# Liquidity Constraint and Fund Size?

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.

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.