Note, the main trade off here is the costs of holding cash rather than being invested for a few months vs trading costs from trading every month. Let's start by understanding investing every month vs every three months. First compare holding cash for two months (at ~0% for most Canadians right now) and then investing on the third month vs being invested in a single stock etf (~5% annually?). At those rates she is forgoing equity returns of around
- first month $2000 * (5%) * (2/12) = ~$16 (2 months forgone)
- second month $2000 * (5%) * (1/12) = ~$8 (1 month forgone)
- third month forgoing nothing as you invest the money at this time.
These costs and the $10 for one big trade give total costs of $16+$8+$10=$34 dollars.
If you were to trade every month instead there would be no cost for not being invested and the trading costs over three months would just be 3*$10=$30. So in this case it would be better to trade monthly instead of every three months.
However, I'm guessing you don't trade all $2000 into a single etf. The more etfs you trade the more trading more infrequently would be an advantage. You can redo the above calculations spliting the amount across more etfs and including the added trading costs to get a feel for what is best. You can also rotate as @Jason suggests but that can leave you unbalanced temporarily if not done carefully.
A second option would be to find a discount broker that allows you to trade the etfs you are interested in for free. This is not always possible but often will be for those investing in index funds. For instance I trade every month and have no brokerage costs.
Dollar cost averaging and value averaging are for people investing a single large amount instead of regular monthly amounts. Unless the initial amount is much much larger than the monthly amounts this is probably not worth considering.
Edit: Hopefully the above edits will clarify that I was comparing the costs (including the forgone returns) of trading every 3 months vs trading every month.