In an effort to resolve the question mentioned yesterday, Testing for Scalability, I pulled a random sampling of U.S. stocks to look at their volume turnover rates.

I pulled the sample in different groups, with market caps above $10 billion, between $1 billion and $10 billion, and between $100 million and $1 billion. I then compared the daily liquidity (average (OHLC price) times shares traded) to their market capitalizations.

I found that the largest group, those above $10 billion in cap, tended to trade about 0.75% of their cap on a daily basis.

Those in the middle group, between $1 and $10 billion, had the highest turnover at about 1.25% of their cap, daily.

In the smallest group, those between $100 million and $1 billion, I found turnover of about 0.90% of their cap on a daily basis.

Therefore, given no cap bias towards any particular trading system, one could say that – generally speaking, of course – target stocks will turn over about 1% of their market cap daily.

Again, while this is a non-trivial and useful answer, it’s still incomplete. If one is interested in a system that is scalable to a particular number of stocks and turnover per period, one has to have a good idea of the percentage of total daily liquidity that, if exercised by one fund, will move the market disadvantageously.

Back to my example of strategy X holding 344 stocks with over $1 bil in cap, turning them over at 18% a month: how fast does that execution need to be?

The backtested results were done at zero slippage, so any execution lag could impact the result, and one assumes that it would be a deleterious impact. “Monday morning at open” is fine for a retail schlub grabbing 20 positions that max at 0.0001% of cap and about 0.01% of daily volume, but in the case of our fund, how big are those positions?

Running “only” $344 million, each position averages about $1 million dollars, and the minimum market cap is $1 billion. Executing the trade inside of one day implies occupying no more than one-tenth of the average daily liquidity, which, to my novice brain, seems imminently do-able. Also, the $1 billion is a market cap filter, with many of the stocks in the system – and the average market cap of its holdings – being larger. I would believe that a skilled day-trader, or prodigious computer algorithm, could accomplish that without moving the market overmuch. If we use that as our hypothetical ceiling, then …

Running “only” $3.4 billion, the fund is trading positions that run to a maximum of 1% of capitalization, and those positions would require 10 trading days – at most – to enter or exit.

Running “only” $7 billion, the fund is running into limiting cases where a stock might enter the list one month, and exit the next, and be at the minimum eligible market capitalization. In that limiting case, with trading at only one-tenth of average daily liquidity, the fund may spend a full month building a position only to turn around and liquidate that position over the next month. Note that the average tenure is about 5.5 months in our case (hypothetical 18% monthly turnover). Also note (again!) that the average cap size is going to be higher than the minimum cap size.

My amateurish take is that this hypothetical system is robust up to managing $1 billion in capital, unleveraged, and that past that point, execution of trades impacts profitability.