Please explain the math behind the DCA. I am confused.

[a298b112]

So, I was DCAing, and at some point in January, 2023 I had 350 CNS (some coins) at 45 USD in average. Then I sold 100 of CNS. So now I have 250 CNS. The question: is the average still 45 USD per CNS? Or how do I calculate average price per coin after selling 100 of them?

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[UchihaSarada]

The question: is the average still 45 USD per CNS

Your average price is the same. After you DCA, all coins you own will have a same average price. If you sell any fraction of your coins, the rest will have same average price like before selling.

Average price only changes if you buy new coins at new prices different than your current average price.

[Coyster]

Well, i don't think anything changes, if you bought the 350 CNS at an average price of 45 U.S dollars per coin, even if you took out 100 of them, the remaining 250 were still bought at 45 U.S dollars per coin. The change in average price would occur if the price of CNS rises and you start to accumulate again, then would the average price per coin change.

Having said that, mind you that DCA is usually best with coins that are sustainable for the long term, if you are using DCA to accumulate a coin that has no actual utility or sustainability, you might run into a huge loss in the future.

[_act_]

Do not confuse yourself, just buy weekly and do not make the calculation hard for yourself.

DCA only just mean that you can buy certain amount of a coin like bitcoin weekly over certain period of time. Assuming the price of bitcoin has decreased, if you are receiving $500 weekly, you can start to use $20 to buy bitcoin every week, that is DCA. Because you do not buy bitcoin at once but buying it weekly at varing price means DCA because you can take average of the bitcoin bought weekly but summing the total coin bought and divide it by the number of times you bought it to get the average price for you to be making profit.

[LeGaulois]

People heard about DCA in crypto, then they advice DCA everywhere.
But of course, they don't do DCA themselves...

The costly myth of dollar-cost averaging
https://web.archive.org/web/20050910142530/http://moneycentral.msn.com/content/P104966.asp

A Note on the Suboptimality of Dollar-Cost Averaging
http://gsbwww.uchicago.edu/fac/george.constantinides/JFQA_1979.pdf

DCA is worse than a buy and hold strategy or rebalancing your portfolio. If it is supposed to lower the risk, there is no measure of risk provided
Marketing stuff created by banks and brokers since people think it's safer and continue to inject money no matter what the market is doing.

[ajiz138]

DCA is buying at an average dollar price for a certain time, for example every week/two weeks/month then you can record the purchase price later, all you have to do is adjust it with the data, maybe it can be a percentage right and that is my way of calculating DCA.

In fact, I have never considered doing DCA in altcoins as such a big risk in the future, while what we often talk about is doing DCA on bitcoin, which is a long-term prospect for years or even in 10 years, the best way is with DCA in a certain period.

But if you count with significant time maybe you can see it in terms of the average.

[Stalker22]

So, I was DCAing, and at some point in January, 2023 I had 350 CNS (some coins) at 45 USD in average. Then I sold 100 of CNS. So now I have 250 CNS. The question: is the average still 45 USD per CNS? Or how do I calculate average price per coin after selling 100 of them?

To calculate the average purchase price of your coins, when you have multiple transactions, you can use the weighted average method.

For example, let's say you purchased 10 coins at $100, sold 5 at $150, and then purchased 5 more at $90. The calculations would be as follows:

Transaction 1: Buy 10 coins at $100
Total cost = 10 x $100 = $1000

Transaction 2: Sell 5 coins at $150
Total cost = Total cost - $750 (5 x $150, but we will subtract that amount since you received money)

Transaction 3: Buy 5 coins at $90
Total cost = Total cost + $450 (5 x $90)

Total cost of all transactions = $1000 - $750 + $450 = $700
Total quantity of coins purchased = 10 - 5 + 5 = 10

Average purchase price = $700 / 10 = $70

Therefore, the average purchase price of your coins in this case would be $70.

Using this calculation method will provide a more precise average price compared to only calculating the purchase price. Essentially, each time you purchase coins at a price below the current average and sell them at a price higher than the current average, your overall average purchase price will decrease.

[coolcoinz]

People heard about DCA in crypto, then they advice DCA everywhere.
But of course, they don't do DCA themselves...

The costly myth of dollar-cost averaging
https://web.archive.org/web/20050910142530/http://moneycentral.msn.com/content/P104966.asp

A Note on the Suboptimality of Dollar-Cost Averaging
http://gsbwww.uchicago.edu/fac/george.constantinides/JFQA_1979.pdf

DCA is worse than a buy and hold strategy or rebalancing your portfolio. If it is supposed to lower the risk, there is no measure of risk provided
Marketing stuff created by banks and brokers since people think it's safer and continue to inject money no matter what the market is doing.

It's not worse in the falling markets, but worse in rising markets. That's what the article from your first link proves. The author invested a lump sum and DCA into the S&P over a period of a few years where the market was rising, so obviously the lump sum investment gave him much greater returns. I don't get why these people try to prove a point by doing such obvious experiments.

OP, your DCA strategy didn't work well because you sold part of your investment at a random time. DCA is a great strat when you don't know where the bottom of the bear market will be, but you want to accumulate anyway. It doesn't work well when you keep buying and selling before the market turns around.

