Daily Tsumetate

[AussiePete]

I have noticed that Rakuten offers the option of daily contributions to a NISA fund, in addition to monthly contributions.

On the plus side, this would seem to provide the closest realization of true dollar cost averaging over the course of the year.

On the down side, one could "lose" one unit per day if unlucky in the rounding of the number of units purchased daily. The law of averages say that this should balance out to equal over the course of the year, but in practice will end up in a small loss or gain over the course of the year.

I ran a search of topics but could not find this having been discussed anywhere in the forum before. Apart from the practical problem of ensuring enough funds are always in the account, is there any other reason not to do this?

[adamu]

viewtopic.php?t=2483

[AussiePete]

Thank you, for some reason that thread did not show up when using the search function.

With respect, I do not necessarily agree with the sentiment in that thread, that getting the funds into the market as soon as possible is the best option. For a long-term tsumitate investment, purchasing the most number of units possible is the goal. Buying as soon as possible (i.e. 1st of each month) is only the best result if the unit price increases every day without fail. As we know, the price fluctuates daily, so it is an exercise in luck whether the day one purchases on will be the cheapest day of the month.

It is a small sample size, but I calculated the possible purchases for the month of December 2022, using the eMaxis Slim all country. There were 22 trading days in the month, so I based my calculations on investing 33,333 yen on one day, or 1,515 each day.

The unit price started high on December 1st at 17,248 and generally declined to finish at 16,024 on December 30th. The lowest point was 15,785 on 21st December.

A person who bought their full allotment on the 1st would have received 19,326 units. A person who bought on December 21st would have been luckiest and got 21,117 units. Meanwhile, buying 1,515 yen's worth of units each day would have resulted in 20,185 - just slightly below the middle point between the high and low. Only those who bought a full month's allotment from the 19th onwards would have produced a better return than spreading purchases across the month.

There is one factor which makes the above calculation inaccurate though. December's 22 trading days is a high number. Rakuten's daily limit this year is 1,626 yen, based on 246 trading days throughout the year. Therefore, when I have some more time available, I will conduct a back-calculation for the entire year of 2022, based on the 244 trading days last year. That should give a better idea whether there is any merit in the idea.

[RetireJapan]

With respect, I do not necessarily agree with the sentiment in that thread, that getting the funds into the market as soon as possible is the best option. For a long-term tsumitate investment, purchasing the most number of units possible is the goal. Buying as soon as possible (i.e. 1st of each month) is only the best result if the unit price increases every day without fail. As we know, the price fluctuates daily, so it is an exercise in luck whether the day one purchases on will be the cheapest day of the month.

The reason that buying as soon as possible is seen as best is that the markets tend to go up about 2/3 of the time. So yes, you could be 'lucky' and have an anomalous month, but daily tsumitate is a negative expected value bet compared to a lump sum at the start of the month.

There's probably not much in it on a monthly basis though, so either is going to be fine in practice.

[AussiePete]

I got impatient and compiled all of the statistics for the eMaxi Slims all countries for 2022, using the historical data from Rakuten's site.

I calculated the returns for a full purchase of 33,333 yen each month on a specific day of the month (between the 1st and 28th), as well as purchasing 1,639 yen on each trading day.

The best performing day last year was (Drumroll......) the 24th, which ended the year with 244,464 units (worth 398,843 as of yesterday's price).
Those making their purchases on the 5th were unluckiest, having purchased 240,738 units (worth 392,764 yen as of yesterday). So there was a 1.65% difference between the luckiest day and the unluckiest day.
Surprisingly, there is a pattern in the dates, with the best five being 24, 23, 27, 25, and 26, and the worst five being 5, 9, 6, 1 and 10.

Less surprisingly, making a purchase every day resulted in 242,109 units. This was just below the average of the 28 days (242,261) but slightly above the median (242,080, on the 13th and 19th). In other words, close to a truer dollar cost average, as I suspected it would be in my original post.

The reason that buying as soon as possible is seen as best is that the markets tend to go up about 2/3 of the time. So yes, you could be 'lucky' and have an anomalous month, but daily tsumitate is a negative expected value bet compared to a lump sum at the start of the month.

There's probably not much in it on a monthly basis though, so either is going to be fine in practice.

Perhaps it is a sign of the market trending downwards last year, but out of the 243 trading days excluding the first day, 118 saw an increase on the previous day, and 125 saw a decrease.

If I ever recover from the trauma of compiling the above numbers manually, I may attempt it again for a year in which the market moved upwards.

[zeroshiki]

Take those numbers and then run them over 20 years.

[TBS]

I may attempt it again for a year in which the market moved upwards.

Here's the numbers since eMaxis Slim all country started on 2018-10-31. Investing as a lump sum has beaten spreading out the investments over each day of the following month on 660 of the 1004 trading days so far. On average the former has beaten the latter in units bought by 0.4%.

Questions like this come up on the forum regularly and there's lots of good links in previous posts.

[zeroshiki]

I remember when I thought I was smarter than the average investor and tried timing the market and buying individual stocks (didn't go well).

[adamu]

If once a month is better than daily, is once a year better than monthly, and once a decade better than annually?

[RetireJapan]

If once a month is better than daily, is once a year better than monthly, and once a decade better than annually?

If you have the cash up front, sure. Lump sum vs dca.

But most people don't, so they put money in when they can.