4. Opportunity cost and the cost of not trading

Costs 2: What you pay and cannot see

One component is left, the slipperiest of them all, and not by chance: it is the only one that leaves no trace anywhere. The spread you can see in the book, slippage you can see by comparing two prices, impact you can see on the chart. The opportunity cost of a trade you decided on and never executed appears nowhere at all, because there is no trade to examine. And yet, in a great many strategies, it is the largest term of the lot.

The piece that was missing from the implementation shortfall

When Perold set out the implementation shortfall, his decisive contribution was not saying that executing costs money, which everybody already knew. It was insisting that the correct comparison is between the complete paper portfolio and the complete real one, and that therefore the trades that were never executed count just as much as the ones that were.

The hole between paper and reality breaks down like this:

• Explicit costs. Commissions and transaction taxes. Billed, visible, easy.
• The execution cost of what you did trade. Spread, slippage and impact on the executed part.
• The opportunity cost of what you did not trade. What the orders that never filled would have returned, or the part of them left unexecuted.

Almost every measurement system stops at the second item, because the third demands keeping a record of what you decided to do rather than of what you did. Anybody who does not record their decisions cannot measure their implementation shortfall; they can only measure their invoices.

The limit order that never fills

The limit order looks like the elegant solution to everything above: if the problem is crossing the spread, name your price and wait for them to come to you. Instead of paying half the spread, you collect it. On paper, an improvement of twenty basis points per complete trade.

The trouble is that it does not always fill, and that when it fills and when it does not is a long way from random. A limit order sitting in the book is, in practice, a free option you have written to the market: anybody can execute it against you when it suits them and nobody will when it does not. Its value grows with the asset's volatility and with the time you leave it there. Larry Harris describes it with that very image, and it is probably the most useful way to remember it: you are not waiting for a better price, you are giving away an option.

Let us do the honest sum. A hundred signals, each with an expected profit of 150 basis points if it executes at the decision price, and a spread of 20 basis points:

• With market orders: all hundred execute, each one paying the full spread. A hundred times 130 basis points, that is, 130 basis points per signal.
• With limit orders: seventy fill without paying any spread, and thirty do not fill because the price left without you. Seventy times 150, divided by a hundred signals: 105 basis points per signal.

The limit order comes out 25 basis points worse per signal. And here is the measurement trap that sinks a great many people: if you look only at the ones that executed, the limit order appears to be running twenty basis points better than the market order. That is true and it is irrelevant. The cost of the thirty that are missing shows up in no execution report, but it is there in full in your return. And in real life it is worse still, because the ones that fill tend to be the worst ones: you get filled when the price was coming toward you, which is to say when you were wrong.

The sign depends on what kind of strategy you have

This comparison has no universal winner, and that is the interesting part.

• Trend-following or momentum strategy. You buy what is going up. The orders that do not fill are precisely the ones that were moving most, which is to say the good ones. The opportunity cost is enormous and it is nearly always better to cross the spread and secure the fill.
• Mean-reversion strategy. You buy what has fallen too far. The orders that do not fill are the ones that carried on falling, which is to say the ones that would have gone badly. Here the failure to execute is a filter working in your favor, and on top of that you collect the spread instead of paying it. The limit order is not merely acceptable: it is part of the strategy.

Before deciding how you execute, you need to know which side you are on. A momentum system that executes with limit orders to save on the spread is paying far more than it thinks.

The cost of impatience, and the horizon

The opposite face is crossing the spread out of fear of being left behind. Say you decide to buy at the open, when spreads are at their widest, and you pay 40 basis points to cross when two hours later, with the book settled, you would have paid about 12. You have charged yourself 28 basis points for being in a hurry.

Is that serious? It depends entirely on the horizon, and here is the honest conclusion of the level:

• If you are going to hold the position for several years, 28 basis points are noise next to what will decide the outcome.
• If you are going to close it this very afternoon in search of 30 basis points, those 28 are the whole trade.

How market and limit orders really compare

To sum up what is worth retaining about the two:

• Market order. A known and bounded cost (half the spread plus whatever impact you cause), guaranteed execution, no opportunity cost. You are paying for certainty.
• Limit order. A lower or even negative execution cost on the ones that fill, but an uncertain total expected cost with an unpleasant tail: the good signals that get away from you.

The rule that follows from the whole level is simple: compare the expected cost across all the decisions, not the price obtained on the executions. That is the number Perold put on the table almost forty years ago and it remains, by some distance, the commonest difference between a strategy that works on paper and one that works with money. And the only lever that acts on all four components of this level at once is the same one: trade fewer times.