My DCA strategy focuses on buying during the bear market and selling the same way by slowly doing a reverse DCA into fiat money in a bull run.
How do I know when there's a bull run? Usually a good indicator is breaking through 50% of the ATH. I did that in 2018 and 2019 where bitcoin was below 10k. That was almost a whole year where I did my DCA. When we broke above 10k USD I begun to slowly DCA back into fiat, but when we fell below again and went to 4k in 2020 I was buying. Then again, when we broke above towards 20k I was DCAing back to fiat and then slowly all the way to the ATH in 2021. When we went below 40k USD I stopped selling and waited for the market to show me what to do. We went to 30k so I started buying again. 

[hatshepsut93]

Your average purchase is not affected by selling. But now you must also calculate your average sell price and combine it with current value. So now you have 100 coins sold at some price and 250 coins at current price. Your average sale is 100/350 * selling price + 250/350 * current price. If it's higher than your average buy price, you are still in green.

[UchihaSarada]

Using this calculation method will provide a more precise average price compared to only calculating the purchase price. Essentially, each time you purchase coins at a price below the current average and sell them at a price higher than the current average, your overall average purchase price will decrease.

Unnecessary to complicate it like this (subtract the value you sold).

Average price is for all coins you have. Assume after you DCA 1 year, you have 10 coins, with average price is $25,000. If you sell 2 coins, the 8 coins left will have same average price at $25,000. If you buy new coins like 2 coins or 5 coins at $30,000, those new coins will be used to calculate your new average price for your total 10 coins or 13 coins.

Buy 2 new coins at $30,000: [(8*25,000) + (2*30,000) ]/10 = 26,000 is your new average price.
Buy 5 new coins at $30,000: [(8*25,000) + (5*30,000) ]/13 = 26,923 is your new average price.

[Doan9269]

DCA means Dollar Cost Averaging and you can easily make a google search on the meaning for more explanation, it's a particular pattern believed to be one of the best method of acquiring bitcoin from the market by buying a particular amount of it on a weekly or monthly basis, this is done in other to ensure a reduced percentage of lost otherwise known to cut lost in case of wjen you buy and the price goes dip or more.

[tjtonmoy]

When you sold 100 CNS, the average price of your remaining coins didn't change, so it's still $45 per CNS. The average cost you initially paid doesn't change based on the number of coins you sell. So, for your remaining 250 CNS, the average price remains $45 per CNS.
If you want to calculate it, then it should be like this.

Total cost of all 350 CNS = 350 x $45 = $15750

You sold 100 CNS at $45 per CNS = $4500

You are left with 250 CNS which worth ($15750-$4500) = $11250

Average cost per CNS = total cost divided by total number of CNS.
                                = $11250 / 250
                                = $45

So, even after selling 100 CNS, the average cost per CNS remains the same at $45.

[palle11]

Having said that, mind you that DCA is usually best with coins that are sustainable for the long term, if you are using DCA to accumulate a coin that has no actual utility or sustainability, you might run into a huge loss in the future.

I think this is the point for op to simply know. If you are thinking of your average you have to know the value of when you bought a unit and how much you are selling it for and like the quoted post, if you have a coin with potential for rising then DCA will be profitable for you but if it is depreciating, that means you are simply going to have a reduce profit or nothing at all if you are selling at lesser price from what you bought thereby running into losses.

[DoublerHunter]

~snip~
Average cost per CNS = total cost divided by total number of CNS.
                                = $11250 / 250
                                = $45

So, even after selling 100 CNS, the average cost per CNS remains the same at $45.

^The same answer and this is right upon my calculation.
Therefore, the average price per coin after selling 100 of them is still 45 USD per CNS.
When calculating your average cost per unit, you need to consider the value of the unit at the time of purchase and the number of units purchased. If you sell some units later on, you also need to consider the value of the units at the time of sale and the number of units sold.

[@sriyan]

So, I was DCAing, and at some point in January, 2023 I had 350 CNS (some coins) at 45 USD in average. Then I sold 100 of CNS. So now I have 250 CNS. The question: is the average still 45 USD per CNS? Or how do I calculate average price per coin after selling 100 of them?

DCA is about how we average the prices in volatile market conditions. First, you have to tell us about the selling price of that 100 CNS.

If you are sold at the same average price(45 USD), then your average price will be the same.
If you are sold at a different price(Assume 60 USD), then your average price will be different.

[teosanru]

So, I was DCAing, and at some point in January, 2023 I had 350 CNS (some coins) at 45 USD in average. Then I sold 100 of CNS. So now I have 250 CNS. The question: is the average still 45 USD per CNS? Or how do I calculate average price per coin after selling 100 of them?

You basically multiply the price per coin into the number of coins you bought at that price and then you add the total values. Finally divided it by total number of coins to get the average per coin. Now in case selling it created issues so there are two things you can do to simplify it. Either assume the same average price as it was before and consider everything you got in access as gain in this time. Otherwise reduce the total sales value from total cost and make this new cost. Basically profit will be booked together in just one time.