reinvest and the gain of 160 is equivalent to a proportional gain of 160%. Look up Ole Peters' ergodicity video 'time for a change', it's fascinating. By the way, trading just loses money due to transaction costs including brokerage and time wasting. Buy and hold is the winning strategy. I'm a finance lecturer and like your videos. But I've seen many smart math, science and engineering brains waste time and $ trading, due to not understanding the principle of weak form market efficiency - prices go up and down due to good and bad news which nobody can predict, therefore past price data is useless for predicting the future. Edit: fixed incorrect calc at top, oops

[@arthurmorgan2961]

The most successful hedge fund in the world based on performance is renaissance technologies, it employs high frequency trading strategies based purely on mathematical models. Please do not mislead people.

[@keithphw]

@@arthurmorgan2961 Read about survivorship bias

[@badrghilani]

@@keithphw Read about Optiver

[@avilash2546]

@@keithphw There are lots of quants and hedge funds that consistently make money from short-term price behavior, not just RenTech. If you believe the efficient market hypothesis, buy-and-hold investing is just not worth it given how accessible information and data is.

[@avilash2546]

@@keithphw Also, because so many traders use technical analysis strategies when trading, it becomes a self-fulfilling prophecy.

[@tomsetberg4746]

If the math is coming out identical to basic averaging is the calculation wrong or is that expected? Essentially its coming out to the same number as doing the sum value of all trades divided by the number of trades.

[@ariston111]

Can you make a video on stochastic calculus and geometric Brownian motion to model stocks?

[@GhostKing6790]

Great… I learned differential equations for basic algebra and stats

[@Tabu11211]

Can you talk about the non array identity of the sma? :D I programmed a simple moving average with an array abut I was reading that you don't need the array because of algebra?

[@12-OneTwo]

3:33 Which books do you recommend to learn this? Is it only Statistics & Probabilities?

[@Adam-kg7ng]

I was just thinking about this while learning ode for the first time

[@TheMathSorcerer]

👍

[@12-OneTwo]

7:51 What about x=1 & y=3? These are conservative numbers when it comes to risk management for placing Stop Loss & Take Profit. How would you estimate the probability of loss & gain in this context for maximized profitability in the long run?

[@abhishekmishra6786]

Thanks sir

[@shaider1982]

Say, what's your thoughts on using fib's on candlesticks on stocks?

[@TheMathSorcerer]

I think they can be very effective!

[@ponzianomanning3071]

Can you do a video on how to use the Kelly Formula for investment sizing?

[@azimuth4850]

Very cool!!!

[@gamershideout89-ke2vn]

Hi does this strategy work? in reaping profits?

[@Re-lx1md]

Is there a course or book on this? applying to the real world of course

[@ColeCoug]

I am curious what your thoughts are on the future of the stock market, considering the exponential growth over the last 20 years in any typical market metric. You know how quickly exponentials can get out of control and if we keep setting company expectations based on the growth we have seen in the past then very soon it will be impossible to seem profitable when expected to grow exponentially forever into the future. This will continue to push companies to cut wages for workers and rely on bailouts and subsidies from the government IMO.

[@nickbregadze4497]

I ve been thinking about this since i took math 54 course at college.

[@user-oi8up4wi7y]

thank u bro

[@ignasa007]

Just a correction which, as a math nerd, I'd like to make - pos/neg expected value doesn't guaranteed you to win/lose in the long run. It just says that almost surely you'll win/lose (see law of large numbers). You can lose/win, but it would happen with prob 0. PS. Correct me if I'm wrong, I only have basic training with this stuff.

[@jodyclaborn]

You are wrong. For example if you know your reward/risk ratio and multiply that by the win rate, then that will allow you to calculate the the average return per trade if you have properly backtested the strategy (whole subject within itself) and have an accurate win rate and reward/risk ratio. Math Sorcerer is absolutely correct. I too am a professional mathematician and make my living from what he just taught.

[@MaximusAlgorithmus]

⁠​⁠@@MrHardzio4Fun I am a professional mathematician as well. The Math Sorcerer and @jodyclaborn is absolutely correct. I recommend you read up on Jim Simons, a mathematician that ran the most successful hedge fund of all time. There is an entire field of professional mathematics that focuses on trading. I promise, everyone of them calculate the win rate and reward to risk ratio for every strategy they trade. Of course there is a lot more analysis that goes into building successful trading strategies, but you must calculate and ensure it has a profitable historical win rate and reward to risk ratio. To not do this in developing a trading strategy would just be foolish. Also, if mathematicians didn’t use historical/experimental/empirical probability and only relied on theoretical probability to construct models or make predictions about the future, we would still be in the Stone Age.

