In essence there are two ways on investing in convertibles. One can buy a convertible outright and accept all the risks inherent within the instrument. The main risks are equity risk, for the bond may well convert into equity, credit risk, because as a debt instrument it is subject to the corporate issuer’s ability to pay, and interest rate risk, because as the risk-free rate changes the bond element will become more or less attractive to hold. Or one can buy a convertible and seek to hedge out these risks on the basis that the convertible’s price does not adequately reflect the returns available from its underlying components of risk. A convertible arbitrageur will seek to monetise that undervaluation.
Recent estimates suggest that the size of the hedge fund universe is $765bn (e624bn). The total capitalisation of stock markets around the world is in the range of hundreds of trillions of dollars. So in the normal course of business hedge funds do not exert a dominant role in the pricing of most market instruments. However, with an estimated 70% of convertible issuance in the hands of convertible arbitrage funds, their parameters for holding inventory are of prime importance in gauging new issue pricing and secondary market trading and cannot be ignored by the long only universe of managers.
A convertible will behave more like a bond or an equity depending on how close the equity is trading to the conversion price. The number of shares into which each bond may convert is (generally) fixed and determines the conversion price, the share price at which the value of shares received upon conversion equals the face amount of the bond. If the stock price is well below the conversion price the convertible will trade as a bond, since the chances of conversion are slim. The market’s estimation of the credit quality of the issuer will be the most important determinant of the price. The price of a convertible will rise as the share rises above the conversion price, ultimately, at prices significantly higher than the conversion price, trading as a proxy for the equity.
Convertibles are bought by long only equity and bond funds when the convertible is felt to offer an attractive alternative to either equity or straight bond of the issuer. Hence it is usually only at the extreme ends of the scale, when the convertible is trading as a bond, or when it is trading as an equity proxy, that a convertible will be attractive to managers of these asset classes. In the middle, its low equity price sensitivity will diminish its attractiveness to equity managers, and its low yield will underwhelm bond managers. Otherwise convertibles are bought outright by managers of specialist funds, whose remit is to exploit the characteristics of the instrument, not to mimic bond or equity-like returns.
A convertible arbitrage fund will buy a cheap convertible on the expectation that its price will increase, relative to its underlying stock and bond components. Typically this cheapness is expressed in terms of implied volatility, meaning that the pricing of the convertible implies a stock volatility below the likely future volatility of the stock price. A convertible bond arbitrage fund buys a convertible and takes short positions in the stock on an equivalent exposure basis, according to a theoretically determined hedge ratio called the delta. As the stock price moves up and down, the delta will change and the manager will adjust the short position in the stock accordingly. Since the manager sells into stock price rises and buys back into stock price falls these delta adjustments are money-making. The activity is called ‘gamma trading’, because the option term for changes in delta is gamma. The greater the stock price volatility, the more the arbitrageur will have to rehedge. For this reason the convertible arbitrage strategy is often termed a ‘long volatility’ strategy, since the arbitrage fund will benefit when stocks are more volatile than the implied volatility of the convertible instrument purchased.
Besides the profits made from gamma trading, the convertible arbitrage fund will also reap returns from positive carry, since the sum of the coupon on the convertible and the interest income on the short stock will typically be greater than the dividends paid by the underlying equity. Another source of returns is if the convertible becomes more expensive, relative to theoretical value, in which case the entire position can be unwound at a profit.

To be confident in his ability to pursue the strategy, the convertible arbitrageur must have a reliable model for the calculation of theoretical value and delta and accurate estimates of credit spreads and forward volatility to use as inputs. Because the returns on individual trades are quite small, of the order of 1% of nominal, the manager must leverage his book to achieve adequate levels of risk and return. Convertible arbitrage funds are at risk to changes in the terms of trade, whether it be withdrawal of financing, a shortage of stock borrow, or corporate events, which might adversely affect the position of convertible holders relative to equity holders.
As opposed to solely exploiting the convertible market’s implicit understatement of equity volatility, long only convertible funds can take a more balanced approach to convertibles, assessing the risks and opportunities from taking positions in credit, interest rates (via duration), equity direction and volatility. But, as Anthony Smouha, managing director of Atlanticomnium, and external manager of the GAM Dollar, GAM Swiss Franc Special Bond and GAM Sterling funds, comments, “in the current relatively stable interest rate environment, we will look for convertibles where we are happy with the credit risk, or both credit and equity”. GAM Dollar fund, which is 35% in convertibles, focuses on yield, value and capital preservation. Smouha takes explicit views on improvements in the credit and/or equity , focusing primarily on convertibles with a good running yield. Smouha will analyse the company issuer’s capability to repay debt out of cash flow and suggests that some of his best bets in the last couple of years have come from exploiting convertible arbitrage funds’ increasing difficulty in hedging credit, which forced some to dump stock at fire-sale prices. At times like these, convertible investing has parallels with distressed investing. When a company is in difficulty, the position of convertible holders is usually preferential to equity holders, since as a debt holder they will have a prior claim on the assets. On the flipside, the convertible still has access to equity returns should the position improve.
As the environment for issuance improved in spring of this year, Smouha participated in a number of new issues, such as Man Group, Hilton and EMI. Within the Sterling fund, Smouha writes call options on the underlying stock against his holding in the convertibles, turning the equity component into additional income. This strategy is especially beneficial when option premiums reflect high expected volatility, and can compensate when convertibles are trading theoretically expensive. By offsetting the option premium against the cost of the bond, the downside risk is also reduced. Despite sharp falls in equity and widening credit spreads, the performance of this fund in 2001 was 1.8%. Performance in 2003 year to date is 14.6%.
