# Convertible Bonds

Convertible bonds, often simply called converts, are usually debentures, which are unsecured bonds, that can be converted into common stock of the corporate issuer within a specified time period at the discretion of the investor. Either the number of shares or the share price is specified in the indenture. The number of shares of stock that each bond can be converted to is known as the conversion ratio. Thus, a bond that can be converted into 10 shares of stock has a conversion ratio of 10 to 1, or simply 10. If the share price is specified in the indenture instead of the number of shares, then the conversion ratio can be found by dividing the par value of the bond —\$1,000 — by the share price. Thus, if a share price of \$20 is specified, then the conversion ratio is \$1,000/\$20 = 50 shares. When the bond is first issued, the conversion price is much higher than the stock price.

Some bonds specify different conversion ratios, or different conversion prices, for different time periods. For instance, the indenture may say that in the first 10 years, the bond may be converted to 20 shares, and after that, they may be converted to 40 shares. There is also an anti-dilutive provision where the conversion ratio or conversion price is changed to reflect any stock splits or stock dividends.

The convertibility factor, like many special bond features, lowers the interest rate that the corporation would otherwise have to pay without this feature, and it appeals to investors who want current income, but would like to take advantage of any growth in the corporation. The bond yield is usually more than any stock dividend — called the yield advantage of the convert — but less than a straight bond from the same issuer. The premium over bond value is the difference in price between the convertible bond and a straight bond without the convertibility feature from the same issuer. Factors that increase the premium over bond value are:

• The demand from life insurance companies and other institutional investors who may be restricted by law from buying stock. Buying converts allows these institutional investors to possibly earn considerable more than just the yield, while having downside protection.
• Transaction costs for buying the bond and converting it into stock are lower than buying the stock itself.
• The longer the duration of the conversion option, the greater the premium.

Higher common stock dividends diminish the yield advantage, thus diminishing the premium over bond value.

Because convertible bonds are callable, the conversion can be forced by the company if bond prices drop. This eliminates debt and interest payments for the company.

The advantages of convertible bonds to an investor is that it offers appreciation potential if the company does well, and its stock rises; but, if the company suffers, and the stock price declines, then the investor can still keep the bond as a bond, and collect interest and principal, or sell it, based on the interest that it pays. If the company ever goes bankrupt, the bondholder will have superior claims over any stockholder.

Disadvantages include a lower interest rate, and the possibility the bond will be called prior to conversion, or even before when it can be converted, since some bonds restrict conversions to certain time frames. Rising interest rates can also have a detrimental effect on convertible bonds since rising interest rates not only cause bond prices to decline, but also stock prices. Therefore, the value of the convertible feature would decline as well, so the convertible feature can cause the price to decline even more with higher interest rates.

Converts can lead the market — like stocks — during a bull market. However, since convertible returns generally fall between those of stocks and bonds, an investor should only buy converts if the stock has a good possibility of appreciation; otherwise, it is better to buy a straight bond.

## Conversion Parity — the Relationship of Bond Price to Converted Stock Price

Conversion parity is a term used to describe the relationship of the stock price, multiplied by the conversion factor, to the bond price. For instance, if the bond is currently selling for \$1,200 and can be converted into 10 shares of stock, and if the current stock price is \$120, then the stock price and bond price are at parity. If the stock is selling for less than \$120, then it is selling below parity, and if it is selling for more than \$120, then the stock is selling above parity.

When the bond is first issued, the bond price is much higher than the conversion parity price. The difference between the bond price and the conversion parity price is the conversion premium (aka premium over conversion value).

Conversion Premium = Bond Price - (Stock Price × Conversion Ratio)

### Example: Calculating the Conversion Premium

If a bond, with a conversion ratio of 20, is currently selling in the secondary market for \$1,200 and the common stock is selling for \$50, what is the conversion premium?

Solution: Conversion Premium = \$1,200 - (\$50 × 20) = \$1,200 - \$1,000 = \$200.

## Convert Valuation Using a Premium Recovery Period or Payback Period

There are several methods for valuating convertibles, but 2 common methods are the cash-flow payback period and the dollar-for-dollar payback period. The premium recovery period or payback period is the amount of time it would take for the bond to earn the conversion premium plus all stock dividends over the period. In other words, what is the opportunity cost of buying the convert over the stock?

The cash-flow payback period is the time it would take for the convertible to earn interest equal to the conversion premium plus the stock dividends if the number of shares specified in the conversion ratio was purchased instead of the convert.

 Cash-FlowPayback Period = Conversion Premium / (1 + Conversion Premium) (Current Yield – Dividend Yield) / (1 + Conversion Premium)

The dollar-for-dollar payback period is like the cash-flow payback period except that the number of shares purchased is the number of shares purchasable at the convert's price.

 Dollar-for-DollarPayback Period = Conversion Premium / (1 + Conversion Premium) Current Yield – Dividend Yield

If the premium recovery period is longer than the term of the bond or the call date — if it is likely to be called — then it only makes sense to buy the convert if there is a good possibility that the stock price will rise above the conversion price during the time that the bond can be converted.

## Arbitrage — Profiting from the Price Difference between Bond and Converted Stock

When the price of the stock is below conversion parity, then the bond price will generally fluctuate with interest rates, just like any other bond. However, when the stock price exceeds conversion parity, then the bond price will increase in direct proportion to the stock price times the conversion ratio.

If Stock Price > Conversion Parity, then Bond Price Stock Price × Conversion Ratio

If the bond price is selling for less than parity, then this creates an arbitrage opportunity, which is the buying and selling of the same or derived securities to profit from a price discrepancy among the different securities. In this case, if the bond is selling for less than the stock price × conversion factor, then an arbitrageur can make money immediately by selling the stock short, and buying the bond. The stock is sold short because the conversion takes time, and if the arbitrageur waited, the price of the stock might decline. Then the arbitrageur simply converts the bond into shares of stock to cover the short. Arbitrage creates demand for the bond, thereby increasing its price, and selling short the stock decreases its price, which maintains conversion parity.

### Example: Arbitrage Profits when the Convert Trades for less than Conversion Parity

A convertible bond that can be converted to 10 shares of stock is selling for \$1,050, and the stock is selling for \$120. Selling short 10 shares of the stock would yield \$1,200, and buying the bond to cover the short would yield a net profit of \$150.

## Forced Conversion of Bonds into Stock

Sometimes a corporation can impel a bondholder to convert his bonds into stocks. If the bond is trading at a premium, above the call price, then the corporation can call the bond at a lower price. However, the corporation must give notice, usually at least 30 days, to the bondholder before it is called. This gives the bondholder the opportunity to convert the bond, if the converted stock is worth more than the call price. Another situation that can cause a bondholder to convert is if the company raises the dividend on the stock, such that the total dividend of the converted shares exceeds the interest paid on the bond.