Real/ Nominal and Pre/ after Tax Returns

CFA Level III Portfolio Management
#1

Hi all,

I am so confusing with the terminology of real, after-tax/ pretax and nominal/ real return in private wealth management. Please correct me my following understanding about 04 following formulas:

Given a situation that you have $1 and invest in 1 year.

Formulas 1

1* (1 + R real pretax ) * (1 + inflation) = 1 * (1 + R nominal pretax )

With tax effect, we have

Formulas 2:

1* (1 + Inflation) + R real pretax * (1 + inflation) * (1 - Tax) = 1 + 1* R nominal pretax * (1 - Tax)

Formulas 3:

(1 + inflation) + R real after tax * (1 + inflation) = 1 + 1 * R nominal after tax

Formulas 4:

R nominal pretax = [R real after tax * (1+ inflation) + inflation] / (1-T)

Thank you all

#2

It all depends on if the investment is taxable or not taxable. if it is taxable, you add inflation and then dividend by (1-T) and if it only the withdraw portion of the return is taxable, you divide by (1-T) and then add inflation. Read the question carefully to know what they want you to do.

  • Fully taxable: R nominal pretax = [( R real after tax + inflation)] / (1-T)
  • Only return portion is taxable (for example a TDA): R nominal pretax = [( R real after tax ) / (1-T)] + inflation
  • Tax Exempt: Take a guess :slight_smile:

Bill’s article on this helped a lot: http://finexamhelp123.wpengine.com/inflation-in-required-rate-of-return-to-tax-or-not-to-tax/

Since this is individual, you’ll want to add inflation rather than multiple to make things simplier :slight_smile: