This doesn't take into account two factors: 1. Buying a house to live in avoids all CGT, which you would be paying on gains through shares. 2. You have to borrow to buy a house, which magnifies your returns. Many would find it too risky to borrow to buy shares.
I'm all for renting and either investing in equities or investment property, however isn't your comparison of the weekly savings disingenuous? 'For example, if you’re paying $650 a week in rent for a place that would have a mortgage repayment of $1378 a week if you bought it' With interest rates around 4% for owner occupier and rental yield around 4% on average for investment property, whether you are an owner or a renter the weekly outgoings are more or less the same. Now you might say the average interest rate over time is more like 6.5% or something, but that's not the case right now.
The only issue here is that by buying, you have locked in the "rent" you pay. Using the example, it is unreasonable to suggest that the rent of $650 per week will remain constant over the life of the loan. Rates and insurance will increase too for an owner, but the mortgage repayment is largely fixed depending on interest rates of course.
What about TAX on the investment income
For the comparison you need to consider how much the value of the house will have appreciated over the 10 years. Lets assume 5% per year for a $1M house equates to be worth $1.62M at the end of 10 years. So $620k v's $435k, the ownership model is superior.
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