4 ms·
> The range of returns across 1-year periods has varied significantly (from negative 37.0% to +53.2%). However, the annualized returns across 20-year periods ha
by retube 4y ago
> The range of returns across 1-year periods has varied significantly (from negative 37.0% to +53.2%). However, the annualized returns across 20-year periods have a much tighter range (from +0.5% to +13.2%)
You'd expect something like this. For a normally distributed iid, the annualised volatility of returns over n years scales as sigma / root(n). So if your one year vol was 10%, the annualised vol over a 20 year period would be 10%/sqrt(20) = 2.23%.
- xapata 4y agoAre they normally distributed?
- pclmulqdq 4y agoAlmost, but the distribution has slightly fat tails.
- ttymck 4y agoIs it correct to say that makes it (slightly) more like a uniform distribution, if viewed as a spectrum between one-point distribution and uniform?
- xapata 4y agoIt's hard to imagine a uniform distribution over an infinite domain, but that sounds right if you're think of it as a half-open spectrum.
- kqr 4y agoI don't think normality is required -- the sqrt(n) scaling factor comes out of variance laws and the definition of the mean. It should be true for any distribution that has a variance, and the 150-year historic return certainly has a variance.
- xapata 4y agoThe sample variance is different from the distribution variance, but I get your point.