In the first quarter of 2005, investors pulled more than 20% of the capital in convertible arbitrage hedge funds. The funds sold bonds to pay them, prices fell below their model values, and losses triggered more redemptions. Three years later the same strategy lost far more when its funding vanished: the investable HFRX convertible arbitrage index fell 58% in 2008, nearly all of it between September and November (NBER, 2007; NBER, 2010). Both episodes trace to the same design: a well-hedged position with little risk per dollar, run with a lot of borrowed dollars. If delta and gamma are new to you, start with delta hedging explained.
What is convertible arbitrage?
Convertible arbitrage is a hedge fund strategy that buys a company’s convertible bonds and sells its stock short, in an amount set by the bond’s sensitivity to the stock, to profit from mispriced optionality, income and volatility rather than from the stock’s direction.
A convertible security, in the SEC’s plain definition, is usually a bond or preferred stock that can be converted into a different security, typically the issuer’s common stock (Investor.gov). FINRA lists convertibles as one class of corporate bond (FINRA). In conventional deals the conversion formula is fixed. The SEC warns that less conventional, market-price-based formulas can protect the convertible holder at the expense of common shareholders through dilution; arbitrage funds mostly trade the conventional kind.
Convertible arbitrage sits in the relative-value family alongside statistical arbitrage, and many of today’s convertible books live inside multi-strategy funds.
How is a convertible bond priced?
A convertible is worth roughly its value as a straight bond (the bond floor) plus the value of a call option on the issuer’s shares, and never less than its conversion value, the number of shares it converts into times the stock price.
Take a hypothetical $1,000 bond maturing in five years with a 1% coupon, convertible into 20 shares, a conversion price of $50. Discounted at a 6% credit-adjusted yield, the coupons and principal are worth about $789: the bond floor. The embedded option is worth 20 calls struck at $50. With the stock at $40, the model prices the bond at about $1,009, a 26% premium to its $800 conversion value.
The curve has three zones. When the stock collapses, the bond is “busted”: the option is nearly worthless and the bond trades on credit, so the floor itself sags as default risk rises. When the stock soars, the bond behaves like stock and its delta approaches the full 20 shares. In the middle, the hybrid zone, the bond’s sensitivity to the stock changes fastest. That middle zone is where arbitrageurs like to be.
How does the delta hedge work?
The arbitrageur shorts the number of shares that matches the bond’s delta, so a small rise or fall in the stock produces equal and opposite moves in the bond and the short.
In the example the model delta at $40 is about 14.6 shares per bond, or 0.73 of the 20 conversion shares. A fund buying 100 bonds ($100,000 face) would short about 1,460 shares. If the stock ticks up $1, the bonds gain about $1,460 and the short loses about the same. The fund now earns three streams of carry: the bond’s coupon, interest on the cash from the short sale (the short rebate), minus the fee to borrow the shares and any dividends owed on them. The delta hedging guide shows the same mechanics for listed options.
| Component | How it is earned or paid | Direction |
|---|---|---|
| Coupon | 1% of face, paid by the issuer | Earned |
| Short rebate | Interest on the short-sale proceeds held by the broker | Earned |
| Borrow fee | Cost of borrowing the shares; rises if the stock is hard to borrow | Paid |
| Dividends on the short | Any dividend the issuer pays on the shorted shares | Paid |
| Financing | Interest on money borrowed to buy the bonds | Paid |
When borrow is tight, the fee can swallow the carry; our guide to stock borrow fees explains why.
What is gamma trading in convertibles?
Gamma trading is rebalancing the short stock hedge as the bond’s delta changes, which mechanically sells stock after rallies and buys it back after declines, and makes money when the stock moves more than the volatility priced into the bond.
Because the bond’s delta rises as the stock rises, a hedge sized at $40 is too small at $50 and too big at $30. In both cases the bond has done better than the short assumed. In the model, an instant drop to $30 leaves the hedged position up about $9 per bond, and a jump to $60 leaves it up about $29, while the unhedged bond would have lost about $137 at $30. Rebalancing locks those gains in: short more after the rally, cover after the fall. That is being long gamma, the same property that makes a long option position profitable in a volatile market. The bill comes as time decay: if the stock sits still, the option inside the bond loses value and the carry has to cover it. Our explainer on gamma covers the trade-off.
A hedged convertible is a bet that the stock will move more than the bond’s implied volatility says, financed by carry. Compare the volatility implied in the bond with the stock’s listed options and its realized volatility; see the implied volatility guide. If the bond’s implied volatility is above both, the optionality is not cheap.
Which risks does the hedge leave behind?
The stock hedge removes directional equity risk for small moves, and leaves credit, volatility, interest-rate, borrow, liquidity and funding risk in the position.
- Credit. If the issuer’s credit weakens, the bond floor falls. A credit default swap or a short position in the company’s straight bonds can hedge it, at a cost.
