Just from intuition DCA would yield less than one lump if the expectation value is larger than 0. But then there is variance. If the asset is volatile enough that even a short period of DCA investing is bringing down the price a bit, I assume.
If the market goes up year and year then obviously lump sum investing is best, but it doesn't. It goes through periods of over and under performance and then returns the mean.
In any case, it's academic for most us investing from our salaries. DCA isn't a choice.
And of course, many of us don't have a big chunk of cash sitting around waiting to get invested.
Most of the time, in the long term, investing a lump sum beats DCA even if you buy at a previous peak.
1. Have a pile of cash to burn and invest it immediately, to maximize time in market
2. Have a pile of cash and sit on it to "time" a later lump sum entry to the market
3. Have a pile of cash and invest it incrementally for some ramped entry to the market
4. Have recurring income and invest it immediately as it becomes available
5. Have recurring income and save/buffer it up to revisit the alternatives (1)-(3)
6. Use credit to obtain a pile of cash ahead of income and revisit the alternatives (1)-(3)
Yes. There's a lot of research comparing dollar cost averaging with lump sum investing. Lump sum investing in a diversified portfolio (total market ETF) almost always wins, even in periods where markets are 'overpriced' (e.g., high CAPE 10 ratios).
Here is a good example: https://www.portfoliovisualizer.com/monte-carlo-simulation
Plenty of the white-papers from the big mutual fund firms give the impression they use very similar analysis methods.
Yes.
Watch https://www.youtube.com/watch?v=X1qzuPRvsM0 and read the papers referenced in the video.