I Is there a way to calculate expected value from probabilistic data?

[Feynstein100]

The average profit should not be higher @FactChecker the graph they put in the original post is a terrible way of visualizing what is going on.

@jbriggs444
Here's the frequency distribution of outputs at the end of each game:

This is without the stop-loss.

This is with the stop-loss at 980. The right side actually goes on for quite a while but I wanted the spike at the stop-loss to be visible.

 

[pbuk]

Rather than play around with this, do you think it would be a good idea to learn about probability and statistics in a more structured way? This would prevent you wasting time going down blind alleys, help you focus on what is important, and perhaps also introduce you to even more interesting problems.

You could look at this open course which covers the material touched on in this post:
https://ocw.mit.edu/courses/18-440-probability-and-random-variables-spring-2014/

Or for a more general introduction to probablity and statistics try here:
https://ocw.mit.edu/courses/18-05-introduction-to-probability-and-statistics-spring-2014/

 

[Feynstein100]

Rather than play around with this, do you think it would be a good idea to learn about probability and statistics in a more structured way? This would prevent you wasting time going down blind alleys, help you focus on what is important, and perhaps also introduce you to even more interesting problems.

You could look at this open course which covers the material touched on in this post:
https://ocw.mit.edu/courses/18-440-probability-and-random-variables-spring-2014/

Or for a more general introduction to probablity and statistics try here:
https://ocw.mit.edu/courses/18-05-introduction-to-probability-and-statistics-spring-2014/

Thanks for the recommendations. I'll check them out. However, I don't see any problem with playing around. There's really no substitute for firsthand experience. For instance, if I hadn't messed around with this, I wouldn't have learned that stop-losses and take-profits don't change the expected value. I can't help but wonder what profound implications that might have for daytrading. But then again, is the stock market inherently probabilistic? I'm inclined to think not. And even if it were, it has a net positive expectation value over time. How does that affect our simulation? Is the simulation even applicable? Those are the kinds of questions that interest me.

 

[Office_Shredder]

Thanks for the recommendations. I'll check them out. However, I don't see any problem with playing around. There's really no substitute for firsthand experience. For instance, if I hadn't messed around with this, I wouldn't have learned that stop-losses and take-profits don't change the expected value. I can't help but wonder what profound implications that might have for daytrading. But then again, is the stock market inherently probabilistic? I'm inclined to think not. And even if it were, it has a net positive expectation value over time. How does that affect our simulation? Is the simulation even applicable? Those are the kinds of questions that interest me.

Anyone with a bit of probability knowledge can immediately tell you that giving the stock positive drift means your stop loss order can only lower the expected value. You don't need to run simulations and ponder whether you got the right result when you understand the underlying concepts.

 

[Feynstein100]

giving the stock positive drift

I don't know what that means But based on personal experience, stop-losses do seem to make a difference in daytrading. How can we explain that?

 

[pbuk]

I don't know what that means But based on personal experience, stop-losses do seem to make a difference in daytrading. How can we explain that?

You could try following the advice I gave a few days ago.

@Feynstein100 you don't need to do any maths to see that the stop loss does not change the expected value if returns are symmetrical, you just need to look at the symmetry. Think about the expected value of the investments you sell at 980.

Once you have thought this through, see if you can predict what a stop loss will do in a rising market, then run a simulation.

 

[BWV]

I don't know what that means But based on personal experience, stop-losses do seem to make a difference in daytrading. How can we explain that?

Maybe your personal experience is not reliable?

But you could try this:
https://eml.berkeley.edu//~anderson/Sources-042212.pdf
https://en.wikipedia.org/wiki/Autoregressive_model

 

[Feynstein100]

You could try following the advice I gave a few days ago.

Yeah I didn't find that helpful at all. I mean, the whole reason I posted here is because based on the symmetry, I anticipated an increasing expected value then couldn't figure out why that wasn't true.
I have no idea what a stop-loss would do in a bull market. I expect it to not even be relevant because if the market is indeed ascending then the stop-loss shouldn't even be triggered. That's kind of the point, isn't it? In a bull market, a stop-loss is basically non-existent. In a bear market, the stop-loss minimizes your losses. Looks good on paper but how does it fare in reality?