[@axii133]

How do you determine both the avg loss and gain per trade? Is it not simply one number, either positive or negative, indicating whether you've gained or lost money from a trade?

[@jodyclaborn]

You will have to backtest the strategy on years of historical data. I personally code it to be backtested to get these numbers.

[@SuperYoonHo]

very nice

[@dosgos]

One interesting way the Casino stacks the deck is by limiting bet size. . .

[@TheMathSorcerer]

Yes!!

[@remlatzargonix1329]

Casinos and bookies set the odds so that no matter which horse wins the the house makes money.....never lose site of that fact and you won't get caught up in a money-losing "greatest strategy in the world" scenario whereby the adherent thinks that they will break the bank at Monte Carlo!

[@manupandit3864]

The cross over needs to happen in which time frame

[@walterreuther1779]

5:06 "In the long run you're guaranteed to be a winner (mathematically)" - I cannot help but to throw in the St. Petersburg Paradox at this point: Flip a coin, if heads flip again, if tails break and get payout of 2^n $ (where n is the number of coin tosses you had). Now this game has an expected value of infinite, but you are going to have to play an enormous amount of time to get this (or even just a positive, assuming you pay for playing) outcome - you are probably going to be ruined before you get the big gain....

[@Sosinvestimenti]

Really interesting. it resembles the so called Kelly criterion

[@shiminglu3940]

Aww I just learnt it in my actuarial science class:)

[@TheMathSorcerer]

Oh wow awesome

[@cornbreadpelicanundertake]

What module was this under?

[@shivammishra-wl4bq]

amazing it is

[@maximosh]

E(x) actually sums to 118.5 which is a profit factor of 1.185 or theoretically 18.5% better than breakeven, without any brokerage costs considered.

[@wr2382]

There is no way to guarantee win/loss percentages. So none of these types of things work, except by chance.

[@dhruva_tara]

we need more of mathematics in stocks.

[@stevenjames5874]

Math Sorcerer, if you see this, how do you feel about going all in on a few index funds and some bonds for young people? I've heard that modest yearly contributions can make somebody a lot of money over a couple of decades. It just takes a long time

[@TheMathSorcerer]

Definitely a good idea IMO.

[@stevenjames5874]

@@TheMathSorcerer thanks for this!

[@fadedflage]

Bonds are very dumb these days in the macroeconomic environment. Stocks should go up in the long run though. Start learning about bitcoin.

[@hohohotszkin]

this is gold , bro wtf , I dident expect that but I'll keep this shit frfr

[@lucaarmstrong6375]

And then you realise your back testing didn’t include commissions

[@manupandit3864]

What could be the drawdown. Say on loses the first 6 trades. So for the winning trades he will need higher capital. And higher percentage to cover the loses and be in profit in the end.

[@brothberg]

I would add that no retail investor should use a quant system with actual money. I've been involved with them since graduating in '68, and I know that virtually all retail investors who do this lose money. The quants who make money are either high speed traders with access to low latency feeds that your viewers cannot get, or longer term hedge funds or CTAs who have backtested thousands of systems over many years. Even they have to change their systems often, as the market sniffs out statistical regularities and arbitrages them.

[@prod.kashkari3075]

I want to become a quant, but I’m a statistics major. Everyone tells me I should have studied math. Any tips on what I need to learn to break into quant?

[@prod.kashkari3075]

@@ProxyAuthenticationRequired what math would you recommend?

[@TubeScavenger]

Price action is king. Actual price action, not what most people call price action. The free webinar Volatility Patterns for Day Traders and Scalpers by Chris Lori will show you just the tiny tip of what actual price action is.

[@AnakinSkywalker-zq6lm]

Careful Mr. Simons

[@GizmoMaltese]

Math Sorcerer, conjure us some money

[@dalisabe62]

Problem is not in the math; problem is in the trade business itself, where it is very difficult to assume anything based on what you are told by the lead players in the market. Just when you know that your assumptions about the market are good enough, some surprise proves you wrong. The stock market lacks the scientific honesty, so science is of little use to it. The biggest problem with stocks is it’s vulnerability to trading activities. More buys raises the stock value, while more sells drops it. A good stock is one that reflects real growth in the company, not mere inflated faith based on trading activities.

[@marktube5732]

The stock market became such a casino, it’s ridiculous. It has always been like that but since 2020, my god.

[@drury2d8]

A friend dropped out of school is a self made millionaire. Math is only one of the several tools out there.

[@ILoveMaths07]

Nice... but I have no clue what the strategy means.

