[baobabKoodaa]

> An 11% return will always beat a 4% return eventually, no matter what the initial conditions are.

No, it won't. I already gave you a very simple and easily verifiable scenario where that 4% return will beat that 11% return because of leverage. If you don't even accept that hypothetical, then you must be arguing just for the sake of arguing.

> But that's only a tiny piece of the money you will spend on the house and ignoring this will obviously lead you to a false conclusion.

That simple example was not supposed to be a realistic model of the world. I'm fine expanding the simple example step by step into a fully realistic model of the world. But there's no point going there if you refuse to accept very basic arithmetic facts in the simple example.

[spacemark]

Hey, I don't view this as arguing at all. I'm sorry you do. I find it valuable as a check on my own thinking and assumptions. If you are feeling negative emotions with this exchange, please walk away!

>if you refuse to accept very basic arithmetic facts in the simple example

I refuse to accept your assertions because they're simply incorrect. Basic power law math - a higher value exponent will always win, eventually.

>Stock market option: $20k with no leverage -> 11% ROI on a $20k investment

P = P_o * e^(r*t)

P = 20,000 * e^(0.11*t)

>Real estate option: $20k of your own money + $80k of the bank's money -> 4% ROI on $100k investment (counting both your money and the loan)

P = 100,000 * e^(0.04*t)

Set these two equations equal to each other and solve for t. This will give you the number of years the 4% return with a 100k initial investment will beat the 11% return with a 20k initial investment.

20,000 * e^(.04*t) = 100,000 * e^(0.11*t)

t = 23 years. After 40 years, the 11% return has beaten the 4% return by 3.3x

If I'm misinterpreting your "very simple and easily verifiable scenario," please let me know. But I don't think so. Your error is in this statement. I'll leave it to you to figure out why, let me know if you need help! ;P

>(counting both your money and the loan) -> 20% ROI on $20k investment (counting only your own money) 20% is better than 11%,*

[baobabKoodaa]

Oh crap, you're right. Sorry about my tone earlier. What I didn't consider properly is that the leverage ratio goes down over time as your equity in the house increases. So even though you start off with a leverage ratio which allows you to beat the returns from the non leveraged stock market investment, after some point the leverage ratio goes down below that point.

I tried to do the math now (independently from your calculations) and I ended up with the number 16 as "years after which the stock market 11% return has beaten the leveraged 4% return". I think your calculation result 23 is different from 16 because it assumes the loan can be kept as "free money" instead of paying it back.

$20.000 * 1.11 ^ 16 - $20.000 ~ $86.218

$100.000 * 1.04 ^ 16 - $100.000 ~ $87.298

[spacemark]

No worries, glad we were able to come to a general agreement!