3. Capacity: why size kills an edge

Level 10: Why it runs out

An investment idea does not have a return. It has a return for each size, and the relationship between the two is the concept that has cost investors who buy funds on their track record more money than any other. We take as read from the costs course that buying moves the price against you. What we need now is the arithmetic of what happens when that gets multiplied.

Return is a property of the pair idea and size

Stating the problem is easy. You buy because you think something is worth more than it costs. In buying, you push the price up. If you buy a little, the push is negligible and you keep almost all the difference. If you buy a lot, a growing part of that difference is eaten by you yourself before you have finished building the position. And then you have to get out, which is the expensive half of the trip.

From that follows something that sounds odd the first time: the same manager, with the same idea and the same talent, gets worse results the more money is entrusted to them. Not because they relax or lose their touch, but because their own order is now part of the price they pay.

Why the cost grows faster than the benefit

Here is the heart of the module. The gross profit of an idea grows more or less in proportion to capital: if with 100 million you made 8% gross, with 200 you expect to make 8% gross on twice the base. But the cost does not behave the same way. The sustained empirical observation is that the cost per euro traded grows approximately with the square root of the size of the order: multiplying by a hundred what you want to buy multiplies by ten what each euro costs you.

Put the two pieces together and the conclusion follows: gross income grows in a straight line with assets, and total cost grows considerably faster, because the number of euros traded and the price of trading each one grow at the same time. Sooner or later the two curves cross.

The full sum, in euros

Let us take an illustrative example, with round numbers chosen so the mechanism can be seen. A strategy manages 100 million, achieves 8% gross and pays 1% in trading costs: 8 million minus 1 million, 7% net and 7 million of profit.

• With 400 million (four times as much), the unit cost doubles to 2%: 32 million gross minus 8 of costs, 6% net and 24 million.
• With 1.6 billion (sixteen times), the unit cost quadruples to 4%: 128 minus 64, 4% net and 64 million.
• With 6.4 billion (sixty-four times), the unit cost reaches 8%: 512 million gross minus 512 of costs. Net return zero.
• The maximum profit in euros is at none of those points: it falls at around 2.8 billion, with about 76 million net and a return of barely 2.7%.

Read that last line again, because it is the most important in the module. The size that maximizes the manager's euros returns less than half as much to their clients as the small size does. There is no open conflict, no lie, no error: just two different objectives pointing to different sizes.

Why the manager grows anyway

If the fee is 1.5% of assets, with 100 million the manager collects 1.5 million and their client keeps 5.5% after the fee. With 2.8 billion they collect 42 million and their client keeps around 1.2%. The manager has multiplied their income by twenty-eight while their clients' result was divided by more than four.

That is the mechanism by which money flows toward a good track record until the edge disappears: the talent exists, but it is captured by whoever charges on assets, not by whoever provides them. And the investor who arrives last is precisely the one funding the stretch in which the edge no longer exists.

How much capacity each type of idea has

As a mental rule, the capacity of an idea is the liquidity of the universe it operates in divided by its turnover:

• Low turnover, a few trades a year, and large companies: enormous capacity, in the tens of billions.
• High turnover, a portfolio refreshed every few weeks, and small companies: tiny capacity, sometimes a few hundred million.
• Doubling turnover roughly halves capacity, because each turn of the portfolio pays the toll again.

Novy-Marx and Velikov analyzed a broad set of anomalies measuring their return net of trading costs and found the expected pattern: the low-turnover ones survive reasonably well, while a good part of the high-turnover ones lose most of their gross edge or all of it. And that calculation is done at modest sizes: on scaling up, the verdict only gets worse.

Real case: the funds that close themselves

The most cited example is that of a US quantitative fund which, according to public reports, capped its assets at around ten billion dollars, returned outside capital and was reserved for its employees, sustaining extraordinary annual net returns for decades, on the order of thirty-something percent. The same firm later ran funds open to the public of far greater size, with ordinary results and one clearly bad year.

The opposite contrast is also historical: a very famous US fund went from a few tens of millions of dollars in the late 1970s to some fourteen billion in the early 1990s, with returns close to 29% a year during that climb, and in the following decades, by then a giant, it looked more and more like the index. Neither story is about talent. They are about arithmetic.