Show HN: Should you buy a house and rent it out?
The math on appreciation rate is a bit off because of how risk adds up to itself over time.<p>For example, if you assumed 3 +&#x2F;- 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% +&#x2F;- 3%.<p>However the normal way this is done in economics and finance is to assume independent increments of return volatility (let&#x27;s say 3% per annum). This gets you:<p>- 1 year out: 3% +&#x2F;- 3%<p>- 10 years out: 3% +&#x2F;- 3% &#x2F; sqrt(10)<p>- N years out: 3% +&#x2F;- 3% &#x2F; sqrt(N)<p>Intuitively, imagine if having a &#x27;good year&#x27; 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 &#x2F; N, the standard deviation of realized annualized return scales at total &#x2F; sqrt(N).<p>Probability cones should always look like sideways parabolas:<p><a href="https:&#x2F;&#x2F;sixfigureinvesting.com&#x2F;wp-content&#x2F;uploads&#x2F;2018&#x2F;11&#x2F;MonteCarlo-vs-theor-simple.jpg" rel="nofollow">https:&#x2F;&#x2F;sixfigureinvesting.com&#x2F;wp-content&#x2F;uploads&#x2F;2018&#x2F;11&#x2F;Mo...</a><p>More here:<p><a href="https:&#x2F;&#x2F;sixfigureinvesting.com&#x2F;2018&#x2F;11&#x2F;predicting-price-ranges-with-historic-volatility&#x2F;" rel="nofollow">https:&#x2F;&#x2F;sixfigureinvesting.com&#x2F;2018&#x2F;11&#x2F;predicting-price-rang...</a><p>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&#x27;re comparing a &#x27;risky&#x27; 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).