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Â In this video we're going to discuss the use of options derivative contracts to

Â ensure against market fault.

Â So, we start from the perspective of

Â an investor who has a long position.

Â So he's holding a portfolio invested in a well-diversified

Â portfolio hold in, for example, the equivalent of a stock index, okay?

Â Let's assume that we have correctly described the optimal asset mix.

Â And the part of the portfolio allocation is constituted by

Â investments in the S&P 500.

Â So we hold all these securities in their appropriate proportions.

Â 1:15

So, the question we are asking here, is how can we actually protect our portfolio

Â against such a detrimental variation in the market?

Â So the first thing that comes to mind, is we could simply sell our possession.

Â We could sell our possession, wait for

Â the market fall that we expect to actually happen, and then buy the possession back.

Â This of course comes with significant transaction costs, and

Â this is particularly true for retail investors.

Â So modify the portfolio structure by selling the entire portfolio and

Â buying it back after the period where we expect to observe a market fall

Â is going to be very costly in terms of transaction costs.

Â Also, if we happen to be wrong, and the market rises.

Â If we have sold our position, obviously we won't be able to benefit from this.

Â So another way of protecting the portfolio against the market fall,

Â is to buy an insurance.

Â So how do we buy an insurance in the context

Â of investment in financial securities?

Â Well, we add a pay off that corresponds to an insurance against the market fall.

Â So, we're going to take the situation of a long position in the S&P 500 that we

Â want to protect.

Â And to do so we're going to buy a derivative contract.

Â 2:35

The question is do we buy a put or do we buy a call?

Â So you've discussed with in the previous video

Â the structure of derivative contracts and what their payoff actually look like.

Â What we know is that a put option is going to benefit the owner of this contract.

Â When the market fall, the good option is a right to sell the underlying

Â at a given price and at a given date, and

Â this right becomes extremely valuable when the underlying value..

Â Okay, so let's see graphically how this situation would look like.

Â The green line on this graph represents the value at,

Â let's say, an horizon of three months, the value of the underlying security.

Â The scale here is just representative and goes from zero to 200.

Â Let's say we start today at 100, somewhere in the middle of the graph.

Â This is the current level of the S&P 500 this year.

Â If things goes well, the S&P 500 goes up,

Â the value of our portfolio goes up along the green line.

Â If things bad, The S&P level falls and

Â the value of our portfolio goes down along the green line again.

Â So we want to add a payoff to this initial situation, our holding of the S&P 500

Â which is going to compensate the losses that we might incur when the market falls.

Â And this is the red dotted line that is added below the green line in this graph.

Â And you see that these corresponds to the pay off of the put

Â option with a strike price equal to 100.

Â So this is a contract that is going to benefits its holder

Â when the market falls below this strike price level of 100.

Â And you see that it will

Â exactly compensate any fall below the level of 100.

Â If actually I add up these two lines to create the pay off generated

Â by holding simultaneously, the position in S&P 500 and

Â they put option written on the S&P 500 with a strike price of a $100.

Â This is the combined payoff that I will obtain.

Â And you see that this combined payoff provides a guarantee.

Â Right?

Â If things go well,

Â we will move up along this blue line on the righthand side of the level of 100.

Â If things go bad, well we stay at a level of 100 and our capital is guaranteed.

Â So by purchasing an option, a put option in this context to protect

Â against market fall, we simultaneously guarantee the initial level of

Â the portfolio and participate in any increase in the market.

Â Okay, so this almost looks too good to be true, but

Â as we have extensively discussed in this course, there are no free lunch.

Â Okay. So the option insurance that we purchase

Â the put option that we purchase of course is not free.

Â And this insurance is going to affect the distribution of the return and

Â is going to come, in the form of cost,

Â which will reduce the overall return of the portfolio.

Â So I'm going to show you in the next graph two return distributions.

Â One in red is going to be the return distribution

Â assuming that we don't have the position.

Â And the other one in blue which will be superimposed will describe

Â the distribution of return if we also purchase the insurance.

Â 6:08

The two distribution are very very different.

Â As you can see, the red distribution goes from minus 100,

Â to a large value, so it means that if things go really really poorly,

Â we could actually lost the entire investment made in the underline stack.

Â The blue distribution.

Â It's a little bit strange, it has such a very big mode, a little bit below zero and

Â apparently there's nothing to the left of the distribution, it is bounded below.

Â And this corresponds to the maximum loss that we can incur by holding

Â simultaneously the stock because the option provides a guarantee

Â there is a minimum level below which we will never fall.

Â Hence, the difference between the red and

Â the blue curve is also manifest in the level of their average.

Â The average of the red distribution, okay so the expected return if we

Â don't hedge is actually going to be higher than the expected return if we hedge.

Â However, the compensation, the risk associated with the blue distribution,

Â the hedged portfolio, it's going to be significantly lower and

Â in particular it's going to remove all that downside risk to

Â the left of the distribution that we actually don't like.

Â And the risk overall is going to be lower for the hedge position.

Â So in conclusion, we can temporarily insure our portfolio

Â against market fall by buying a put option.

Â Now this can be done only if there exists trade and securities, traded

Â derivative securities written exactly on the underline that we want to protect.

Â 7:49

We can protect the evolution of the market, the evolution of the specific

Â stock, but not necessarily the evolution of an entire portfolio.

Â It might be the case that we have long position

Â in stocks that have no derivative contract traded on it.

Â And therefore in these cases, we cannot purchase interest contract.

Â But in general, if we think about hedging against market variation,

Â against market fall, these contracts are very liquid.

Â It's very easy to trade them, and they're accessible on financial markets.

Â And we can add them to the portfolio allocation to protect against

Â the outsiders.

Â