4. Valuing a Convertible Bond
The convertible bond has three main parts: its value as a straight bond, called the
investment value; its value as a stock, called the conversion value; and the theoretical
fair value. The investor must dissect the convertible security to understand the valuation
process. The three factors are interdependent, and each must be considered for a proper
valuation of a convertible security. In this section, we begin the process of evaluating
convertibles by dissecting the convertible bond into its various parts.
What is the investment value?
A convertible bond’s investment value is its value as a bond. This is the fixed-income
component of the convertible. Keep in mind that investment value refers to this one
aspect of convertible valuation and is not the same as the convertible security’s market
value. Conceptually speaking, it is the value of the bond without the conversion feature.
It is calculated by determining what the value of the bond would be if it were not
convertible, according to standard fixed-income analysis—company fundamentals, type
of bond (collateral or debenture), coupon and maturity date, sinking fund requirements,
call features and yield to maturity. The market value of a straight bond fluctuates with
any changes in these factors. However, since the investment value of a convertible bond
is embedded and is a component of the total market value of the convertible, changes in
fixed-income determinants may not directly affect its market price.
Figure 4.1 shows the relationship between the common stock price and market price of
the bond investment value graphically as a horizontal line for normal price fluctuations.
With the convertible value shown on the vertical axis and the stock price shown on the
horizontal axis, the effect of changes in the variables is easily determined.
The investment value of a bond remains stable over a wide range of stock prices, if
we assume stable interest rates for the sake of simplicity. The financial stability of
the company and most of the other bond quality factors change slowly, if at all. Since
investment value, therefore, remains constant over relatively short periods of time, it
appears as a horizontal line on the graph. The bond value is not affected by increases
in the value of the common stock, although the market price of the convertible will be
affected. In situations of deteriorating creditworthiness, the stock price begins to sink
to zero. The obvious probable cause for this is a not-so-normal deterioration of company
financial fundamentals, which causes the expected recovery of the full principal to come
into question. As show in Figure 4.1, the value of a convertible bond must also approach
its bankruptcy value.
The decline of a particular stock due to overall negative market sentiment should
not influence the investment value especially in the short run. The investment value
will continue to provide an investment floor below the convertible market price,
and the convertible bond should not fall below its investment value as long as the
creditworthiness of the issuer remains unchanged. This provides the essential safety
element in convertible bonds. Furthermore, the convertible feature should ensure
that convertible securities will always be more valuable than income-equivalent nonconvertible
Figure 4.1. A Convertible’s Investment Value
Source: Calamos Investments.
Establishing the investment value of a convertible requires rigorous credit research, above and beyond any available third-party credit ratings.
However, there are a number of factors that do influence the investment value of a
convertible security. If the common stock declines due to company factors (unsystematic
risk), poor earnings, or other causes, the bond’s investment value will be influenced,
similar to the way the value of a straight bond is influenced by a ratings downgrade. In
fact, deterioration of company fundamentals should cause a ratings downgrade. A stock
decline caused by such factors will also cause the investment value to decline, reflecting
the possibility that the company may not be able to pay the coupon or principal of the
bond. In the ultimate case, both the value of the firm and the bond investment value
would approach zero. Studies have shown that dramatic changes in the fundamentals of a
company will have an immediate effect on bond investment value. Investors who ignore
these fundamentals in evaluating convertibles will be at a distinct disadvantage
in the marketplace. Rating agencies may assist in this effort, but may not always be
In approaching this mathematical analysis of convertible securities, it’s convenient to
assume a stable investment value over the short term and that stock price fluctuation is
due to general market sentiment. The investment value does fluctuate over the longer
term, and it must increase to par value by the time the bond matures, regardless of how
the common stock is changing.
Of course, interest rates affect the investment value of convertibles like they affect the
value of straight bonds. As interest rates increase, the investment value will decline; as
interest rates decrease, the investment value will rise. The investment value fluctuates in
tandem with the price of straight corporate bonds of similar quality.
