Section 1.5

The universal building block

12 min

Essential question

The zero-coupon bond is the indispensable tool for guaranteeing the capital of a capital-guaranteed product. But it is also used in many other products. For what reasons?

ConstructionCapital guarantee and collateral

The zero-coupon bond is the indispensable tool for guaranteeing the capital of a capital-guaranteed product. Yet it is found in many other products, including products with no guarantee, where its function is different: it makes it possible to buy the underlying at the agreed price if the option is exercised, in a Reverse Convertible for instance. The zero-coupon bond therefore acts as collateral for the options sold, and makes it possible to honour the financial commitments if they are exercised.

Role 1 · Funding the options of a guaranteed product

A capital-guaranteed product is built in two steps. You set aside what is needed to return the capital, the zero-coupon bond, and you spend all the rest on options. That "rest" has a name: the balance available, also called the option budget.

Option budget = 100 − price of the zero-coupon bond

5-year ZC at 3.3% = 84.79 → that leaves 15.21% to buy the performance engine and pay the fees.

100 invested: an allocation to the zero-coupon bond, and the option budget into the risky asset to generate performance

Zero-coupon · 84.79

15.21

Guaranteeing the capital (returning 100 at maturity) Option budget: options + fees

These two blocks are complementary by construction: every percent gained on the price of the zero-coupon bond is one percent more for the engine. The structurer does not decide the size of the blue block: rates impose it.

The complete example, end to end

The capital to be guaranteed. 100% of the nominal at 5 years, issuer at 3.30% → the ZC costs 84.79.
The option budget. 100 − 84.79 = 15.21%.
The fees. A structuring commission of, say, 2% → that leaves 13.21% to spend on options.
The performance engine. A 5-year at-the-money call on the index costs about 18% (that is the subject of module 1B).
The participation. 13.21 ÷ 18 = 73%. The investor will receive 73% of the rise in the index, with a 100% capital guarantee at maturity from the issuer.

That figure of 73% is not a commercial decision. It is an arithmetic result. To raise it, there are only five levers: lengthen the maturity, accept a more expensive issuer, change currency, cut the structuring commission, or lower the guarantee level.

Worth keeping in mind

That 73% only means something set against the rates the issuer would have paid over the same period. So the only question that matters is this one: are we convinced that a 73% exposure to the risky asset will do better than those rates?

Whether the exposure shown is 10%, 73% or 200% is not what counts. What counts is the performance potential of the underlying, adjusted for the exposure on offer and set against rates. Offering 200% of the rise in an index sells better than 100%, but the level of rates and the volatility of the underlying alone determine what is achievable: a high participation is not necessarily a better deal.

This table gives the exposure to the risky asset by level of capital guarantee. Maturity 5 years, rate 3.30%, ATM call at 18%.
Redemption = zero-coupon bond + if the performance of the underlying is positive: participation × performance. The detailed workings will be covered in the chapter devoted to capital-guaranteed products.
Guarantee level	ZC price	Option budget	After 2% of fees	Participation
100%	84.79	15.21%	13.21%	73%
95%	80.55	19.45%	17.45%	97%
90%	76.31	23.69%	21.69%	120%
80%	67.83	32.17%	30.17%	168%

The same product, three periods: at 100% capital guaranteed, what exposure to an equity-index risky asset?

100% capital guaranteed at 5 years, on the same equity-index risky asset. **An identical product offered 107% of exposure in 2007, 3% in 2021 and 73% in 2024.** The structurer has not changed method; the level of rates has changed. For the sake of the exercise we assumed a similar option price (which was not the case).
Period	5-year rate + funding	ZC price	Budget	After fees	Exposure Risky asset
2007 · pre-crisis	4.8%	78.66	21.34%	19.34%	107%
2021 · rates at the floor	0.5%	97.53	2.47%	0.47%	3%
2024 · rates are back	3.3%	84.79	15.21%	13.21%	73%

Negative rates: when the budget turns negative

Between 2015 and 2021, 5-year rates in CHF and in EUR went below zero. At −0.40%, a 5-year zero-coupon bond does not cost 97, it costs 102.02: guaranteeing 100 at maturity costs more than 100 today.

The option budget turns negative. The investor would have to be charged for having their capital guaranteed. As a result, capital-guaranteed products disappeared from the offering.

