Reverse Convertible

A reverse convertible looks like a bond with an unusually generous coupon — say 8% a year when savings accounts pay 2%. The catch sits at maturity: if the linked stock has fallen below a set level, you don't get your money back. You get the shares instead, at their now-lower value.

So the deal is: heads, you collect a fat coupon and your capital back; tails, you collect the fat coupon and become a reluctant shareholder of a stock that just dropped. The coupon is paid in every scenario — it is the price the issuer pays you for taking on the stock's downside.

Where does the big coupon come from? You have, without necessarily realising it, sold a put option on the stock. The option premium is chopped up and handed back to you as interest. In Germany, where these notes are a retail staple, the name says it plainly: Aktienanleihe — "share bond".

The construction

A classic reverse convertible on stock \(S\) with strike \(K\) (usually the stock price at issue) decomposes exactly into two positions:

Redemption at maturity \(T\), with \(N\) the par amount and \(n = N/K\) the share count:

The barrier variant

Most modern issues are barrier reverse convertibles: shares are only delivered if the stock traded below a barrier \(B\) (say 70% of the initial price) during the note's life and finishes below the strike. The embedded option becomes a down-and-in put — cheaper than a vanilla put, so the coupon is smaller, but the investor keeps par through moderate declines. Swiss private banks issue these by the billion.

What drives the coupon

• Volatility: higher implied vol → richer put premium → bigger coupon. The juiciest coupons appear on the most dangerous stocks, exactly when they are most dangerous.
• Barrier level: a barrier at 80% pays more than one at 60% — you are insuring closer to the money.
• Dividends and rates: expected dividends raise put values (bigger coupon); higher rates raise the bond part's contribution.

Pricing and the volatility skew

Fair value is par minus the put the investor is short (rates aside):

where the put \(P\) is priced on the skew: equity index and single-stock smiles make downside strikes trade at implied vols several points above at-the-money. The issuer buys that put back cheaply through its structuring desk while the marketing materials quote the coupon as if vol were flat — the skew is a structural margin source. For barrier versions, the down-and-in put is priced with a local-vol or stochastic-vol model; barrier proximity makes vega and vanna (sensitivity of delta to vol) spike, which is what the issuer's book actually manages.

Why investors persistently buy them

The behavioural finance literature calls the pattern skewness-seeking in reverse: the note converts an uncertain equity distribution into a high probability of a visible gain (the coupon) and a low probability of a large, psychologically deferrable loss ("I'll just keep the shares"). Issuance data show volumes peak after calm markets — when coupons are lowest and the insurance sold is cheapest — and collapse after crashes, when selling puts would actually pay.

Risk anatomy

• Delta: near zero at issue for deep barriers, snapping toward 1 as the barrier approaches — the investor is increasingly "just long the stock" precisely as it falls.
• Issuer credit: the note is a senior unsecured claim; Lehman's reverse convertibles taught European retail that the "bond part" has a default risk of its own.
• Worst-of baskets: multi-underlying versions ("worst-of RC" on three stocks) pay even fatter coupons because the investor is short the minimum of correlated assets — a hidden short-correlation position that concentrates losses in crises, when correlations rise.

The formulas above are standard textbook formulations, simplified for teaching. They explain the mechanism — they are not a valuation tool, and they will not reproduce a dealer’s price.