Convertible Arbitrage: How Funds Hedge Convertible Bonds, and Why the Trade Broke in 2005 and 2008

Convertible arbitrage is a hedge fund strategy that buys a company’s convertible bonds and sells short the company’s stock against them, so the position keeps the bond’s income and the value of its embedded call option while hedging away most of the exposure to the share price. Professionals run it as a relative-value trade: they buy convertibles that look cheap against a pricing model, hedge them, and earn the gap as it closes, plus whatever they make from rebalancing the hedge.

In short: a convertible bond is a corporate bond plus a call option on the issuer’s shares. A convertible arbitrage fund owns the bond and shorts roughly delta shares of stock per bond, which leaves it long the option’s gamma and volatility, long the bond’s income, and exposed to credit spreads, interest rates, liquidity, and financing. Because the hedged position moves very little day to day, funds lever it several times over with money borrowed from prime brokers. That leverage is what turned two “market-neutral” episodes, the redemption wave of 2005 and the financing collapse of 2008, into large losses. The academic record on both is unusually good, and it is mostly about capital, not about the bonds.

This piece assumes you know how a call works (see call options explained) and what delta measures (see delta explained). It describes how professional funds operate. It is not a recommendation, and the strategy depends on financing, borrow, and pricing infrastructure that individuals do not have.

A common misconception: “it’s arbitrage, so it’s riskless”

The word “arbitrage” is aspirational. Mark Mitchell and Todd Pulvino, practitioners at CNH Partners who also publish academic work, put it bluntly in “Arbitrage Crashes and the Speed of Capital” (Journal of Financial Economics, 2012): convertible arbitrage and its relatives are not true arbitrage strategies, because the securities in the trade are “merely related rather than nearly identical.” A hedged convertible removes most stock risk. It does not remove the risk that the bond gets cheaper relative to its model value, that its credit spread widens, that the stock becomes impossible to borrow, or that the lender financing the position asks for its money back. Those are exactly the risks that showed up in 2005 and 2008.

What a convertible bond is

A convertible bond pays a coupon like an ordinary corporate bond, and the holder can exchange it for a fixed number of shares, the conversion ratio. A few terms matter:

Conversion price: face value divided by the conversion ratio. A $1,000 bond convertible into 16 shares has a conversion price of $62.50.
Conversion value (parity): conversion ratio times the current share price. At $50 a share, 16 x $50 = $800.
Investment value (bond floor): what the bond would be worth as a straight bond with no conversion right, discounted at the issuer’s credit spread.
Conversion premium: how much the convertible trades above conversion value.

Deep in the money, convertibles trade like the stock; far out of the money (“busted”), like credit. Arbitrageurs concentrate in the “balanced” zone in between, where the option is worth the most per dollar of stock exposure.

Why issuers sell them and why funds own them

Companies issue convertibles because they can raise money quickly at a lower coupon than straight debt. Mark Mitchell, Lasse Heje Pedersen and Todd Pulvino (“Slow Moving Capital,” American Economic Review Papers and Proceedings, 2007) describe how this works: since SEC Rule 144A took effect in 1990, almost all convertibles have been sold privately to qualified institutional buyers, with one to two days from announcement to closing and often less than 24 hours, against at least a month for a registered public deal. Someone has to absorb that supply overnight, and the natural buyer is a fund that can hedge the stock risk immediately. The same paper reports that convertible arbitrage funds accounted for up to 75% of the convertible market, and that convertibles are often issued below fundamental value as compensation for providing that liquidity.

That last point is the economic engine of the strategy. The arbitrageur is not finding free money. It is being paid a new-issue concession, and later an illiquidity discount, for warehousing a security other investors do not want to hedge.

How professionals value a convertible

Desks value convertibles with lattice or finite-difference models that handle the features a simple formula cannot: early conversion, issuer calls, investor puts, and the fact that the bond and equity pieces carry different credit risk. Mitchell, Pedersen and Pulvino describe the inputs their model used: the stock price, a volatility estimate drawn from historical and options-implied volatility, a credit spread estimated from credit default swaps, straight-debt yields and ratings, and the yield curve.

A widely used approach (Tsiveriotis and Fernandes, Journal of Fixed Income, 1998) splits the convertible into two pieces on a binomial tree: an equity component, discounted at the risk-free rate because the shares it converts into are not a claim on the issuer’s credit, and a cash component (coupons and redemption), discounted at the risk-free rate plus the issuer’s credit spread. At each node, the holder converts if conversion value exceeds the value of continuing.

