Manager has $250 million in assets under management (AUM). Share of company A has a market capitalization of $3.0 billion, an index weight of 0.20%. Give the index weight constraint below:
Index weight: The maximum position weight must be less than or equal to 10 times the security’s weight in the index.
What’s the maximum position size?
The answer is “Index weight constraint = $250 million × (0.20% × 10) = $5.0 million”
I don’t quite understand how AUM is related to index weight? What does “index weight” mean?
Equity indexes are comprised of fictional “shares” of the each stock in the index, which is important to ensure they behave like normal positions with respect to performance, splits, dividends etc. This attribute ensures that managers can replicate the index.
As an example, the S&P 500 (aka SPX) “holds” 7,728,915 shares of MSFT, which today equates to an index weight of roughly 3.69%. If you manage a $250M SPX index fund, you need to own approximately $9.225M notional value in MSFT, or 87,267 shares to remain in line with the index.
In the example you provided, the index weight is used as the percent of the portfolio that should be held in company A in order to perfectly replicate the index. The portfolio has a fairly large active weight constraint that each position can be up to 10 times the index weight, or 2.00% in this case. Thus, to hold the position at index weight the manager would need to buy $250M*0.002 = $500k in the stock. The maximum position size is 2% however, so we can hold up to $250M*0.02 = $5.0M.
The piece of information regarding market cap is unimportant to answer the question, but tells you that if the index in question is market cap weighted like SPX is, the total market cap of the index is $1.5 trillion (i.e. $3.0B/0.002 = the sum of the market cap of every company in the index).