## What Is Super-Hedging?

Super-hedging is a strategy that hedges positions with a self-financing trading plan. It utilizes the lowest price that can be paid for a hedged portfolio such that its worth will be greater or equal to the initial portfolio at a set future time.

Super-hedging requires the investor to create an offsetting replicating portfolio for a given asset or series of cash flows. Super-hedging is a risk management strategy that in theory will help investors construct a portfolio that remains profitable regardless of the market's ups and downs.

### Key Takeaways

- Super-hedging is a risk management strategy traders use to hedge their positions.
- Super-hedging requires the trader to build an offsetting replicating portfolio for the asset or the series of cash flows they are trying to hedge.
- Super-hedging strategies are self-financing, which means the trader finances the purchase of a new asset with the sale of an old one.
- Setting up an optimal super-hedge can be challenging because replicating portfolios are rarely an exact replication of the original.
- Transaction costs to build and maintain the hedge can also add up, reducing the overall profit potential.

## How Super-Hedging Works

Traders can use a hedging transaction to limit the investment risk of an underlying asset. To accomplish this, they can purchase options or futures. These are bought in opposing positions to the underlying asset in order to lock in a certain amount of gain. The super-hedging price of Portfolio A is equivalent to the smallest amount necessary to be paid for an admissible Portfolio B at the current time so that at some specified point in the future the value of Portfolio B is at least as great as Portfolio A.

In a complete market, the super-hedging price is equivalent to the price for hedging the initial portfolio. In an incomplete market, such as options, the cost of such a strategy may prove too high. The idea of super-hedging has been studied by academics. However, it is a theoretical ideal and is difficult to implement in the real world.

## Super-Hedging vs. Sub-Hedging

The sub-hedging price is the greatest value that can be paid so that in any possible situation at a specified point in the future, you have a second portfolio worth less than or equal to the initial one. The upper and lower bounds created by the sub-hedging and super-hedging prices are the no-arbitrage bounds, which specify the limits of the portfolio's price.

The no-arbitrage price bounds are an example of what traders call good-deal bounds, which represent the price range that a trader deems they will be getting a good deal based on their individual preferences.

Some traders attempt to establish optimal super-hedging and sub-hedging bounds as part of a strategy in trading exotic options, such as quanto options, basket options, and knock-out options.

## Super-Hedging and Self-Financing Portfolios

A self-financing portfolio is an important concept in financial mathematics. A portfolio is self-financing if there is no external infusion or withdrawal of money. In other words, the purchase of a new asset must be financed by the sale of an old one.

A self-financing portfolio is a replicating portfolio. In mathematical finance, a replicating portfolio for a given asset or series of cash flows is a portfolio of assets with the same properties.

## Hedging and Replicating Portfolios

Given an asset or liability, an offsetting replicating portfolio is called a hedge. It can be static or dynamic. For the most part, a static hedge does not require the trader to rebalance the portfolio as the price or volatility of the securities it hedges fluctuates. This is because the static hedge consists of assets that mirror the cash flows of the underlying asset and do not require the trader to make adjustments to maintain the hedge.

This contrasts with a dynamic hedge, which requires the trader to frequently adjust the hedge as the price of the underlying asset moves. Dynamic hedges are built by purchasing options that have "Greeks" that are similar to those of the underlying asset.

Creating the optimal replicating portfolio may require the trader to engage in a more active approach to portfolio management. In some cases, this can become a time-consuming and complex activity that is best suited for more advanced traders.

In practice, replicating portfolios are seldom, if ever, exact replications. Dynamic replication is imperfect since actual price movements are not infinitesimal. Because transaction costs to change the hedge are not zero, the trader should consider these potential costs when deciding to pursue a super-hedging strategy.