Investments & Securities Chapter 19 Analysis Convertible Bonds Summary This Focuses Convertible Bonds Explain

CHAPTER 19

ANALYSIS OF CONVERTIBLE BONDS

CHAPTER SUMMARY

This chapter focuses on convertible bonds. We explain methodologies for analyzing convertible

bonds, beginning with a review of the basic provisions.

CONVERTIBLE BOND PROVISIONS

A convertible bond is a corporate bond with a call option to buy the common stock of the

issuer. Exchangeable bonds grant the bondholder the right to exchange the bonds for the

common stock of a firm other than the issuer of the bond. The number of shares of common

stock that the bondholder will receive from exercising the call option of a convertible bond or an

exchangeable bond is called the conversion ratio.

conversion ratio

Along with the conversion privilege granted to the bondholder, most convertible bonds are

callable at the option of the issuer as of a certain date. This standard type of call option in

a convertible bond is called an unprotected call.

There is another type of call feature that is included in some convertible bond issues: The bond

may only be called if the price of the underlying stock (or the average stock price over some

number of days) exceeds a specified trigger price. This type of call is known as a protected call.

Another convertible that was at one time issued for its favorable tax treatment is one with

a contingent payment provision, nicknamed “CoPa” bonds. Unlike a traditional convertible

bond whose coupon rate is fixed over the bond’s life, a CoPa bond pays a higher coupon rate if

the price of the underlying stock prices reaches a specified threshold (say, 125% of the

conversion price).

Special Conversion Provisions

An investor must look carefully at the conversion privilege because not all bonds allow

a straightforward conversion privilege. Two types of convertible bonds issued prior to 2008 that

departed from the traditional conversion privilege are the net share settlement convertible and the

contingent conversion convertible.

CATEGORIZATION OF CONVERTIBLE SECURITIES

The U.S. convertible bond market is by far the largest convertible bond market. Most U.S.

convertible bonds are issued as private placements under Securities and Exchange Commission

(SEC) Rule 144A. Lehman Brothers publishes the Lehman U.S. Convertible Indices. The main

index is the Lehman Convertible Composite Index.

A convertible preferred is a preferred stock that can be converted into common stock.

Amandatory convertible is a convertible security that converts automatically at maturity into

shares of the issuer’s common stock. This automatic conversion differs from convertible bonds

where conversion is optional.

BASIC ANALYTICS AND CONCEPTS FOR CONVERTIBLE BOND ANALYSIS

Consider the following convertible bond with dividends per share = $1; current market price of

XYZ common stock = $17; current market price of XYZ bond = $950; par value = $1,000;

conversion ratio = 50; coupon rate = 10%; and, maturity = 10 years. If this convertible bond is

neither callable nor putable, then the conversion price for the XYZ bond is:

Minimum Value of a Convertible Bond

The conversion value of a convertible bond is the value of the bond if it is converted

immediately. It is expressed as:

conversion value = market price of common stock × conversion ratio.

Illustration

For the XYZ bond given above that has a current market price of $17 and a conversion ratio of

50, what is its conversion value?

We have:

straight value of the convertible bond would be $896. The minimum price for the convertible

bond must be its straight value in this case because that is a value higher than the conversion

value of $850.

Market Conversion Price

conversion ratio

An investor who purchases a convertible bond rather than the underlying stock typically pays

a premium over the current market price of the stock. This premium per share is equal to the

difference between the market conversion price and the current market price of the common

stock. That is,

market price of common stock

The market conversion premium per share can be seen as the price of a call option. The

difference between the buyer of a call option and the buyer of a convertible bond is that the

former knows precisely the dollar amount of the downside risk, whereas the latter knows only

that the most that can be lost is the difference between the convertible bond price and the straight

value.

