# How do you define the market cap of an ETF?

I'm hesitating between these 2 solutions:

1. The conventional calculation:

MCAP = #shares * SharePrice

1. Perform the weighted average of the MCAP of each stock in the ETF

MCAP = sum(iStockWeight * iStockMCAP)

• what is iStockWeight here? – Kamster Jul 2 '15 at 2:08

An ETF’s assets will fluctuate based on both changes in the value of the underlying securities and the creation of new shares or redemption of existing shares. It is worth noting that there may be a difference between an ETF’s market capitalization and the net asset value (NAV) of its underlying securities. The difference results in either a discount or a premium in the trading price of the ETF.

The market capitalization at time $t$ is therefore the number of shares at $t$ times the price of those shares at $t$. The net assets are the total value of all the assets in the fund at 't': $$Net\ Assets_t = U_{t} \cdot NAV_t = U_{t} \cdot \sum_{i} (S_{i,t} \cdot weight_{i,t})$$ where $S_{i,t}$ is the value of a share of stock $i$ at time $t$, $weight_{i,t}$ is the fraction of the index invested in stock $i$ at time $t$, and $U_{t}$ is the number of shares of the index. Or equivalently:

$$Net\ Assets_t = \cdot \sum_{i} (S_{i,t} \cdot q_{i,t})$$ Where $q_{i,t}$ is the number of shares of stock $i$ at time $t$ held by the ETF. This sounds simpler but it is often easier to find index weights than exact share holdings measured in number of shares.

But for open-ended funds that allow creation and redemption or have minimal expenses these NAV and market price based approaches will give similar answers.

One problem you should see with the way you are calculating market cap for ETF is by the following example:

Assume there are 100 shares of Stock A for \$5 per share (MKTCAP for A = \$ 500) and 200 shares of stock B for \$10 per share (MKTCAP for B = \$ 2000) .

Say ETF1 contains \$100 worth of stock A and \$100 worth of stock B. And ETF2 contains \$200 worth of stock A and \$200 worth of stock B.

By your formula, MKTCAP for ETF1 is equal to MKTCAP for ETF2 since both contain same weights (0.5, 0.5). Instead the formula should be

$$\sum_{i} \left(\frac{\textrm{# of shares in ETF for Stock }i}{\textrm{# of total shares of Stock }i}\right)\textrm{MKT CAP}_i$$

• Note: that if you work out the math in equation provided by @BKay , you get same answer as one that I provided. I would say that BKay equation is probably easier to use in practice since stocks prices is relativiely easy to find and is consistently updated and number of shares of index and weights is easily known – Kamster Jul 2 '15 at 2:12

MCAP = sum(iStockWeight * iStockMCAP)