What it means
A convertible bond contains an option over the issuer's shares, and options do not move in a straight line with the share price. The trader isolates that curvature by holding the bond and shorting enough shares to cancel out the first slice of any price move.
The number of shares to short comes from the delta, which measures how much the convertible's value changes for a small change in the share price. A delta of 0.60 means the bond captures about 60 cents of every dollar the shares move, so the trader shorts 60% of the shares the bond would convert into.
The profit comes from three places: the coupon on the bond, the interest earned on the cash raised by the short sale, and the gains from rebalancing the hedge as the share price moves around. Because the bond gains more when shares rise than it loses when they fall, active shares move in either direction can be turned into money.
The strategy is not risk free despite the name. Credit risk is the main danger, because a bond bought at $1,000 can fall a long way if the issuer's finances deteriorate, and no equity short position will cover that.
Practical frictions matter too. Shares must be borrowable at a sensible cost, the convertible must be liquid enough to exit, and the whole position usually runs on borrowed money, so a funding squeeze can force a sale at the worst possible moment.
In practice
Real-world examples.
Example
A hedge fund buys convertibles issued by a volatile technology company and shorts 55% of the underlying shares. Over six months the shares swing wildly but end roughly where they started, and the fund books a profit purely from rebalancing the hedge through each swing.
Example
A specialist desk takes a position in a mid-cap engineering convertible and adds a credit default swap to cover the issuer's default risk. The equity exposure is hedged with shares and the credit exposure with the swap, leaving the desk with a nearly pure bet on volatility.
Example
A fund is forced to close a convertible arbitrage position early when the borrow cost on the issuer's shares jumps because a rival is short-selling heavily. The trade was sound in theory but the cost of maintaining the short wiped out the expected return.
Formula
Calculation
Shares to short = Conversion ratio x Delta x Number of bonds held.
A fund buys 100 convertible bonds at $1,000 each, a total outlay of 100 x $1,000 = $100,000. Each bond converts into 25 shares, and the desk's model puts the delta at 0.60. The shares trade at $40.
Shares to short = 25 x 0.60 x 100 = 1,500 shares. Selling 1,500 shares short at $40 raises 1,500 x $40 = $60,000 in cash, which sits with the broker earning interest.
The shares then fall 10% to $36, a drop of $4. The short position gains 1,500 x $4 = $6,000. A straight-line estimate would put the bond's loss at 0.60 x 25 x $4 x 100 bonds = $6,000, exactly offsetting the short. In reality the convertible's delta falls as the shares drop, so the bond only declines to $972, a loss of $28 x 100 = $2,800.
Net result on the price move = $6,000 - $2,800 = $3,200, on top of the coupon income and the interest on the short proceeds. The trader would now reduce the short position to match the lower delta and wait for the next move.Case study
Seen in the real world.
This is an illustrative case study about a fictional firm. Aldergate Capital, an invented hedge fund, ran a convertible arbitrage book of $200,000,000 across two dozen issuers, hedging each position with a delta-weighted short in the underlying shares. For two calm years the strategy delivered steady mid single-digit returns from coupons and rebalancing.
A credit shock then hit the market. Convertible prices fell far more than the equity hedges gained, because investors were pricing in default risk rather than share price moves, and Aldergate's supposedly market-neutral book lost money on both sides at once. Its lenders cut leverage at the same time, forcing sales into a market with almost no buyers.
Aldergate survived by cutting the book in half and adding credit protection to its remaining positions. The lesson from this fictional example is that convertible arbitrage hedges equity risk well and credit risk not at all, unless you pay separately for that cover.
Watch out
Common mistakes.
- Believing the word arbitrage means the trade is risk free. Credit deterioration, funding withdrawal and share borrow costs can all cause serious losses even when the equity hedge works exactly as designed.
- Setting the hedge once and leaving it. Delta changes constantly as the share price moves, so a static hedge slowly turns into an unintended directional bet.
- Ignoring the cost and availability of borrowing shares. If the borrow is expensive or gets recalled, the short leg cannot be maintained and the whole structure of the trade falls apart.
Questions
People also ask.
Who actually runs this strategy?
Almost entirely hedge funds, bank trading desks and a small number of specialist funds, because it needs leverage, short selling and constant monitoring.
Where does the return really come from?
Mainly from the coupon, the interest on short sale proceeds, and gains from rebalancing the hedge as the shares move, rather than from any single directional view.
Does the strategy work better in calm or volatile markets?
Volatile but orderly markets suit it best, since frequent share price moves create rebalancing profits, while disorderly credit-driven selloffs are the worst environment for it.
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