The currency is not a detail: rates are different from one to another

The risk-free rate is the rate of the product's currency. Same underlying, same maturity, same issuer: three currencies, three budgets.

ATM call at 18%, 2% of fees. The option budget is **4.6 times** higher in USD than in CHF (18.13% against 3.92%); since the 2% of fees are taken out of that budget, the participation gap climbs to **eight times** (90% against 11%). That is the real reason why dollar products look more generous, and one then has to talk about the cost of hedging the currency (quanto), which takes back part of the gap.
The benchmark, however, remains the one we have been discussing since the previous module: the rate of the currency. In CHF, rates are lower, so the **rate to beat is lower**. A participation of 11% in CHF and of 90% in USD cannot be compared directly: each is judged against the rate of its own currency.
Currency	5-year rate	ZC price	Option budget	Participation
USD	4.0%	81.87	18.13%	90%
EUR	2.8%	86.94	13.06%	61%
CHF	0.8%	96.08	3.92%	11%

Role 2 · Acting as collateral for the options sold

There are several families of products whose capital is not guaranteed. They too, however, contain a zero-coupon component or something equivalent.

We will not describe how they work here, each will be the subject of a dedicated chapter. We limit ourselves to one question: what is the zero-coupon bond for in these products?

In these structures the investor does not buy an option, they sell one, typically a put. That sale can oblige them to buy the risky asset at an agreed price. For example, a product may commit the investor to buying share ABC at CHF 100 under certain conditions. To be sure that the investor can honour that commitment, those CHF 100 have to be available at the maturity of the product.

That is exactly what the zero-coupon bond makes possible. The capital invested is lent to the issuer, which keeps it for the whole life of the product and uses it as collateral. In this type of product the zero-coupon bond therefore no longer guarantees the investor's capital at maturity, but it does guarantee that the investor will be able to honour their commitment, namely to buy the underlying at the agreed price if the option is exercised.

That collateral is not a frozen asset for all that: it also earns part of the compensation paid to the investor. For the family of yield products, which pay coupons, the compensation comes from two sources: the premium of the put sold, and the return on the zero-coupon bond acting as collateral.

Again, the aim here is not to go into the detail of how the products work, but by way of introduction, here are three questions investors often ask about the coupon paid by yield products:

The coupon has two sources, not one. Part of it comes from the premium of the option sold, the other part comes from the zero-coupon bond, that is from the rate and the funding. An "8% coupon" is not 8% of option premium. This can have tax consequences in some countries. For Swiss residents for instance, only the part of the premium linked to interest rates is taxed.
The coupon has to be compared with the risk-free rate. A coupon of 8% when rates are at 0%, as they were between 2015 and 2021, does not have the same value as a coupon of 8% when rates are at 3%. In the first case, all of it comes from the option premium, and therefore from the risk taken on the underlying; in the second, a good part simply comes from the zero-coupon bond.
The commitment is 100% covered. The structured product fully covers the optional commitment taken by the investor. In other words, the investor cannot lose more than what was invested in the product.

Period	Rate leg (the ZC)	Premium of the put sold	Annual coupon	Share of the coupon coming from the ZC
2021	0.5%	4.5%	5.0%	10%
2024	3.3%	4.7%	8.0%	41%

Key message

In a product whose capital is guaranteed by the issuer at maturity, the zero-coupon bond returns the capital and its gap to par funds an exposure to the risky asset through options bought. In a product without a guarantee, it ties up the capital as collateral for the options sold and feeds part of the coupon in yield products. In both cases the "rate" component is an essential element in the construction of the structured product.

Mini-quiz · Section 1.5

5 diagnostic questions

~4 min · immediate feedback

Question 1 / 5

In a 100% capital-guaranteed product at 5 years, the zero-coupon bond costs 84.79% and the fees 2%. What do the remaining 13.21% represent?

Question 2 / 5

With a budget of 13.21% and an option at 18%, the participation comes out at 73%. How should that figure be read?

Question 3 / 5

An identical product offered 107% of exposure in 2007, 3% in 2021 and 73% in 2024, at an assumed unchanged option price. Which factor explains those gaps?

Question 4 / 5

In a product with no capital guarantee, where the investor sells a put, what is the zero-coupon bond for?

Question 5 / 5

A yield product shows a coupon of 8%. How should it be read?

0 / 5 answers

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