In this workout on structured products, we are asked to calculate first of all, the funds available to the bank to purchase call options to hedge their risk, and also to calculate the payoff to the client if the S&P 500 ends up at either 2,400 index points or 2,575 index points at maturity of this principle-protected note.

The workout also informs us that the principle on the principle-protected note is $1,000, and that the initial value of the S&P 500 is 2,500 index points. Also, within the principle-protected note, the formulaic payoff to the client is that for every one index point above its current level of 2,500, the client will receive 40 cents worth of extra payoff, and that the cost of a 1-year zero-coupon U.S. Government bond, that matures at the same time as the principal-protected note does in one year's time, is $985. So, in terms of the bank being able to manage their risk, the client here in purchasing the principle-protected note, will pay the bank $1,000. The bank can then use that $1,000 to go out and buy the 1-year zero-coupon U.S. Government bond.

That will only cost them $985, leaving $15 left over to purchase equity call options.

At the maturity of this principle-protected note, if the S&P 500 is 2,400 points only, then the client is only owed the par value. They will get their money back for sure, even though the equity index has fallen in value, the options that the bank has purchased to manage their risk will expire out of the money and therefore be abandoned. However, if the S&P 500 increases over the year to the maturity of this principle-protected note, and increases to 2,575 index points, then the client will be owed not only the money they initially invested, which the bank will be able to afford through the maturity of the 1-year zero-coupon U.S. Government bond, but they are also owed on the formulaic basis, the difference between the value of the index at maturity and the value of the index at the inception of the principle-protected note. So a 75 index point increase, and they are owed 40 cents per index point above the 2,500 level at inception. So the client will be owed $1,030, The extra $30 the bank can afford, through the exercise of the equity call options purchased at inception to manage their risk.