Two different bubbles. You're worried about a stock market bubble which may or may not be happening. I'm talking about your real estate situation which distinctly sounds like a bubble but may collapse with little to nothing happening to the stock market.
I think the reason why I should not invest house downpayment in stock market is because of possible stock crash. Is my understanding correct?
I think there are a few possibilities:
a) stock crashes and house market crashes. In this case, since both go down, I can still use the money left in stock market to buy a house. What's more, consider my 200k becomes 100K, and the 1M house become 700k. I can borrow less from the bank (800k vs 600k). So, I think this case is acceptable.
b) stock does not crash but house crashes. In this case, I can definitely use my down payment to purchase a house.
c) stock crashes and house does not crashes. From my understanding, the possibility is little. Also as you mentioned, the housing market is more likely to be a bubble. However, it is true that I will face the risk that I do not have money to buy a house at that time.
d) both stock and housing market go up. If I do not invest in stock, there is no possibility I can catch up with the crazy housing price. In other words, there is still risk here if I keep the money in CD. (my husband bought our current condo in 2011 for about $300k. Now it's more than $550k. Even stock market could hardly catch the housing price).
To summarize, the risk investing house down payment in stock market is from case (c). From my personal analysis, the possibility of (c) is small and I can accept that risk. Rather, there is risk of not investing the down payment in stock market in case of (d).
I will not put my money in the stock market at once. I think my dollar cost average strategy will take at least 1.5 years to put most cash in stock/bonds.