Cut-Throat said:
Can you explain in detail these formulas to me. I excelled in Algebra, but admit to not understanding how you arrived at yours - log - which I assume is short for logrithum?
I am guessing that at least 75%+ on this forum does not understand this?
-25% is the worst case yearly decrease
7% is the average yearly portfolio increase
both number are
already discounted by inflation
4% is drawn so 3% is the average portfolio increase.
after n average years the value of 1 dollar is (1.03)^n.
assuming that one year a catastrophic -25% occurs the value will be .75*(1.03)^n
how many years of increase will you get your dollar back? 1=.75*(1.03)^n
take the logarithm on both sides and know that
log(a*b)=log(a)+log(b) and that, log(a^n)=n*log(a), log(1)=0
n=-log(.75)/log(1.03)=9.6
you will get your result of
9.6 YEARS to recoupe your portfolio if you withdraw 4%. If you don't withdraw it would take
4.2 YEARS
you can use log, Log or Ln on any calculator or excel.
NB: Contrary to my initial post you have to use .75, which is not 1/1.25 to reach the correct value. Which explains that a 25% decrease needs to be compensated by a 33% increase!!!!
Also contrary to my initial post the average 7% and the worst case -25% are already corrected for CPI. (those are my own calculation based on historical market return and CPI since the past 100 years or so.