Convertible Arbitrage

Convertible Arbitrage Definition

Convertible Arbitrage refers to the trading strategy used in order to capitalize on the pricing inefficiencies present between the stock and the convertible where the person using the strategy will take the long position in the convertible security and the short position in underlying common stock.

It is a long-short trading strategy favored by hedge funds and large-scale traders. Such an approach involves taking a lengthy method in convertible security with a simultaneous short position in the underlying common stock to capitalize on pricing differences between the two securities. A convertible security is one that can be converted into another form, such as a convertible preferred stock, which can be changed from a Convertible Preference share to an Equity share/Common stock.

Why use Convertible Arbitrage Strategy?

The rationale for adopting a convertible arbitrage strategy is that the long-short position enhances the possibility of gains is made with a relatively lower degree of risk. If the value of the stock declines, the arbitrage trader will benefit from the short positionShort PositionA short position is a practice where the investors sell stocks that they don't own at the time of selling; the investors do so by borrowing the shares from some other investors to promise that the former will return the stocks to the latter on a later more in stock since it is equity and matter flows in the direction of the market. On the other hand, the convertible bond or Debentures will have limited risks since it is an instrument having a fixed rate of income.

However, if the stock gains, the loss on the short stock position will be capped since the profits on the convertible security will offset it. If the stock is trading at par and not going either up or down, the convertible security or the debenture will continue to pay a steady coupon rate, which shall offset the costs of holding the short stock.

Another idea behind adopting a convertible arbitrage is that a firm’s convertible bonds are priced inefficiently relatively to its stock. This can be since the firm may lure investors into investing in the debt stock of the firm and hence offer lucrative rates. The Arbitrage attempts to profit from this pricing error.

Also, look at Accounting for convertible bonds.

What is Hedge Ratio in Convertible Arbitrage?

A critical concept to be familiar with convertible arbitrages is the hedge ratio. This ratio compares the value of the position held through the use of the hedge compared to the whole place itself.

E.g., if one is holding $10,000 in foreign equity, this does expose the investor to FOREX risk. If the investor decides to hedge $5,000 worth of the equity with a currency position, the hedge ratio is 0.5 (50/100). This culminates that 50% of the equity position is prevented from exchange rate risksExchange Rate RisksExchange Rate Risk is the risk of loss the company bears when the transaction is denominated in a currency other than the company operates. It is a risk that occurs due to a change in the relative values of more.

Convertible Arbitrage Risks

Convertible Arbitrage is trickier than it sounds. Since one generally must hold the convertible bonds for a specified amount of time before conversion into equity stock, it is critical for the arbitrageur/fund manager to evaluate the market carefully and determine in advance if market conditions or any other macroeconomic factors can have an impact during the time frame in which conversion is permitted.

For instance, if a fund has acquired a convertible instrument of ABC Co. with a lock-in period of 1 year. However, post one year, the countries Annual budget is going to be announced whereby they are expected to impose a 10% Dividend Distribution tax on the dividends declared by the company on the equity shares. Such a measure will have an impact on the market and also the question of holding a convertible stock over the long run.

Arbitrageurs can fall victim to unpredictable events with no limits to the downside effects. One instance was during 2005, when many arbitrageurs held long positions in General Motors (GM) convertible bonds and short positions in GM stock. The expectation was that the present value of GM stocks would fall, but the debt will continue to earn revenues. However, the debt began to be downgraded by the credit rating agencies. A billionaire investor attempted to make a bulk purchase of their stocks, causing the strategies of fund managers to a tailspin.

