Broadly I think part of what you are trying to say is true. In order for JPY-based DCA to win, it needs the combined effect of the market movement
and the forex movement to be a drop. So if the subsequent forex movement after a LS investment is a drop (yen getting stronger), that's a good thing for the chance of DCA winning.*
However the reasoning you then use to argue that DCA is therefore a good option for Jan 2023 contains basic flaws. Working backwards:
northSaver wrote: ↑Tue Aug 22, 2023 9:12 am
4. Then I wondered what the results would be when the USD.JPY rate is at least 5 yen higher at the start of the 12-month DCA period than at the end. This roughly simulates a falling yen. Here they are:
USD LS wins = 66% (97/147). JPY LS wins = 46% (67/147).
This calculation leaks information from the future back to the point you have to decide between LSI and DCA. You'll need to know what the exchange rate will be in Jan 2024 when you make your decision in Jan 2023 for this calculation to be relevant.
It's like saying you analyzed tennis matches where the underdog was 2 sets up, and found they were more likely to then go on to win the match than the favorite. So therefore that's evidence that in future tennis matches, before even any points or sets have been played, that underdogs are more likely to win than favorites.
northSaver wrote: ↑Tue Aug 22, 2023 9:12 am
3. Then I wondered what the results would be when the USD.JPY rate is relatively high, like it is now. This reduces the dataset considerably but here they are:
USD.JPY > 120: USD LS wins = 63% (72/115). JPY LS wins = 51% (59/115).
USD.JPY > 130: USD LS wins = 61% (33/54). JPY LS wins = 48% (26/54).
USD.JPY > 140: USD LS wins = 47% (8/17). JPY LS wins = 29% (5/17).
Similar here, the analysis uses information about the exchange rate from the full period to decide what a "high" and "low" yen is. However the "strength" of the yen at each point should only be judged on the data before that point.
Moreover, you chose to ignore all the exchange rate & USA market data from before the period you chose, because...??? probably because it wouldn't support your argument
northSaver wrote: ↑Tue Aug 22, 2023 9:12 am
2. Then I noticed that USD DCA outperformance is -2.6%, which is a lower magnitude than the LS performance (2.6 < 3.3). But after rounding they're the same number: +- 3%
"So relatively LSI did 27% better than DCA in magnitude (3.3/2.6-1), but because they round to the same whole number that's evidence that their performance is actually the same"
Also, could you explain a little more how you calculated 3.3 & 2.6? Intuitively they feel wrong too me - magnitudes are too small if they are meant to be the average outperformance of LSI when it wins, and for DCA when it wins.
northSaver wrote: ↑Tue Aug 22, 2023 9:12 am
1. First I verified that your stated results are correct with the data given. Nothing personal of course, I would always do this before continuing!
Thanks, did you find any issues?
* it's not a sufficient thing to guarantee that DCA will win, as a market movement upwards could outpace the rate of yen strengthening and the LS investment will wins.