Illustration

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market conversion premium ratio =

17$

2$

= 0.117647 or about 11.76%

CURRENT INCOME OF CONVERTIBLE BOND VERSUS STOCK

As an offset to the market conversion premium per share, investing in the convertible bond rather

than buying the stock directly generally means that the investor realizes higher current income

from the coupon interest paid on the convertible bond than would be received as dividends paid

premium payback period =

market conversion premium per share

favorable income differential per share

where the favorable income differential per share is equal to

Illustration

For the XYZ convertible bond where the coupon rate is 10%, the conversion ratio is 50, the

dividend per share is $1, and the market conversion premium per share is $2, how long would it

take an investor to recover the market conversion premium per share?

We first compute the favorable income differential per share, which is found by first computing

the coupon interest from the bond. We have: coupon interest from bond = (coupon rate)(par

value) = 0.10($1,000) = $100. Inserting the given values, the favorable income differential per

share is:

( ) ( )

coupon rate par value conversion ratio dividend per share

conversion ratio

 − 

=

( )

$100 50 $1

50

−

= $1.

The premium payback period can now be computed. We have:

favorable income differential per share

1$

Thus, without considering the time value of money, the investor would recover the market

conversion premium per share in two years.

Downside Risk with a Convertible Bond

straight value





The higher the premium over straight value, all other factors constant, the less attractive the

convertible bond.

Illustration

Earlier, we said that if comparable nonconvertible bonds are trading to yield 14%, the straight

value of the XYZ bond would be $788. The premium over straight value for bond XYZ would

be:

straight value





OPTION MEASURES

Because a convertible bond embeds a call option on the underlying common stock, we can

estimate the sensitivity of a convertible bond’s price from measures used in option theory. The

measures we describe are delta, gamma, vega, and implied volatility.

The measures are calculated by using a theoretical model to value the price of an option (the

most common for options on common stock is the well-known Black–Scholes option pricing

model) and determining how the theoretical value changes when a factor (holding all other

factors constant) changes.

Delta

The delta is used to estimate the impact of a change in the price per share of the underlying stock

on the convertible bond’s value as follows:

approximate change in a

convertible bond’s value = change in stock price per share × conversion ratio × delta

Multiplying the delta by the conversion ratio of 50 gives 30. This means that 30 shares must be

shorted in order to obtain a market neutral position. For example, suppose the price of the

underlying shares increases by $0.128. This means the short position consisting of 30 shares of

stock will lose $0.128 × $30 = $3.75.

Gamma

Duration is the first approximation of how the bond’s price will change when interest rates

change. The convexity measure shows for larger change in interest rates what the additional

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role as convexity. In the case of a convertible bond, gamma is the additional change in the

convertible bond’s value for a larger change in the price of the underlying stock.

Vega

An option’s vega is the sensitivity of the option’s price to a change in expected volatility for the

underlying. For a convertible bond, it is an estimate of the sensitivity of the convertible bond’s

price to a change in the expected volatility of the stock’s price.

Implied Volatility

PROFILE OF A CONVERTIBLE BOND

In describing how to categorize convertible securities at the outset of this chapter, one way to

categorize is by the convertible’s profile. Basically, by profile we mean the factors that dominate

the performance of the convertible such as the stock price of the issuer or the level of interest

rates and spreads. The categories according to Lehman Brothers are (1) typical, (2) equity

PROS AND CONS OF INVESTING IN A CONVERTIBLE BOND

One disadvantage of buying the bond is that the conversion price is higher than the price at the

time the convertible bond is purchased. Thus, the return will be lower unless the interest

payments for the length of ownership of the convertible bond are great enough to cover (i) the

higher price paid per share and (ii) any dividends that are forgone for the length of time.

Call Risk

Convertible issues are callable by the issuer. This is a valuable feature for issuers, who deem the

current market price of their stock undervalued enough so that selling stock directly would dilute

Takeover Risk

CONVERTIBLE BOND ARBITRAGE

Because of the investment characteristics of convertible bonds that we have described in this

chapter, their payoff characteristics allow the creation of different positions that can benefit from

the mispricing of a convertible bond. Seeking to capitalize on the perceived mispricing of

a convertible bond issue is referred to as convertible bond arbitrage.

