>Let's ignore future cash flows and how those are invested, just consider the initial investment of $20k.
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.
Anyway, you don't have to agree with the numbers. I can link you to articles where Warren Buffet also points out the same thing, but you don't have to believe him either. Or you can Google rent vs buy calculators and do the full picture math yourself, if you're really that interested.
An 11% return will always beat a 4% return eventually, no matter what the initial conditions are. The question is just when.
> 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.
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%,*
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.
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.
Anyway, you don't have to agree with the numbers. I can link you to articles where Warren Buffet also points out the same thing, but you don't have to believe him either. Or you can Google rent vs buy calculators and do the full picture math yourself, if you're really that interested.
An 11% return will always beat a 4% return eventually, no matter what the initial conditions are. The question is just when.