3. Market impact: your own order moves the price

Costs 2: What you pay and cannot see

The previous two modules dealt with costs the market charges you for existing. This one deals with a different cost: the one it charges you for being big. Once your order is bulky enough relative to what normally trades in that asset, it stops being a drop in the ocean and becomes part of the tide. You move the price yourself, and always against yourself.

The two impacts and why they are worth telling apart

When you send a large buy order two things happen at once, and they are opposite in nature.

• Temporary impact. You eat the available liquidity: you exhaust the offer at the best price, then the next level, then the one after that. The price rises while you buy because you are consuming the inventory of whoever is quoting. When you stop buying, that inventory is replenished and the price tends to come back. It is a cost that is real and reversible at the same time: you pay it, and whoever sold to you keeps it.
• Permanent impact. The rest of the market notices there is an insistent buyer and concludes that he knows something. Those quoting raise their prices for good, and the price does not come back. It is the part of the move you caused by revealing information through your own activity.

Larry Harris, in the standard work on microstructure, puts this tension usefully: liquidity is a service somebody renders you, and like every service it has a price, one that goes up the more you need it.

Why impact grows faster than size

Here is the point almost everybody's intuition gets wrong. There is an empirical regularity documented across a multitude of markets and periods, known as the square-root law: the impact of an order, measured as a percentage of the price, grows roughly with the square root of the fraction of daily volume it represents, scaled by the asset's daily volatility.

This reads two ways, and both need to be understood properly.

Per share, impact is concave: multiplying the order by a hundred does not multiply the overpayment by a hundred, but by ten. Executing big is proportionally more efficient than executing small.

But the total bill in euros is that overpayment multiplied by the number of shares, so it grows with size raised to a power of roughly 1.5: more than proportional. Doubling the order does not double the total cost, it multiplies it by about 2.8, nearly 180% more.

Let us see it with figures. Take a security with 5 million euros of daily volume and daily volatility of 2%, and use a coefficient of 1 to keep things simple (the real coefficients that get estimated tend to sit in the region of unity, but they vary by market and by method):

• An order of 5,000 euros, 0.1% of daily volume. The square root of 0.001 is 0.032. Impact: 2% times 0.032, some 6 basis points. In euros: about 3 euros.
• An order of 500,000 euros, 10% of daily volume. The square root of 0.10 is 0.316. Impact: 2% times 0.316, some 63 basis points. In euros: about 3,150 euros.

A hundred times the size, ten times the cost per share and a thousand times the cost in euros. That factor of a thousand is why size is the natural enemy of any strategy.

Capacity: why an idea stops working as it grows

Straight out of the above comes the notion of capacity: the largest sum a strategy can manage before its own execution costs devour its theoretical edge.

Stay with the same security. Suppose a strategy with a gross edge of 60 basis points per complete trade. Since it pays impact going in and coming out, it can afford at most 30 basis points of impact a side before it is left with nothing. Solving the law above: 0.30% equals 2% times the root of the volume fraction, which gives a root of 0.15, that is, a fraction of 2.25% of daily volume. On 5 million, some 112,500 euros per position.

If the strategy holds twenty simultaneous positions of similar size, its point of death is somewhere around 2.25 million euros under management. And long before it gets there, at half that size, it will already have given away a substantial part of the edge. That same system running 10,000 euros notices absolutely nothing: its impact is a few basis points and the edge arrives almost intact.

This is exactly the phenomenon Marcos López de Prado describes when he insists that capacity is a property of a strategy every bit as important as its return, and that ignoring it is the commonest way of selling results nobody can reproduce with real money. A strategy that works with 10,000 euros and not with 100 million is not a fraud: it is the arithmetic of impact doing its job.

What this protects and what this punishes in a small investor

Out of this comes the most interesting asymmetry in the level, and it cuts both ways.

It protects you on the impact front. An order of 2,000 euros in a large security is literally invisible: it moves nothing, it reveals nothing and it does not have to be sliced across several days. You can trade in illiquid corners where a large fund simply cannot get in without destroying the very price it wants to exploit. The anomalies that survive scrutiny usually survive precisely because they do not scale, and not scaling stops being a problem when what you manage is small. It is the private investor's only genuine structural advantage.

It punishes you in everything else. Those same illiquid corners carry spreads of 50 or 100 basis points, and those you do pay in full. Commissions with a per-trade minimum weigh proportionally far more on small orders. You have no execution algorithms to spread the order out and no access to several trading venues.

Put another way: your capacity advantage lives on exactly the terrain where the invisible costs are highest. It is a real advantage, but it is not free, and collecting it demands measuring very carefully what getting in and out costs.