I won't call you an idiot or economically illiterate, but I'll suggest a different approach. Take your own circumstances and see if this would work better for you:
1. Buy a home, and calculate the difference between the monthly payment on a 15-year mortgage and the monthly payment on a 30-year mortgage. We'll call this figure X.
2. Sign a 30-year mortgage on the home, and make regular monthly payments on it.
3. Take the difference between the two mortgage payments every month (X) and invest it in a diversified portfolio of investments that lean toward conservative (a mix of stocks and bonds, but stocks should be concentrated in index funds).
4. At the end of the nine years you described, your mortgage will have a balance that we'll call Y. Your investments will have a balance that we'll call X'.
The advantage of this approach is that after the nine years are up, you now have the flexibility to do a lot of different things -- like selling the home, refinancing the mortgage for another 30 years, taking some or all of your X' and making a lump-sum payment against the principle, etc. I'd recommend refinancing for another 30 years, because you can then start the whole process all over again -- and your new X will be higher because your monthly mortgage payments will likely be lower.
Give it a shot on paper and see how it works for you. You should also take into account the tax deductibility of your mortgage interest payments, which basically means that you're borrowing money at a preferred (and effective subsidized) interest rate to finance your investments of X.
The investments sunk into X would need to average more than my interest on the loan. That may or may not happen.
120K over 15 years vs 30 costs 51K vs 120K in interest. After 2 years, the 15 year loan has you paying off $500/month in principle, while the 30 year loan has you paying off $159/month on your principle.
During your third year of ownership, that works out to paying off 6,000 and paying off $1900.
You can decide if you think your stock investments will outperform that. Over a 30 year period, the answer is probably. Over 5-10 years, maybe not. The additional value in your home is something tangible being purchased, vs stocks that are here today and may be gone tomorrow.
Of course, if you are stupid enough to buy at the top of a bubble, your house will lose value - but it is much easier to see a housing bubble than a stock market one.