Yes. A larger down payment means you're choosing to invest your money in real estate versus stocks. Additionally, a larger mortgage lets you invest with more leverage, which gives you more upside (and downside) potential.

The ideal scenario:

Imagine you want to buy a house worth $500,000, and you have $500,000 on hand you want to invest. Annually, over the next 30 years, real estate will appreciate 3% and markets will appreciate 5%.

Option A: Purchase the property outright. 30 years from now, that investment will be worth approximately $1.2M.

Option B: Purchase the property with a mortgage and a 20% down payment of $100k, and put the remaining $400k into an index fund tracking the stock market. In that case, after 30 years your stock will be worth $1.7M, your house will be worth $1.2M, and you'll have spent $0.7M on the mortgage, for a $2.2M net.

Option B is significantly better.