## Multi Bonus Certificates

Multi bonus certificates are identical structures to bonus certificates, except that they are based upon several underlying assets and that the payoff is based upon the worst performing one. The name is somewhat misleading, as it suggests that the product is based on a basket, hence we will call them for what they are henceforth: worst-of bonus certificates. Indeed, an embedded worst-of option makes sure that if only one of the included assets breaks through the predefined barrier, the protection as well as the bonus are disabled.

###### Payoff

The issue price of the worst-of bonus certificate is most of the time equal to 100% of the weighted average price of the underlying assets. As long as the barrier is not breached, the redemption at maturity will be the greater of

- the bonus
- the weighted average performance of the basket

However, if the barrier has been breached anytime during the life of the product by at least one underlying asset (in case of an American style barrier, which is the most commonly used barrier type), the bonus and the protection disappear and the redemption at maturity will be based on the worst performing asset.

It is not possible to correctly represent the payoff diagram of a worst-of bonus certificate, unless the upside participation is also based on the worst-performing asset (which is not a common product, but a variant as explained below). To the right is represented the payoff of a classical bonus certificate.

It is worthwhile to note that while one asset can break through the barrier, it is by no means sure that the payoff at maturity will be based on that particular asset, as it could recover between the moment of the barrier breakthrough and the maturity, while another asset declines to below the original spot price. Once the barrier is broken, no matter which asset breaks it, the payoff at maturity will be based on the worst-performer.

###### Numerical example

Consider the following structure:

- Underlying assets: BASF, Total, Generali Assicuranzi (weighted 33.33% each)
- Currency: EUR
- Maturity: 12 months
- Monitoring: continuous (=American style barrier)
- Bonus: 110%
- Barrier: 60% of spot
- Participation: 100% of the basket
- Issue price: 100% of weighted average spot

At maturity:

- Scenario 1: if none of of the three stocks ever crossed the barrier, the product is redeemed in cash at the greater of 110% or the weighted performance of the basket (Basket
_{Final}/ Basket_{Initial}). - Scenario 2: if at least one of the three stocks ever crossed the barrier, the product is redeemed in the shares of the worst performing stock (Asset(i)
_{Final}/ Asset(i)_{Initial}).

###### Variants

Note that the formulation of the payoff at maturity may vary according to each issuer. In particular, several variants are common:

- Redemption of the product in cash even in case a barrier breach occurred.
- Upside participation based on the worst-performing stock even if no barrier has been breached (makes the product more attractive, as either the bonus level or the barrier can be ameliorated).
- Redemption based on the basket even if a stock has breached the barrier (fairly uncommon; makes the product look less attractive).
- All other classical bonus certificates variants apply as well (capped bonus certificate, bonus certificate with European barrier style (observed only at maturity), etc.)

In practice (particularly in Germany), multi bonus certificates are often based on several stocks, but in theory, all kind of assets can serve as underlying : indices, commodities, interest rates etc.

###### Correlation

In addition to the implied dividend yield, the imperfect correlation between the assets is used to generate the bonus and the barrier. Correlation is a statistical measure quantifying how much two assets move in relation to each other. The maximum correlation between two assets is 100% , or +1. The minimum is -100% or .-1. If the correlation is high (close to +1), then if one asset rises, the other rises by more or less the same amount; the also tend to fall together. if it is low, then they move independently (correlation close to zero). If the correlation is negative, then, if one rises the other falls (correlation close to -1). The lower the correlation, the higher the value for the investor and the better the bonus certificate will look.

The correlation is sold by the investor, which means that a concentration of risk on one of the included underlying assets occurs. This makes portfolio management more difficult, as it is not possible to know beforehand on which asset the final payoff will be based.

Useful to know as well is that the extracted correlation value of each additional asset diminishes (because of the cross-correlations). Hence, it is seldom advisable to invest in worst-of bonus certificates with more than two assets. In any case, avoid those with more than three assets.

###### Do's and don'ts

- Do invest in a worst-of bonus certificate if the correlation is low and expected to increase,
*without*either asset expected to fall by more than the barrier. - Do invest in a worst-of bonus certificate to either ameliorate the barrier or reduce the maturity. remember that the bonus mechanism does not "grip" until nearly three quarters of the lifetime of the product are over.
- Don't invest in a (worst-of) bonus certificate with more than three underlying assets.
- Don't invest in a worst-of bonus certificate with a maturity over two years. Stay preferably under 18 months.