Convertible Bond Arbitrage

What this topic is

Convertible bond arbitrage is a relative value strategy. You buy a convertible bond, which is a corporate bond with an embedded call option on the issuer's stock, and short the number of shares that neutralises the position's first-order sensitivity to the stock price. What remains is a position that is long volatility, long or short credit depending on how you hedge it, and exposed to the cost and availability of funding and stock borrow.

Why it matters

Convertible issuance is one of the largest sources of primary market volatility supply. Issuers sell options embedded in bonds because it lets them borrow cheaply, and they are not primarily option sellers, so the embedded options have historically been issued below the price a pure options market would set. Hedged buyers capture that difference. The strategy also teaches something more general than itself: how to decompose an instrument into its parts, hedge the part you do not want, and be honest about the residual risks you cannot hedge.

Who should learn it

Credit and equity derivatives practitioners, multi-strategy and relative-value fund analysts, corporate treasurers and CFOs deciding whether to issue a convertible, and anyone who wants to see option theory applied to a live instrument with real financing constraints.

What you will understand

• How to decompose a convertible into a bond floor plus an equity option, and compute the hedge ratio
• Where the return actually comes from: cheapness, gamma, carry, and how each is measured
• Why credit is the risk that turns a well-hedged book into a loss, with a worked scenario
• The structural features - soft calls, make-whole tables, dividend protection, capped calls - that decide whether the theoretical trade survives contact with the document

Prerequisites

• Game Theory at the Negotiating Table
• Sources and Uses

Common misconception

The word arbitrage is doing a lot of unearned work. There is no riskless profit here and never was. A delta-hedged convertible is short nothing and long several things at once: the issuer's credit, the availability of stock borrow, the level of financing rates, and the difference between the volatility the market implied and the volatility the stock actually delivers. In the worked example in this lesson, a well-constructed hedge produces about $7 of gain on a 20% fall in the stock if credit is unchanged - and a loss of about $71 on the same stock move if the issuer's credit spread widens by 250 basis points at the same time. Since equity falls and credit widens together, that correlation is not a tail event. It is the ordinary case.