Taxable Investing > Details > Geometric Returns

Geometric Returns as after-tax returns in a multi-period horizon account for management fees and taxes, and also for cash inflows and outflows.  This is due to the geometric return comparing the Starting Market Value in the first period to the Ending Net in the last period as follows:


rGM = (End Net Last Period / Start Value First Period) ^(1/N) - 1

rGM = geometric return

N = number of periods


Portfolios with significant expenditures can often have near zero or even negative geometric returns even though the per period before-tax returns, marginal after-tax returns and actual after-tax returns are all positive.


Geometric returns are useful for investigating a portfolio’s ability to support different levels of spending over time.  The table to the right shows two different spending streams for a $10 million portfolio over ten years.


Starting Value $10 million $10 million
Spending Per Year $300,000 $600,000
Before-Tax Return Target 6.32% 6.32%
Marginal After-Tax Return 5.33% 5.33%
Actual After-Tax Return 4.39% 4.48%
Geometric Return 1.49% (2.69%)
Ending Net Year 10 $11.6 million $7.6 million