 

[BWV]

Yeah I didn't find that helpful at all. I mean, the whole reason I posted here is because based on the symmetry, I anticipated an increasing expected value then couldn't figure out why that wasn't true.
I have no idea what a stop-loss would do in a bull market. I expect it to not even be relevant because if the market is indeed ascending then the stop-loss shouldn't even be triggered. That's kind of the point, isn't it? In a bull market, a stop-loss is basically non-existent. In a bear market, the stop-loss minimizes your losses. Looks good on paper but how does it fare in reality?

Define bull vs bear market - how do you know which state you are in until after the fact?

 

[jbriggs444]

The way I see it, there are only a few ways to make money in the stock market.

You can be smarter than most everyone else. That is hard to arrange. It is even harder if you give up and try to pretend that it's all just random.

You can be faster than most everyone else. Also hard to arrange. Fast switches, routers and algorithms.

You can know more than everyone else. Sometimes, that's doing your homework. Other times, it's called insider trading.

You can manipulate news articles and such and thereby manipulate market prices.

You can buy and hold and trust that the companies whose stock you bought will make make a good return on investment.

You can convince someone else that you are skilled enough so that they will pay you to invest their money for them.

My impression is that day trading is like poker. You make your money off of people that think that they are good enough to make money off of you. But it is a negative sum game. Somebody has to lose.

 

[Feynstein100]

Define bull vs bear market - how do you know which state you are in until after the fact?

Well, you don't. That's kind of why we're doing all this? If you knew beforehand whether you were going to get a heads or tails, you wouldn't have to worry about the probabilities now, would you?

 

[pbuk]

But it is a negative sum game. Somebody has to lose.

A rising market is not a negative sum game.

Well, you don't. That's kind of why we're doing all this? If you knew beforehand whether you were going to get a heads or tails, you wouldn't have to worry about the probabilities now, would you?

No we don't have perfect knowledge, so we make assumptions, build a model, make predictions using the model, and test them. This is science.

Just throwing guesses around is not science, it is a waste of time.

 

[BWV]

A rising market is not a negative sum game.

outperforming a rising market is zero sum before fees and expenses, negative sum after

 

[pbuk]

outperforming a rising market is zero sum before fees and expenses, negative sum after

But the game we are discussing here is the market itself (which by definition when rising is positive sum before fees and expenses), not outperformance of the market.

 

[jbriggs444]

A rising market is not a negative sum game

With daytrading, it is.

 

[Feynstein100]

With daytrading, it is.

That sounds interesting. Would you care to elaborate?

 

[jbriggs444]

That sounds interesting. Would you care to elaborate?

Every time you make a trade, some money rubs off. Trade often enough and the amount of money that rubs off will exceed any reasonable ROI that would accrue from a "buy and hold" strategy.

 

[Feynstein100]

Every time you make a trade, some money rubs off. Trade often enough and the amount of money that rubs off will exceed any reasonable ROI that would accrue from a "buy and hold" strategy.

I don't think that applies to commission-free trading we have these days

 

[BWV]

I don't think that applies to commission-free trading we have these days

Google bid/ask spread

 

[Feynstein100]

Google bid/ask spread

No, I know what that is. Unless you're a high-frequency trader, it doesn't really make much of a difference from what I know.

 

[Arqane]

Pro poker players often do things to reduce standard deviation. This lessens their vulnerability to a run of bad luck, which they say WILL happen anyway. I think these bets also reduce their expectation, but they say it's worth it.