However, due to the unique nature of convertibles, a change in the investment value of the
convertible bond may not necessarily mean a change in the market price. The investment
value may fluctuate, but the market price of the convertible bond remains relatively
stable because changes in interest rates are just one of many factors that may be affecting
the market price at any given moment. A bond that is trading close to its investment value
will be relatively more affected by changes in interest rates than one that is trading close
to its conversion value and well above its investment value. If the underlying stock is
increasing in value as interest rates are rising, the convertible bond will be driven by its
equity component rather than by its fixed-income component and will increase in value.
It is important to recognize that the investment value of a convertible bond at issuance
is rarely near par. The convertible bond is not discounted at its coupon rate, but rather
must be discounted at a rate appropriate for the issuing company’s non-convertible debt.
For example, if the company has issued a convertible with a 2% coupon and its nonconvertible
debt is at 5%, then the investment value of the convertible will be discounted
at 5%. On a five-year bond, the investment value will be $868.72 for a bond with a $1,000
Arriving at a proper estimate of the investment floor is critically important in evaluating
a convertible bond; it constitutes the minimum value below which the convertible
bond should not fall, regardless of common stock fluctuations, and influences all other
calculations in the mathematical analysis of convertibles. Because investment value is
the hinge on which all other calculations depend, it’s important to understand how the
various factors affect it.
What is the investment premium?
The convertible bond’s investment premium is the difference between the convertible’s
market price and its investment value, expressed as a percentage. An important measure
of the basic value of the convertible is its premium over investment value. At this point,
we determine the convertible’s market value by calculating the difference between the
convertible’s market price and its investment value, expressed as a percentage. This
value is important because it indicates the level of downside risk and can be monitored
as market prices change. For example, in the case of a bond with a par value of $1,000 and
an investment value of $868.72, the investment premium is ([$1,000-$868.72]/$868.72),
which is equal to 15.1%.
The higher the investment premium, the more sensitive the market price of the convertible
is to a decline in the underlying common stock. A high market price relative to investment
value is caused by increases in the value of the underlying stock such that the convertible’s
market value depends on the value of the stock. There is less downside protection because
the stock would have to decrease in value by a significant amount before the market price
of the convertible would approach the investment value and offer protection.
Delta is a measure of a convertible security’s sensitivity to its underlying equity, with higher deltas indicating greater sensitivity.
Similarly, when the investment premium is small, a small decrease in the value of the
underlying stock would result in the market price reaching the investment value. At that
time, the investment value floor provides downside protection. Furthermore, when the
investment premium is small, the convertible is more interest rate sensitive rather than
equity sensitive and will typically be vulnerable to changes in market interest rates.
What is the conversion price?
The convertible’s conversion price is the effective price for conversion into the stock
with the bond at par. At the time of issue, the offering prospectus indicates the common stock
price equivalent to the value of the bond at par. This price in turn determines
the number of shares of stock into which each bond at par can be converted; this is the
Confusion often arises among investors because the conversion price is specified in the
bond documents, but the conversion ratio is not; it must be calculated. The conversion
price is meaningful only when the bond is at par, and it can be calculated by dividing the
par value by the conversion price. For example, if the common stock price at which the
bond can be converted is $50, then each convertible bond represents 20 shares of stock
(par value of $1,000 divided by stated conversion price of $50 = 20).
Investors often focus on the conversion price when they should be paying more attention
to the conversion ratio. From the moment the bond is brought to market, it trades either
above or below par value, depending on the market forces. Since the conversion rate
remains the same whether the bond is at par or not, it is the more important number for
What is the conversion ratio?
The conversion ratio determines the number of shares of common stock a convertible
bondholder would receive if the bond were converted into stock. The conversion ratio is
set at the issuance of the security and is typically protected against dilution. It may well
specify partial shares (i.e., 21.3 shares).
The conversion ratio is usually adjusted for stock splits and stock dividends. The initial
conversion ratio in our example was 20 shares of stock per each convertible bond. The
conversion ratio would be adjusted to 22 following a 10% stock dividend. Prior to 2003,
convertible bondholders were rarely protected against normal cash dividends. Today,
they are generally protected against normal cash dividends as well as special dividends
and spin offs. (We discuss this in greater length on page 21.)
