Lesson 6 of 6
The drag of turnover
Paying tax each year rather than at the end costs 13.6 percent of the ending value over twenty years, at an assumed 8 percent return and 20 percent rate.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- Tax paid each year is money that stops compounding. Tax deferred to the end compounds for you until then.
- The gap is small over a few years and large over decades, because it is itself a compounding effect.
- None of this is an argument for holding anything. It is the arithmetic that makes a pre-tax return an incomplete number.
Two investors earn the same 8 percent a year on the same money for the same twenty years. One realises the gain every year and pays tax on it. The other realises nothing until the end. The pre-tax return is identical and what they keep is not.
One dollar after twenty years, two ways
- Tax paid every year$3.4581
- Tax paid once at the end$3.9288
The two paths, computed
One dollar, 8 percent a year, twenty years, an assumed 20 percent rate
- Deferred path: 1.08 to the power 20 is 4.6610. That is the gross ending value.
- The gain is 4.6610 minus 1, which is 3.6610.
- Tax at 20 percent on that gain: 0.7322.
- Net ending value: 4.6610 minus 0.7322, which is 3.9288.
- Annual path: 8 percent taxed at 20 percent leaves 6.4 percent compounding each year.
- 1.064 to the power 20 is 3.4581.
- The difference is 0.4707, which is 13.61 percent more ending value on the deferred path.
Every line can be recomputed. The whole effect comes from step five: an investor paying tax annually compounds at 6.4 percent instead of 8, for twenty years.
Why the gap grows with time
The drag is not a fixed percentage. It is itself compounding, so it starts negligible and becomes large.
Where the intuition goes wrong
Most people estimate this by comparing rates: 8 percent against 6.4 percent, a difference of 1.6 points, and expect something proportional. What actually happens is that the 1.6 points compound against you for the whole period, which is why the gap at thirty years is twenty times the gap at five.
The second thing people get wrong is the direction of the comparison. The deferred path still pays the tax. It is not avoided, and this is not a lesson about avoiding it. It is paid later, and the money owed did work in the meantime.
The three qualifications that matter
Turnover has other costs. Every realisation is also a round trip through a spread and a commission, and those are paid whatever the tax position. The tax drag is one part of a larger cost of trading.
Realisation is sometimes correct. A thesis that broke is a reason to sell, and the arithmetic above is not an argument against it. Holding a deteriorating position to defer tax is a decision about a smaller number at the expense of a larger one.
The rates are assumed. Every figure here uses 8 percent and 20 percent because round numbers can be checked. Neither is a rate anyone should expect, and the actual treatment depends on the jurisdiction, the account and the holding period.
What to take from it
That a pre-tax return is an incomplete description of an outcome, and the size of the incompleteness depends on how often gains are realised and over how long. When comparing two records, the turnover of each is part of the comparison.
Check yourself
At 8 percent a year with tax paid annually at an assumed 20 percent, what rate actually compounds?
- 8 percent
- 6.4 percent
- 1.6 percent
Show the answer
Answer: B.
Twenty percent of the 8 percent gain is paid out each year, leaving 6.4 percent to compound. The whole effect in this lesson follows from that one substitution.Why is the deferred advantage 0.87 percent over five years and 28.30 percent over thirty?
- Because tax rates rise with time
- Because the annual drag itself compounds, so it grows faster than the horizon
- Because the deferred path avoids the tax entirely
Show the answer
Answer: B.
The 1.6 point difference in the compounding rate is applied every year, so the gap between the two paths widens at an increasing rate. The deferred path still pays the tax, at the end.Your thesis on a holding has broken but selling would realise a gain. What does this lesson say to do?
- Hold, to defer the tax
- Sell, to avoid further loss
- Nothing: it supplies the arithmetic, and the decision is not its subject
Show the answer
Answer: C.
The lesson measures a cost. It does not weigh that cost against the reason for selling, and it is not advice. A decision like this belongs with the investor and, where tax matters, a qualified adviser.Sources
- IRS Topic no. 409, Capital gains and losses, and IRS Publication 550, Investment Income and Expenses: the realisation principle that makes the deferral in this lesson possible.
What this leaves out
- This is not tax advice. It describes general US mechanics. Rules differ by country, by state, by account type and by individual circumstance, and they change.
- Every figure is invented arithmetic at an assumed 8 percent return and an assumed 20 percent rate, chosen so a reader can recompute each line. Neither number is a rate or a return anyone should expect.
- The model assumes one rate on all gains, no dividends, no losses to offset, and no change in the rules over thirty years. All four of those assumptions are false in practice and each would change the result.
- Nothing here is a recommendation to hold, to sell, or to choose any strategy, and nothing here is advice about any security.