Hi Kris, and thank you for your interesting articles (which I just recently found).
I believe the key to why normal distribution can be used to model long-term annualized returns is the fact that compounding over time involves adding log returns.
The fact that log returns are additive over time means that the law of large numbers applies to geometric (log) instead of arithmetic returns implying the average annualized return over time converges to geometric expectation.
On the other hand, adding a large number of short-term log returns over time and calculating their yearly mean implies that central limit theorem can work its magic and make the distribution approximately normally distributed no matter what the original log return distribution was.
Back when I made the comment about survivorship bias, it wasn’t meant to be dismissive. I think the show is fantastic; I’ve probably read 4-5 biographies since I started listening - I have a newfound admiration for the genre and what it can bring a reader. The show is also quite inspirational and I think your description of its merits hit the mark.
"What Negative Skew?" What about monthly and daily drawdowns? (Max DD & Max MD). I think the long period with the arbitrary year end obscure some of the negative skew..
Hi Kris, and thank you for your interesting articles (which I just recently found).
I believe the key to why normal distribution can be used to model long-term annualized returns is the fact that compounding over time involves adding log returns.
The fact that log returns are additive over time means that the law of large numbers applies to geometric (log) instead of arithmetic returns implying the average annualized return over time converges to geometric expectation.
On the other hand, adding a large number of short-term log returns over time and calculating their yearly mean implies that central limit theorem can work its magic and make the distribution approximately normally distributed no matter what the original log return distribution was.
Back when I made the comment about survivorship bias, it wasn’t meant to be dismissive. I think the show is fantastic; I’ve probably read 4-5 biographies since I started listening - I have a newfound admiration for the genre and what it can bring a reader. The show is also quite inspirational and I think your description of its merits hit the mark.
"What Negative Skew?" What about monthly and daily drawdowns? (Max DD & Max MD). I think the long period with the arbitrary year end obscure some of the negative skew..