© Copyright 2000 Rogers Media. The following article first appeared in the February 2001 edition of BENEFITS CANADA magazine.

Convertible bond arbitrage

Offering attractive current income and the opportunity to profit from volatility, convertible bond arbitrage hedge funds are solid performers--even in bear markets.

By Robert Parnell

Convertible bond investors generally expect to earn a return equal to about two-thirds of the underlying equity market over the long term, and based on the past six years, they cannot be too disappointed.

In the six-year period ending Dec. 31, 2000, global convertible bonds earned 11.4% while U.S. converts earned 18.8%. Not bad for an asset class with a principal guarantee and a higher yield than common equity.

Last year, however, all was not well in convertible bond land. The UBS Warburg Global Convertible Bond Index was off 10.4% in 2000 while the U.S. sub-index declined 11.2%. With equity market exposure and frequently below-investment-grade credits, many convertible bonds performed poorly as equity markets corrected.

It appears that convertible bonds were simply the wrong place for investors to be last year--unless they happened to be a hedge fund. Despite dismal performance in the global convertible bond market, convertible arbitrage hedge funds shone.

The CSFB/Tremont Convertible Arbitrage Index (an asset-weighted benchmark of convertible hedge funds) produced a return of 25.1% in the first 11 months of 2000, beating the convertible bond indexes by more than 35%. Many pension funds and other institutions have invested in convertible arbitrage hedge funds over the years no doubt, in part, because of their ability to perform well even in a down market.

So, how does convertible arbitrage work? And why did convertible arbitrage hedge funds perform so well last year when the convertible bond market performed so poorly?

There are currently over 120 hedge funds focused on convertible arbitrage. Collectively, they represent about US$10 billion in net assets. The managers of these funds exploit arbitrage opportunities not only in convertible bonds, but other convertible securities including convertible preferreds, zeros and mandatory convertibles.

Convertible bond prices hinge on three main factors: investment, conversion and option value. The investment value is a theoretical measure of where the bond would trade if it were not convertible, such as a straight bond. This value represents the bond's floor value--it should never trade below this level. Even if the bond experiences no equity participation, it should at least pay coupons and the principal amount at maturity.

The conversion value represents the value of the common stock that the bond can be converted into. If the bond is convertible into, say, 50 shares of common and each share has a market value of $20, then the conversion value would be $1,000. Obviously this changes as the price of the common fluctuates.

The conversion value represents only upside because the holder of the bond has the right, but not the obligation, to convert. If the share price is too low, the investor will choose not to convert and hold the bond for its fixed income payoff. In this situation, the investment value dominates. Conversely, if the share price is very high, conversion becomes more likely and the conversion value dominates.

The investment as well as the conversion value act as price boundaries for the convertible bond. With few exceptions, the convertible bond price should never be less than either value. In fact, convertible bond prices usually exceed the investment and conversion values because the investor has the right to choose whether or not to convert. This ability to choose also has value--it is the time value of an option.

Take for example, Internet company AOL's zero coupon converts due Dec. 6, 2019. These bonds are convertible into 5.8338 shares of AOL stock. With AOL common stock trading at $34.80 on Dec. 31, 2000, the conversion value was $203 (5.8338 x 34.80). As the conversion value is significantly below the investment value (calculated at $450.20), the investment value dominated and the convertible traded at $474.10. When, or if, the stock trades above $77.15, the conversion value will dominate the pricing of the convertible because it will be in excess of the investment value.

MADE TO MATCH

In a typical convertible bond arbitrage position, the hedge fund is not only long the convertible bond position, but also short an appropriate amount of the underlying common stock. The number of shares shorted by the hedge fund manager is designed to match or offset the sensitivity of the convertible bond to common stock price changes. This is known as delta hedging in hedge fund parlance.

In the AOL example, the delta for the convertible is approximately 50%. This means that for every $1 change in the conversion value, the convertible bond price changes by 50¢. To delta hedge the equity exposure in this bond we need to short half the number of shares that the bond converts into, for example 2.9 shares (5.8338 ÷ 2).

The combined long convertible bond/short stock position should be relatively insensitive to small changes in the price of AOL's stock. As the price of AOL rises, the profit in the convertible bond should be offset by the loss on the short AOL stock position. Conversely, as the price of AOL declines, the loss on the convertible bond should be offset by the gain on the short equity position. This relatively simple adjustment allows convertible arbitrage hedge fund managers to create portfolios that are less dependent on market direction.

There is another important consequence of delta hedging a convertible bond. It can help a hedge fund profit from something that traditional investment managers would generally like to avoid--volatility.

Although the short stock position provides a reasonably good hedge for small stock price movements, the accuracy of the hedge breaks down for large stock price movements because the bond price does not move linearly with the stock price.