Figure 4.2. A Convertible’s Equity Value
Source: Calamos Investments.
Equity analysis is the lynchpin for determining conversion value.
What is the conversion value?
Conversion value represents the equity portion of the convertible bond. It is what the
convertible bond would be worth if it were converted into common stock at current
market prices. In Figure 4.2, the diagonal line indicates the conversion value. For any
stock price, the conversion value is found by multiplying the given stock price times
the stated number of common shares received per bond. For example, if a bond can be
converted into 20 shares of stock and the stock currently sells at $42 per share, the
conversion value of the convertible bond is $840. As we have said previously, the number
of shares each bond can be converted into is the conversion ratio and is set at the time the
bond is issued.
Like bond investment value, conversion value is a minimum value or price at which the
security is expected to sell. If the market price fell below the conversion value, specialists
and market makers would quickly take advantage of the situation; the arbitrageur would
buy the bond and simultaneously sell an equivalent number of shares of the underlying
common stock. The difference between these two values would be a risk-free profit to the
arbitrageur. Because of this, conversion value, like investment value, becomes a minimum
value, below which the convertible’s market price should not fall.
Figure 4.3. A Convertible Bond’s Conversion Premium
Source: Calamos Investments.
Through modeling and convertible analysis, the active manager establishes the fair value price track for a convertible.
What is the conversion premium?
The equity value of a convertible bond was determined to be its conversion value. Conversion premium can be calculated easily by simply taking the difference between the current market price of the convertible and the conversion value and expressing it as a percentage. Since the convertible bond is more secure than common stock and generally pays higher interest than the stock dividend, the convertible bond buyer is willing to pay a premium over the conversion value. Market forces determine the amount of premium that a particular convertible may command in the market place. However, it should make sense that, as a convertible bond price increases above its investment value, its fixed-income attributes give way to equity characteristics, decreasing the conversion premium. On the other hand, if the stock price declines, the convertible bond price approaches its fixed-income value and the conversion premium increases. Convertible bonds that are trading near their fixed-income values with substantial conversion premiums are called “busted converts.” Their equity component is of little value, and they trade mainly on their fixed-income characteristics.
Figure 4.3 depicts a typical convertible price curve, with the shaded area denoting
conversion premium. Notice that as the stock increases in value, conversion premium
gradually decreases until it becomes zero. At that point, the convertible market price and
the conversion value are equal. As the common stock declines in value, the convertible
gains conversion premium because it is approaching its investment value.
From another perspective, the market value of the convertible should always be higher
than either the conversion value or the investment value. If we were to hypothesize a
convertible with a market value that exactly equaled its investment value, the investment
premium would have a value of zero and the convertible would be trading as if it were
a straight non-convertible bond. However, a convertible security has an implicit option,
and as long as there is time remaining before the option expires—thereby providing the
holder with equity potential—the option will have some value in itself.
The convertible price curve can be either an estimate of how much conversion premium
a particular convertible security would command at various stock prices or a historical
depiction of how a convertible has actually traded as the common stock has fluctuated
over time. It is an extremely important consideration in evaluating convertible
securities because it determines the upside potential versus the downside risk. Detailed
mathematical formulae are needed to estimate the convertible price curve accurately.
It is inadequate to rely on simple historical price relationships to properly analyze the
fairness of the conversion premium level.
What is the relationship between conversion value and
To illustrate the relationship between the conversion value and the investment value of
the convertible bond, we will disregard many of the realities of the marketplace. Figure
4.4 shows the relationship between movements in stock price (horizontal axis) and their
effect on the convertible bond’s market price (vertical axis). The arrow indicates the
ideal price at which this convertible bond may be purchased. At this price, if the stock
increases in value, the convertible bond’s value will increase at the same percentage. On
the other hand, if the common stock were to decline in value, the convertible bond would
be supported by its investment value and would maintain its market value.
Figure 4.4. Ideal Convertible Bond
Source: Calamos Investments.
