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Let us say that there is some stock which a year from now will have some value V.

A replicating portfolio is a portfolio which will always equal V a year from now.

Clearly, both the stock and the replicating portfolio must cost the same today.

So far, so good.

However, I have heard many people call this replicating portfolio for a "hedge".

Why is it a "hedge"?

The way I understand a "hedge" is when we enter a contract so that in the future, we are protected from some extremely bad events.

But how is the replicating portfolio then a hedge? Buying and selling it just corresponds to buying and selling the stock: but I already own the stock, so what do I need the replicating portfolio for?

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The way I understand a "hedge" is when we enter a contract so that in the future, we are protected from some extremely bad events.

Not exactly. A hedge is something that reduces a specific risk. One possible hedge is one that reduces extreme downside risk (like a put option), but that's just one example.

In the case of your example, if you "short" this replicating portfolio, then you are no longer exposed to any value loss from your stock. No matter what the price is, your replicating portfolio will offset any loss (or gain). In other words, you have reduced "price risk".

Buying and selling it just corresponds to buying and selling the stock: but I already own the stock, so what do I need the replicating portfolio for?

It depends on how the portfolio was constructed. If, for example, it was constructed with options, it might reduce price risk but might have volatility risk, meaning that the replicating portfolio might change value if the volatility of the underlying stock changes.

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Some background information about options to facilitate the example in my answer. There are 6 basic synthetic positions relating to combinations of put options, call options and their underlying stock in accordance to the Synthetic Triangle. They are all variations of:

Stock + Put = Call

which is the core of put/call parity (details not important here). This equation can be factored 3 ways and since you can be long or you can be short, that makes 6 outcomes.

Synthetic Long Stock = Long Call + Short Put

which means that if you buy a call and sell a put with the same strike price and the same expiration, you have a combination option position that mimics the behavior of long stock or as you called it, a replicating position. This combo has the almost the same P&L as owning the stock.

The cost of this position would effectively be the risk free interest rate, ignoring dividends. Dividends lower a call's premium while increasing a put's premium so the larger the dividend, the less the synthetic position would cost... and the combo could possibly be done for a small credit if the dividend was large enough. For all intents and purposes, let's just pretend that the cost of the synthetic long is zero.

If long term options were used to create the combo, the P&L of the two positions (combo versus stock) would be approximately the same at all times. Option volatility would tend to have minimal effect since premium change would offset (you are long one option and short the other). In comparison, the cost of the respective positions would be vastly different. Therefore, they would NOT cost they same today and they would both NOT be worth the same amount a year for today. However, their P&L would be the same.

A hedge is any non correlated position that reduces the risk of an adverse price movement in your asset, albeit in varying degrees. Some examples of hedging long stock are covered calls, long puts, option collars, a short position in another stock, inverse securities, etc.

Regarding your question, if the replicating portfolio was truly 1:1, then being long the stock and short the replicating portfolio would be a hedge but since they are respectively plus and minus 100 delta, they would offset each other at 100% and there would be no profit or loss potential while both positions were on. Or as you stated: "Buying and selling it just corresponds to buying and selling the stock: but I already own the stock, so what do I need the replicating portfolio for?" The only reasonable answer I can offer is that usage of this might be to defend a greatly appreciated stock during a market decline where you don't want to sell and incur a large tax bite. The size of the correction would determine the efficacy of this.

Where this gets beyond the scope of this Q&A is that there are some arbitrage possibilities for natural and the replicating portfolio but that's much higher on the food chain than we are (professional traders, investment banks, etc.).

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