2. Turnover: the number that multiplies all your costs

Costs 6: The full bill

The previous module ended with a difference of almost three and a half points between two portfolios of the same size and with access to the same markets. Nearly all of that difference comes out of a single variable, and it is not the investor's skill or the quality of his ideas. It is turnover: how much you buy and sell over the course of a year. This module works through its arithmetic, because that is what turns unit costs that look ridiculous into the largest item on the bill.

What turnover actually measures

Annual turnover relates the volume you trade to the size of your portfolio. Turnover of 100% means that over a year you have replaced the equivalent of your entire holdings: if you have 50,000 euros, you have sold some 50,000 and bought another 50,000. It does not mean you have changed all your positions, because you can go in and out of the same share three times, nor that December's portfolio is any different from January's.

It is worth knowing the two conventions in circulation. The fund industry's takes the lesser of purchases and sales and divides it by average assets; some brokers add both together and divide by two. They give similar but not identical figures unless you buy and sell exactly the same amount, so you should never compare your number, worked out one way, with a fund's, worked out the other. As a reference point, a large-cap index fund typically turns over between 2% and 10% a year; a traditional active fund, between 30% and 100%; a quantitative strategy with monthly rebalancing comfortably exceeds 400%.

The cost of one full round trip

The second half of the arithmetic is the round-trip cost: what it costs to buy something and sell it again, counting everything. It is the right unit, because a position you open is a position you will sooner or later close. You already know its components:

• The commission going in plus the commission going out, with the warning about the per-trade minimum: if the broker charges a 5-euro minimum and your trade is 1,000 euros, your effective commission is 0.5%, not the advertised rate.
• The full spread. You buy near the offer and sell near the bid, so on a round trip you pay the whole spread, not half of it.
• Slippage and market impact, twice over: on the way in and on the way out (level 2).
• Currency conversion, also twice if the asset trades in another currency.

A very liquid ETF in a large account might have a round trip of 0.10%. A European mid-cap share in an ordinary account, between 0.25% and 0.50%. A small, thinly traded or emerging-market share, more than 1%. These ranges are orders of magnitude stated as assumptions, not price lists.

The multiplication

The formula is brutally simple: annual friction cost = turnover x round-trip cost. With two cost scenarios, one cheap and one ordinary, the table writes itself:

• Turnover of 20%: 0.05% a year on the cheap round trip; 0.12% on a round trip of 0.60%.
• Turnover of 100%: 0.25% and 0.60%.
• Turnover of 300%: 0.75% and 1.80%.
• Turnover of 1,000%: 2.50% and 6.00%.

Notice what is happening: the unit cost has not changed at any point. It is still a number that looks insignificant —a quarter of a point in the cheap scenario, six tenths in the normal one—, something nobody would quibble over when sending an order. What changes is how many times you pay it. Turnover is not a matter of style: it is the multiplier that decides whether your friction bill is a footnote or the dominant line on your income statement.

How much gross edge you need just to draw level

Here is the consequence that kills the illusion of frequent trading. If your strategy turns over 800% a year on a round trip of 0.55%, it drags a weight of 4.4 percentage points a year. To draw level with sitting still in an index, your decisions have to generate 4.4 points of gross edge every year. To genuinely win, more.

Look at it per trade as well, because that is where it hurts. Suppose your average trade, counting winners and losers, leaves 0.45% gross. If each round trip costs 0.30%, the cost takes two thirds of your profit and you are left with 0.15% net per trade. All it takes is for the cost to rise to 0.45%, which happens simply by trading slightly less liquid securities, for your strategy to go from making money to making nothing at all, without its ability to pick correctly having deteriorated one jot.

William Sharpe set out the general version of this in a very short piece on the arithmetic of active management: since active investors between them own the market, their average gross return is necessarily the market's, and therefore their average net return is below an index tracker's by the difference in costs. It is not an empirical result that future research might refute: it is arithmetic. And turnover is exactly the variable that decides the size of that difference. Charles Ellis developed the same idea with a different metaphor, the game you win by not losing: when the gross edge is small, whoever accumulates the fewest errors and the fewest tolls finishes in front.

Measure your real turnover

Nobody estimates their own turnover well from memory; everybody underestimates it. The calculation takes a minute:

• Add up the euro value of all your purchases for the year.
• Divide it by the average value of your portfolio over that period.
• Multiply by your estimated round-trip cost, minimum commission included.

The result is the toll you pay for trading the way you trade, in percentage points a year. Set it beside your expected return. It is almost always the most uncomfortable figure in a portfolio, and also the easiest to change: halving your turnover halves that item, immediately and without depending on getting anything right.