Attributes of Issues for Use in a Convertible Bond Arbitrage Strategy

In screening the candidate list of convertible bond issues for a convertible bond arbitrage

strategy, the manager will prefer those with certain attributes for the underlying common stock

and for the convertible bond issue itself.

For the convertible bond itself, the following attributes are desirable in a convertible bond

arbitrage: (1) good liquidity, (2) low conversion premium, (3) high convexity, and (4) low

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arbitrage trades, typically a long position is established in the convertible bond, and

simultaneously, a short position is established in the underlying stock.

The objective in a volatility trading strategy is that regardless of how the price of the

underlying stock price changes, the mispriced convertible bond’s value will outperform the value

of the short position in the underlying stock’s value.

As with most option trading strategies, the position of a strategy must be changed as the price of

the underlying changes. There are option strategies that involve capitalizing on the expected

change in the delta of an option.

key factor is the expected price volatility of the stock: the more the expected price volatility, the

greater the value of the call option. As a first approximation to the value of a convertible bond,

the formula would be

convertible bond value = straight value + price of the call option on the stock.

The price of the call option is added to the straight value because the investor has purchased

movements of these two variables must be estimated and incorporated into the model.

KEY POINTS

• A convertible bond grants the bondholder the right to convert the bond into a predetermined

number of shares of common stock of the issuer. The number of shares is called the

conversion ratio.

in describing the investment characteristics of convertibles. These measures include delta,

gamma, vega, and implied volatility.

• Convertibles are classified according to their investment profile: typical convertibles (also

referred to as balanced convertibles), equity sensitive convertibles (also referred to as equity

substitute convertibles), busted convertibles, and distressed convertibles.

ANSWERS TO QUESTIONS FOR CHAPTER 19

(Questions are in bold print followed by answers.)

1. In the November 28, 1995, prospectus summary of the Staples 10% convertible

subordinated debentures due 2003, the offering stated: “Convertible into Common Stock at

a conversion price of $60 per share . . .” If the par value is $1,000, what is the conversion

ratio?

Let us rearrange the equation for conversion price to solve for the conversion ratio. We have:

conversion price =

par value

conversion ratio

➔ conversion ratio =

par value

conversion price

.

par value

conversion price

60

2. What are the similarities and differences between a soft put and a hard put in

convertible bonds?

Along with the conversion privilege granted to the bondholder, most convertible bonds are

callable at the option of the issuer. Some convertible bonds are putable. Put options can be

classified as hard puts and soft puts. Soft put and hard put are similar in the sense that both of

3. Upon exercise of the conversion option for a convertible bond, all issuers must exchange

shares of stock for the bond. Explain whether you agree or disagree.

When the holder of a convertible bond exercises the option to convert, the traditional outcome

was that the issuer exchanged the bond for the number of shares as indicated by the conversion

ratio. So in terms of a “traditional” bond, one could agree with the statement. However, one can

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treated favorably in the calculation of the issuer’s earnings per share. However, the change in the

financial accounting rules that were put into place in 2008 no longer made this type of financing

attractive to corporations. To see the popularity of these bonds before then, since 2005 when they

first became popular, $120 billion of the $171 billion of U.S. convertible bonds contained this

provision.

4. What is the difference between a mandatory convertible bond and a non-mandatory

convertible bond?

5. This excerpt is taken from an article titled “Caywood Looks for Convertibles,” which

appeared in the January 13, 1992, issue of BondWeek, p. 7:

Caywood Christian Capital Management will invest new money in its $400 million high–

yield portfolio in “busted convertibles,” double– and triple-B rated convertible bonds of

(a) What is a busted convertible?

(b) What is the premium over straight value at which these bonds would trade?

