Let's say I want to buy a house worth £400k. I can get a mortgage up to £300k, and I have £150k cash sitting in the bank. Which would be my best option:
1) Take out the maximum mortgage of £300k and add £100k in cash deposit to buy the house, then invest the remaining £50k in stocks.
2) Take out a mortage of only £250k and add all my £150k in cash deposit to buy the house, with nothing left over to invest.
I am interested in which one will be typically the most financially profitable option overall on average, without going into the micro details such as volatility of the stock market, fluctuating interest rates, fluctuating house prices, the fact that I would have no cash in the bank to spend... I would just like an overall idea of whether putting more cash into buying a house is better than spending that money in investments.
My intuition is that it is better to take out the maximum mortgage, because mortgage repayment rates are likely to be lower than with standard loans, because the bank has less risk due to the property it partially owns. Therefore, if I wanted to invest $50k in stocks, it would be better for me to "borrow" that via the mortgage, and invest my own cash, rather than borrow £50k ordinarily and invest that. Am I correct?