PORTAX After-Tax Portfolio Analysis

An investment typically generates two sources of return: income and capital appreciation.  This creates a before-tax total return decomposition of

r_T = r_I + r_G

r_T = before-tax total return
r_I = before-tax income return
r_G = total before-tax capital gains return

On an after-tax basis, this return decomposition yields: 

r_AT = (1 - t_I )(r_I - mf )+ (1 - Tt_G ) r_G

 r_AT = after-tax total return
t_I = income tax rate
r_I = before-tax income return
mf = management fee
T = turnover
t_G = capital gains tax rate
r_G = before-tax capital gains return

Note that this after-tax return assumes the cost basis equals the market value.  Additionally, this after-tax return assumes that there is no market value tax.  These assumptions are for introductory purposes.