I’m having a tough time understanding the concept that derivatives transform the performance of the underlying. The book doesn’t go into very much detail and the only example in the forwards section hasn’t gleaned any light on the matter for me. Google has been no help also. Can anyone please explain this concept to me?

With a forward contract, you agree to buy (or sell) an underlying at a specified price on a specified day. The spot price of the underlying on the delivery day may have gone up, down, or not changed since you entered the forward, but you have locked in to the specified price. If you agreed to buy the underlying and the then current spot price is above (below) the agreed forward price, you have made a profit (loss): in the former, you’re buying something below the spot market price, while in the latter you are paying more than the spot market price. Similarly, if you agree to sell forward and the then current spot price is below (above) the agreed forward price, you have made a profit (loss): in the former, you’re selling something above the then current market price, while in the latter you’re selling below the then current market price.

Take the example of (A) a simple long position in the underlying vs (B) a protective put (i.e. a long in the underlying combined with a long put). Let’s assume the put has a strike (exercise) price of $50.

in (A), your payoff is the value of the stock - so, if the price goes below $50, so does your payoff.

in (B), the total payoff will never be less than $50 - as the price of the underlying goes below $50, the value of the put position increases to offset the decrease in value of the underlying.

Graph the payoffs of (1) the value of the stock, (2) The value of the put, and (3) The combined value of the put and the stock. You’ll see that the payoff (performance) of (1) and (3) are radically different.

Here’s a simple example from everyday life:

You own a car. A tree jumps out in the middle of the road and your vehicle gets totalled. What is the difference in your financial situation with and without car insurance?

I think I get it.

could you please explain it,I have the same doubt, what does transform the performance of the underlying and pass through the returns of an underlying mean???

The return on a call option isn’t the same as the return on the underlying.

The return on a put option isn’t the same as the return on the underlying.

And so on.