From the December 01, 2008 issue of Futures Magazine • Subscribe!

Exploiting the limits of convertible bonds

Convertible bonds are hybrid securities that provide advantages to both issuers and investors. Corporations realize a number of advantages from issuing convertibles. They obtain long-term financing at coupon rates significantly lower than current market rates, indirectly increase equity capital while delaying dilution of current earnings per share, issue stock at above-market prices, and finance with unsecured debt because most convertibles are debentures — that is, a debt vehicle not backed by collateral.

Investors in convertible bonds own securities that combine the attributes of a bond and a call option on the issuer’s common stock.

The bond, or straight-debt portion may be valued at any time by discounting the future stream of coupon interest and principal payments back to present value at the market yield for the issuer’s unsecured long-term debt. On top of the straight-debt value is a call whose value depends on the current stock price and the market’s assessment of future movements in the issuer’s common stock price.


Each convertible has an assigned conversion price, the price at which the holder can convert the bond into common stock. Alternatively, the bond has a conversion ratio, the number of shares into which the bond is convertible. Because the principal value is usually $1,000, a conversion ratio of 20 (for example) would correspond with a conversion price of $50. Conversion ratios at the time of issue may be adjusted later for stock splits, stock exchanges due to mergers, and changes in the issuer’s capital structure.

The straight-debt value of a convertible is considered to be a floor price for the instrument, acting as support when the stock price falls and the option value is reduced. The debt value provides only a flexible floor, however, because a falling stock price together with a lower credit rating for the issuing corporation can lead to a declining straight-debt value.

Conversion value, equal to the conversion ratio times the current stock price, provides another base for the bond price. The conversion value is a stronger support than the debt value because of the possibility of arbitrage involving a short sale of the underlying stock and simultaneous covering with the undervalued convertible bond.

When the common stock price is lower than the conversion price, the ultimate base value is the straight-debt value; however, the principal value becomes a de-facto floor price for many convertibles even when the stock price falls far below the conversion price. As the stock price rises above the conversion price the conversion value becomes the relevant bond price support.

“Convertible bond prices” shows a sample of convertible bonds whose prices are supported by either the straight-debt value or conversion value.

In some cases, support is provided by both the debt value and conversion value. To the right of the intersection of $1,000 and the conversion value line, the primary base price is the conversion value. To the left of the intersection, the bond prices tend to relate more to the $1,000 principal value than to the straight-debt value, although the debt value would soften any further decline caused by falling stock prices.


The convertibles shown on “Convertible bond prices” are representative bonds chosen from those listed by the Mergent Bond Record in several months over the years 2005-08. The bonds have different conversion prices and conversion ratios, as well as separate implied call option strike prices. The securities are standardized by using ratios of stock price-to-strike price (S/E) and option price-to-strike price (W/E). These ratios are applied to a single conversion price, $25, conversion ratio, 40:1, and stream of stock prices from 0 to $50. The bond prices are the original prices listed by Mergent Bond Record. The resulting chart shows the bonds as if they had identical conversion terms.

To calculate the ratios of stock price and option price to the strike price, the strike price for each bond is equal to the conversion price less the per-share difference between the $1,000 principal value and the estimated straight-debt value. The straight-debt value is the zero price base of a convertible call option. Because the conversion value ascends at a 45-degree angle, the distance between $1,000 and debt value can be subtracted from the conversion price to find the strike price, the stock price at which the conversion value equals the straight-debt value.

There are two possible zero price lines, or horizontal axes, for the embedded call option. One is the lower level provided by the straight-debt value and the other is the $1,000 principal value of the bond. As shown on “Convertible bond prices,” the market frequently considers the principal value as the more relevant base line.


The method used here to compare convertible bonds based on their relation to the conversion value and straight-debt value support levels may be extended to evaluate other convertibles. One objective of this comparison is to select bonds for investment or hedging that are close to conversion value and at or slightly below the $1,000 principal. At this location, an increase in the price of underlying common stock should result in a corresponding increase in the convertible, while decreases in share price result in the convertible moving to the left, supported by the principal and straight-debt values and falling more slowly than the stock price.

Two convertible bonds illustrate typical market pricing. The bond prices for Best Buy on three dates show the convertible close to the conversion value when the stock price is above the conversion price and near the principal value when the stock price is lower. Merrill Lynch convertibles are LYONS (liquid yield option notes). These have an additional feature in giving the holder several dates on which the bond can be put back to the issuer at the principal value. This feature provides an assist to the bond’s price, which is near $1,000 when the stock price is considerably below the conversion price. On Merrill Lynch, the alternative straight-debt value for the LYON convertible is adjusted for the nearer maturity of the put option, 2012 instead of 2032.

Following the purchase of Merrill Lynch by Bank of America in September 2008, it is possible that changes will occur in the conversion terms or other features of the LYONS security.


“Convertible bond arbitrage” shows the results of a hypothetical hedging or arbitrage strategy using the Best Buy convertible bond, 2.25% coupon rate with maturity of Jan. 15, 2022. On Jan. 3, 2008, it is noted that the bond’s market price, $1,153, is close to the conversion price of $1,152. This means that an increase in the common stock price should be approximately matched by a gain in the bond price. The hedger will hold sufficient debentures to cover a short sale of 100 shares of Best Buy common stock.

The hedge uses five of the convertibles because the conversion ratio is 21.74-to-one. The main risk in this hedge is related to a potential decline in the bond price that may exceed a drop in the stock price; therefore, the strategy is to just cover the short sale against a rising stock price and not buy more bonds than necessary for that purpose.

The results from the hedge strategy are positive in this example, with the convertible bonds covering the short sale, and with the bonds declining just to the principal value while the conversion value continues down to $870. If the stock price had increased instead of falling, the five convertibles should have more than covered the loss on the shares sold short. This is because the conversion ratio is larger than one-to-one, and the coupon yield would add positive cash flow.


Volatility is an important variable in pricing shorter-term options. The differences in heights of price curves for stock and futures options are mainly attributed to expected volatilities of underlying assets. These effects are diluted when applied to longer-term convertible bond options, where the primary cause of a higher-than-normal option value is likely to be either a large coupon rate or short maturity, or both.

The convertible bond market lacks the liquidity and smooth price transitions of the equity and futures option markets. This poses problems for the usual option pricing models, but need not prevent carrying out profitable hedging and arbitrage strategies.

Because there are many different combinations of conversion ratios, conversion prices, coupon interest rates or zero coupons, delays in convertibility and other features, it is important to become acquainted with the prospectus for any convertible under consideration. Although there are certain basic similarities between various issues, it is best to treat each convertible as an individual before analyzing it along with other bonds in this general class.

Paul Cretien, CFA, is an investment analyst and financial case writer. E-mail him at

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