|
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 |
|