In this simplified example, when the convertible bond is priced at this ideal point, it is
obviously a superior buy because it offers the same upside potential as the common stock
with none of the downside risk. The real world, of course, will not allow investors such
easy profit opportunities. In the financial marketplace there exists a trade-off between
the safety of the bond investment value and the opportunity of the conversion value. How
much an investor is willing to pay for that trade-off creates a premium above conversion
value, as well as a premium above investment value, and it becomes the most complicated
aspect of convertible investing. A measure of that value is the convertible security’s
There are two basic scenarios for holding a convertible bond. First, if the company stock
does well, the convertible increases in value—and can increase greatly in value as a bond
without equity conversion. Many investors who are new to convertibles don’t realize
that it is not necessary to convert to the underlying common stock to realize a profit. The
market price of a convertible varies with changes in the stock price, and the bond can be
sold at any time. The increased value of the stock will be reflected in the market price of
the convertible. Of course, the bondholder also has the option to convert the bond into
stock, although that is not necessary. Conversion occurs only at the request of the holder.
Second, if the stock does not do well, the bondholder retains the bond and collects the
coupon interest (which is almost always higher than the stock dividend), and par value
is repaid at maturity. When the stock stays flat or falls, the bondholder still retains
the investment value of the bond, which constitutes a floor value for the security;
theoretically, in an adverse equity market, the bond would not decline in price as much as
the underlying stock because of this investment value. Furthermore, if interest rates rise,
the bond principal is protected to some extent by the convertibility feature.
Although simple in principle, convertibles can be complex to manage. The dual nature of
convertibles—that is, they have characteristics of both stocks and bonds—is part of what
makes them so difficult to analyze, and the evaluation process must take both parts into
consideration. However, their dual nature is also what makes them so attractive as an
The investor can calculate the value of both the bond and the equity portions of the
convertible security, but that still doesn’t tell the entire story. The final piece of the
evaluation might be the hardest: pricing the security itself. The investor must determine
the bond’s theoretical fair value or normal expected price, the value at which it is fairly
valued in the marketplace, taking into consideration both its bond and its equity value, as
well as its call terms, volatility, and the term structure of interest rates. This theoretical
fair value is then compared to the market price to determine profit opportunity and
market advantage. The convertible can be over- or underpriced relative to the stock.
Figure 4.5. Convertible Bond Theoretical Price Curve
Source: Calamos Investments.
Actual trades differ from the theoretical price track, which highlights the importance of ongoing research and monitoring.
Figure 4.5 shows the history of a convertible bond’s actual prices with a theoretical
convertible price track overlaid. As the stock declined in value, investment value also
declined, because of credit deterioration. It indicates the importance of credit and
The investor must also evaluate how much the bond will rise or fall under different
market scenarios. The risk/reward characteristics of the individual security depend on
its value relative to its equity and bond values. This in turn determines the performance
of both the security and the portfolio within which it is included.
The proper selection of convertibles requires careful analysis, and simple rules of thumb
are likely to result in disappointing performance. Examples of such rules are: “Buy converts
only when the conversion premium is below 20%,” or “buy only when the time to break
even is less than three years.” Additionally, scenarios that may hold true in one interest rate
environment may break down in others. For example, the yield curve of the 1970s and the
yield curve of 2015 would have wildly different ramifications for convertible valuation.
What are the different types of convertible call provisions?
The call provision, which is standard in most bond indentures, is one of the most important
features affecting the price of a convertible security. The issuing corporation retains the
right to call the bond for redemption prior to final maturity. A call option gives the issuer a
certain amount of control over the convertible issue. Call terms and provisions are outlined
in the security’s indenture and determined at or prior to issuance. The call terms typically
indicate the circumstance under which the security can be called, the date, and the price.
Call protection can be either hard or soft. Hard or absolute call protection protects the
issue from being called for a certain period of time, no matter the circumstances. Soft (or
provisional) call protection allows the issuer to call the security immediately under certain
circumstances. Convertibles can be issued with either or both types of call protection.
When interest rates decline, issuers like to have the flexibility to be able to call an issue
if they think they can refinance it more cheaply. This is true in general for all corporate
bond issues. Convertible issuers have another reason for wanting a call option: calling an
issue forces bondholders to convert debt into equity, which can reduce debt levels and
have a beneficial effect on the balance sheet.
