WHEN SHOULD YOU REALIZE GAINS?
Fischer Black
on
TAXES
Vol. 1, No. 2
February, 1981
Last time, we found that when trading costs are zero and when you have no
special information about stocks, it pays to realize losses whenever they
occur. It pays to realize losses this year rather than next year, and short
term rather than long term; and it pays to realize a loss early in any tax
year rather than waiting till the end.
Let me emphasize the assumptions needed for these results: no trading costs
and no ability to pick stocks that will do better than other stocks or worse
than other stocks. If we relax these assumptions, it may sometimes pay to
wait till later to realize losses.
For now though, we will continue to make the same assumptions. If the portfolio
is large enough, realized losses that can't be used to offset this
year's ordinary income will soon be generated. We'll have a backlog of
realized losses; enough to use the maximum loss deduction for one year, or
several years, or many years in the future.
The stocks that remain in the portfolio will all show unrealized gains. Some
will be large, and some will be small. Some will be short term, and some
will be long term. But all the stocks we hold will show gains.
Does it ever pay to realize a gain? Does it pay to realize a gain as soon as
it becomes a long term gain? Or does it always pay to wait for death to
wipe out all unrealized capital gains?
Fischer Black on TAXES Page 2
A Backlog of Realized Losses
Let us assume that there is a backlog of realized short term losses big
enough to carry into at least the next tax year. Realized losses will
normally be short term if we follow the policy of realizing them as soon
as they become losses.
This means that long term gains will look just like short term gains.
There won't be any difference. Any realized gain will cut the size of
the backlog of losses dollar for dollar.
Initial Realized Final
Backlog Gain Backlog
(all dollar amounts in $ thousands)
50 a 50
50 1 (short term) 49
50 1 (long term) 49
Thus the decision to realize or not to realize a gain will not depend on
whether the gain is short term or long term. Will it depend on the size
of the backlog?
When the backlog is large, the losses cancelled out when a gain is taken
probably won't be used until years in the future. The present value of
a given tax saving is lower, the farther the tax saving is pushed into
the future. Thus the larger the backlog, the lower the cost of a given
realized gain.
At the same time, a large backlog means lower benefits from realizing a
gain. The potential benefits come from replacing the existing stock with
a new stock that is more likely to give an added short term loss. But the
larger the backlog, the less an added loss will be worth.
Fischer Black on TAXES Page 3
In fact, a large backlog reduces the tax cost of realizing a gain and the
tax benefits of replacing the old stock with a new one in exactly the same
proportion. So long as we continue to assume zero trading costs, the
size of the backlog won't affect the decision to realize a gain.
Cost of Benefit of
Initial Realizing Starting
Stock Backlog Gain Over Decision
(years) ($ thousands) ($ thousands)
A 7 2 4 sell
A 14 1 2 sell
B 7 6 4 hold
B 14 3 2 hold
Similarly, neither the investor'~ tax bracket nor prospective changes in
tax rates will affect the decision. A high tax rate means a high cost
for realizing a gain, but also a hi7,h benefit from buying a stock that may
give an added short term loss.
In fact, when trading costs are zero the only things I can think of (other
than the amount of the potential realized gain) that will affect the
decision are the level of interest rates and the volatility of stocks
generally. Higher interest rates means higher dollar expected returns on
stocks, and thus a smaller chance oi realizing a short term loss on the
replacement stock. Higher volatility on the replacement stock means a
larger chance of realizing a short term loss.
This also means that in choosing a replacement stock, other things being
equal, it's better to choose a high volatility stock than a low volatility
Fischer Black on TAXES Page 4
stock. The other things that must be kept equal, though, include the
diversification of the portfolio and the overall volatility of the whole
portfolio.
The Trigger Price
When there's a backlog of realized short term losses, the cost of realizing
a gain is independent of whether it's a long term gain or a short term
gain. The cost is independent of the length of time the stock has been
held.
The benefit of selling the stock and replacing it with a new stock is not
independent of its holding period, though. The longer the stock has been
held, the less likely it is, compared to the replacement stock, to give
rise to a short term loss. If tile s tack has been held more than a year,
it will never give rise to a short term loss.
The original stock and the replacement stock will both cancel short term
losses if gains are realized, but tl,e r"placement stock is more likely to
give realized short term losses. When the cost of switching is zero, the
replacement stock will be better (a~suming it is at least as volatile as
the original stock).
When the price of the original stock equals its cost, there is no tax
burden from selling it. If trading costs are zero, it must pay to switch
to the replacement stock. Switching has no disadvantages.
Since it clearly pays to switch when price equals cost, there must be prices
above cost where it will pay to switch also. The longer the original
stock has been held, the larger the gain from switching if price equals cost,
and thus the higher the price at which it will still pay to switch.
No matter how long a stock has been held, there is ah,ays a trigger price
below which it should be sold. At first, the trigger price is equal to
Fischer Black on TAXES Page 5
cost: it should be sold if that will generate a short term loss. The
trigger price gradually rises until the stock has been held a year, and
then tends to stay at the same level except for shifts due to interest
rate and volatility changes.
Trigger
Price
one
year
Holding
Period
Every stock in the portfolio has a trigger price when trading costs are
zero. If the stock falls below that price, it should be sold. The trigger
price is always equal to or higher than the original cost of the stock, so
the short term losses are generated by stocks that fall below cost before
they can be sold. Any stock in the portfolio selling below cost should
be sold.
When we put in positive trading costs, we will lower the trigger price.
In fact, as we will see, with high enough trading costs a stock may not
have any trigger price.
Fischer Black on TAXES Page 6
One final point. When there is a backlog of realized losses, the end of
the tax year has no special significance. A stock should be sold when it
falls below its trigger price whenever that happens. Only when there is
no backlog might the end of the tax year make a difference. If we expect
to realize short term losses next year, it may pay to realize long term
gains this year, even though that means paying extra taxes this year. If
we wait, the long term gains may be wasted as offsets to short term losses
next year or in later years.
If you have any questions or comments, please call me at 617-253-6691, or
write me at 50 Memorial Drive, Cambridge, MA 02139.