Re:U.S. stock market returns – a history from the 1870s to 2022
by xapata on Friday January 06, 2023 @02:39PM
(#34279799)
Are they normally distributed?
Re:U.S. stock market returns – a history from the 1870s to 2022
by pclmulqdq on Friday January 06, 2023 @03:12PM
(#34280331)
Almost, but the distribution has slightly fat tails.
Re:U.S. stock market returns – a history from the 1870s to 2022
by ttymck on Friday January 06, 2023 @04:41PM
(#34281599)
Is it correct to say that makes it (slightly) more like a uniform distribution, if viewed as a spectrum between one-point distribution and uniform?
Re:U.S. stock market returns – a history from the 1870s to 2022
by xapata on Friday January 06, 2023 @05:07PM
(#34281944)
It'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.
Re:U.S. stock market returns – a history from the 1870s to 2022
by kqr on Friday January 06, 2023 @04:43PM
(#34281622)
I 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.
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%.