Fischer Black
on
TAXES
Vol. 1, No.1
January, 1981
SHOULD YOU WAIT TO REALIZE TAX LOSSES?
You buy a stock, and it goes dOl.n. In the light of what you now know about
the firm, you are neither bullish nor bearish on the stock. Your tax bracket
is high, and you expect it to remain high. If you realize a loss, you may
not be able to use it fully this year, but you expect to be able to use it
fully to offset capital gains or ordinary income within the next few years.
Trading costs are modest compared to the potential tax saving. Should you
realize the loss now, or should you wait?
I claim you should almost always realize the loss now. You shouldn't wait
till next year. You shouldn't wait till it becomes long term. You shouldn't
wait until the year in which you will be able to use the deduction. You
shouldn't even wait till the end of the year.
You might wait if trading costs are high compared to the potential tax
saving, or if your tax bracket is likely to rise substantially in the future,
or if you are bullish on the stock and there are no good substitutes for it.
For now, we will ignore these factors. We will assume that trading costs
are zero, that your tax bracket is constant at 50%, and that you are currently
neutral about the stock.
Year End Tax Trading
The simplest case is the one in which you are going to sell the stock anyway,
and it's near the end of the year. Should you sell the stock now, so that
Fischer Black on TAXES Page 2
some or all of the deduction can be taken this year, or should you wait till
next year?
The answer, of course, is that you should sell it this year. Assuming that
the tax saving will be the same whether you sell it at the end of this year
or at the start of next year, you will gain by interest on the taxes by
selling this year. If you sell at the start of next year, you may have some
saving in estimated taxes, but most or all of your saving is likely to
be deferred until the end of next year. Thus you lose a year of interest on
most or all of the tax saving.
To be more concrete, letts look at an example. Assume that the stock was
bought for $50 and is now selling for $40. The interest rate is 10% per
year before taxes, or 5% per year after taxes. Selling the stock "ill give
you a $10 deduction and a $5 tax saving.
Realized Loss ($50 - $40)
Tax Saving (50% of loss)
Present Value (at 5%)
Sell
Now
$10
5
5
Sell
Later
$10
5
4.75
Thus the present value of the tax saving is higher if you sell now (at the end
of the year) than if you sell later (at the start of the next year).
Realizing Short Term Losses
Assume now that the choice is between realizing a short term loss now, or
waiting a little and realizing a long term loss. If you have already realized
Fiscner Black on TAXES Page 3
net long term gains, the choice may not matter, but if you will use the loss
to offset short term gains or ordinary income, it will. It will be worth
twice as much if it's short term.
Let uS again assume that a stock bought at $50 is now selling for $40. We
will assume that the deduction will be this year whether the stock is sold now
or later. Assume the long term capital gains tax rate is 40% of the short
term rate.
Sell Sell
Now .L-a-te-r
Realized Loss ($50 - $40) $10 $10
Tax Saving (50% or 20%) 5 2
Present Value (no discounting) 5 2
Thus the advantage of selling now to realize a short term loss rather than
selling later to realize a long term loss can be great: much greater than
the advantage of realizing a loss this year rather than next year.
Limited Deductions
What if you have no realized capital gains this year? What if you have already
realized enough capital losses to offset the maximum amount of ordinary income?
Is there any advantage to realizing more capital losses this year?
Yes, there is. First, of course, you gain from realizing short term losses
rather than long term losses. But even if the losses will be short term
whenever they are realized, there is an advantage to realizing them now.
This is because the cost basis of the stock won't change. while the market
value is expected to rise. If you realize the loss later. you will expect it
Fischer Black on TAXES Page 4
to be smaller than if you realize it now. If you realize the loss now,
and stocks grow as expected, you will end up with a large loss and an
unrealized gain in the substitute stock rather than a smaller loss and no
unrealized gain.
Even though the loss won't be usable until some future year, the amount of
the loss will be greater if it is realized now than if it is realized later.
For an example, let us aSSume that the loss will be realized either this
year or next year, but that the tax benefit of the loss will come next yearˇ
in either case. Assume that the after-tax interest rate is 5%, and that
both the stock you hold and its potential substitute will grow 5% over the
next year.
Realized Loss (sell at $40 or $42)
Tax Saving (50% of loss)
Present Value (at 5%)
Sell
Now
$10
5
4.75
Sell
Later
$ 8
4
3.80
It is likely, of course, that the unrealized gain in the substitute stock if
we sell now will have a negative value, because we might realize it and pay
taxes, or because it is less likely to turn into a realized loss. This will
reduce, but not eliminate, the advantage of selling now rather than later
when the deduction will only be taken later.
Early Tax Trading
For similar reasons, it pays to take a tax 108s as early in the year as
possible. If you wait till the end of the year, you will expect a smaller
tax loss. If you act now, you will eKpect a IB.rge:r: tax loss comhiueu with
~n unrertlized gain in the substitute stock.
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In the previous section, we compared selling at the end of this year with
selling at the end of next year, and assumed that the deduction ,,,auld be
taken at the end of next year. Let us keep all the same assumptions, except
that we will compare selling at the start of this year with selling at the
end of this year, and will assume that the deduction will generate a tax
saving at the end of this year in either case.
Realized Loss (sell at $40 or $42)
Tax Saving (50% of loss)
Present Value (at 5%)
Sell
Now
$10
5
4.75
Sell
Later
$ 8
4
3.80
Thus there seems to be more value J.n early tax trading than in selling at
the end of one year rather than the start of the next year (assuming that
the loss can be used in either year).
Options Analysis
The investor has a series of options with each stock: the option to realize
a gain or loss now or to wait. These options are valuable. Normally, the
best strategies are to realize a short term loss, or to realize a long term
gain, or to let an unrealized gain remain unrealized.
Selling a stock to realize a loss has two benefits. The realized loss is
worth more now than later, as shown above. And the options are generally
worth more in the substitute stock than in the original stock. For one
thing, going to the substitute stock starts the clock over for short term
losses. For another thing, the option element is worth more when cost equals
market value than when cost is far from marKet value.
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Suppose, for example, that the stock will either go up 12 points or d01;u 12
points with equal probabilities. It starts at $40. The change will occur
right away, the loss will be realized right away, and the tax saving will
occur right away. If the original stock goes up 12 points, it will be
above cost (of $50), and the gain will not be realized. If the substitute
stock goes up, its gain will not be realized.
Sell Now Sell Later
A B A B
Realized Loss (original) $10 $10 $0 $22
Realized Loss (substitute) 0 12 0 0
Tax Saving (total) 5 11 0 11
Present Value (total) $8.00 $5.50
The example is extreme in the sense that large mOves in the stock are assumed
in a short period of time. The example is typical, though, in that it shows
a large effect from uncertainty about the future value of the stock. The
benefit from starting the holding period over with a substitute stock where
cost equals market value can be greater through the options effect than from
any of the other effects mentioned above.
Thus the options analysis strengthens all of the other analyses. It makes early
realization of a capital loss even more attractive. It appears that a taxable
investor should almost always be quick to realize a short term loss, at
least under the assumptions of zero trading costs and a neutral prediction
for the growth in the stock price over time.
If you have any questions or comments, please call me at 617-253-6691, or
write me at 50 Memorial Drive, Cambridge, MA 02139.