Warrants, turbos and certificates: what they are and what you pay on top

In depth12 min read · 15 sources

Warrants, turbos and certificates are debt securities issued by a bank whose payout is linked to an underlying. Almost every one of these products can be broken down into two basic building blocks: a bond of the issuer and one or more options. Valuing the building blocks separately shows what a product is fairly worth and how much you pay on top through margin, spread, volatility, financing and dividends. With recalculated examples and the state of research.

The principle: an issuer bond plus options

Legally, a certificate is a bearer bond: the issuer pays according to a formula that depends on the underlying. This formula can be replicated, using a bond of the issuer and options that the issuer sells to you or you sell to the issuer. It follows that:

The industry association BSW (German Structured Securities Association) divides the market into investment products with 100% capital protection, investment products without capital protection, and leverage products such as warrants, knock-out warrants and factor warrants (BSW 2024). For valuation, the breakdown is what counts: if you are the writer, you sell volatility in return for a discount or coupon; if you buy options, you pay time value.

Warrants: conversion ratio, premium, leverage and omega

A warrant is an option securitised by a bank. The issuer is itself the writer, continuously quotes bid and ask prices (market making) and hedges itself in the market. The conversion ratio states how many units of the underlying one warrant refers to. Three metrics help with comparisons:

• Premium: for a call, (strike + price / conversion ratio − share price) / share price. This is the rise the underlying needs by expiry for you to break even.
• Leverage: share price × conversion ratio / price.
• Omega (effective leverage): delta × leverage, the change in percent per 1% change in the share price. It corresponds to the lambda among the Greeks.

The spreads on bank-issued warrants are often tighter than on the futures and options exchange (Bartram et al. (2008), see below). But a tight spread does not mean a warrant is cheap: the margin lies in the level of the prices, not in the gap between them.

Turbos and mini futures: knock-out, financing, gap risk

A turbo certificate, called a knock-out warrant by the industry association, tracks the underlying minus a loan: a long turbo is worth roughly (share price − strike) × conversion ratio. If the price touches the knock-out barrier, it expires. In option theory this is a down-and-out call with the barrier at the strike (a formula for down-and-out options was already derived by Merton (1973)); without interest it is worth exactly the share price minus the strike, regardless of volatility, with no time value and a delta of one. With an open-end turbo, which has no fixed term, the issuer shifts the strike daily; that is how you pay for the loan:

On top of this comes gap risk: if the index opens at 17,800 after a weekend, the turbo is worthless, even though the index has only lost 11%. With a mini future with a stop-loss at 18,300, the issuer pays a residual value after it is triggered; if the position is unwound at 18,250, roughly (18,250 − 18,000) × 0.01 = €2.50; if the price jumps below the strike, nothing remains here either.

Factor certificates (called factor warrants by the industry association), on the other hand, keep the leverage constant and adjust it daily like a leveraged ETF; many also reset it intraday after sharp moves. They lose in sideways markets through volatility decay and charge financing costs and fees.

Investment certificates: discount, bonus, reverse convertible, express, capital protection

With most investment certificates you are the writer: you give up upside or dividends in return for a discount or coupon. The simplest example is the discount certificate.

With a bonus certificate, by contrast, you buy an option: the share without dividends is combined with a down-and-out put with the strike at the bonus level. With a bonus level of €120, a barrier of €75 and otherwise the same assumptions, the put is worth €10.63 in the barrier model; the fair value is 97.04 + 10.63 = €107.67. The dividends of just under €3 pay for only part of the bonus protection; with a cap, you additionally sell a call and the price falls.

With a reverse convertible, you sell the issuer a put: if the share closes below the strike, you receive shares instead of cash. With a nominal value of €1,000, a strike of €90 and otherwise the same assumptions: the put on 11.11 shares is worth €60.66, and a fair coupon would be 8.21%. If the issuer offers 7.00%, it keeps €11.85 per €1,000, or 1.20%. This advertised coupon, the “headline rate”, is the subject of Célérier and Vallée (2017).

An express certificate (autocallable) is redeemed early with a coupon if the underlying is above a threshold on an observation date. At maturity a barrier protects you; below it, you bear the price loss. Broken down: a bond plus digital calls (the coupons) minus a down-and-in put; because the term depends on the price path, valuation requires simulation or trees. With a capital protection certificate, it is the other way round: a zero-coupon bond of the issuer secures the nominal value, and the rest buys a call. At a 2% interest rate and five years, the zero-coupon bond costs €905.73 per €1,000; that leaves €94.27 for the call and the margin. The lower the interest rate, the less call you get. What is more, the protection only holds as long as the issuer pays.

What you pay on top: the cost components

• Issuer margin: the mark-up on the fair value, hidden in the issue or ask price.
• Spread (bid-ask spread): often just one cent, but relative to the price it weighs more the cheaper the warrant, and it applies on every trade.
• Volatility above or below the market: if you buy options (warrant, bonus, capital protection), the margin lies in an implied volatility that is too high; if you sell them (discount, reverse convertible, express), in one that is too low. Compare with exchange-traded options (volatility).
• Financing spread: for turbos, the mark-up on the money market rate; for factor certificates, financing costs and fees. The longer you hold, the more expensive it gets.
• Dividends: discount and bonus certificates pay none; what is priced in is the dividend the issuer expects. For turbos on shares, the issuer adjusts the strike. Whether gross or net is stated in the product terms.
• Credit risk: the fair value depends on the issuer's credit spread (see issuer risk and CVA).

