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I am recently studying mathematical finance, and I am not really familiar with how the financial system works. This might be a naive question: when reading some books on mathematical finance, "hedging" acts as a core concept. I understand that in some cases hedging does make sense, e.g., a farmer who wants to sell his wheat a few months later might prefer to short a forward to hedge against the risk. However, there are some cases that I really don't understand.

For example, "delta-hedging" seems to be a very important strategy. I can understand it mathematically, but I don't know why in practice people needs to implement delta hedging, because by the arbitrage free condition, a perfect delta-neutral hedging (rebalance the portfolio continuously to make it delta-neutral) is no more than making it a risk-free asset. Then why don't we directly buy a risk free asset? What's more, in practice perfect delta-hedging is impossible, then to hedge the portfolio, we have to finance more money...

It looks to me unreasonable that an investor bother to long/short some derivative and then hedge against the position, so I would like to know about some circumstances in the real world that we really need to hedge against the derivatives. Could you explain to me some reasons? Thanks in advance!

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    long/short some derivative and then hedge against the position Are you sure this is the case, as it seems to go totally against the whole idea of derivatives ? Which book and which relevant part mentions this ? – DumbCoder Dec 28 '14 at 11:43
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    Better on Quantitative Finance ? – AakashM Jan 27 '15 at 12:37
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Sometimes hedging is used if you have a position and you feel the market is going against your position, so one would hedge that position in order to protect their capital and possible profits instead of closing the position and incurring capital gains tax.

Personally if the market was going against a position I had open I would get out of that position and protect my capital/profits instead of using more capital to hedge against my position. I would rather take a profit and pay some capital gains tax than watch my profits turn into a loss or use up more capital to try and protect a bad position.

Hedging can be useful in certain circumstances but I think if you feel the market is going against your position/s for the medium to long term you should just get out of your positions instead of hedging against them.

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In general, when you open a position or make an investment in the financial markets, you are expecting a return on your investment based on a set of assumptions.

For example, if you were buying stock in a utility company, you might expect the company to continue to pay dividends for the foreseeable future.

However, there may be some aspects that you cannot predict and that you don't want to include in your set of assumptions. For example, there might be the risk that the company might cut its dividend. If it were to do so, one would expect the stock price to drop significantly, so a 'hedge' against that possibility would be to buy a put option in the company.

Hedging allows you to remove some of the risks that you are not including in your set of assumptions.

You are correct - if you eliminated all of your risks through hedging, you wouldn't make any money - in fact, the hedge would probably cost more than you would make. However, by using various hedging 'tools' you can use them to reduce risks that you can't predict.

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I don't know why a financial investor or a retail trader would do this. But I can guess why a market maker in options would do this.

Let us say you buy an option from an option market maker and the market maker sold the option to you. He made a small profit in the bid-ask spread but now he is holding a short position in the option with unlimited risk exposure. So to protect himself, he will take an offsetting position in the underlying and become delta neutral, so that his position is not affected by the moves in the underlying.

In the end, he can do this because he is not in the market to make money by betting on direction, unlike the rest of us poor mortals. He is making money from the bid-ask spread. So to ensure that his profits are not eroded by an adverse move in the underlying, he will continuously seek to be delta neutral.

But once again, this is for a market maker. For market takers like us, I still don't understand why we would need to delta hedge.

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There are a number reasons to hedge a position. Here are some of the more common:

  • Delta hedging can be used to make a temporary position change cheaper. Once an option position is traded it can often be expensive to trade out of that position and then back into the position if you think the position will have a temporary setback. Instead managers will temporarily delta hedge using the underlying which can be significantly cheaper.
  • You might even be able to approximately delta hedge a whole portfolio with a single liquid index which may be much, much cheaper than to trade all the positions.
  • Also, delta hedging only hedges the linear effects for small moves. Delta hedging can be used to take out the linear risk and bet on exclusively the non-linear part of the derivative (i.e. gamma for options).
  • Victor123 has a nice write-up on arbitrage in another answer. Essentially, as you mention you do get a risk free asset but if you trade well you might be able to capture a risk-free portfolio that is at a rate slightly higher then the prevailing risk-free rate.
  • As Victor mentions there can be tax reasons for temporary hedging to avoid realizing capital gains. Though the treatment of gains in derivative positions can be complicated and even cancel out occasionally.
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Hedging of one derivative position with other derivative is common case. It does not remove risk, but it cuts the volatility of portfolio. For example you have 1 contract of oil futures, then you sell one contract of oil, for different date. Your delta positioning is near zero, but your position is not zero. You still own one +1 and one -1 contract, even if these will follow spot price and overall your position will be "frozen".

It is not "hedging" in common sense, to reduce risk. When you buy stocks, you reduce your risk of inflation, for example. It is different. You only reduce volatility.

  • In finance terms, volatility and risk are basically the same thing... – Grade 'Eh' Bacon Oct 26 '18 at 14:55
  • @Grade'Eh'Bacon as much as you could ever be wrong, you are – sanaris Oct 26 '18 at 15:02

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