# Practice problem Vol.3 Reading 18, Example 7, Part 2 - AUM affected by liquidity & concentration constrains

Andrew Isaac runs a \$100 million diversified equity portfolio (about 200 positions) using the the Russell 1000 as his investable universe. The total capitalization of the index is approximately \$20 trillion. Isaac’s strategy is very much size agnostic. He consistently owns securities along the entire size spectrum of permissible securities. The strategy was designed with the following constraints:
●● No investment in any security whose index weight is less than 0.015% (approximately 15% of the securities in the index).
●● Maximum position size equal to the lesser of 10× the index weight or the index weight plus 150 bps
●● No position size that represents more than 5% of the security’s average daily trading volume (ADV) over the trailing three months The smaller securities in Isaac’s permissible universe trade about 1% of
shares outstanding daily. At what level of AUM is Isaac’s strategy likely to be affected by the liquidity and concentration constraints?

Solution :
Based on the index capitalization of \$20 trillion, the size constraint indicates that the smallest stocks in his portfolio will have a minimum market cap of about \$3 billion (0.015% × \$20 trillion). The ADV of the stocks at the lower end of his capitalization constraint would be about \$30 million (1% × \$3 billion). Because Isaac does not want to represent more than 5% of any security’s ADV, the maximum position size for these smaller-cap stocks is about \$1.5 million (5% × \$30 million). It appears that Isaac’s strategy will not be constrained until the portfolio reaches about \$1 billion in size (\$1.5 million ÷ 0.15% = \$1 billion). If the level of AUM exceeds \$1 billion, his position size constraints will require
the portfolio to hold a larger number of smaller-cap positions. There is room to grow this strategy.

Could some please explain this question in some other way. I am having a hard time understand the solution, especially this part → \$1.5 million ÷ 0.15% = \$1 billion. why is it divided by .15% and where is it coming from.

1 Like

0.15% = 0.015% × 10.

0.015% comes from bullet point 1. 10× comes from bullet point 2.

portfolio\ size × 0.15\% ≤ \\$ 1.5\ million
portfolio\ size ≤ \dfrac{\\$ 1.5\ million}{0.15\%} = \\$1\ billion

Thank you Magician!

My pleasure.

That example has been a source of immense frustration amongst candidates.

How to get average daily trading volume(ADV)? Min market cap(3 billion) *1% was used in the solution. Could you please give me more clues to understand these Magician? Super appreciate!

3bn is minimum amount to trade and 1% of ADV is condition given in the problem.

Sorry for coming back to this again.
My question is what if AUM now is \$1.2 billion? Why do we then face liquidity and concentration constraints? Do we need to make the assumption that the extra AUM ( 1.2-1) billion needs to be allocate to some smaller cap and then breaching the limit related to DAV?