(c) Why does Mr. Caywood seek convertibles with higher investment-grade ratings?

A higher investment-grade implies a lower probability of default. This means that the convertible

bond will be around for awhile and longevity implies a longer horizon for achieving conversion.

(d) Why is Mr. Caywood interested in call protection?

6. What is the limitation of using premium over straight value as a measure of the

downside risk of a convertible bond? What is the premium over straight value for a bond if

the market price of it to be $200, and the straight value is $160?

Investors usually use the straight value of the bond as a measure of the downside risk of a

convertible bond because the price of the convertible bond cannot fall below this value. Thus the

straight value acts as the current floor for the price of the convertible bond. The downside risk is

7. This excerpt comes from an article titled “Bartlett Likes Convertibles” in the October 7,

1991, issue of BondWeek, p. 7:

“Bartlett & Co. is selectively looking for opportunities in convertible bonds that are

trading cheaply because the equity of the issuer has dropped in value, according to Dale

Rabiner, director of fixed income at the $800 million Cincinnati-based fund. Rabiner said

8. Consider a convertible bond as follows:

par value = $1,000; coupon rate = 9.5%

market price of convertible bond = $1,000

Answer the below questions.

(a) Calculate each of the following (1) conversion value, (2) market conversion price,

(3)conversion premium per share, (4) conversion premium ratio, (5) premium over straight

value, (6) favorable income differential per share, and (7) premium payback period.

(1) conversion value = market price of common stock × conversion ratio = $23 × 37.383 =

$859.809 or about $859.81.

market price of convertible bond

$1,000

(4) market conversion premium ratio =

conversion premium per share

market price of common stock

=

$3.57

$23

= 0.155217

or about 15.52%.

conversion price

26.750127

insert all of our given values into our favorable income differential per share to get:

( ) ( )

coupon rate par value conversion ratio dividend per share

conversion ratio

 − 

=

( )

$95 37.383 $0.75

37.383

−

= $1.7912621 or about $1.79.

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(7) premium payback period =

market conversion premium per share

favorable income differential per share

=

$3.5701127

$1.7912621

= 1.993071 or about 1.99.

(b) Answer the below questions if the price of the common stock increases from $23 to $46.

(1) What will be the approximate return realized from investing in the convertible bond?

First, we need to compute the conversion value for the bond. We have: conversion value =

market price of common stock × conversion ratio = $46 × 37.383 = $1,719.62. Assuming the

cost

par value

$1,000

The return would probably be slightly higher because the convertible bond would trade at a

slight premium to its conversion value. For example, at the time of the conversion, the rate

of return is:

conversion price

$26.75013

(2) What would be the return realized if $23 had been invested in the common stock?

The rate of return is:

current market price investment price

investment price

−

=

$46 $23

$23

−

= 1.0000 or 100.00%.

(3) Why would the return on investing in the common stock directly be higher than

investing in the convertible bond?

The reason for the lower return by buying the convertible bond rather than the stock

directly is that the investor has effectively paid $26.57 – $23 = $3.57 per share more for

(1) What will be the approximate return realized from investing in the convertible

bond?

There is currently no conversion value and with such a low price of $8 it is doubtful if the

convertible bond is selling at much of a premium. However, there is a 9.5% coupon

(2) What would be the return realized if $23 had been invested in the common stock?

(3) Why would the return on investing in the convertible bond be higher than investing in

the common stock directly?

The convertible bond has little downside risk as bond values do not have as much volatility

of common stock. This is because they have senior claims on cash flows compared to

9. A Merrill Lynch note structure called a liquid yield option note (LYON) is a zero-

coupon instrument that is convertible into the common stock of the issuer. The conversion

ratio is fixed for the entire life of the note. If investors wish to convert to the shares of the

issuer, they must exchange the LYON for the stock. As a result, the conversion price

increases over time. Why?

