A third idea, sort of, would be to invest $300 to 325 of the $375 proceeds over the next year (plan on leaving $50-75k liquid).
As far as lump sum vs $ avg, just do whichever makes you feel more comfortable. In either case, history suggests you are more likely to come out ahead just dumping it into the market, but this is also on a 10+ yr horizon. If it helps you sleep at night, just set up an automatic contribution of $5k/week, so whether the market goes up or down, you can still participate AND sleep better at night.
In either case, your gains/losses from one strategy vs the other are not going to be significantly different.
The notion that you are better off by dumping into the market is wrong, because the studies I have seen suggest two options: a) Dump all money at one, b) $ avg into the market over 12-24 months (but do not value the real option I describe below).
Your chances of outperforming are actually better if you $ avg, here's why:
- If the market jumps 15%, it becomes even more likely those gains are transient, and will likely revert to "normal" levels at some point in the future. You can hold back the majority of your funds, and wait for a better point of entry.
- If the market tanks 15%, it will be obvious that this is at least a somewhat favorable point of entry, and you can pour in your funds on the way down at a rapid pace ($10k/week, $20k/week, whatever you feel depending on how steep the drop). Most studies do not include the value of this real option in the calculation.
This is why I believe $ avg is the better strategy when investing a large % of your assets in a relatively short period of time.
Also, you didn't ask this, but to ease your sleep even more, I'd just plan on investing all but $50k of your initial purchase (so $110 cash total projected), so you have the majority of a future down payment on hand and can move quickly if the bank(s) give you lip-service, just offer to put down 25% or 30% and they'll likely shut up (worked for me in the past).
Then, you can just continue investing as your normally do, without wondering about how to fund a down payment.
It's just easier that way, IMO.