In the short-term, there could be some advantages one way or the other. For example, if you start a dollar cost average (DCA) plan and we start an 18-month bear market a week after the first investment, you will likely be a bit better off with the DCA plan because you will be getting more shares for the money on the way down. The flip is that if you invested in one-large chunk, and we started a bear market the next week, you'd wish you had DCA'd the money in.
Conversely, if you DCA the money and the markets are going up, you might be a bit worse off in the short term because you will be buying fewer shares on the way up, and if you had just put a lump sum in, you would have seen a higher short-term return.
However, in the long-run (assuming we are talking about 10, 15, 20, 30+ years), it probably isn't going to make a huge difference as to whether you invest $10,000 at one time, or do $1,000 per month for 10 months.
The key is that if you invest a large chunk and things don't go well in the short-term you don't want to panic, sell (locking in losses), and ultimately get away from your long-term plan. If you feel that you won't do that, then it probably won't make a difference which route you go from a long-term perspective. If you worry that you might panic should you invest $10,000 and see it decline 10% in a short-period (or something like that), then I would suggest using a DCA approach.
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