Convertible Arbitrage Hedges Away the Stock and Keeps the Rest
A convertible bond contains an embedded equity option. The strategy separates them, hedging away the stock exposure to isolate what the option was really worth.
What Is Being Separated
A convertible bond is debt that can be converted into a defined number of shares. It therefore contains two things: a bond, and a call option on the issuer equity.
Issuers sell convertibles because the embedded option lets them pay a lower coupon than straight debt would require. The buyer accepts less income in exchange for equity upside.
Convertible arbitrage buys the bond and shorts the underlying shares in the amount implied by the option delta, which removes the equity direction exposure and leaves the rest.
What remains after hedging the stock is a position in the credit and the volatility. The strategy is a bet that those two were priced too cheaply inside the convertible.
Why the Opportunity Exists
Convertibles are frequently issued cheaply relative to the value of their components.
The reason is structural rather than mysterious. Issuers want the deal completed and priced attractively enough to sell quickly. Many natural buyers of straight bonds do not want equity exposure and many equity investors do not want a bond, so the pool of buyers for the combined instrument is narrower than for either part.
Arbitrageurs are the buyers who can take the whole instrument and hedge away the part they do not want, which is why they are a substantial share of the primary market for new issues.
Where the Returns Come From
| Source | Detail |
|---|---|
| Cheapness at issue | Instrument priced below component value |
| Gamma trading | Rebalancing the hedge as the stock moves |
| Coupon income | Bond pays while held |
| Short rebate | Interest on short sale proceeds |
| Credit spread narrowing | If the issuer improves |
Gamma trading is the part that resembles the options material. Because the hedge ratio changes as the stock moves, the arbitrageur sells shares as the stock rises and buys as it falls, capturing small profits on the rebalancing. A more volatile stock produces more of these, which is why the strategy is long volatility.
The Financing Dependency
The strategy is leveraged, because the returns on unlevered capital are modest. That leverage is provided by prime brokers against the convertible bonds as collateral.
This is the critical vulnerability. When financing conditions tighten, haircuts on convertible collateral widen and leverage must be reduced, which means selling convertibles.
Because the same participants hold similar positions, everyone sells at once into a market with few natural buyers, and prices fall well below any reasonable estimate of component value.
The 2008 Demonstration
The strategy suffered severe losses in 2008, and the cause was not the analysis being wrong.
Prime broker financing contracted, short selling of financial stocks was temporarily banned in several jurisdictions, which broke the hedge for issuers in that sector, and forced deleveraging drove convertible prices to levels implying implausible credit assumptions.
Positions were, on the analysis, extraordinarily cheap. Many funds could not hold them, because the financing had gone. The instruments largely recovered in 2009, which benefited whoever was still there.
It is a clean illustration that a correct valuation is insufficient if the position cannot be maintained.
What to Assess
The credit quality of the issuer, since the bond floor is what limits downside and a deteriorating issuer removes it. The implied volatility embedded in the convertible against comparable listed options. Borrow availability and cost on the underlying, since the hedge requires shorting. And the terms of the financing arrangement, which determine whether the position can be held through stress.
The Bottom Line
Convertible arbitrage buys a convertible bond, shorts the stock to remove direction, and holds the resulting exposure to credit and volatility, which issuers frequently sell too cheaply. Returns come from that cheapness plus gamma rebalancing. The strategy depends entirely on leverage remaining available, and 2008 showed that correct valuations do not survive a financing withdrawal.