Replicating portfolio
A replicating portfolio for a particular asset or a series of cash flows in mathematical finance is a portfolio of assets sharing the same properties as the reference assets.
The replicating portfolio, which is also called a hedge, can be static or dynamic and building such a portfolio is referred to as static or dynamic hedging.
In case with a static hedge, a trader does not have to rebalance the portfolio and make adjustments, because the price of the assets it hedges fluctuates. It happens because the static hedge includes the assets, mirroring the cash flows of the underlying asset.
In contrast, a dynamic hedge presupposes that the trader would re-adjust the portfolio. Dynamic hedges are usually constructed by acquiring options that have “Greeks” that are similar to those of the underlying asset.
The Replicating portfolio method is related to a super-hedging strategy that is aimed to help investors build a profitable portfolio regardless of the market’s upward and downward movements.
Building an effective replicating portfolio may force the trader to get involved in an active portfolio management. The process is rather complicated and requires time. Therefore, it is considered more suitable for experienced traders.
Replicating portfolio example
Let’s presume that a brokerage house sells an option on a particular stock. They are going to sell (or buy) shares of the stock if the call (or put) buyer exercises his right to sell (or buy) the option, when the price of the underlying stock is higher (or lower) then the strike price.
In this case the brokerage house decides to hedge the risk of a short option position. They create a long option, in other words a replicating portfolio with the same payoff of the option it sold.
This portfolio will consist of 