Amortization, tax, and yield curve (short end vs long end) issues aside, this is the problem you have. Choose between two alternatives:
Alt 1: Put 20% down, take a loan equal to 80% of the purchase price, and pay mortgage at rate, rate_1,
Alt 2: Put 0% down, take a loan equal to 100% of the purpose price, and pay mortgage at rate, rate_2.
In Alt 2, suppose you are able to invest your 20% at investment rate, rate_3.
The breakeven condition for choosing Alt 2 is the following:
20% * rate_3 >= 100% * rate_2 - 80% * rate_1,
OR
20% * ( rate_3 - rate_2) >= 80% ( rate_2 - rate_1),
OR
( rate_3 - rate_2) >= 4 *( rate_2 - rate_1).
In other words, if the difference (rate_2 - rate_1) is say 1%, then the investment rate of your own assets, rate_3, must EXCEED rate_2 at least 4 times that difference. So, if:
rate_1 = 5.5%,
rate_2 = 6.5%,
then rate_3 must be at least 4*1% + 6.5 = 10.5%.
You can modify my analysis to account for tax consequences and amortization. However, the general principle is that the investment rate of your own assets must far exceed the difference in the two rates (0% downpayment rate and 20% downpayment rate).
With respect to housing prices keeping up with inflation, that is a totally orthogonal consideration. Once you own the house, it does not matter what loan structure you have - you own that asset, and are subject to that assets price fluctuation risk. Whether you have more equity in it or less has no consequences on the normal or real appreciation pace of that house.
My advice would be the same as chocula's: choose Alt 1, i.e., put 20% down and get the best possible interest rate without PMI. AND, invest the recurring stream of money equal to the difference in the payments between Alt 1 and Alt 2.
Here is an advice of a different kind: if you are a first time homebuyer, depending on your income and state, you might qualify for some downpayment assistance. Such downpayment assistance sometimes comes in the form of grants and sometimes in the form of a 0% second mortage which does not need to be paid (amortized) until you sell it, and if you sell the house at a loss, some or all of that mortgage might be forgiven. I don't know if you would qualify to such programs with assets equal to 20% of the house, but might be worth to investigate.