In Part I and Part II of the series, we looked at the different DCA strategies and their pros and cons. To my surprise, ETH was better accumulated by a monthly DCA strategy over the last year, which was different from BTC and LINK. The conclusion was, for any given coin, monthly DCA strategy is riskier for higher volatility coins (I know all coin prices are volatile, but some are more so than others). Weekly DCA allows us to reduce the variance in how much we can accumulate over time, whereas monthly DCA potentially results in higher gains during bull runs.

Based on the comments to the previous posts, I will expand the analysis to two areas:

• Dynamic DCA (i.e. if we were to buy different amounts every time)
• Timing of the DCA

Although I initially thought I'd post on Dynamic DCA, it turned out to be more involved than I anticipated. There's a lot of literature out there that I need to investigate. The timing of DCA was a side thought but a lot of people mentioned that it's best to buy on Sundays, and I was really interested in if this could be true. Personally, I've been DCAing on Wednesdays and I'll show that this was a terrible idea.

For this analysis, we will use the timeframe 8/1/2017 - 7/31/2021 (a 4-year window seemed reasonable, but does not change the results). I had daily Open/High/Low/Close data for BTC and ETH, so we will look at daily patterns. If anyone has hourly data, I'd be happy to look at hourly analysis as well.

First, some assumptions:

• Daily average is the best proxy for these analysis but we do not have that.
• Using daily Low value would give the best case scenario, however it is not realistically possible to time the market to purchase at the lowest price of the day
• An average of daily High and daily Low is prone to significant outliers if the price jumps within the day (compared to daily average).
• Daily Close is a good enough proxy and it will keep the buying time of the day consistent - we will use that.
• Week is defined as starting on a Sunday and ending on a Saturday.

Best Day to buy BTC

During the 4-year period. BTC gained value in 118 weeks, and lost value in 89 weeks. The lowest Close price during the week is when we should buy it for DCA. Below is the pareto chart for lowest Close prices.

Count of lowest Close prices

As you can see, Sundays have indeed the lowest Close price of the week much more often than any other day. In fact, it is twice more likely to buy at the lowest price on Sunday than Monday, which is the next more likely lowest day. Wednesdays (my DCA day) are the worst since it has the lowest likelihood to be the lowest price of the week. We can even look at if this holds over time, i.e. if this has always been the case or it it is changing during these 4-years.

BTC lowest price of the week

We look at the lowest price of the week across 4-years in above figure, and see that Sunday has had consistently the lowest price except a brief period in 2018 and the last couple of months.

However, a good data scientist always questions his/her assumptions, and the last assumption is really bugging me. Since "week" is a construct of our minds, it can start any day. If we start to count the weeks on Mondays, then this whole analysis would flop. So we need another way of confirming if Sundays are best. For this, we look at the weekly price changes over the same period and try to find the lowest weekly change. It will tell us the least likely day to see a daily spike, therefore the best day to buy. Remember that we want to buy as cheap as possible in any given week. According to the below figure, it is again Sunday!

Average weekly price change

Best Day to buy ETH

Count of lowest Close prices for ETH

As you can see, Sunday is the best day to but ETH as well. There's high correlation between BTC and ETH in this regard. However, if we look at the change over time, we see that it hasn't always been the case for ETH. After 2021, Sundays become the most dominant lowest price point. If we look at the weekly price changes, Sunday seems to be the best time to buy as well.

Average weekly price change for ETH

This confirms the well-known urban legend of buying Sunday! In lieu of this I've changed my weekly buys to Sunday starting last week.

We are in a great time to be an investor. Enjoy your DCA and cheers!