After-tax, after-cost long-run average rate of return is the total return for a portfolio after deducting taxes and costs of investing, calculated over a long-term holding period, divided by the number of years in the holding period.  We calculate total return for the portfolio as total cash flows associated with owning the portfolio divided by the beginning market value of the portfolio.  Cash flows over the holding period include income (dividends and interest earned) plus capital gains (end value of the portfolio minus beginning value of the portfolio) minus costs of investing (advisor fees, fund management fees, plus trade execution costs), minus taxes due.

As an example, suppose the beginning market value of a portfolio is $100,000.  Over a 7-year holding period, suppose the portfolio generates total dividend payments of $30,000 and interest income of $45,000.  Typically, such income streams would be earned monthly or quarterly throughout the holding period.  The income streams might or might not be reinvested throughout the holding period.  In this hypothetical example the investor pays fees totaling $7,000 for portfolio management and trade execution over the holding period.  The portfolio has a market value of $116,000 at the end of the 7-year period.  Total taxes due over the 7-year period total $19,500.  Given these hypothetical cash flows, the after-tax, after-cost long-run average rate of return for this portfolio would be

	$	116	,000	Ending market value of the portfolio
—	$	100	,000	Beginning market value of the portfolio
	$	16	,000
+	$	30	,000	Dividend income paid over the 7-year holding period
+	$	45	,000	Interest income paid over the 7-year holding period
-	$	7	,000	Cost of investing over the 7-year holding period
-	$	19	,500	Taxes paid over the 7-year holding period
=	$	64	,500	Total cash flows of the portfolio
÷	$	100	,000	Beginning market value of the portfolio
		=0	.645	Total after-tax, after-cost rate of return over the 7-year holding period
		÷	7	Holding period in years
		=0	.0921	After-tax, after-cost long-run average annual rate of return = 9.21%