Worked example: Maple Widgets 1% convertible

Take a hypothetical issue. Maple Widgets Inc. trades at $50 and pays no dividend. Its five-year convertible has a $1,000 face, a 1% annual coupon, and converts into 16 shares. Assume 30% volatility, a 4% risk-free rate, and a 3% credit spread. Pricing it on a Tsiveriotis-Fernandes tree (1,200 steps, averaged with a 1,201-step tree to smooth the lattice noise; no call or put features), with the Greeks estimated by bumping the inputs and averaging across tree sizes:

Measure	Value
Theoretical value	$985.68
Investment value (straight bond at 7%)	$745.42
Conversion value (16 x $50)	$800.00
Conversion premium over parity	23%
Delta	11.05 shares per bond (69% of the 16-share conversion ratio)
Gamma	about 0.15 shares per $1 move in the stock
Vega	+$6.44 per bond per volatility point
Credit sensitivity	-$23.50 per bond for +100 basis points of spread

The bond sits about $240 above its bond floor because of the conversion option. The delta of 11.05 shares is the hedge: a fund that buys one bond sells 11.05 shares short.

The core trade: long the bond, short delta

Here is what the hedged position does if the stock jumps instantly and the bond is marked at model value:

Stock move	New stock price	Bond P&L	Short-stock P&L (11.05 shares)	Net hedged P&L
-30%	$35.00	-$142.53	+$165.75	+$23.22
-20%	$40.00	-$100.45	+$110.50	+$10.05
-10%	$45.00	-$52.55	+$55.25	+$2.70
0%	$50.00	$0.00	$0.00	$0.00
+10%	$55.00	+$57.46	-$55.25	+$2.21
+20%	$60.00	+$119.12	-$110.50	+$8.62
+30%	$65.00	+$182.96	-$165.75	+$17.21

That shape is the reason the strategy exists. Because the fund owns the option, the hedged position is long gamma: it makes money on large moves in either direction, and it can harvest smaller moves by rebalancing (buying stock back after a fall, selling more after a rise). The same mechanics are covered in detail in delta hedging and gamma scalping. If the stock’s realized volatility over the life of the trade matches the 30% in the model, those rebalancing gains roughly pay for the option’s time decay. The edge comes from buying the bond below its theoretical value, or from realized volatility coming in above the volatility implied by the bond’s price.

The table hides an asymmetry. It holds the credit spread fixed. In reality a stock that falls 30% usually has a wider credit spread too, because equity and credit are claims on the same firm. Rerun the -30% case with the spread widening from 3% to 6% and the bond is worth $759.46: the hedged position loses $60.47 per bond instead of making $23.22. The bond’s downside depends on credit, and a pure stock hedge does not cover it.

The other hedges

Mitchell, Pedersen and Pulvino list the extra hedges arbitrageurs may add: shorting government bonds against rate risk, shorting the issuer’s straight bonds or buying credit default swaps against credit risk, and selling listed options against volatility risk. Each costs money and adds basis risk. A convertible asset swap separates the pieces outright: a credit investor takes the bond’s credit and coupon stream, and the arbitrageur keeps a call on the convertible. Either way, the fund owns the cheap option and lays off what it is not paid to hold.

How the trade is financed

A hedged convertible is a low-volatility position, and low-volatility positions get levered. Mitchell and Pulvino (2012) define leverage as the long market value of convertibles divided by fund capital, and report that 4 to 6 times was considered normal in the years before 2008, with up to 20 times possible on very high-delta bonds whose hedged risk was minimal.

The plumbing runs through a prime broker:

The fund buys the bond and posts only a haircut (a margin percentage). The prime broker lends the rest.
The prime broker funds that loan partly by rehypothecating the fund’s securities, pledging them to its own lenders, such as large banks.
The fund borrows the shares it sells short from the prime broker’s stock-loan desk. It earns a short rebate on the cash proceeds, the cash rate minus a borrow fee. Hard-to-borrow stocks pay little or even negative rebates.

Worked example: one year of carry at 4x leverage

Suppose the fund buys the Maple Widgets bond at 2% below model value, $965.97, at 4x leverage (a 25% haircut), so it puts up $241.49 of capital and borrows $724.47. Assume the loan costs 4.5%, the short rebate on the $552.50 of short-sale proceeds (11.05 shares x $50) is 3.5%, the stock ends the year unchanged, and nothing is rebalanced:

Item, per bond, one year	Amount
Change in the bond’s model value with one year less to run	+$3.40
Coupon	+$10.00
Short rebate (3.5% x $552.50)	+$19.34
Interest on the loan (4.5% x $724.47)	-$32.60
Subtotal: carry with no convergence	+$0.14
Cheapness closes from 2% to zero	+$19.71
Total	+$19.85

On $241.49 of capital, carry alone earns less than 0.1%, far below the 4% the capital could earn in Treasury bills. With convergence, the trade earns 8.2%, or about 4.2% over cash. This is a deliberately plain example (no rebalancing gains, no transaction costs, no borrow recall), but the shape is realistic: the return of a levered convertible book is mostly the cheapness closing, multiplied by leverage. The same multiplier works in reverse when cheapness widens.

