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

So you've discussed with in the previous video

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

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

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

at a given price and at a given date, and

this right becomes extremely valuable when the underlying value..

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

The green line on this graph represents the value at,

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

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

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

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

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

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

If things bad, The S&P level falls and

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

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

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

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

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

option with a strike price equal to 100.

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

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

And you see that it will

exactly compensate any fall below the level of 100.

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

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

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

This is the combined payoff that I will obtain.

And you see that this combined payoff provides a guarantee.

Right?

If things go well,

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

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

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

against market fall, we simultaneously guarantee the initial level of

the portfolio and participate in any increase in the market.

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

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

Okay. So the option insurance that we purchase

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

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

is going to come, in the form of cost,

which will reduce the overall return of the portfolio.

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

One in red is going to be the return distribution

assuming that we don't have the position.

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

the distribution of return if we also purchase the insurance.