# Chapter 13 (Barrier) Reverse Convertibles

## 13.1 Reverse Convertibles

Reverse Convertibles are among the most popular yield enhancement products in Switzerland and are suited for investors who are anticipating a sideways or slightly upward trending market.

The holder of a reverse convertible gives up the potential upside exposure to the underlying asset in exchange for an enhanced coupon. The holder of the product remains exposed to the downside exposure.

The enhanced coupon of the reverse convertible is paid in any case. Because of this, the product will always outperform its underlying asset to the downside. The product will also outperform if the asset does not rise by more than the coupon. Hence, the ideal market scenario for reverse convertibles is the prospect of a sideways trending market.

### 13.1.1 Payoff

In its most basic form, the reverse convertible is constructed by means of a short put and a money-market placement. In most cases, the strike is placed ATM. Obviously, the lower the strike, the lower the value of the put option and the lower the guaranteed coupon.

The below graph shows the payoff of a 1y reverse convertible with a ATM Put and a guaranteed coupon of 10.5%.

The price of this reverse convertible is 99.81%, which is composed of:

- Long 1y Zero-Coupon Bond: 98.02% (assuming 2% interest rate for the sake of the example).
- Short 1y ATM put option: 8.50% (assuming 20% implied volatility and 3.5% of dividends).
- Guaranteed coupon: 10.5% paid at maturity –> PV(10.5%) = 10.29%.

Let us assume that the 19 bps left (100% - 99.81%) are earned by the bank as a commission.

### 13.1.2 Risk Analysis

As you can see, there is no discontinuity in a reverse convertible because the coupon is not conditional. The risk analysis is therefore similar as a short put and very straightforward. The relative size of the coupon with respect to the risk-free rate of the product maturity will give you an idea of the risk of the product. The higher this difference, the more valuable the put, the riskier the product!

Since an investor buying this reverse convertible is selling a put option, he is selling volatility and should therefore invest when volatility is high or expected to fall.

The holder of a Reverse Convertible will incur a loss if the loss of the sold put option is larger than the sum of the guaranteed coupons received.

## 13.2 Barrier Reverse Convertibles

Barrier Reverse Convertibles (BRC) are a special variant of the classical Reverse Convertibles.

The holder of a barrier reverse convertible gives up the potential upside exposure to the underlying asset in exchange for an enhanced coupon. The holder of the product is not exposed to the downside exposure, unless the underlying asset breaks through a predefined barrier set at the inception of the product.

The enhanced coupon of the barrier reverse convertible is paid in any case. Because of this, the product will always outperform its underlying asset to the downside. The product will also outperform if the asset does not rise by more than the coupon. Hence, the ideal market scenario for reverse convertibles is the prospect of a sideways trending market. All else remaining equal, a BRC pays a lower coupon than a reverse convertible, because of the conditional capital protection provided by the barrier.

### 13.2.1 Payoff

The barrier reverse convertible is constructed by means of a short Down-and-In put and a money-market placement. In most cases, the strike is placed ATM but more conservative versions placed it OTM. The barrier is usually ranging between 50% to 80% of the spot price. Obviously, the lower the barrier and the strike, the lower the value of the put option and the lower the guaranteed coupon.

As long as the underlying asset does not cross the barrier, the BRC remains capital protected. Once a barrier breach occurs, the capital protection is lost, and the BRC transforms itself in a classic reverse convertible.

The below graph shows the payoff of a 1y reverse convertible with a ATM 80% Down-and-In Put and a guaranteed coupon of 8.4%.

The price of this barrier reverse convertible is 99.76%, which is composed of:

- Long 1y Zero-Coupon Bond: 98.02% (assuming 2% interest rate for the sake of the example).
- Short 1y ATM 80% DIP: 6.50% (assuming 20% implied volatility and 3.5% of dividends).
- Guaranteed coupon: 8.4% paid at maturity –> PV(8.4%) = 8.23%.

Let us assume that the 24 bps left (100% - 99.76%) are earned by the bank as a commission.

### 13.2.2 Risk Analysis

Since the coupon is guaranteed, it does not bring additional risk. The risk analysis is therefore similar as a short Down-and-In put and is quite straightforward if you read **chapter 12**.