Q1 How leveraged ETFs achieve their leverage:
Depending on the fund house's strategy, leverage is typically achieved by investing in futures, swaps, by borrowing funds, or a combination of above. You should refer to the prospectus for an ETF's investment strategy. For the example of TQQQ, as Freelunch has answered and according to its prospectus, it principally invests in Nasdaq stocks, swaps, futures, and money market instruments.
Q2 Do they primarily use stock options of the underlying asset to gain the leverage:
They can invest in stock options if the prospectus says so. In practice it is uncommon.
Q3 What methodologies can achieve 3x leverage on a single stock
- You can borrow 2x of your fund and buy 3x worth of stock.
- You can invest in 3x notional of single stock futures
- You can enter a swap agreement with 3x exposure
- You can go synthetic long in 3x notional by buying ATM calls selling ATM puts
Q4 Can you achieve 3X weekly or 3X monthly performance instead of daily?
If you rebalance weekly, you will have 3x weekly return by the time you rebalance. If you rebalance monthly, you will get 3x monthly return. Rebalance frequency determines what time period your leverage is achieved on.