[@bernardtruchet]

l''expression "buy when the 5 days SMA crosses the 20 days SMA" est fausse car le 5 days SMA peut croiser le 20 days SMA "en montant" donc le marché est haussier et il faut effectivement acheter ou "en descendant" le marché devient baissier et là il faut vendre. Définir une stratégie à partir du calcul des gains et des pertes est très délicat, je pense que la meilleure solution est de passer des ordres d'achat ou de vente avec perte limitée et gain illimité; c'est à dire acheter une option d'achat (call) dans un marché haussier et acheter une option de vente (put) dans un marché baissier, dans les deux cas la perte est limitée au montant de l'option. Sur 10 opération si vous êtes gagnant 4 fois et perdant 6 fois le solde doit être positif

[@huckleberryfinn8795]

Just DCA and sit on it for a few decades.

[@TheMathSorcerer]

👍

[@High_Priest_Jonko]

In The Legend of Zelda, there's a money-making game which costs 100 rupees to play. You choose one of three boxes and get either 1 rupee, 20 rupees, or 300 rupees. The expected value is (1)(0.33) + (20)(0.33)+(300)(0.33) = 107 rupees. Pretty mediocre.

[@TheMathSorcerer]

Ahh Zelda!!❤️

[@MrPeterJin]

For trading, I'd check out Inner Circle Trader's KZbin channel. I guess you could use math to trade, but it works better with other methods in my opinion.

[@12-OneTwo]

How would you maximize your profitability in the long term?

[@Sugurous]

The market always change so having a static strategy will not be efficient, so you should implement new strategies and used past strategies depending on the market.

[@user-vt6td9hp3g]

All of the casino games except Poker.

[@1dantown]

This is a mechanical system. The stock market runs on fear and greed. It is a psychological framework. Not criticizing.

[@TheMathSorcerer]

👍

[@serkratos1216]

Everything in life runs on fear and greed

[@freebornjohn2687]

You could have a strategy like this and in a bull run and think you are genius. Try doing this in a bear market and see how good your model is.

[@paulstudier5706]

The size of the bets compared to your capital can make or break any system. From Wikipedia: In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet), is a formula that determines the optimal theoretical size for a bet. It is valid when the expected returns are known. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate. en.wikipedia.org/wiki/Kelly_criterion

[@fredrik8806]

The market is a 180 iq behemoth that the layman will never one up

[@TheMathSorcerer]

👍👍

[@quantronin]

In the stock market strategy, the expected value you use is not only unnecessary (just compute the average), but also misleading. Your expected amt is NOT approaching $10. This is because the probabilities you are using in your example are EMPIRICAL (i.e. estimates that are derived from data) not THEORETICAL

[@AndersBjornTH]

Ignores transaction costs and churning

[@TheMathSorcerer]

👍👍

[@TronSAHeroXYZ]

Indicators on Tradingview use math. By default.

[@da-mealish]

I was searching gold and i found diamonds 😅

[@Taigokumaru]

I'd like to see a video from you relating stock strategies to use of the "harmonic mean" in calculating arbitrage opportunities. I learned about that while studying for a Financial Math Actuarial exam a few years ago. It was a short single page example on sports betting, and when I dissected the calculations the harmonic mean formula came into play. It was used to accomplish two things: 1. Normalize "winning amounts" for all competitors the player bet on to make player indifferent to who wins. (E.g. 2-horse race where $100 is split into 2 betting amounts with one amount for each horse, and either horse yields winnings of $120.) 2. That singular outcome value was "favorable" in that it is higher than what the player started with. ($120 > $100) This is apparently possible whenever the harmonic mean for the set of betting odds values (for all included competitors) is greater than the # of those competitors. (H_n > n) In an oversimplified 2-horse race it boils down to: Is the 'product' of the betting odds of both horses greater than their 'sum' ? If yes, math can be done to decide the betting amounts to put on both horses to make the player profit regardless of who wins.

[@remlatzargonix1329]

Beware of "simple examples" of how to easily make money when investing!.....An unsophisticated person who follows such examples ends up broke! Economics is a social science and the models and results generated are only as reliable as the assumptions and approximations which underpin those models......unfortunately those assumptions are often very heroic (I.e unrealistic) and the models are not at all robust (I.e. If the assumptions are relaxed the models fall apart).... So, if you do not want to lose your shirt, then be careful blindly following "formulas".

[@xyzct]

If you want a risk-free guaranteed return, just stop spending your money on stupid stuff, like eating out, spending $12 every morning at the cafe, alcohol, etc..

[@whatitmeans]

you have a huge mistake, and it is assumming that the amount of your budget invested don't affect the longterm result, and also that the process is ergodic and it isn't (since is multiplicative). The proper aproach is using the long term time average defined by Thorp process when looking for the Kelly Criterion.