Resurrecting the thread a bit. This is quite true with a whole lot of pro poker players. They play it safe because eventually they still almost always gain money. Ironically it makes them fairly easy to play against because of the consistency. I played similarly, minimizing most hands and actually losing more often than winning, but maximizing my returns on wins. Not much different than most pros, but instead of sticking with the highest odds on the starting cards, I more frequently started with the lower odds. Playing Texas Hold Em, the odds change substantially on the flop when the bets are still low. So although my odds were a bit lower initially, I played the odds after the flop which also had the benefit of getting much higher pots because of the expectations of them starting with a better hand (which they very often did).
Most people don't play this way, so the pros still consistently make their money. But shifting the time that I reduced my deviation was very effective against someone who kept their deviation low from the very beginning. So how does this tie in with the OP? It's a version of stop-loss where I'd cut my losses unless the gains were more likely. But the only reason why I gained more than I lost in the vast majority of these cases was because of external decisions by the other players. In a truly random game I'd end up at 0 (or really below since I started with a bad strategy), but when you have emotions involved or other external factors, this type of system can work. It really requires that external part, though.

 

[Feynstein100]

Resurrecting the thread a bit. This is quite true with a whole lot of pro poker players. They play it safe because eventually they still almost always gain money. Ironically it makes them fairly easy to play against because of the consistency. I played similarly, minimizing most hands and actually losing more often than winning, but maximizing my returns on wins. Not much different than most pros, but instead of sticking with the highest odds on the starting cards, I more frequently started with the lower odds. Playing Texas Hold Em, the odds change substantially on the flop when the bets are still low. So although my odds were a bit lower initially, I played the odds after the flop which also had the benefit of getting much higher pots because of the expectations of them starting with a better hand (which they very often did).
Most people don't play this way, so the pros still consistently make their money. But shifting the time that I reduced my deviation was very effective against someone who kept their deviation low from the very beginning. So how does this tie in with the OP? It's a version of stop-loss where I'd cut my losses unless the gains were more likely. But the only reason why I gained more than I lost in the vast majority of these cases was because of external decisions by the other players. In a truly random game I'd end up at 0 (or really below since I started with a bad strategy), but when you have emotions involved or other external factors, this type of system can work. It really requires that external part, though.

That's an interesting take and kind of my notion on why daytrading differs from pure gambling. There are too many variables, including other, most often fallible players, market forces and what nots. It kind of seems inescapable that in a game of pure chance, you can't do anything to change the expected value. However, daytrading isn't a game of pure chance. Which should leave some room for other things.

 

[Arqane]

That's an interesting take and kind of my notion on why daytrading differs from pure gambling. There are too many variables, including other, most often fallible players, market forces and what nots. It kind of seems inescapable that in a game of pure chance, you can't do anything to change the expected value. However, daytrading isn't a game of pure chance. Which should leave some room for other things.

Well with daytrading, emotion makes up an absolutely huge part of it. Can't tell you how many times I've gotten in and out of Tesla and still made good money after the taxes because of how fickle people are with it. The stock market is still essentially gambling in the way most people use it, since they don't use it for the little value basis it has by supposedly owning a portion of the company. Stock loses most of that basis as soon as it's sold by the company to a shareholder. But you're right that it's not a pure chance gambling game. Not even sure where people would think that comes from. It's just that the risk is more against other investors' feelings and not the basis of the company the stock represents.

 

[Feynstein100]

Well with daytrading, emotion makes up an absolutely huge part of it. Can't tell you how many times I've gotten in and out of Tesla and still made good money after the taxes because of how fickle people are with it. The stock market is still essentially gambling in the way most people use it, since they don't use it for the little value basis it has by supposedly owning a portion of the company. Stock loses most of that basis as soon as it's sold by the company to a shareholder. But you're right that it's not a pure chance gambling game. Not even sure where people would think that comes from. It's just that the risk is more against other investors' feelings and not the basis of the company the stock represents.

Well said. There's also the fact that wealth is being created in the stock market, which is why stock prices rise over time. Because of this fact, it's a positive sum game and thus everyone can win, unlike the zero sum game of gambling.

 

[Arqane]

Well said. There's also the fact that wealth is being created in the stock market, which is why stock prices rise over time. Because of this fact, it's a positive sum game and thus everyone can win, unlike the zero sum game of gambling.

I definitely wouldn't go as far as saying that. Supposedly most of the stocks are purchased with cash that was gained elsewhere and exchanged for that stock. For any money that is loaned for the purpose that doesn't exist, that's equivalent to printing money. You could try to say that the money is being used to provide additional goods and services by the company, but that's a very weak link at best (and part of why I don't like the stock market). The added money has nothing to do with the business itself unless it borrows money against the inflated cost, or does a stock buyback. Otherwise the transaction is completely between two outside parties that are usually determining value by emotion and not even the underlying numbers of the business.

