Structured Equity Products

Abstract

Structured equity products have been a feature of the equity markets for many years. But what is a structured product? In general terms, a structured product is an investment whose risk-return profile cannot be easily replicated by the end investor. Broadly speaking there are two ways of structuring this type of instrument. Some can be ‘engineered’ by combining different instruments; for example, a basic capital protected note can be replicated by a zero coupon deposit and a long call option. On the other hand, some so-called exotic structured products are designed with a specific investor payout in mind and the payoffs are modelled using a Monte Carlo simulation.

Appendix

Many thanks to David Oakes for his significant contribution to this appendix.

Section 12.2 introduced a shortcut technique to convert an OTC index option premium into a monetary equivalent without the use of a cash multiplier. The premium in index points is divided by the strike price which is then multiplied by the certificate’s notional amount to determine the cash equivalent and the associated participation rate. The purpose of this appendix is to illustrate the logic behind this approach.

Listed index options make a payoff that is calculated by applying a cash multiplier to the option payoff which is expressed in index points; equally the cash value of the option premium is calculated by multiplying the option price in index points by the cash multiplier. To understand how this logic could be applied to an OTC option, assume, without loss of generality, that this cash multiplier is $1. In the base case scenario in Sect. 12.2, if the option costs 262 points it would cost $262 to buy an option that would pay $1 for every point that the index finishes above the strike. The investor invests $1000 in the note, but $960.98 of this is needed to fund the capital protected amount, leaving just $39.02 to purchase the option that will fund the supplemental payoff. This will allow the bank to buy 0.1489 (calculated as $39.02/$262) of an option that would pay $1 per index point above the strike, so the payoff that the investor will receive on the option will be just $0.1489 for each point that the index finishes above the strike.

Suppose that the index finishes at 2100. This is a percentage gain of 5 % above the strike (calculated as (2100 − 2000)/2000). The supplemental payoff the investor receives from exercising the option, however, will be $14.89 (calculated as (2100 − 2000) x $0.1489). Since the supplemental payoff is:

$$ \$1,000\times \mathrm{participation}\;\mathrm{rate}\times \mathrm{percentage}\;\mathrm{in}\mathrm{crease}\;\mathrm{in}\;\mathrm{in}\mathrm{dex}\;\mathrm{relative}\kern0.28em to\kern0.28em \mathrm{the}\;\mathrm{strike} $$

This can be rearranged to solve for the participation rate:

$$ \begin{array}{l}\begin{array}{l}\mathrm{Participation}\;\mathrm{rate}=\\ {}\mathrm{supplemental}\;\mathrm{payoff}/(\$1,000\times \mathrm{percentage}\;\mathrm{in}\mathrm{crease}\;\mathrm{in}\;\mathrm{in}\mathrm{dex}\;\mathrm{relative}\kern0.28em \end{array}\hfill \\ {}to\kern0.28em \mathrm{the}\;\mathrm{strike})\hfill \end{array} $$

Inserting the relevant values gives:

$$ \$14.89/\left(\$1,000\times 0.05\right)=\$14.89/\$50=29.79\% $$

Now consider the case where the strike is increased to 2100. This reduces the option price to 228 points, so it now costs $228 to buy an option that will pay the investor $1 for every point by which the index finishes above the strike. The capital protection costs the same as in the base case, so the bank will still have only $39.02 to buy the option. This means that the bank can buy 0.1711 (calculated as $39.02/$228) of an option that would pay $1 for every point that the index finishes above the strike. Put another way, the investor will receive $0.1711 for every point by which the index finishes above the strike.

To facilitate comparison between the two cases, suppose that the index finishes at 2205. This index level is 5 % above the strike price of 2100 (calculated as (2205 − 2100)/2100). If the index finishes at this level, the investor will receive a payoff of $17.97 (calculated as (2, 205 – 2, 100) × $0.1711). Using the same formula as in the base case, we can calculate the participation rate as:

$$ \begin{array}{l}\begin{array}{l}\mathrm{Participation}\;\mathrm{rate}=\\ {}\mathrm{supplemental}\;\mathrm{payoff}/(\$1,000\times \mathrm{percentage}\;\mathrm{in}\mathrm{crease}\;\mathrm{in}\;\mathrm{in}\mathrm{dex}\;\mathrm{relative}\kern0.28em \end{array}\hfill \\ {}to\kern0.28em \mathrm{the}\;\mathrm{strike})\hfill \end{array} $$

Inserting the relevant figures returns the following participation rate:

$$ \$17.97/\left(\$1000\times 0.05\right)=\$17.95/\$50=35.94\% $$

Using a ‘percentage of spot’ shortcut, the participation rate can be calculated as: participation rate = (nominal amount – amount required for capital protection)/((option premium/spot index level × nominal amount)).

For the base case, this gives participation rate as:

$$ \left(\$1000-\$960.98\right)/\left(\left(262/2000\right)\times \$1000\right)=29.79\% $$

Using the ‘percentage of strike’ shortcut, the answer is the same because the spot and the strike are the same. But consider what happens if the strike is increased to 2100. The ‘percent of spot’ shortcut now gives the participation rate as: participation rate = (nominal amount − amount required for capital protection)/((option premium/spot index level) × nominal amount).

Inserting the relevant figures returns a value of:

($1000–$960.98)/(228/2000) × $1000) = 34.23 %which is the wrong answer! If, instead, the ‘percent of strike’ shortcut is used, the participation rate is: participation rate = nominal amount − amount required for capital protection)/(option premium/strike index level × nominal amount).

Using the relevant market data returns:

$$ \left(\$1000-\$960.98\right)/\left(\left(228/2100\right)\times \$1000\right)=35.94\% $$

which is the right answer.