I was watching an interview of Edward Thorpe in which he mentally calculated
his annualized return on stocks over a 35 year horizon by computing the 35th root
of 250 (percentage return) by taking e^(5.6/35) to get approximately 1.17, which
is the right answer.
Does anyone know where he got the 5.6 from and why the natural log?
OK - you get a point for posting your question in the right forum. e^5.6 is roughly 250 (well, it’s actually 270), and since taking the 35th root is the same as raising to the power of 1/35 , e^(5.6/35) is approximately one plus the annual return. Since 5.6/35 is a little less than 1/6 we can call it .16 and a second order approximation of the exponential gives you 17% and change. Where the rabbit went into the hat was when Thorp memorized tables of logarithms, which makes quick calculations like these relatively straightforward.