8.10 Valuation and analysis of convertible bonds

8.10.1 Defining features of a convertible bond

A convertible bond is a hybrid security that presents the characteristics of an option-free bond and an embedded conversion option.

The conversion option is a call option on the issuer's common stock, which gives bondholders the right to convert their debt into equity during a pre-determined period (known as the conversion period) at a pre-determined price (known as the conversion price).
The number of shares of common stock that the bondholder receives from converting the bonds into shares is called the "conversion ratio."
Investors usually accept a lower coupon for convertible bonds than for otherwise identical non-convertible bonds because they can participate in the potential upside through the conversion mechanism-that is, if the share price of the issuer's common stock (underlying share price) exceeds the conversion price, the bondholders can convert their bonds into shares at a cost lower than market value.
The issuer benefits from paying a lower coupon. In case of conversion, an added benefit for the issuer is that it no longer has to repay the debt that was converted into equity.
Convertible bonds can have a call or a put option.

8.10.2 Components of a convertible bond's value

The conversion value or parity value of a convertible bond indicates the value of the bond if it is converted at the market price of the shares.

Conversion value = Underlying share price x Conversion ratio The minimum value of a convertible bond is equal to the greater of the following:

Conversion value and Value of the underlying option-free bond

Theoretically, the value of the straight bond (straight value) can be estimated by using the market value of a non-convertible bond of the issuer with the same characteristics as the convertible bond but without the conversion option.
In practice, such a bond rarely exists. Thus, the straight value is found by using the arbitrage-free framework and by discounting the bond's future cash flows at the appropriate rates MARKET CONVERSION PRICE AND PREMIUM The market conversion premium per share allows investors to identify the premium or discount payable when buying the convertible bond rather than the underlying common stock.

Market conversion premium per share = Market conversion price – Underlying share price The market conversion premium ratio expresses the premium or discount investors have to pay as a percentage of the current market price of the shares:

Theoretically, the value of the straight bond (straight value) can be estimated by using the market value of a non-convertible bond of the issuer with the same characteristics as the convertible bond but without the conversion option.
The market conversion price represents the price that investors effectively pay for the underlying common stock if they buy the convertible bond and then convert it into shares.
As the underlying share price falls, the convertible bond price will not fall below the straight value. Viewed in this context, the market conversion premium per share resembles the price of a call option.
In practice, such a bond rarely exists. Thus, the straight value is found by using the arbitrage-free framework and by discounting the bond's future cash flows at the appropriate rates.

DOWNSIDE RISK AND UPSIDE POTENTIAL OF CONVERTIBLE BONDS Many investors use the straight value as a measure of the downside risk of a convertible bond and calculate the following metric:

The upside potential of a convertible bond depends primarily on the prospects of the underlying common stock.
Thus, convertible bond investors should be familiar with the techniques used to value and analyze common stocks
Despite its use in practice, the premium over straight value is a flawed measure of downside risk because, as mentioned earlier, the straight value is not fixed but rather fluctuates with changes in interest rates and credit spreads.

8.10.3 Valuation of a Convertible Bond is Valued in an Arbitrage-Free Framework

The most commonly used model to value convertible bonds is the arbitrage-free framework V lue of co vertible bo d V lue of str ight bo d V lue of c ll optio o the issuer's stock Value of callable convertible bond = Value of straight bond + Value of call option on the issuer's stock – Value of issuer call option Value of callable putable convertible bond = Value of straight bond + Value of call option on the issuer's stock – Value of issuer call option + Value of investor put option No matter how many options are embedded into a bond, the valuation procedure remains the same. It relies on generating a tree of interest rates based on the given yield curve and interest rate volatility assumptions, determining at each node of the tree whether the embedded options will be exercised, and then applying the backward induction valuation methodology to calculate the present value of the bond

8.10.4 Risk-Return Characteristics of a Convertible Bond, Straight Bond and Underlying

Common Stock When the underlying share price is well below the conversion price, the convertible bond is described as "busted convertible" and exhibits mostly bond risk-return characteristics. In contrast, when the underlying share price is above the conversion price, a convertible bond exhibits mostly stock risk-return characteristics. In between the bond and the stock extremes, the convertible bond trades like a hybrid instrument.

When the underlying share price is below the conversion price and increases toward it, the call option component increases significantly in value as the underlying share price approaches the conversion price. The return on the convertible bond during such periods increases significantly but at a lower rate than the increase in the underlying share price because the conversion price has not been reached yet.
When the underlying share price is above the conversion price but decreases toward it, the relative change in the convertible bond price is less than the change in the underlying share price because the convertible bond has a floor. This floor is the minimum value of the convertible bond, which in this case is equal to the value of the underlying option-free bond.

BOND ANALYTICS

Some market participants, in particular financial institutions, develop bond analysis system in-house.
How can a practitioner tell if such a system is adequate?
The system should be able to report the correct cash flows, discount rates, and present value of the cash flows. The discount rates can be verified by hand or on a spreadsheet.
Even if it is difficult to verify that a result is correct, it may be possible to establish that it is wrong by doing the following checks:
Check that the put-call parity holds
Check that the value of the underlying option-free bond does not depend on interest rate volatility.
Check that the volatility term structure slopes downward

Lesson Wrap-Up

This lesson should leave you able to explain the valuation and analysis of convertible bonds in a fixed-income context and connect it to the decisions made by issuers, investors, or analysts.

Review Prompts

Explain defining features of a convertible bond in your own words.
Explain components of a convertible bond's value in your own words.
Explain valuation of a convertible bond is valued in an arbitrage-free framework in your own words.
State one exam-style risk, valuation, or market implication of the valuation and analysis of convertible bonds.