For advanced readers: fair values, barriers and the life cycle

Three subtleties: first, barriers depend on the volatility near the barrier, not at the strike: with a volatility smile like that of equity indices, a down-and-in put far below the current price is more expensive than a flat volatility suggests. The writer of an express certificate then receives too little. Second, many barriers only apply to the closing price; the correction by Broadie et al. (1997) shifts them for calculation purposes. Third, the issuer is usually the only dealer in its product and steers its prices over the term.

This leads to the life cycle hypothesis, which goes back to Stoimenov and Wilkens (2005): at first investors buy, towards the end they sell back. The issuer therefore charges high mark-ups early on and low ones later; Wilkens et al. (2003) found such an effect. The discount example shows how sensitive the fair value is: if you calculate with 23% instead of 25% volatility, it rises to €83.44, and the margin shrinks to 0.68%.

What the research shows

• Wilkens et al. (2003) compared reverse convertibles and discount certificates on the DAX and NEMAX with their replication from Eurex options: almost all traded at a clear premium; its size differed by issuer and depended on moneyness and remaining term.
• Baule et al. (2008) took the banks' credit risk into account and found rather low overall margins for discount certificates in the secondary market, a substantial part of which is attributable to credit risk.
• Entrop et al. (2009): for open-end turbos, the announced adjustment formula strongly favours the issuer, even allowing for credit and jump risk. Baule and Blonski (2015): among similar warrants, investors choose the one with the lower margin, but they do not react to the general level of margins.
• Bartram et al. (2008): bank-issued warrants on the EUWAX had tighter spreads than comparable Eurex options. There, market makers have to protect themselves against better-informed traders; this adverse selection accounts for at least half of the spread.
• Henderson and Pearson (2011) examined 64 issues of a popular US structured product: the issue prices were on average almost 8% above the fair value from option models, and the expected return was slightly below zero. This is consistent with the hypothesis that issuers exploit complexity at the expense of poorly informed investors.
• Célérier and Vallée (2017) analysed the payout formulas of 55,000 retail structured products in Europe from 2002 to 2010: as interest rates fell, the headline rates, i.e. the advertised best-case returns, moved away from the interest rate level, and the products became more complex, riskier and more profitable for the distributing banks.

Regulation: key information document and product intervention

For packaged retail investment products, which include certificates and warrants, a key information document (KID) is mandatory. It contains a summary risk indicator, scenarios and the costs in euros and percent (PRIIPs Regulation 2014). The investment firm must also state all costs to you as an amount and a percentage, and afterwards annually as well (European Commission 2017). Compare them with your own calculation.

For the riskiest products, the supervisors intervened: in 2017, BaFin issued a general administrative order prohibiting the offer of CFDs with an obligation to make additional payments to retail clients (BaFin 2017). In 2018, ESMA decided on a ban on binary options for retail investors and, for CFDs, leverage limits of 30:1 to 2:1, a close-out at 50% of the minimum margin, negative balance protection (the account cannot go into the red) and a risk warning; according to ESMA, 74 to 89% of retail accounts lose money (ESMA 2018). This did not affect warrants and turbos, because with them the loss is limited to the stake.

Limits and common mistakes

• Confusing leverage with omega: the simple leverage of a warrant overstates the effect; what matters is the delta.
• Mistaking a discount for safety: discount and coupon are premiums for options you have sold. If the share falls sharply, you lose almost as much as with the share itself.
• Misunderstanding a barrier as a stop-loss: price jumps make turbos expire with no residual value; a bonus certificate that hits the barrier loses the bonus for good.
• Forgetting issuer risk: all these products are debt securities; if the bank defaults, you face a total loss, even with capital protection.
• Taking the model value as the truth: two volatility points shift the fair value in the example by more than half the margin.

This article is not investment advice and recommends neither issuers nor individual products.

How Portfolio Lab calculates it

The option pricer values the building blocks: European calls and puts with Black-Scholes-Merton and a continuous dividend yield, barrier options in closed form according to Reiner and Rubinstein (continuous or with a correction for discrete monitoring), digital options and the implied volatility for a given price (for a warrant, using the price per unit of the underlying, i.e. price / conversion ratio). Under Strategies you combine up to eight legs: a discount certificate is a call with a strike close to zero (the share without dividends) minus a call at the cap; the underlying itself as a leg would include the dividends. Details: option pricer methodology.

Not modelled are the issuer's default risk (you calculate the discount e^(−s × T) yourself), autocallables with several observation dates and the strike adjustment of open-end turbos. You can replicate daily adjusted leverage as in factor certificates in the Backtest using leverage per security (see leverage in a portfolio).

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.