How/How much does volatility effect dollar cost average?

Question

Notice that this question does not involve lump sum investing.

Background/Own research:

Since it is hard to come across someone/a website selling funds/stocks/... who does not tell you about dollar cost averaging, I wondered how big the effect is/whether it would be beneficial to take to take the fund with the higher volatility when investing regularly for the next 10 years when both have the same return but a different volatility. When searching about 99% of the results were just marketing without or only artificial numbers. From the remaining most websites used something like Monte Carlo and showed that a higher volatility resulted in lower results and one showed about 0,5-1% higher results when using historical data compared to steady increase with 0 volatility (I sadly can't find this one again). If those using Monte Carlo were right, it would mean, that dollar cost averaging would have a negative effect contrary to the claims of the sales people. But I also heard that Monte Carlo often produced different results than real world data because it doesn't include things like mean reversion. For the website using historical data it could be the result of survival bias, selection bias, limited data, ... . As I am not a professional financial expert I don't know which is more realistic if anyone and what pitfalls to watch out for. Therefore I would be happy to gain knowledge from people better than me.

Example for better understanding:

Let us assume there are 2 funds A and B (or stock or similar) that are identical, especially for the return, but have different volatility and I would make regular investments into it like 100€ per month. Here with the special case with A having no volatility, only a steady increase.

Shareprice of A	number of shares of A	Shareprice of B	number of shares of B
100	1	100	1
110	1,90909090909091	115	1,8695652173913
121	2,73553719008264	105	2,82194616977226
133,1	3,48685199098422	140	3,53623188405797
146,41	4,16986544634929	150	4,20289855072464
161,051	4,79078676940845	161,051	4,82381987378379

Final value of shares of A: 771,561

Final value of shares of B: 776,881

With these made up numbers B would have been better although both had an average return of 10%.

Question:

Would a higher or lower volatility be better under a realistic circumstances for dollar cost averaging (using metrics like median)? (If the answer uses historical data and uses suspicious start-/endpoints like February to April 2020 it should provide the reason for this to remove the doubt of fudging the numbers)

Bonus question: How much would be the difference and does it differ when talking about average past returns or expected future returns?

Answer 1

Dollar cost averaging (DCA) doesn't profit from volatility, it just diminishes it. If you invest over the next 10 years in a large number of small investments, then the number of shares you have when you're done is related to the average price over 10 years. The 10-year average price is less volatile than the daily price.

If you invest a lump sum, the number of shares you get is based on the price right now.

Calling something an "investment" means you believe it will appreciate over time. It follows that the average price over the next 10 years will probably be higher than the price now. So for the same money, you will receive fewer shares with DCA than with a lump sum.

The argument that DCA is superior because it "buys more when the price is low" doesn't make much sense, because it also buys less when the price is high. You have to consider the upside and the downside. And again assuming you believe prices will generally appreciate, the implication is DCA will realize more of the downside (buy less when the price is high) than the upside (buy more when the price is low).

So what you get with DCA is a less volatile price, but a later entry into the market.

DCA or not, it would never make sense to choose a more volatile investment if you could get a less volatile investment for the same return. It might make more sense to choose a more volatile investment if and only if it offers a higher return, depending on your objectives.

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If you want a proof that DCA doesn't profit from volatility, consider a mutual fund (let's call it VOTX) which primarily invests in an S&P 500 index fund. Except, to increase volatility, randomly some of the value of the fund is taken out and "hidden" (decreasing its price) and at other random times that value is put back in (increasing its price). This fund has the same average returns as the S&P 500 index fund, but higher volatility.

Now, another savvy fund manager knows that DCA turns volatility into profit, and so constructs another fund, let's call it DCAVOTX. DCAVOTX works by purchasing VOTX, but with DCA. Since increased volatility implies higher returns with DCA, the returns of DCAVOTX must be higher than VOTX.

Not to be outdone, another fund manager creates VOTDCAVOTX, which invests in DCAVOTX and does the same volatility-generating trick of randomly hiding and restoring value.

So, DCAVOTDCAVOTX buys VOTDCAVOTX but with a DCA strategy, offering yet higher returns.

This seems like a tidy scheme: just keep repeating this pattern and returns can be as high as you like!

So either:

1. I just figured out a way to generate infinite money, or
2. there is something wrong about the premise that more volatility implies higher returns when using a DCA strategy.

In summary, you should seek the highest risk adjusted return you can find. DCA can reduce some kinds of risk (the risk that you invest all your money at a bad time), so if you believe in market efficiency, it must offer a lower return. It might be a better risk adjusted return, but that's not really something that can be "proven" since everyone has different objectives, which means a different definition of "risk".