- Volatility (vega). The fund is long the option inside the bond, so it loses if implied volatility falls.
- Interest rates. The bond floor has duration; rising rates lower it. Some funds short Treasury futures against it.
- Borrow and recall. If the lender recalls the shares or the fee spikes, the hedge becomes expensive or impossible.
- Liquidity and funding. Convertibles trade less often than stocks, and leverage depends on prime brokers. This is the risk that dominated 2005 and 2008.
Mitchell and Pulvino report that leverage, measured as the long market value of convertibles divided by a fund’s net assets, of 4 to 6 times was considered normal before 2008, and up to 20 times for very high-delta bonds. Hedged positions with low risk per dollar invite leverage, which is why the strategy belongs in any discussion of gross vs net exposure.
What happened to convertible arbitrage in 2005?
In 2005 the strategy suffered a redemption-driven sell-off: investors withdrew capital, funds sold bonds to meet redemptions, bonds cheapened, and losses fed more redemptions.
According to Mitchell, Pedersen and Pulvino, more than 20% of capital was redeemed from convertible arbitrage funds in the first quarter of 2005, citing the Barclay Group. A sample of 28 specialist funds had sold 35% of their convertible holdings by the end of 2005, and assets managed by convertible arbitrage funds had fallen by half by the first quarter of 2006. Bonds traded at a median discount to theoretical value of up to 2.7% in mid-May 2005, and the discount peaked around investor redemption-notice deadlines. Convertible hedge funds returned −7.2% from January to May 2005, roughly what a 2.7% cheapening implies at 3-to-1 leverage. The authors’ point is that capital was slow to come back: it took months for prices to recover even though the bonds were cheap.
What happened to convertible arbitrage in 2008?
In 2008 the strategy suffered a funding crash: prime brokers failed or pulled financing, hedge funds were forced to deleverage, and convertibles fell far below their model values.
Mitchell and Pulvino report that the HFR convertible arbitrage index lost 34% in 2008, nearly all from September to November, against losses of only 2% in 2005 and 4% in 1994, its only other negative years since 1990. The investable HFRX version, which is free of survivorship bias, fell 58%. Their measure of convertible cheapness reached 10.9% in November 2008, more than three times the 2005 peak, and took well over a year to return to normal. In the published version, the authors argue that when arbitrageurs lose access to debt capital, they cannot keep similar assets priced alike (Journal of Financial Economics, via AQR). The hedge leg also failed in some names: on September 19, 2008 the SEC banned short selling in 799 financial companies (SEC), removing the usual hedge for convertibles issued by those firms.
Treating “hedged” as “safe” and levering it up. A hedged convertible can still lose several percent when every holder sells at once. At five times leverage, that is a large share of the fund’s capital, and the losses arrive exactly when lenders are cutting credit lines. The same pattern shows up in the Treasury basis trade.
Why do companies issue convertible notes, and who buys them?
Companies issue convertibles to borrow at a lower coupon than straight debt by giving investors a share of the upside, and they can raise the money in days. The main buyers are arbitrage funds that hedge by shorting the stock.
Mitchell, Pedersen and Pulvino note that convertible arbitrage and multi-strategy funds have accounted for up to 75% of the convertible market and that nearly all convertibles have been issued under Rule 144A, often in one or two days. Rule 144A resales go to qualified institutional buyers, broadly institutions that own and invest at least $100 million in securities (17 CFR 230.144A). So the arbitrageur is, in effect, financing the company and passing the equity risk to the stock market through its short.
What does convertible arbitrage mean for an executive with concentrated stock?
Two things. If your employer issues convertibles, arbitrage funds will short its stock to hedge, and that short interest will rise with each issue. And the strategy’s logic of owning optionality and hedging delta is a useful lens on your own position.
When a company you hold announces a convertible, read the terms: the conversion premium, any capped-call purchase, and the potential dilution, which the SEC flags as a key risk for common holders. Expect hedge-related short selling around the issue. More broadly, most executives with large stock positions are short optionality without realizing it: selling covered calls for income is the mirror image of the arbitrageur’s long-gamma book. That can be the right trade, but it pays you for accepting the big moves rather than profiting from them. Buying protection, as in a collar, puts some of that convexity back on your side. Proflex’s approach to concentrated tech positions starts with exactly this question: which Greeks are you long, which are you short, and are you being paid enough for the ones you sell?
What should you check before investing in a convertible arbitrage strategy?
- Ask how the manager measures leverage and what it was in the worst month of 2008 or 2020.
- Find out how much of the book is in hybrid, busted and equity-like convertibles.
- Check how credit and interest-rate risk are hedged, and at what cost.
- Ask about borrow: concentration in hard-to-borrow names and plans for a recall or a short ban.
