# How to calculate leveraged ETF rebalancing?

So let's say that we have a market-cap weighted ETF (free-floating shares) that tracks an index comprised of stocks A and B. Stock A has a share price of 10 and there are 100 outstanding shares and stock B has a share price of $50 and there are 5 outstanding shares. Let's add that the divisor of the index this ETF tracks is 100. The goal of the ETF at inception is to provide 2:1 long (Bull) leverage. First question: The ETF has 2500 dollars worth of exposure (because of 2:1 leverage), and with the divisor of 100, would each share of the fund have a price of 12.5 or 25 at the time of ETF origination? Second question: Does it make sense to say that there are 500 available shares of the ETF? Would we then set the price of each of the shares to$5 (2500/5) or would that make the market cap of the etf greater than the market cap of the stocks it attempts to track (500*12.5). What is the maximum number of shares that this fund can create?

Third question: If this is a 2:1 leveraged etf - let's take a look at how it rebalances after a day of trading.

Assuming the price of the etf is 12.5, we buy 8 shares for total assets of 100. The etf, however, gives us 200 dollars worth of exposure (16 shares of A and 0.8 shares of B). Stock A rallies 5%, and stock B rallies 10%. Our exposure is now: 168 (from A) + 44 (From B) = 212. We now have $112 in assets, which means our shares increased in price from 12.5 to 14 dollars. The fund now needs to buy an additional$12 (112*2=224-212) dollars worth of stocks to rebalance at the end of the day. It needs to buy these according to the new market cap weightings: 10.5*100+55*5 = 1325. Stock A will take up (1050/1325)% of this purchase (about 79%), or 9.48 dollars which is 9.48/10.5=-.902 shares of stock A. We buy 2.52 dollars of stock B, which is 2.52/55=0.045 shares of stock B. Thus we have exposure to:

16.902 shares of stock A and 0.845 shares of stock B. Is that correct?

In general I'm pretty loose on my understanding of this topic. Any information or resources are greatly appreciated.

• To start an ETF you need some money, which usually comes from the ETF sponsor(s). This amount is arbitrary (but usually small, much less than the value of outstanding stock). Let's say they give you 100 USD to get you started, you borrow another 100 from you prime broker and then you buy 200 worth of stocks. NAV= LongExposure - MarginDebt. When you rebalance you raise additional debt (or repay debt) as necessary to keep the leverage at 2:1. That is the essence of it. – Alex C Apr 30 at 21:10
• Thank you Alex, that clears up a lot of the confusion. – HowtoETF101 May 1 at 15:08