2005: when investors pulled capital

Mitchell, Pedersen and Pulvino document the 2005 episode in “Slow Moving Capital.” The key facts, all from the paper:

In early 2005, large institutional investors began withdrawing from convertible hedge funds, reportedly because of low returns in 2004. Citing the Barclay Group, the authors report that more than 20% of capital was redeemed from convertible arbitrage funds in the first quarter of 2005, and that by the first quarter of 2006 assets managed by these funds had fallen by half.
Using SEC Form 13F filings, they identify 28 specialist convertible arbitrage funds holding about $40 billion of convertibles at the end of 2004, roughly 15% of the US market. By the end of 2005 those funds had sold 35% of their convertibles, and 41% by the third quarter of 2006.
On a sample of 550 US convertibles, the median bond traded at a maximum discount of 2.7% to theoretical value in mid-May 2005, about 2.5 standard deviations from the 1985-2004 average and the largest gap since LTCM liquidated its convertible book in 1998. The discount peaked around investor redemption notice deadlines, 45 days before the end of June and of December.
Convertible hedge funds returned -7.2% from January to May 2005. The authors note that this is roughly what a 2.7% cheapening would produce at a typical 3:1 leverage: 2.7% x 3 = 8.1%.
Volatility and credit spreads changed little, and convertible prices rebounded in 2006. The authors conclude that the losses were driven by capital flows, not by deteriorating fundamentals.

The most striking finding is about who did not step in. Multi-strategy hedge funds, whose stated advantage is moving capital to the best opportunity, did eventually add convertibles: the 27 multi-strategy funds with convertible holdings increased them by 36% by the end of 2005. But that increase was driven largely by one fund, and more than half of the 27 actually reduced their exposure. The authors’ explanation is that information barriers inside a firm can impose the same capital constraints on a losing trading desk that outside investors impose on a losing fund. Amaranth Advisors, they note in a footnote, sold more than half its convertible book after convertibles reached their cheapest level in 2005 and expanded its energy trading instead; it lost $6 billion on energy bets in September 2006 and shut down.

Using Hedge Fund Research data, Mitchell and Pulvino (2012) put the HFR convertible arbitrage index’s 2005 return at -2%, one of only two negative years (with 1994, at -4%) between 1990 and 2007.

2008: when lenders pulled financing

The 2008 episode was larger and had a different cause. In 2005 the funds lost equity capital. In 2008, they lost debt capital.

Mitchell and Pulvino trace the chain. When Lehman Brothers filed for bankruptcy on September 15, 2008, the lenders that had financed Lehman’s prime brokerage through rehypothecation were left holding its hedge-fund clients’ collateral. Those lenders held only the long side of hedged trades: a deep-in-the-money convertible, which is low-risk when hedged, is almost pure equity risk without the short. So they sold collateral quickly. Lenders to other prime brokers, worried the same could happen to them, pulled back too, and prime brokers in turn forced their clients to cut leverage. Moving to a healthier prime broker was not a practical option, because new relationships take weeks to set up and the surviving brokers were reluctant to take on more securities. The authors report, as anecdote, that margin requirements on illiquid hedged convertible positions (small and credit-sensitive issues) rose from 10-15% to 50-75%.

The results, from the same paper:

HFR’s convertible arbitrage index lost 34% in 2008, almost all from September to November. HFR’s investable HFRX convertible arbitrage index, which is free of survivorship bias, fell 58%.
On their measure, equity-sensitive convertibles traded on average 0.5% cheap to theoretical value from 1990 to 2010. In November 2008 the median cheapness reached 10.9%, which the authors calculate as 8.7 standard deviations from the January 1990 to August 2008 mean, with a daily maximum of 13.7% on December 4, 2008. That is more than three times the 2005 level, and it took well over a year to return to normal.
Small issues (under $250 million outstanding) went from 10.6% cheap at the end of August 2008 to 39.7% at the end of November; larger issues went from 7.2% to 27.4%.

