What it means
A convertible bond is really two instruments bundled together: an ordinary bond paying interest, and a call option letting the holder exchange it for shares. Because the two parts are sold as one package, the combined price sometimes sits below the value of the parts added up separately.
The arbitrageur buys the bond and then short sells shares to neutralise the equity exposure, keeping only the pieces they actually want: the interest, the volatility in the option, and any mispricing in the package. The number of shares to short is set by the hedge ratio rather than guessed.
That hedge ratio comes from delta, the sensitivity of the convertible's price to a $1 move in the share, multiplied by the conversion ratio, which is how many shares each bond converts into. Delta changes as the share price moves, so the hedge has to be adjusted regularly, a process called rebalancing.
Rebalancing is where much of the profit comes from. If the share price swings around, the trader sells more shares short as the price rises and buys some back as it falls, which mechanically banks small gains; more share price volatility therefore means more profit, which is why the strategy is described as being long volatility.
The risks are real and are mostly not about share prices. Credit risk is the big one, because if the issuer's finances deteriorate the bond falls in value while the short position may not gain enough to compensate, and liquidity risk bites when convertibles become hard to sell at any sensible price.
For a business, the relevance runs the other way. Companies issuing convertible bonds should understand that a large share of the buyers are arbitrage funds who will short the shares immediately, which typically puts short term pressure on the share price but also creates the demand that makes the low coupon possible.
In practice
Real-world examples.
Example
A hedge fund buys a five year convertible issued by a mid sized biotechnology company and shorts 55% of the underlying shares. The share price halves after a trial disappointment, but the short gain and the bond's remaining value as debt leave the fund with a small profit.
Example
A convertible fund holds a position in an engineering group whose shares swing between $28 and $36 for several months. Each rebalancing trade banks a small gain, and the accumulated rebalancing profit exceeds the coupon income for the year.
Example
A listed company issues $200,000,000 of convertible bonds at a 1.5% coupon, far below the rate on its ordinary debt. Its shares drop 4% in the week of issue as arbitrage buyers establish their short hedges, and the finance director had budgeted for exactly that reaction.
Think of it
“Convertible arbitrage profits from convertible bonds being mispriced relative to the stock they convert into.
Formula
Calculation
Shares to short per bond = delta x conversion ratio
A fund buys 1,000 convertible bonds at par with a face value of $1,000 each, so $1,000,000 in total, paying a 3% coupon. Each bond converts into 20 shares, and the current delta is 0.6, so the hedge is 0.6 x 20 = 12 shares short per bond, or 12,000 shares in total. With the share trading at $45, the short position raises 12,000 x $45 = $540,000.
Suppose the share price falls to $40. The short position gains 12,000 x $5 = $60,000. The convertible loses roughly delta x conversion ratio x the price move, which is 0.6 x 20 x $5 = $60 per bond, or $60,000 across 1,000 bonds. The two offset almost exactly, leaving the position close to flat on the share move.
Meanwhile the fund keeps the coupon of 3% x $1,000,000 = $30,000 a year, plus interest earned on the short sale proceeds. The offset is only approximate, because delta shifts as the share price moves, which is exactly why the position must be rebalanced.Case study
Seen in the real world.
This is a fictional and illustrative example. Calder Point Capital, an invented convertible arbitrage fund, ran a portfolio of forty positions and reported steady returns of about 8% a year for six years with very small monthly swings. Its investors began describing the strategy as low risk.
Then a credit shock hit. Convertible bonds fell far more than their equity hedges gained, because buyers disappeared and prices were marked on where dealers would actually trade rather than on any model.
Calder Point, which had used three times leverage to amplify its modest gross returns, faced margin calls and was forced to sell positions into a market with almost no bidders. The fund lost 26% in a single quarter.
The illustrative lesson is not that the strategy was unsound; the surviving positions largely recovered over the following two years. It is that a strategy hedged against share price movement was never hedged against credit and liquidity, and that leverage turned a difficult quarter into a permanent loss for investors who redeemed at the bottom.
Watch out
Common mistakes.
- Describing convertible arbitrage as risk free because the equity exposure is hedged, when credit, liquidity and financing risks remain fully in place.
- Setting the hedge once and leaving it, when delta changes continuously and an unadjusted hedge quickly stops offsetting the share position.
- Judging the strategy on gross return without accounting for the leverage used to produce it, which hides how much risk is actually being taken.
Questions
People also ask.
Why do convertible issuers accept arbitrage funds as buyers?
Because those funds create reliable demand that allows the company to borrow at a much lower coupon than on ordinary debt, in exchange for some short term share price pressure.
What does being long volatility mean here?
It means the position profits when the share price moves a lot in either direction, since larger swings produce more rebalancing gains and raise the value of the embedded option.
Can a private investor run this strategy?
Realistically no, because it needs the ability to short shares cheaply, access to convertible bond pricing and inventory, and financing arrangements that individuals cannot obtain.
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