[@Jkauppa]

mindless system, no

[@kodfkdleepd2876]

This is wrong. The stock market is manipulated. It's been manipulated for decades. Also, all indicators are lagging(nothing can know the future). 1. the market makers are legally allowed to naked short(counterfeit shares) which they do to steal from retail. 2. Criminals are not punished. Go look at the SEC filings and you will see that none of them that are "caught" are ever charged more than they steal or are punished with jail time. JPM, for example, has stolen billions. They literally have been caught manipulating metals just a few months ago and paid a fraction of the cost and did not have to admit guilt and no one was charged. The markets are 100% rigged. Go look at HKD, a company with 10 employee's that went up 32000% in a week and it is an NYSE listed company. There are others too like AMTD and MEGL. Spoofing, front running, quote stuffing, naked shorting, PFOF, FUD, swaps, and many other means are used to steal from you. There is ZERO way to win in a game that is rigged so you lose. Sure you might win some of the time but in the long run you WILL lose.

[@kodfkdleepd2876]

The only way to actually profit is to learn how they cheat and that takes year of study. They use AI that tracks their losses and gains and they get all the data while feeding you fake data. They know exactly how much money is flowing in and how much has flowed out and set the price and it's direction based on that. They don't care if you get lucky and buy the dip and the sell at a peak before they dip it because they got 100 other people buying in that they just dipped on and who will paper hand. The other way to get rich in the stock market is buy GME and BBBY. Why? Because these are the only two stocks that have investors who are not selling and who are buying and DRSing. Why? Because supply and demand does not exist in the fraud market due to counterfeiting and shorting. GME investors are buying up shares and DRSing them as to take away the shares from the manipulators and GS/RC is helping them know how many they have. Once the float is locked this means there technically can be no shares trading unless the price rises(technically we need to lock the entire outstanding but there is some wiggle room). This means if there is trading that the stock is being manipulated. There are actually many people who have experienced this such as Eagletech when one guy bought the entire outstanding and the next day still had the entire stock trading like nothing happened and the price was still tanking(how when he owns all the shares? this was due to counterfeiting). The market is a fraud. There is no mathematical strategy that can let you win. Maybe AI can figure out their schemes and learn too profit off them but all they have to do is switch them. Since they have all the info(such as when they will manipulate), are protected by the government(who is part of it), and have all the money(backed by the FEDs) they can do what they want. The stock marketed is a rigged casino and, by extension, so is the entire world economy. BBBY, about a week ago, was 5$... it hit 13$ yesterday, they tanked it today to 9. If you bought in BBBY knowing that it could not go much lower due to fundamentals and that they've been shorting it since 16$ you could have profited off it like I did. Also if you know that RC bought in at 15$ and bought calls at 80 for jan23 you would know that it is likely, if you trust RC, going to go past 80$ by jan23. There is far more going on in the fraud market than just buying low and selling high. You could invest in a good company and in a day see your investment tank 50% for absolutely no reason and if you sell you lose out... else you have to wait months and hope they don't cellar box or infiltrate the company and steal your $$$. Criminals run the fraud market. Virtually all the billionaires involved have some type of record of doing crime but are never punished. E.g., Ken Griffin who runs the market and steals trillions(he's the money man for the largest billionaires) was kicked out of China for manipulation and has been caught many times in the US but he's still allowed to process 90% of retail's orders and to do PFOF along with running hedge funds and other stuff. GME has a tone of DD(research) on what is going on if you know where to look(I can't give a link since the comment will be deleted).

[@iiiiiiiiiiiiiiiiiiiiiiiiii2458]

Nah. the Stock market is rigged. Ask Nanci.

[@madalisomwanza3214]

I think that this is were math fails unfortunately. Strategy is more important than expectations. There are too many factors and if statistics really works, it would not be taught at uni. It's good for other things but not this.

[@wilhelmtaylor9863]

I see arithmetic and algorithms but not a single trace of "math". Crunching numbers is not mathematics.

[@joelong4042]

And moving average is lagging indicator so don't rely to that in the first place or you will lose all your funds

[@Siegefya]

You pretty much created a baseline for an algorithm that could make trades for you. You'd have to code it... but this is a start of a algorithm based trading system. Interesting video. When I trade, only math I do is basic ➕➖✖️➗ lol.

[@TheMathSorcerer]

👍

[@KRYPTOS_K5]

This is the idea of hedge funds plus the broad investments in all types of stocks. The original idea of hedge funds was to defend against inflation not to get real profits. Today it changed a bit... However hedge funds only work better than any traditional fund in the short run during an inflation crisis if ceteris paribus. Brasil