Convertible Arbitrage faces the following risks –

Convertible Arbitrage

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  1. Credit Risk: The majority of the convertible bonds can be below investment grade or not rated at all, promising extraordinary returns. Hence a significant default risk exists.
  2. Interest Rate Risk: Convertible bonds with longer maturity are sensitive to interest rates. While stocks with a short position are a solid hedging strategy, lower hedge ratios may require additional protection.
  3. Manager Risk: The manager may incorrectly value a Convertible bond resulting in the arbitrage strategy to be questioned. If the valuations are wrong and/or credit risk increases, the value from bond conversion could be reduced/eliminated. Manager risk is also inclusive of the firm’s operational riskOperational RiskOperational risk is the business uncertainty a company comes across in the industry while executing its everyday business operations. Such risks arise due to internal system breakdown, technical issues, external factors, managerial problems, human errors or information gap. read more. The manager’s ability to enter/exit a position with minimal market impact will have a direct impact on profitability.
  4. Legal Provision & Prospectus Risk: The prospectus provides many degrees of potential risks arising in such strategies like early call, special dividendsSpecial DividendsThe term "Special Dividend" refers to an amount distributed to shareholders in the name of a dividend that is in addition to the regular dividend. Companies do this in the event of an unexpected inflow of cash or more expected, late interest payment in the event of a call, etc. Convertible arbitrageurs can best protect themselves by being aware of the potential pitfalls and by adjusting the hedge types to adjust such risks. One also needs to be aware of the legal implications and volatility applicable in the stock markets as well as the bond markets.
  5. Currency Risks: Convertible arbitrage opportunities often cross multiple borders, which also involve multiple currencies and exposing various positions to currency risks. Arbitrageurs will thus need to employ currency futures or forward contracts to hedge such risks.

Convertible Arbitrage Example

Let’s take a practical example of how a convertible arbitrage will work:

The initial price of a convertible bond is $108. The arbitrage manager decides to make initial cash investmentCash InvestmentCash investment is the investment in short-term instruments or saving account generally for 90 days or less that usually carries a low rate of interest or the return with a comparatively low rate of risk compared to other forms of more of $202,500 + $877,500 of borrowed funds = Total investment of $1,080,000. The debt to equity ratioDebt To Equity RatioThe debt to equity ratio is a representation of the company's capital structure that determines the proportion of external liabilities to the shareholders' equity. It helps the investors determine the organization's leverage position and risk level. read more, in this case, will be 4.33:1 (Debt being 4.33 times the equity investment amount).

The share price is at 26.625 per share, and the manager shorts 26,000 shares costing $692,250. Also, a Hedge ratio of 75% is to be maintained, and therefore the bond’s ratio of conversion will be (26,000/ 0.75) = 34,667 shares.

We shall assume a 1-year holding period.

The Total return can be shown with the help of the below table:

Cash Flow in Convertible Arbitrage

Return SourceReturnAssumption/ Notes
Bond Interest Income (on Long)$50,0005% Coupon on $1,000,000 face amount
Short Interest Rebate (on Stock)$8,6531.25% interest on the proceeds of $692,250 based on the initial hedge ratio of 75% [26,000 shares sold at $26.625 = $692,250, relative to the 34,667 shares of the bond equivalency].
Cost of Leverage($17,550)2% interest on $877,500 borrowed funds
Dividend payment (Short stock)($6,922)1% dividend yieldDividend YieldDividend yield ratio is the ratio of a company's current dividend to its current share price.  It represents the potential return on investment for a given more on $692,250 (i.e. 26,000 shares)
Total Cash flow……… (1)$34,481

Arbitrage Return

Return SourceReturnAssumption/ Notes
Bond Return$120,000Purchased at a price of 108 and assuming sold at a price of 120 per $1,000
Stock Return ($113,750)Sold equity stock at $26.625 and stock rose to $31.00 [i.e. Loss of $4.375*26,000 shares]
Total Arbitrage Return. (2)$6,250
Total Return (1) + (2) $40,431(Total $ return of $40,431 is a 20% ROE of $202,500)

The sources of the ROE can be shown with the help of the below table:

Return SourceContributionNotes
Bond Interest income (Long)4.6%Interest of $50,000 earned/bond price of $1,080,000*100 = 4.6%
Short Interest Rebate (Stock)0.8%Interest of $8,653 earned/bond price of $1,080,000*100 = 0.8%
Dividend payment (Stock)-0.6%Dividends of $6,922 paid/bond price of $1,080,000*100 = -0.6%
Cost of Leverage-1.6%Interest of $17,550 paid/bond price of $1,080,000*100 = -1.6%
Arbitrage Return0.6%Return of $6,250 earned/bond price of $1,080,000*100 = 0.6%
Unlevered Return3.8%Total Return of $40,431 earned/bond price of $1,080,000 = 3.8%
Contribution from Leverage16.2%Contribution from Leverage is very significant.
Total Return20.0% 