I'd be interested in hearing a counterpoint, though.

 

[BWV]

I definitely wouldn't go as far as saying that. Supposedly most of the stocks are purchased with cash that was gained elsewhere and exchanged for that stock. For any money that is loaned for the purpose that doesn't exist, that's equivalent to printing money. You could try to say that the money is being used to provide additional goods and services by the company, but that's a very weak link at best (and part of why I don't like the stock market). The added money has nothing to do with the business itself unless it borrows money against the inflated cost, or does a stock buyback. Otherwise the transaction is completely between two outside parties that are usually determining value by emotion and not even the underlying numbers of the business.

I'd be interested in hearing a counterpoint, though.

While stock trades don't directly impact the company, ultimately the stock’s value derives from ownership of the cash flows generated by the business

 

[Feynstein100]

I definitely wouldn't go as far as saying that. Supposedly most of the stocks are purchased with cash that was gained elsewhere and exchanged for that stock. For any money that is loaned for the purpose that doesn't exist, that's equivalent to printing money. You could try to say that the money is being used to provide additional goods and services by the company, but that's a very weak link at best (and part of why I don't like the stock market). The added money has nothing to do with the business itself unless it borrows money against the inflated cost, or does a stock buyback. Otherwise the transaction is completely between two outside parties that are usually determining value by emotion and not even the underlying numbers of the business.

I'd be interested in hearing a counterpoint, though.

Hmm I beg to differ. The way I see it, stocks create wealth in a similar way that banks do. Now how it works with banks is quite simple: they reduce uncertainty/risk. I like to think of it as an interaction between 3 parties: the lender has too much money. He could just let the money sit there and hoard it, of course. But that's not very useful. Instead, he could help himself and others by sharing that money, provided he gets the money back along with the interest. Otherwise there's no incentive to do so. So we discover investing, which is just sharing done right.
Next, we have the borrower who needs money but doesn't have it. Why he needs the money is a bit of a complicated topic but in the best case, he needs the money to try out a new idea, which will lead to increased efficiency and better functioning of the economy. Now, he could wait until he's saved enough money by himself to test the idea but that might take a very long time. Instead, what he can do is borrow the needed money from someone who has too much of it.
Ideally, this is a win-win for both parties. The lender receives a monetary reward for sharing his money and the borrower saves time by having the money now instead of decades later.
However, we do have uncertainty. What if the idea is bad and the borrower is unable to pay? The lender loses his money and thus any incentive to share it, encouraging hoarding. Instead, what the lender could do is spread out his risk. Instead of lending all his money to a single party, he could lend small fractions of it to different borrowers. That way, the risk of all of them defaulting is quite low. Of course, the more borrowers, the better. But depending on how much money the lender has, he can only divide it into so many pieces before the pieces become impractical.
This is where banks come in. By acting as a buffer between the lender and the borrower, they reduce the lender's risk to almost zero. The lender would never have been able to do this on his own. It also saves him a lot of time and effort on having to find the right borrowers and keeping track of his earnings/losses. This is also better for the borrower because it almost guarantees him a supply of needed money. He also saves time and effort on finding a willing lender. Overall, everyone wins.
Sidenote: usually, middlemen just increase inefficiency and thus should be eliminated but banking seems to be an exception where the middleman actually increases efficiency.
Stocks function in a similar way. By raising revenue for the company, the company can now use this revenue to expand and increase efficiency, thus benefitting themselves and the investors in the process. You're basically betting that the money you've given to the company will be used for fiscal gain. Now there's no guarantee that this will happen, but in general, companies are motivated by self-interest too. Hence they have an incentive to use the stock revenue to increase their profits. Stocks are betting done right. Ultimately there are no guarantees and it's all probabilistic. However, 90/10 odds are much better than 50/50 for all parties involved imo Sorry about the lengthy reply. I wanted to be as thorough as possible and help you see things from my perspective.