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.