Convertible Arbitrage Fund Manager’s Expectations

In general, convertible arbitrageurs look for convertibles that exhibit the following characteristics:

Convertible Arbitrage Fund Manager's

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  1. High Volatility – An underlying stock that demonstrates above average volatility as this gives them a greater likelihood of earning higher profits and adjusting the hedge ratio.
  2. Low Conversion Premium – A conversion premium is an additional amount paid for convertible security over its conversion value measured in %. In general, a convertible with a conversion premium of 25% and below the same is preferred. A lower conversion premium indicates lower interest rate risk and credit sensitivity, both of which very difficult to hedge than equity risk.
  3. Low or No Stock dividend on the Underlying shares – Since the hedge position is short on the underlying shares, any dividend on the stock must be paid to the long stock owner since the anticipation of the strategy is the falling of share price. Such an instance will create a negative cash flow in the hedge.
  4. High Gamma – High gamma means how rapidly the delta changes. Delta is the ratio comparing the change in the price of an underlying asset to the corresponding change in the price of a derivative contract. A convertible with a high gamma offers dynamic hedging opportunities more frequently, thus offering the possibility of higher returns.
  5. Under-Valued Convertible – Since the hedged convertible position is a long position, the arbitrageur will be seeking issues that are undervalued or trading at implied volatility levels below average market returns. If the convertible possesses the future of coming back to normal returns, then this will be an appropriate opportunity for the manager to cash in.
  6. Liquidity – Issues which are highly liquid are preferred by the arbitrageur since it can be used for quickly establishing or closing a position.

Convertible Arbitrage Common Trades

There are many convertible arbitrage trades, but some of the common ones are:

Convertible Arbitrage Trades

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  • Synthetic Puts: These are highly equity sensitive trades that are “in-the-money” trading conversions of less than 10% premiums. These are convertibles with a high delta, reasonable credit quality, and a solid bond floor. The bond floor is the rate which the bonds are offering and is a fixed rate of return (a bond component of convertible security based on its credit quality, expressed in %).
  • Gamma Trades: Such trades arise by establishing a delta-neutral or possible biased position involving convertible security with reasonable credit quality and the simultaneous short sale of the stock. Since such stocks are volatile due to their nature, this strategy requires careful monitoring by dynamically hedging the position, i.e., continuous buying/selling shares of the underlying common stock.
  • Vega Trades: Also known as “volatility trades,” involves establishing a long position in the convertibles and selling appropriately matched call options of the underlying stock trading at high volatility levels. This also requires careful monitoring of the positions involving listed call options as the call option strike price and the expirations must match as close as possible to the terms of the convertible security.
  • Cash Flow Trades: The aim of such trades is to garner maximum cash flows from the arbitrage opportunities. This strategy focuses on convertible securities with a reasonable coupon or dividend income relative to the underlying common stock dividend and conversion premium. It offers profitable trading alternatives where the coupon from the long position or dividend/rebate received from the short position offsets the premium paid over a period of time.

Also, look at Top Hedge Fund Strategies


The convertible arbitrage strategy has produced attractive returns over the past two decades, which are not correlated with the individual performance of the bond or the equity market. The deciding factor for the success of such a strategy is the manager risk rather than directional equity or bond market risk. Additionally, high leverage is also a potential risk factor since it can reduce the returns earned.

In 2005, investor redemptions had a significant impact on the strategy’s returns, although the maximum drawdown remains significantly less as compared to traditional equity and bond markets. This is in contrast to the good performance for the convertible arbitrage strategy during 2000-02 when the markets were highly volatile due to the dot com crisis. The strategy still appears to be a good portfolio hedge in situations of volatility.

Such strategies are known to be very beneficial in choppy market conditions since one is required to take advantage of price differences. It is essential to continuously monitor the markets and take advantage of situations whereby the bond/stock is undervalued. The returns from the bond are going to be fixed, which keeps the manager in a relatively safer position but is required to predict the market volatility also for maximizing their returns and extract maximum benefit from simultaneous hold and sell strategies.

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