The following constraints are given:
- With liquidity constraint, the maximum position size is 3% of average daily volume.
- The smallest shares in the permissible universe trade on average 1% of shares outstanding each day.
- With benchmark weight size minimums, no positions are allowed in securities that make up less than 0.5% of the benchmark index.
- With benchmark weight size maximums, no positions are allowed that are greater than 5 times the benchmark weight.
- The total capitalization of the benchmark index is $1 trillion.
Question is: Based on the constraints relating to capacity issues, what is the fund size at which the strategy is likely to be impaired by liquidity issues.
Answer given:
The benchmark weight size constraint implies the capitalization of the smallest shares, that can be held by the fund, is 0.005 × $1 trillion = $5 billion.
The smallest stocks will trade on average 0.01 × $5 billion = $50 million of daily volume.
The liquidity constraint means the fund cannot trade more than 0.03 × $50 million = $1.5 million per day.
The benchmark weight size maximum means that, for the smallest securities, the maximum weight in the fund is 5 × 0.5% = 2.5%.
If assets under management (AUM) are so large that AUM multiplied by 2.5% is greater than $1.5 million, then the manager cannot take the maximum weight in small securities due to liquidity constraints.
Therefore, the maximum AUM = $1.5 million / 0.025 = $60 million.
I am struggling with the last part. If I have a fund that’s $100 million - my position size limit is $2.5 million. Sure I can only trade a max of $1.5 million per day but why would that prevent me from effectively carrying out my strategy? I can still build or completely liquidate my position in 2 days.
It may involve the opportunity cost that you cannot complete your desired position.
^ Riding on the heels of his answer but a bit more context…
I think you misinterpreted the information provided / given inputs … the fund’s maximum position size in any small-cap held by the index would be 3% of the small cap’s average daily volume (i.e. the maximum total dollar value position the fund can hold in any small-cap is $1.5 million total, NOT a maximum daily trade constraint of $1.5 million)…
This way, if you hypothetically had a fund with $AUM of $100 million as you used in your question at the bottom … and you applied the same fund max % weight in any position of 2.5%, then the maximum dollar value according to the weight % constraint = $2.5 million (100 x .025)
Now going back and comparing this to the maximum total dollar value the fund can hold in any position (3% of ADV = $1.5 million), the implication in this scenario is that:
The maximum $ value position imposed by liquidity constraints of $1.5 million is LESS than the maximum weight % permitted of $2.5 million if you had a AUM of $100 million… so a fund manager with $AUM of $100 million would never be able to scale his position in the small-cap to the $2.5 million maximum allowed per the maximum benchmark weight multiple constraint (again, if measuring this according to his hypothetical $100 million $AUM value… but any value above the AUM impairment level of $60 million in this question would apply the same concept)
Might help grasp the idea better if you look at the “x% of $ADV” liquidity constraint (in this case holding no more than 3% of $50 million ADV = $1.5 million) as a “ceiling/cap” that overrides the “max % weight of AUM as per the benchmark multiple provided” constraint… so there’s essentially a disconnect between the two constraints that impairs the fund strategy… in other words, continuing with the $AUM = 100 million ... on one hand, the hypothetical max position is 2.5% = 2.5 million per the benchmark specifications, but on the other hand, the ADV liquidity constraint is also saying the max $ position can’t exceed $1.5 million for the small-cap … so if you put yourself in the shoes of a manager with a $AUM = $100 million, you wouldn’t be able to scale this position to your theoretical max weight of $2.5 million because the “% of ADV” constraint stops you out at $1.5m, or only 60% of your theoretical max position per the benchmark requirements (1.5/2.5 = 60%).
So why take this trade and incur trading costs + potential market impact costs (particularly with less liquid small-caps that don’t require as much buy volume to absorb sell limit orders sitting above the stock’s current market price… in other words, small-caps require less buy pressure to move upwards in price very quickly … relative to mid/large cap stocks…the quick surges in price from relatively low buy volume in small-caps increases your fund’s average cost basis because you’ll be buying at constantly increasing prices from your own buy pressure - and higher ACB = lower returns… it’s more beneficial for the fund to “style shift”, adjusting the fund’s strategy to mid-caps or similar, and your now in a position to have the ability to scale larger positions in more liquid stocks that won’t jump in price as quickly while you’re buying/adding onto your position… without being stopped from buying up to your max weight % permitted if its a high-conviction long trade.