ETF Replication, Hedging, and Pricing Through Arbitrage

# ETF Replication


# ETF Replication












I have a question regarding the ETF replication methods. I know there are two main methods, namely physical and synthetic replications, but I would like to understand how an ETF trader can :

- Replicate this ETF (what position, what P&L)

- Hedge his replicating portfolio

- Price the ETF

Thanks !

## Answer by AlRacoon (score 3, accepted)

https://quant.stackexchange.com/a/43564

1) Physical Replication would entail taking actual positions in the full or subset of instruments that comprise the ETF. This method would necessarily require a list of the holdings and weights of the ETF or the Index which the ETF attempts to track. Alternatively, in order to minimize the costs of replication, some will use an optimization approach by taking a subset of the holdings in weights that minimize the tracking error to the ETF. Sometimes this involves utilizing a set of factors that are tradable and taking positions that represent these factors.

Synthetic Replication would entail taking derivatives positions the would mimic the ETF performance. The most basic would be a Total Return Swap on the ETF. A broker/dealer would agree to pay the Total Return on the ETF in exchange for an interest payment. Another synthetic replication would be a futures position in the underlying. And yet another would be position in options that would replicate the ETF (long call and short put on the ETF).

2) The hedge to these replicating portfolios would be the actual ETF.

3) The price of the ETF would be the mark to market or price of the ETF. This should be about the same price as the combined mark to market of each of the underlying components of the ETF. There is a redemption/creation mechanism in the ETF market that would keep these two prices in line with each other, taking into account transaction and other frictional costs. The replicating portfolios in part 1 of your question should also be in line and can serve as an approximation of the price of the ETF. Arbitrageurs would look to trade the replication vs the ETF to taking advantage of any dislocations between these prices. Based on your question, it looks like you are looking to do this.

## Answer by TomDecimus (score 0)

https://quant.stackexchange.com/a/43560

Regarding the replication, there are two main "views". Local replication (cashflow) and Dynamic Replication (greeks).

Local Replication: Asume a -mostly- linear relationship between the ETF and a class of assets. Commonly this is a subset or cluster of the main holdings of the ETF. We are basically replicating the price and therefore the returns. To asume a relationship between an ETF and some other stock is a strong hipothesis but plausible when we actually know what the ETF investments are (so the relationship can hold over time).

Dynamic Replication: what we want to replicate is the sensibility of the asset to some other factors (and the price of course). This means we are trying to create a synthetic asset with the same delta, gamma, theta, etc. so we get the same exposure to the market.

If we can replicate the ETF, we can hedge the position by taking the inverse order on the market.

If we can replicate, we can price the ETF based on the replication price. This is the basic idea behind derivatives valuation -> get a replication portfolio, and if the portfolio gives the same payoff, the derivate should have the same price based on the non Arbitrage Principle.