Which strategy? Upgrade your home or borrow to invest?

A few months ago, a reader of this blog asked me to analyse two options. Option one is to borrow more money to fund an upgrade of your family home and consequently enjoy tax-free capital gains. The second option is to invest in property. The reader wanted to know which is the best option, net of all taxes such as capital gains and land tax?
Widen the scope of the questionI’d like to widen the scope of this question and add one more option – investing in shares. I have concerns with investing large amounts of borrowed funds in the share market, which I will discuss below. However, as an independent financial advisory firm, it is important that we always provide a balanced view – even if some of the options we are comparing are more of an academic comparison, than a practical one.
Interest rate assumptionOne of the key assumptions in my financial modelling is interest rates. Normally, I like to adopt a conservative long-term interest rate assumption of 6.5% p.a. However, I realise that this might be less appropriate when interest rates around the world are making their way to zero (or are already there) and central banks are pursuing quantitively easing. It is very likely that interest rates will remain persistently low for an extended period of time. That said, it’s also not impossible that interest rates will rise sometime in the future too.
As such, in this analysis I have assumed that the variable interest rate is 3.7% for investment loans and 2.9% p.a. for home loans and will remain at this level for the next 3 years. I have then assumed rates will rise by 3% p.a. over the following decade (on a straight-line basis) and remain at that level.
What is most important is that I have used the exact same assumptions when comparing all options.
The quantitative analysisI financially modelled three scenarios:Option 1: Borrowing $1 million to fund a home upgrade from $1 million to $2 million. This allows you to move to a superior location thereby enjoying a superior capital growth rate.
Option 2: Borrow $1 million to invest in a property that generates gross income of 2% (rental yield before expenses) and capital growth of 7% p.a.
Option 3: Borrow $1 million and invest in shares which generate 4.0% p.a. in

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