After-tax real return - how to calculate

CFA Level III
#1

if we first get pre-tax nominal return and want to solve for after-tax real return

we use (pre-tax nominal return-inflation) * (1-%tax) ______1

or pre-tax nominal return*(1-%tax) - inflation ______2

from the CFA text i think method1is correct what im confused is

if we have to use method 1 , if we have to revert ( solve for after-tax nominal , given after-tax real)

then we have to : [after-tax real / (1-%tax)] + inflation then multiply with (1-%tax) again , right?

please help , may be hard to understand my typing (i’m suck in english)

but i think it’s quite confusing.

when we solve for pretax nominal return > we use (after-tax real return /(1-%tax) right?

so if the exam ask after-tax nominal return > do we have to revert (after-tax real return)/(1-%tax) to pretax real return then add inflation and multiply with (1-%tax) again?

or just simply add inflation to after-tax real return

#2

This has been covered many times, most recently:

http://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/91321885

#3

oh it’s my bad , i got it now

so if account is taxable (inflation is taxed)

so if the exam ask after-tax nominal return and we got after-tax real return first

we have to revert (after-tax real return)/(1-%tax) to pretax real return , then add inflation and finally multiply with (1-%tax) again

such a cumbersome task :frowning:

am i right ? S2000magician

#4

Your first formula can be rewritten as:

(pre-tax nominal return) * (1-tax) = after-tax nominal return

or

(pre-tax real return + inflation) * (1 - tax) = after-tax nominal return

So it is more intuitive to look at it this way. Your portfolio grows at least at the inflation rate, all of which is taxable in a regular taxable account. To illustrate, say, you have $1M portfolio. Its value grew by 5%, part of which is due to inflation. So your real return is 2%. The taxes would be imposed on the entire gain, not just the real portion.

I am not sure about a deferred account, though… I dont know why we need to speak in real terms here… you will be taxed on the entire gain when you retire… so I am confused here a bit…