ETFs: the arbitrage mechanism, and why leveraged ones decay

The in-kind mechanism — An authorised participant can hand the fund a basket of the underlying securities and receive new ETF shares, or hand back ETF shares and receive the basket. That makes the ETF and its basket convertible in both directions, so any gap between the ETF price and the value of the basket is a trade rather than an opinion.

If the ETF trades above the basket, buy the basket, create, and sell the ETF. If it trades below, buy the ETF, redeem, and sell the basket. The premium or discount is therefore bounded by the cost of doing that — the basket’s spreads, the creation fee, and the borrow if any leg must be shorted.

Holds when

• Liquid equity ETFs trade within a basis point or two of net asset value.
• Bond and emerging-market ETFs can sit at wider premiums, because the underlying is harder to trade — and in stress the ETF price is often the *better* price, since it is the one actually trading.
• A persistent premium that nobody arbitrages usually means the basket cannot be assembled, not that traders have missed it.

A 2x daily ETF rebalances to two times exposure every day, which makes its path matter.

1. $$\text{Index: } +10\%, \text{ then } -10\% \Rightarrow 1.10 \times 0.90 = 0.99$$

   The index is down 1%.

2. $$\text{2x fund: } 1.20 \times 0.80 = 0.96$$

   Down 4%, not the 2% a naive reading expects.

3. $$\text{shortfall} = 0.98 - 0.96 = 0.02$$