|
Marginal after-tax returns account for the management
fees, income taxes and capital gains taxes under the assumption that market
value equals cost basis.
rAT
= (1 - tI )(rI - mf )+ (1 - TtG )rG
rAT
=
marginal after-tax total return
tI
=
income tax rate
rI
=
before-tax income return
mf
=
management fee
T
=
turnover
tG
=
capital gains tax rate
rG
=
before-tax capital gains return
The before-tax capital gains return,
rG
represents the expected price appreciation based on the starting market value at
the start of the current period. The
assumption that the cost basis equals the market value means that the turnover
only converts unrealized gains and losses to realized gains and losses based on
the expected price appreciation.
Furthermore, any reduction in market value at the start of the period for either
investor expenditures or portfolio reweighting has no tax impact and therefore
no impact on marginal after-tax returns.
Technically, this means that marginal after-tax returns are invariant to changes in
portfolio weights. This is an
important feature discussed in Optimizing with Taxes in the Complexities
Section.
The table to the right shows a simple example.
Due to the market value equals cost basis assumption the marginal
after-tax return equals the actual after-tax return.
|
|
|
Before-Tax Income Return |
2.5% |
|
Management Fee |
50 basis points |
|
Income Tax Rate |
35% |
|
Before-Tax Capital Gain Return |
5.0% |
|
Turnover
|
50% |
|
Capital Gains Tax Rate |
35% |
|
|
|
|
Starting Cost Basis |
$1,000,000 |
|
Starting Market Value |
$1,000,000 |
|
Ending Capital Appreciation |
$50,000 |
|
Ending Income |
$25,000 |
|
Management Fees |
($5,000) |
|
Income Taxes |
($7,000) |
|
Capital Gains Taxes |
($8,750) |
|
Ending Net |
$1,054,250 |
|
Marginal After-Tax Return |
5.4% |
|
Actual After-Tax Return |
5.4% |
|