https://ofdollarsanddata.com/how-to-invest-a-lump-sum/, posted Feb '19 by peter in finance math
In a paper from 2012, Vanguard found that 66% of the time it is better to invest your money right away (“Lump Sum”) rather than buying in over 12 months (“DCA”). I don’t disagree with Vanguard’s results (my results were strikingly similar), but I don’t think they went deep enough in explaining why this is true.
The main reason Lump Sum outperforms DCA is because most markets generally rise over time. Because of this positive long-term trend, DCA typically buys at higher average prices than Lump Sum. Additionally, in those rare instances where DCA does outperforms Lump Sum (i.e. in falling markets), it is difficult to stick to DCA. So the times where DCA has the largest advantage are also the times where it can be the hardest for investors to stick to their plan.