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Re:Fred Wilson: The Buy and Hold Mindset by aqme28 on Monday November 28, 2022 @06:27PM (#33781378)
You can simplify the mathematical argument a lot by looking at DCA as forcing a relative "buy low sell high." When the price of the asset is lower, your DCA buys more, when it's higher you buy less. Relative to a single purchase at the average price, this is equivalent to buying low and selling high.
Re:Fred Wilson: The Buy and Hold Mindset by DelaneyM on Monday November 28, 2022 @10:22PM (#33783308)
A single purchase at the weighted average price is the same as the DCA'd purchase. In both cases you buy X shares for Y$.
Re:Fred Wilson: The Buy and Hold Mindset by sokoloff on Tuesday November 29, 2022 @06:41AM (#33786315)
Imagine you commit to buying $100 on each of date A, B, and C. On A, the price is $10. You buy 10 shares. On B, it’s $100. You buy 1 share. On C, it’s $1. You buy 100 shares. You have 111 shares at a cost-basis of $300 (or $2.70/share).

The time-weighted average price was $37/share.

Re:Fred Wilson: The Buy and Hold Mindset by DelaneyM on Tuesday November 29, 2022 @09:46AM (#33788217)
> DCA takes a lot of that psychological pressure off...

Yes, that exactly. It's a psychological trick (if you have all the money upfront) and not a financially sound one.