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The math on appreciation rate is a bit off because of how risk adds up to itself over time. For example, if you assumed 3 +/- 3% appreciation, then the calcula

The math on appreciation rate is a bit off because of how risk adds up to itself over time. For example, if you assumed 3 +/- 3% appreciation, then the calculator applies that range to every single future year, whether 1 year or 20 years, e.g. 20 years later, the realized appreciation seems to be 3% +/- 3%. However the normal way this is done in economics and finance is to assume independent increments of return volatility (let's say 3% per annum). This gets you: - 1 year out: 3% +/- 3% - 10 years out: 3% +/- 3% / sqrt(10) - N years out: 3% +/- 3% / sqrt(N) Intuitively, imagine if having a 'good year' were simply a coin flip, e.g. either you get 6% in a year or 0%. Over N years, the sum of your total return is a binomial distribution with standard deviation that grows with sqrt(N). Since your annualized return is approximately total / N, the standard deviation of realized annualized return scales at total / sqrt(N). Probability cones should always look like sideways parabolas: https://sixfigureinvesting.com/wp-content/uploads/2018/11/MonteCarlo-vs-theor-simple.jpg https://sixfigureinvesting.com/wp-content/uploads/2018/11/Mo... More here: https://sixfigureinvesting.com/2018/11/predicting-price-ranges-with-historic-volatility/ https://sixfigureinvesting.com/2018/11/predicting-price-rang... One more thing: the chart has no provision for inputing stock market volatility, which (historically) is quite a bit higher than real estate volatility. You're comparing a 'risky' bet to an assumed 7% riskless bet when stocks are also at an all-time high. The better thing to do would be to model the volatility of the stock market (historically ~15% per year), then show the distribution of (real estate return - stock market return) (with some correlation assumption).

usaar333 8y ago
The math on appreciation rate is even worse than you write because the reporting is showing the compounded values as normally distributed which is not valid when a compounding rate is normally distributed. (normal distribution times normal distribution isn't normal). The way people normally work around this is to use a log-normal distribution, which stays lognormal over time. The appreciation math consequently is massively off for any high variance input. I completely distrust the results.
refrigerator 8y ago
Hey, thanks for taking the time to write a detailed comment! Everything in the model runs by simulation, so we don't do any maths on appreciation rates. Since it's a simulation, I believe the combinatorics sort themselves out! However... it's possible that something we are miscommunicating something — what gave you the impression that the appreciation maths was off? You're right about the chart — we wanted the baseline model to be an extremely rough guide to compare the buy-to-rent scenario with, so didn't want to add volatility there.
- smallnamespace 7y ago
  > we don't do any maths on appreciation rates. Since it's a simulation, I believe the combinatorics sort themselves out! That is never a valid inference. At the risk of sounding harsh, you cannot simply throw up your hands and say 'the simulation said so!' without understanding what is actually being simulated, or else you will get nonsense results. > what gave you the impression that the appreciation maths was off The 'probability cone' is clearly the wrong shape. > so didn't want to add volatility there Many fields the calculator, such as appreciation, have distributions attached to them. The way returns in real life get a distribution is via volatility, so it's highly misleading to both have a distribution width and say that you don't want to add volatility. This is what your simulation is actually doing: 1. Pick a single normally distributed number 2. Pretend that is the return of your investment, linearly applied over many years. E.g. if the number I drew in step 1 is 4%, then I assume I got 4% return every single year until year N. 3. Repeat a number of times and graph the boundaries By contrast, this is the norm in finance and financial economics: 1. Actually simulate a financial return process over a number of years. E.g. in year one, I returned between 0-6%, repeat for year 2 ... N, and keep track of the entire history 2. Repeat many times 3. Draw the distribution Note that the 'correct' simulation procedure draws paths that go up and down, just like asset prices do in real life, while your simulation procedure only ever creates asset price paths that grow or shrink at a constant rate. I strongly recommend either you give up on simulating returns entirely and make it a single point estimate, or do the simulation properly, otherwise your results are badly misleading. Here's a (very simplified) simulation approach: https://www.investopedia.com/articles/07/montecarlo.asp https://www.investopedia.com/articles/07/montecarlo.asp

usaar333 8y ago

The math on appreciation rate is even worse than you write because the reporting is showing the compounded values as normally distributed which is not valid when a compounding rate is normally distributed. (normal distribution times normal distribution isn't normal). The way people normally work around this is to use a log-normal distribution, which stays lognormal over time. The appreciation math consequently is massively off for any high variance input. I completely distrust the results.

refrigerator 8y ago

Hey, thanks for taking the time to write a detailed comment! Everything in the model runs by simulation, so we don't do any maths on appreciation rates. Since it's a simulation, I believe the combinatorics sort themselves out! However... it's possible that something we are miscommunicating something — what gave you the impression that the appreciation maths was off? You're right about the chart — we wanted the baseline model to be an extremely rough guide to compare the buy-to-rent scenario with, so didn't want to add volatility there.

smallnamespace 7y ago
> we don't do any maths on appreciation rates. Since it's a simulation, I believe the combinatorics sort themselves out! That is never a valid inference. At the risk of sounding harsh, you cannot simply throw up your hands and say 'the simulation said so!' without understanding what is actually being simulated, or else you will get nonsense results. > what gave you the impression that the appreciation maths was off The 'probability cone' is clearly the wrong shape. > so didn't want to add volatility there Many fields the calculator, such as appreciation, have distributions attached to them. The way returns in real life get a distribution is via volatility, so it's highly misleading to both have a distribution width and say that you don't want to add volatility. This is what your simulation is actually doing: 1. Pick a single normally distributed number 2. Pretend that is the return of your investment, linearly applied over many years. E.g. if the number I drew in step 1 is 4%, then I assume I got 4% return every single year until year N. 3. Repeat a number of times and graph the boundaries By contrast, this is the norm in finance and financial economics: 1. Actually simulate a financial return process over a number of years. E.g. in year one, I returned between 0-6%, repeat for year 2 ... N, and keep track of the entire history 2. Repeat many times 3. Draw the distribution Note that the 'correct' simulation procedure draws paths that go up and down, just like asset prices do in real life, while your simulation procedure only ever creates asset price paths that grow or shrink at a constant rate. I strongly recommend either you give up on simulating returns entirely and make it a single point estimate, or do the simulation properly, otherwise your results are badly misleading. Here's a (very simplified) simulation approach: https://www.investopedia.com/articles/07/montecarlo.asp https://www.investopedia.com/articles/07/montecarlo.asp