The dominant role of hedge funds in convertible pricing has changed the structure of the convertible market so currently few new issues meet the requirements of the dollar fund. In a low interest rate environment, there is a tendency towards small coupons and high premiums. Convertible bonds have been launched with negative redemption yields and a zero coupon. However, specialist convertible manager Adrian Hope, of Jefferies Asset Management, disagrees with the suggestion that convertibles have become more expensive, suggesting that apparently high implied volatilities are due to a mispricing of credit at too wide a spread, understating the improvement in the credit market. Hope remarks, “often the lack of differentiation of hedge funds provides us as a minority participant greater opportunity”. Hope cites the example of a convertible whose underlying stock cannot be borrowed, putting it outside the universe of hedge managers. Such a bond will trade extremely cheap relatively to theoretical value, since its mispricing is impossible to extract via gamma trading. “The bond will still perform if the equity rises, and if stock borrow becomes available down the line there will be an immediate uplift to the convertible price,” explains Hope.
Jefferies runs $920m in convertibles, split between segregated mandates, some of which are Swiss pension funds, and three convertible bond funds. The firm employs a top-down framework to determine overall portfolio structure, and uses bottom-up analysis to identify individual bonds. It measures its funds against its own Jefferies Active Convertible Index (JACI) benchmark, which has been calculated since 1993. JACI takes US, European, Japanese and Asian component indices to create a global benchmark. Liquidity and price transparency are the main criteria for inclusion. The index retains the key feature of downside protection by omitting those convertibles that have become equity proxies. Jefferies has published material comparing the returns of this benchmark with those of bonds, equities and a 50:50 equity/bond portfolio over the period 1993-2002. Over this period, the maximum drawdown of the JACI was 13%, the annual return 6.5% and risk 8.5%. Over this period the best performance came from BB bonds, with annual return of 7.3% and risk of 5.1%. Equities suffered a far worse maximum drawdown, at 48.5%, and lower annual returns at higher risk than convertibles. Surprisingly to some, the risk/return profile of the 50:50 bond/equity portfolio was also inferior to the convertible portfolio, with maximum drawdown 20.2%. The results are even more impressive if one considers only the European component, where convertibles kept pace with the 50:50 portfolio from 1993-1997, but suffered a far smaller maximum drawdown during the more challenging 1997-2002 period, and annual returns similar to a 100% bond portfolio.
Considering this analysis, Hope highlights that the structure of the convertibles market automatically adjusts in response to changing market conditions. Whereas in 2002 the funds had large credit bets, simply by virtue of a lack of equity content in the market, as the equity markets started to perform, in the second quarter of 2003, the equity content of the existing portfolio increased and was augmented by new issuance. Now the equity content of the JACI benchmark is 32%, against 17% in March 2003. Equally the risk factors of the convertible market changes over time as it becomes more attractive to issuers from different industry sectors, as Hope elaborates, “convertible bond issuance follows general capital markets activity but as the convertible universe requires constant regeneration its composition will be dictated more by recent issuing trends than other asset classes. That should be a good thing for investors.”
In the second quarter 2003 when US convertibles were trading with implied volatilities of 40% in the US, many convertible arbitrage managers were questioning whether future volatility could justify these levels. Not surprisingly the corporate side were tempted by the terms available and a flood of new issues poured out. Some of these new issues were sizable, for example the $4bn General Motors, which was launched around theoretical value. This caused the market to cheapen off rapidly over the summer, resulting in losses of 2% per month for some managers. Funds that emerged from this period relatively unscathed were probably taking more directional bets, or indulging in allied varieties of arbitrage, such as capital structure arbitrage. Currently option implied volatility is less than 20% in the US, and in the mid-twenties in Europe, but convertible implied volatilities are on average still above 30%. With a number of existing bonds being put, called or redeemed, convertible arbitrage funds have cash available to soak up new issues, and this is supporting the secondary market in the near term.
CSFB/Tremont publishes the most widely quoted index of convertible arbitrage funds, under the brand name HedgeIndex. Since 1994, the HedgeIndex Convertible Arbitrage index, which is an asset-weighted universe of managers, has yielded 10.46% average annual return, with a standard deviation of 4.81%. The maximum drawdown of 12.04% occurred during the 1998 LTCM crisis. Even applying some discount for the shortcomings of hedge fund index construction, these are impressive numbers. With new issues coming ever more expensive, can convertible arbitrage continue to generate this level of performance? Marcel Massimb, head of research and risk management at fund of fund manager LJH Global Investments, warns, “a potential source of trouble looking forward is managers’ increasing exposure to credit, because of the lack of opportunities for gamma trading. Credit spreads are very tight and might widen again as interest rates rise”. However, Massimb considers longer term that the strategy will continue to show positive returns.
Daniel Wood, portfolio manager with Concordia Funds, a $1.4bn multi-strategy manager that has been active in convertible arbitrage for 10 years, is more sanguine on future performance from the strategy. “I feel there is plenty of potential on the upside,” declares Wood, highlighting the fall in premium levels, and increased equity sensitivity of the market. “Now that the market is more balanced and the credit market is stable it is a more benign environment, despite the apparent lack of value. The higher equity content of convertibles, with average delta of 50%, means that managers have more risk factors to exploit.” Wood suggests that representing managers as rigorously applying theoretical models is misleading. Comments Wood, “convertible arbitrage has typically had its best returns when expectations for future volatility were positive. But in the last year managers have made money from improving credit. Although it might appear that convertibles are currently expensive, in reality the market rarely trades at the extreme ends of the volatility range. When volatility is high convertibles appear cheap and as volatility falls to the bottom end of the range they appear expensive. No manager is ever fully hedged; he will always have exposure to the relationship between credit and equity volatility.”