A further shock came from regulation. On September 18, 2008, the SEC issued an emergency order (Release No. 34-58592) prohibiting short sales in a list of financial companies, effective until October 2, 2008 unless extended, with a narrow exception for bona fide market makers. For a convertible arbitrageur, the short sale is the hedge, so new hedged positions in affected issuers could not be put on in the normal way.

The Priceline example

Mitchell and Pulvino give a concrete case. On November 28, 2008, Merrill Lynch’s capital markets desk offered, on behalf of a client, $25 million face of Priceline.com’s 0.50% convertible due September 2011 at $166.56 per $100 face. With the stock at $67.66 and a conversion ratio of 24.7647 shares per $1,000, the conversion value was 24.7647 x $67.66 / 10 = $167.56 per $100. The bond was offered one point below what it could be converted into, while the authors’ model valued it at $185.30 (their measure: an 11.3% discount). Why not just convert? Conversion would forfeit accrued interest (only $0.08 per $100 here) and take about a month. The seller needed cash now, and apparently no buyer had the balance sheet to pay even conversion value.

Worked example: how leverage converts cheapening into losses

Take the Maple Widgets bond held at its model value of $985.68, and mark it to the median cheapness of 2005 or 2008, ignoring any hedge or credit loss. Because capital is the position divided by leverage, the loss on capital is the cheapening times the leverage:

Leverage	2005: bond 2.7% cheap	2008: bond 10.9% cheap
3x	-8.1% of capital	-32.7% of capital
4x	-10.8%	-43.6%
6x	-16.2%	-65.4%

The 3x figure is the same 2.7% x 3 arithmetic Mitchell, Pedersen and Pulvino used for 2005. Now add the financing squeeze. Take a fund with $100 million of capital running $500 million of convertibles at 5x (a 20% haircut). A 10% fall in the book’s value costs $50 million, halving capital to $50 million. If the haircut then rises to 50%, $50 million of capital supports only $100 million of positions. The fund must sell $350 million of its remaining $450 million book, into a market where every other levered holder faces the same arithmetic. That forced selling is what pushed cheapness from a few points to double digits.

What the evidence says about the strategy

Mitchell, Pedersen and Pulvino argue that their findings do not fit the frictionless view, under which a capital shock to a small group of specialists should barely move prices because new money would flow in. Instead, prices dropped relative to fundamentals and “the rebound took months.” They blame three frictions: information barriers between investors and managers, the cost of keeping capital and staff idle while waiting for opportunities, and the extra return demanded for supplying liquidity in illiquid markets. The 1998 LTCM liquidation, which they also study, produced a discount of more than 4% in their convertible sample, followed by the same months-long recovery. For a convertible fund, normal-times returns are partly a payment for being the liquidity provider of last resort, and the cost is exposure to exactly the moments when it can least afford to provide liquidity.

What can go wrong

Cheapening from forced selling. The dominant risk in both 2005 and 2008. The hedged position can lose money even when nothing about the issuer has changed, and leverage multiplies it.
Financing withdrawal. Haircuts are set by lenders and can change overnight. A hedged book can be forced out by a margin call rather than by losses on the positions themselves.
Credit and the downside. A stock hedge does not protect against spread widening, and spreads tend to widen when the stock falls. Defaults can wipe out much of a bond’s value while the short stock gain covers only part of it.
Borrow risk. The short leg needs borrowable stock. Borrow can be recalled, fees can spike, and regulators can ban short sales, as the SEC did for financial stocks in September 2008.
Model and volatility risk. The “cheapness” signal depends on volatility and credit inputs that are estimates. If realized volatility comes in below the volatility paid for, the long-gamma position bleeds.
Liquidity, crowding, and contract terms. Convertibles trade over the counter in a market dominated by hedge funds, so exits are simultaneous. Issuer calls and takeovers can also cut off the option’s value early.

The short version

Convertible arbitrage buys a bond that contains a call option and sells delta shares against it, keeping the option’s convexity and the bond’s income while hedging most stock risk. The trade is paid for supplying liquidity to issuers who need cash fast and to holders who need to sell. Because the hedged position is quiet, funds lever it, and the profit in normal times is mostly cheapness closing, multiplied by leverage. The academic record shows that the risk is not the bonds but the capital behind them: in 2005, investor redemptions pushed convertibles to a 2.7% median discount, and in 2008 the collapse of prime brokerage financing pushed it to 10.9%, with funds losing a third or more. It is a professional strategy that depends on financing relationships, stock borrow, and pricing models, and it is described here as a mechanism, not as something to copy.