If the stock price increases significantly, profits on the convertible bond accelerate and start to exceed losses on the short stock position. Conversely, if the stock price declines significantly, losses on the convertible bond decelerate and are more than offset by gains on the short position.

The fortunate result of this imperfect delta hedge is that trading profits can often be realized from a convertible bond arbitrage if the stock price is volatile in either direction. This quality of convertible arbitrage explains some of the impressive returns reaped using the strategy in 2000.

Because convertible arbitrage positions can profit from stock volatility in either direction, they are sometimes described as having synthetic put or call option characteristics. Hedge fund managers can structure put trades that behave more like a put option, or call trades that act more like a call option. In a bearish market, a hedge fund manager can bias the portfolio towards put trades and take a defensive position.

Although volatility can certainly add to convertible arbitrage returns, for most hedge fund managers, it's usually the icing on the cake. The cake itself is current income, and most convertible arbitrage positions are selected because they offer an attractive current income yield.

Consider online discount brokerage company E-Trade's 6%, Feb. 1, 2007 convertible bonds. On Dec. 29, 2000 they had a price of $54.45 for a current yield of 11.02%. For a hedge fund manager, this rather attractive yield is further enhanced by interest earned on the proceeds from the short sale of E-Trade's common shares (known as the short sale rebate).

Assuming no movement in the underlying stock price, the convertible arbitrage position should produce a standstill return of about 12% to 13%, before transaction costs and assuming no leverage of the bond position. Equity volatility could add to this return. Most convertible arbitrage hedge fund managers want to set up trades with attractive standstill returns and then profit from delta trading opportunities as market volatility permits.

On a risk-adjusted basis, convertible arbitrage has produced relatively attractive returns over the past seven years. Despite difficult years in 1994 and 1998, the CSFB/Tremont Convertible Arbitrage Index produced a net annualized return of 10.59% from Dec. 31, 1993 to Nov. 30, 2000 (see "Performance snapshot," page 52). This return compares favourably with the 9.18% return from global convertible bonds during the same period. While U.S. equities have produced higher returns, they have done so with over three times the volatility of the convertible arbitrage index.

Convertible arbitrage hedge funds also provide reasonable protection against market declines. In August 1998 when the Standard & Poor's 500 index declined 14.6%, the CSFB/Tremont Convertible Arbitrage Index was down by only 4.64%. And, once again, convertible arbitrage outperformed both convertible bonds and equity last year as the markets corrected significantly.

CONSIDER THE RISKS

Numerous risks await an investor in convertible arbitrage hedge funds and they should not be taken lightly. Despite their equity upside, convertible bonds are still bonds and accordingly, they are subject to interest rate risks, credit spread expansion and ultimately default risk.

The convertible bond market as a whole is also prone to liquidity risk as demand can dry up periodically, and bid/ask spreads on bonds can widen significantly. Because convertible bond arbitrage also involves the short sale of underlying common stock, the strategy is also subject to stock-borrow risk. This is the risk that the hedge fund manager will be unable to sustain the short position in the underlying common shares.

In addition, convertible arbitrage hedge funds use varying degrees of leverage, which can magnify both risks and returns. While some conservative convertible arbitrage hedge funds may use only one times leverage, most are leveraged four to seven times capital.

Irrespective of the strategy, hedge fund investors are perhaps most vulnerable to manager risk. The majority of hedge fund portfolios are critically dependent on the performance of a star manager, so manager risk is always present. The fortunes of a convertible arbitrage portfolio or any other hedge fund strategy depend largely on the skill of the manager. If the manager gets it wrong, it doesn't matter if the market environment for arbitrage is favourable.

On the positive side, hedge fund managers can, and often do, minimize certain risks in their portfolios. For example, short treasury positions can be used to reduce interest rate exposure and credit swaps can reduce credit risks. In most circumstances, portfolios are well diversified by issue, industry and sector.

With approximately 120 hedge funds focused on convertible bond arbitrage, manager selection and due diligence is a daunting task. As with any asset class, there is a significant performance gap between top quartile and bottom quartile managers. Manager selection is clearly important.

Overall, investing in hedge fund strategies such as convertible arbitrage should be considered as part of a diversified portfolio of hedge fund strategies. Convertible bond arbitrage has a low correlation with other arbitrage and long/short strategies, and pension funds can benefit from this diversification.

Robert Parnell is president of Toronto-based Tremont Investment Management, Inc. rparnell@tremontinvestment.com.This article is the second in a series on alternative investments.

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Performance snapshot

Despite difficult years in 1994 and 1998, convertible arbitrage has produced relatively attractive returns on a risk-adjusted basis over the past seven years. U.S. equities have produced higher returns, but they have three times the volatility of the convertible arbitrage index.

Dec. 31, 1993 to Nov. 30, 2000

All returns are in U.S. dollars.

SOURCE: Tremont Investment Management Inc.

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