Hey, maybe we haven't communicated this well, but we are actually doing exactly what you've described as "the norm in finance and financial economics". We run 1,000 simulations to produce the model output. In each simulation, there are 30 years. Each year, we sample a new "Annual Appreciation" rate. So each simulation does indeed have paths that go up or down.
I didn't mean to suggest that simulations are always correct. Just that I believe ours is, in this case :)
Can you help me understand your point about the "probability cone" please?
I think you're right, just did some careful testing and it looks like the 'probability cone' (basically, the shape you see if you only look at the shape drawn out by the 1 std dev / 2 std dev lines) does have the right shape. My apologies for jumping to conclusions there :)
However, I can't replicate the numbers that you create for a simple test case:
Here we've basically zeroed out rent, mortgage, and everything else, in order to purely isolate the appreciation factor, and your calculator shows a year-30 range of $1m +/- 285k at 95% confidence.
However, if you take 30 independent draws using a 0% +/- 3.2% range @ 95% confidence, that implies each draw has 1.63% std deviation (3.2% / 1.96).
The 95% CI for the sum of 30 independent draws with 1.63% stddev is given by (1.63% * sqrt(30) * 1.96) = +/- 17.5% return.
Applied to your initial amount, I'd expect to see a $1m +/- $1m * e^(17.5%) = ~$190k range for the 95% CI, not the +/- $285k range that you show.
Note the power of just using basic stats and identifying edge cases to validate whether your simulation is giving reasonable results -- here I think either an input or output might be mislabeled (is the input really 3.2% at 95% CI, or is a different confidence?).
I didn't mean to suggest that simulations are always correct. Just that I believe ours is, in this case :)
Can you help me understand your point about the "probability cone" please?