While a corporation’s preference is for the shortest possible call protection, giving
it the maximum amount of control over the convertible bond, it is just the opposite
for investors. Call protection acts to increase the value of the warrant feature of the
convertible bond since it allows a longer period of time for the stock to increase in value
and for the bondholder to convert the bond to the stock at a profit. While waiting for the
stock to increase in value, convertibles typically provide more income than the stock.
Without call protection, this income stream could be called away at any time, making
the convertible much less attractive. Provisional call protection helps ensure that the
investor will receive a certain level of capital gain before the issue can be called.
Before 1970, most convertibles did not have call protection. However, the tide turned
when a leading technology company issued a convertible in 1970 and called the issue
before it paid a single interest payment. Institutional investors were furious. Although
the convertible had increased in value due to the sharp increase in the value of the
common stock, many felt that the 20% premium they paid at the time of issue entitled
them to at least a few interest payments. This case and others brought enough pressure
on underwriters to demand call protection.
Soft call protection was introduced in 1982. This variation provided that the bond
could not be called unless the underlying stock increased to a certain level for 20 or 30
consecutive trading days. This level is typically defined as 140% to 150% above the
conversion price. The underlying common stock would have to increase somewhere
between 60% and 100% before the call could be effected.
A variation of soft call protection, the soft call with a make-whole provision, emerged in
the late 1990s and has evolved since. Such an issue becomes callable when the common
stock meets a certain price, but the issuer pays a make-whole premium, such as the
present value of the remaining coupons or some other compensation.
What antidilution protections do convertible bonds carry?
An antidilution clause protects the convertible security holder by allowing the conversion
ratio to be raised or lowered in certain situations. Historically, convertibles typically have
provided protection against stock splits by proportionately adjusting the conversion ratio
for the amount of a stock dividend. If a convertible had a conversion ratio of 30 shares
per bond prior to a two-for-one spilt, the conversion ratio would become 60 shares per
bond after the spilt. In cases of stock takeovers, convertible bond holders also have long
received antidilution protection, albeit to varying degrees.
Antidilution protections have strengthened in recent decades. While convertible
bondholders have long been protected against dilution resulting from stock splits and
stock takeovers, it was not until relatively recently that convertible bondholders were
protected from the dilutions resulting from cash dividends or cash takeovers. These
enhanced protections were driven largely by one company. In 2003, a casino issued a cash
dividend shortly after bringing a convertible to market, and the resulting dilution caused
an uproar among the arbitrage investors who held the convertible. In the wake of this
action, market participants basically forced underwriters to add protections in cases of
cash dividends. Dividend protection protects the bondholder in case the issuer raises or
initiates a dividend after issuing the convertible. If this happens, the issuer increases the
conversion ratio to offset the increase in the dividend. This adjustment then happens for
any subsequent dividends at the higher rate.
A year later, the same casino was purchased for cash and once again, convertible bond
holders were not protected. To ensure that a similar situation would not occur again,
investors began demanding antidilution protection in cases of cash takeovers as well.
Cash takeover protection is to essentially make the investor whole for the economic loss
they would otherwise suffer. Each convertible issue has what is known as a matrix as
shown in Figure 4.6 (also called a make-whole table). If a convertible issuer is acquired for
cash, the convertible holder can convert and receive additional shares from the matrix,
over and above what the holder would get from the conversion ratio. The idea is to offset
the loss of the time value of the embedded call option of a convertible. This matrix is also
used frequently for the make-whole for soft call protection for some bonds.
These changes marked a significant enhancement in bondholder protection and make
convertibles today more valuable than those issued prior to 2003, all things being equal.
The following table shows the number of additional shares by which the conversion rate will
be increased per $1,000 principal amount of notes for each stock price and effective date.
Figure 4.6. Hypothetical Convertible Issue Matrix
Source: Calamos Investments. The hypothetical illustration has been provided for illustrative purposes only and is not intended to project or predict the outcome of any particular investment.