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i don't quiet understand the result of the quantity of shares based on the ATR calculation

(800(capital) * 3%(risk) / (2 * 0.44(ATR)) = 27, would the result be in shares?, because based on my risk per trade of 24 dollars per trade, i would not be able to afford 27 shares if the stock price is $4.4

so i obviously dont understand something of how this calculation works and what the results actually mean and i hoping someone would explain?

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  • $\begingroup$ I don't know where you are getting your example. Generally this type of rule is used for leveraged trading (which is not for everybody) where you can have a position bigger than your equity. 27 shares at 4.40 a share cost 1188 so indeed you would be leveraged 1188/800 = 1.49 to 1. So you would be buying on margin. (But I would add 800 in capital is really a very small amount, I wouldn't recommend that). $\endgroup$ Commented Apr 29, 2024 at 9:11
  • $\begingroup$ I'm trying understand, wouldn't you being on margin anyway? Even if you had a higher equity amount? and could you provide example of what you mean. Im really trying to understand this properly. The example was just a calculation based on equity I have a available, and yes the equity is not alot $\endgroup$ Commented Apr 29, 2024 at 13:09
  • $\begingroup$ A very small account can easily be wiped out by transation fees and slippage and it forces you to get out of trades very early. But that's not the main point. What wouldyou like to understand about the formula you gave? $\endgroup$ Commented Apr 29, 2024 at 17:04
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    $\begingroup$ This post needs to state the assumptions made and how they are being tested. Use algebraic notation for the formula. ‘Risk’ looks like a bet size, but as the bet size depends on expected return, something is missing here. See Kelly formula. $\endgroup$ Commented Apr 30, 2024 at 4:58
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    $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$ Commented Apr 30, 2024 at 4:58

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I will attempt an explanation of this formula. This is an overview. If you need more detail you should give more information about the problem you are trying to solve.

First let's talk about gambling. The first rule of gambling is that if there is a negative expectation, you should not bet at all. If you have a positive expectation and you have finite capital, then it is generally a good idea to make several bets, not just one. This is because of the Risk of Ruin issue: you could be wiped out due to bad luck on the first one or a few consecutive trades. There is a mathematical theory of RoR, but to keep it simple you could just adopt a rule that you want to survive 20 losing trades, so you would bet 5% of your initial capital on each bet. This is just a rule of thumb, if you are daring you might bet 10% and if you are cautious you might bet 3% (as you rule does). Nothing very scientific here, it is a subjective preference.

Now let's talk about trading financial instruments. The main difference is gambling has a binary (win/loss) outcome while trading has a continuous outcome. So risk measurement is more difficult. We can't use the worst loss because the worst that can happen to a stock is it goes to 0 and that's a 100% loss, though its rare. A rule based on the worst outcome would say we should not bet at all. To get around this we might say: I want to survive 20 "really bad trades" (RBTs) where a RBT is a big loss but not a complete wipeout. For example Value at Risk is defined as a loss that is exceeded fewer than 5% of the time. (Again a "magic 5%" that someone pulled out of the air, though it seems plausible and is commonly used). For intraday trading a plausible RBT would be a trade where you buy at the high of the day and sell at the low of the day. The range (=high-low) is a random variable but we could estimate it using the ATR (average true range, over say the last 60 days). Since the range (and risk in general) fluctuates over time and the ATR is an average measured in a past period, we could use really_bad_loss = 2*ATR to be on the safe side for the future.

The result of all this "reasoning" is the formula you gave for the number of shares to hold:

N = (0.03 capital) / (price_per_share / (2*ATR))

capital is in USD, price_per share is in US/shares and ATR is a pure number, so dimensionally the result is shares, as we wanted.

Note the following limitations:

It assumes day trading: once you get in you have to get the $\bullet$ out (GTFO in polite language) the same day. That limits your flexibility. For multi-day trading you would need more capital (you need to survive a price excursion of more that 2 ATR).

It assumes you will use leverage, and computes for you how much leverage you will use. If the leverage ratio is > 1 (as in your numerical example) you will be buying on margin, which is not always a good idea (it increases the risk of ruin). If you don't use margin you cannot use this rule.

It is an example of a "risk only" position sizing rule, which looks only at the down side and does not take into account the (assumed positive) expectation. Because estimating the expectation is difficult, this is quite common in position sizing. VaR is another example. But there are also rules (such as the Kelly Rule mentioned in a comment above) that take the expectation in account. It is a static rule, based on the initial capital and not on the current capital as it evolves over time (another feature of the Kelly rule).

The coefficients 0.03 in the numerator and 2 in the denominator are somewhat arbitrary, as discussed.

Hope this helps. Seeing the reasoning behind the rule could be helpful, since it also shows the limitations. No one should rely on a mathematical formula without understanding the justification behind it.

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  • $\begingroup$ first off, i appreciate you helping and trying to simplify the issue and risk management as a whole . Im trying to understand this specific formula because i was planning on putting in my program for trend following. Now you said that ATR is for day trading, but trend followers like the turtle traders used it. are you saying that i should not be using ATR because of the method of trading im using and the low equity, and if yes, what other risk management would i be able to use? $\endgroup$ Commented Apr 30, 2024 at 19:52
  • $\begingroup$ Good you mention Trend Following (that was new info to me). In TF risk is controlled with a Position Size rule AND a Stop Loss rule, you have not mentioned the Stop Loss but it is important. My issue is: is 2 ATR a good measure of a reasonably sized loss? Or to put it more bluntly: how the heck was "2" chosen instead of another number. It MAY be allright with the right Stop Loss, but I don't know. And it is frustrating to answer, like reading portions of someone else's undocumented code and trying to guess what it does, without seeing all of it and knowing the context or talking to the author. $\endgroup$ Commented May 1, 2024 at 10:14
  • $\begingroup$ i was also thinking of using the stop loss, just haven't decided whether to use 2, or a higher number to multiply by the ATR, because most stocks im looking at have a low ATR because of lower stock price .i still have a couple questions im trying to understand with ATR 1). the result of the ATR, is it just telling you how much you should leverage or how many shares you should buy, because what i don't understand, is when you use the formula, it calculates more shares than you can afford 2) what would be the difference between using ATR and just a fixed percentage $\endgroup$ Commented May 1, 2024 at 16:11

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