- Read the redemption terms; 2005 showed that matching investor liquidity to asset liquidity matters.
- Compare implied volatility in the convertibles held with listed options on the same stocks.
- Review prime broker arrangements and how many financing counterparties the fund uses.
Frequently asked questions
How does convertible bond arbitrage work?
The arbitrageur buys a convertible bond and shorts the issuer’s stock in an amount equal to the bond’s delta, the number of shares whose price moves match the bond’s. Small stock moves then roughly cancel. The position earns the bond’s coupon plus interest on the short sale proceeds, and profits from rebalancing the hedge when the stock moves a lot.
What is a delta-neutral convertible position?
It is a long convertible bond paired with a short stock position sized to the bond’s delta, so the combined position has little exposure to small stock moves. Because a convertible’s delta rises as the stock rises and falls as it falls, the hedge must be adjusted, and that adjustment is where gamma profits come from.
What are convertible bond Greeks?
Delta is how much the bond moves for a $1 stock move, measured in shares. Gamma is how fast delta changes. Vega is sensitivity to the stock’s volatility. A convertible also has interest-rate duration and credit-spread sensitivity, because the bond floor is a corporate bond.
What is gamma trading in convertibles?
Gamma trading means rebalancing the stock hedge as the bond’s delta changes: shorting more shares after the stock rises and buying shares back after it falls. That sells high and buys low mechanically, and it earns money when the stock moves more than the volatility implied in the bond’s price.
Why did convertible arbitrage lose money in 2005 and 2008?
In 2005 investors pulled more than 20% of capital from convertible arbitrage funds in the first quarter, forcing bond sales that cheapened convertibles. In 2008 prime broker failures and lost funding forced deleveraging; the HFR convertible arbitrage index fell 34% and the investable HFRX version 58%, mostly from September to November.
Why do companies issue convertible notes?
Convertibles let a company borrow at a lower coupon than straight debt by giving investors upside in the stock. Many are sold quickly to qualified institutional buyers under Rule 144A, and the arbitrage funds that buy them hedge by shorting the stock, which is why the strategy supplies capital to issuers.
Can individual investors do convertible arbitrage?
Rarely in practice. Most new convertibles are sold to qualified institutional buyers, trade in large sizes and require continuous hedging, stock borrow and modeling. Individuals usually get exposure through funds, and can learn the same delta and gamma ideas with listed options.
Key takeaways
- Convertible arbitrage buys a convertible bond and shorts the issuer’s stock in proportion to the bond’s delta.
- The hedged position is long gamma and long volatility: it gains on big stock moves either way, before time decay.
- Income comes from the coupon plus interest on short-sale proceeds, minus borrow costs and dividends owed on the short.
- What the hedge leaves behind is credit, volatility, rates, borrow and funding risk, and those are what hurt in a crisis.
- 2005 was a redemption-driven sell-off; 2008 was a funding crash, with the HFRX index down 58%, nearly all of it from September to November.
- Leverage of 4 to 6 times was considered normal for the strategy before 2008, which turned small mispricings into large losses.
Sources and method
- Investor.gov (SEC), Convertible Securities — definition; fixed vs market-price conversion formulas; dilution
- FINRA, Bonds — convertibles as a class of corporate bond
- 17 CFR §230.144A, Private resales of securities to institutions — qualified institutional buyer definition ($100 million in securities)
- Mitchell, Pedersen and Pulvino, Slow Moving Capital, NBER Working Paper 12877 (2007) — 2005 redemptions, 35% of holdings sold by year-end, 2.7% discount, −7.2% Jan–May 2005, up to 75% market share
- Mitchell and Pulvino, Arbitrage Crashes and the Speed of Capital, NBER conference paper (2010) — HFR −34% and HFRX −58% in 2008; 10.9% cheapness; leverage of 4 to 6 times
- Mitchell and Pulvino, Arbitrage Crashes and the Speed of Capital, Journal of Financial Economics (2012), via AQR — loss of debt capital and price dislocations in convertible arbitrage
- SEC press release 2008-211, SEC Halts Short Selling of Financial Stocks — September 19, 2008 emergency short-sale ban on 799 financial companies
Charts 1 and 2 and the worked example are illustrative: a hypothetical $1,000 five-year convertible with a 1% annual coupon and a conversion ratio of 20 (conversion price $50). The bond floor discounts coupons and principal at an assumed 6% credit-adjusted yield (about $789) and tapers toward an assumed $400 recovery value as the stock falls. The convertible price is the bond floor plus 20 Black–Scholes calls struck at $50 with 30% volatility and a 6% rate, floored at conversion value. Delta is the model’s numerical derivative at a $40 stock price; Chart 2 shows instant moves with volatility, credit and time held constant. Chart 3 uses figures reported in the cited NBER papers, which in turn cite HFR, HFRX and fund-index data.