The formula for conversion ratio is:

conversion ratio = par value of bond / conversion price.

Rearranging we get:

10. Answer the below questions.

a. Suppose that a convertible bond has a conversion ratio of 20 and a delta of 0.70. For a

price change of $0.125 for the stock price per share, what is the approximate change in

the convertible bond’s value?

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approximate change in a convertible bond’s value =

change in stock price per share * conversion ratio * delta

For our problem, we have a conversion ratio is 20, a delta of 0.70, and a price change of $0.125

for the stock price per share. Inserting in these values, the approximate change in the

convertible bond’s value is: $0.125 * 20 * 0.70 = $1.75

b. How many shares of the stock must be shorted in order to create a market neutral

position by holding the convertible bond and shorting the stock?

The combined position of the convertible bond and the short position in the stock is said to be

delta hedged, delta neutral, or market neutral. The number of shares that should be shorted is

11. Why would you expect that a distressed convertible would have a delta of zero?

Delta ranges from 0 to 1. The delta can help describe the character of the convertible bond. At

one end of the spectrum is a delta of 1, which means that the convertible bond will mirror the

12. Suppose that the price of the underlying stock for aconvertible bond is considerably

higher than theconversion price. What would expect that convertiblebond’s delta to be?

Delta ranges from 0 to 1. The delta can help describe the character of the convertible bond. At

one end of the spectrum is a delta of 1, which means that the convertible bond will mirror the

13. The following quotes are from Mihir Bhattacharya, “Convertible Securities and Their

Valuation,” Chapter 51 in Frank J. Fabozzi (ed.), The Handbook of Fixed Income

Securities: Sixth Edition (New York: McGraw-Hill, 2001).

(a) Bhattacharya states:

“Increased debt market volatility has driven home the point of duration risk inherent in

any security with a fixed income component, including convertibles. The increased

What message is the author is trying to convey to investors?

The author is conveying that investors in convertible debt (or any fixed income security) should

not take lightly the value of its straight debt component, i.e., the straight value therefore acts as a

(b) Bhattacharya states:

“Convertibles have equity and interest rate options, and occasionally, currency options,

embedded in them. Issuers and investors are becoming even more aware that option

valuation is driven by, among other factors: (a) equity volatility; (b) interest rate volatility;

Explain why the factors mentioned in the quote affect the value of a convertible bond and

why the factors interact.

First, convertibles have equity options. The convertible can be converted at a profit into equity if

the price of equity rises above the conversion price. The probability of converting increases as

the volatility increases. As debt, a convertible issue can fall in value as interest rates increase.

This is because bond prices are inversely related to changes in interest rates. Spread volatility

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a higher yield from an increase in spreads. In fact, the stock price and the yield required by

investors are not independent. When the price of the stock drops precipitously, the perceived

credit worthiness of the issuer may decline, causing a decline in the straight value. In any event,

although the straight value may decline, it still is a floor (albeit a moving floor) for the

convertible bond price.

14. Why is a volatility trading strategy considered to be a non-directional strategy?

The objective in a volatility trading strategy is that regardless of how the price of the

underlying stock price changes, the mispriced convertible bond’s value will outperform the value

of the short position in the underlying stock’s value. Hence, this convertible bond strategy is

a non-directional strategy. That is, the performance of the strategy is based purely on the

volatility of the underlying stock price not the direction in which the stock price moves.

15. What is the difference between a busted convertible and a distressed convertible?

When the price of the underlying stock is very far below the conversion price, the convertible is

said to be a busted convertible. A distressed convertible can be viewed as a special type of

busted convertible where the price of the underlying stock has fallen so far below the conversion

16. What is a cash flow arbitrage strategy involving convertible bonds?

The cash flow from a convertible bond differs from the cash flow from a stock. The idea behind

a cash flow arbitrage strategy is to create equivalent positions in the convertible bond and

underlying stock so that any additional cash flow available from the convertible bond can be