Valuing Converts And Preferreds
New tax laws and market factors have whetted investors' appetites.
Izzy Nelken, president of Super Computer Consulting, shows how to price
these tricky instruments.
On October 20 the federal Reserve Treasury Board agreed that capital
coming from preferred shares will count as equities (Tier 1 capital) and
not bonds. This creates an enormous incentive to issue preferred shares
by allowing companies that issue them to improve their capital-to-debt ratios.
The IRS, moreover, continued to consider the interest the company pays as
a tax deductible cost. As a result, the after-tax cost of paying an 8 percent
coupon on its preferred shares would only be about 5.5 percent.
The costs of issuing these securities have dropped dramatically because
of competition on Wall Street-from 3 percent three years ago to about 1
percent today. Since these securities are sold in institutional rather than
retail markets, the costs and underwriting commissions are low.
In the last two months of 1996, we've seen more than $10 billion invested in these "tax preferred" securities issued. They are marketed
as private placements under rule 144a. Investors like them because of the
high coupon that is payable every three months and the chance they offer
to participate in any equity gains. The coupon on these securities is about
150 basis points above Treasuries and 30 to 40 basis points above similarly
rated corporate bonds. Investors rarely notice that the company may defer
coupon payment for up to five years without going into default.
Despite their attractiveness, the investors do not have voting rights,
may be delayed in receiving their interest and also own securities similar
to subordinated debt. The market, moreover, expects that in 1997 the tax
"loophole" will be shut off. Interest on these securities will
no longer be tax deductible.
Preferred shares and convertible bonds have many common features. Since
these are hybrid instruments, they require special analytical techniques.
It is instructive to look at a qualitative graph of the price of a convertible
bond with respect to the price of the underlying share.
This is a qualitative graph, not the price graph of any particular instrument. We assume here that the convertible can be converted into one share. Let's
make a few observations.
When the underlying stock price is at $100, the convertible's price is
about $125. This is $25 more than the bond price. The difference between
the price of a convertible bond and the price of an equivalent nonconvertible
bond is called the "conversion premium." Investors are willing
to pay more for the convertible since they hope to gain if the share price
will rise in value. This is known as the "hybrid region," the
place where most convertible bonds are first issued.
As the share price declines from $100 to $80, $60, $40 even $30, the
convertible bond keeps most of its value. This is because the coupons and
the principal associated with the convertible have an intrinsic value in
themselves. At these levels, known as the "bond equivalent" region,
the conversion premium almost disappears and we can treat the convertible
as a normal bond.
If the share price tumbles even more, however, and heads toward $10 and
lower, we notice a new effect. Investors now fear that the company will
become bankrupt and will not be able to pay its liabilities. As we can see,
normal bond prices decline drastically but the convertible's price suffers
even more. Usually, a nonconvertible bond ranks senior to the convertible,
so in case of bankruptcy the nonconvertible bond holders may recover more
than holders of the convertible. Because of the drastic nature of this decline
in the convertible's price, this is known as the "waterfall effect,"
which occurs in the "bankruptcy region."
Now, assume that the stock has appreciated from $100 to $120 and $140.
The convertible bond's price will appreciate with the price of the underlying
share. This is because the holders of the convertible are always allowed
to convert into common stock. Eventually, as the underlying common gains
in price, the convertible's price will converge with the price of the share.
At high stock-price levels, the convertible is said to be "trading
off the stock."
Risk and reward
We can tabulate the annualized returns and standard deviations of various indices from January 1988 through June 1996. A high Sharpe ratio means that
the return was high and the standard deviation was low.
Convertibles returned 83 percent of the S&P 500 but their volatility was only 57 percent of the S&P 500.
In most cases, the convertible's price will never reach levels as high
as $160. Many of the convertibles are also callable by the issuer. For example,
assume that an issuer decides to call the bond at par and announces its
intention to do so with the conversion value of the bond at $120. In this
case, the investors would rather convert the bond into shares and receive
$120 than wait for the call date and receive only $100.
In this "forced conversion" scenario, the issuer forces holders to convert their bonds into equity.
We can almost think of the converts market as a game between two opponents: the holder of the bond tries to maximize its value at all times while the
issuer of the bond tries to minimize its value. Issuers usually prefer to
force conversion, as they would rather pay in shares than in cash. As a
result, the issuer typically allows the share price to appreciate to a level
beyond the conversion threshold before announcing the call. The purpose
of allowing the stock to climb higher is that even if the share price falls
somewhat during the call period, investors would still choose to convert
over accepting cash. In the example above, the issuer waited for the conversion
value to become $120 before calling the bond.
Variations and effects
There are several important variations on this basic structure. In some
cases, convertible bonds are issued with "put options." The investor
may put the bonds to the issuer. In other words, the issuer is obliged to
purchase the bonds at a predetermined price on certain dates. Put options
increase the price of the bond. Some convertible bonds are issued in the
form of zero-coupon bonds. They pay no coupon and are sold at a discount.
Such instruments are known as "Lyons."
When an investor converts and receives shares, the shares may be distributed either from the corporation's existing stock or from a new issue of shares.
In the latter case, we have to account for a "dilution effect."
There are now more company shares for the same capital base. Even when it
is financially advantageous to do so, however, some investors may refrain
from converting. This may be because of tax considerations or perhaps forgetfullness.
In these cases, we note a "partial dilution."
Some of the more recent issues are convertible into shares of different
issuers who may be in different countries. For example, there are several
U.S. convertible bonds whose underlying shares trade in Japanese yen or
Thai bhat. In this case, the investor must also consider the currency risk
Dividends also affect the share price and, as such, they make an impact
on the price of the convert. At times we may want to model a certain dividend
yield. In other circumstances, the yield may be a cash amount that is fixed
regardless of the price. In many situations the next few dividends may be
modeled as known cash dividends and, thereafter, it is more appropriate
to model a dividend yield. Still, in other cases we may know some part of
the dividend for sure and model the rest as a dividend yield. The estimation
of future dividends is a complex field of study in itself.
Many bonds exhibit step-up (or step-down) coupons in which the coupon
rate varies with time. These changing coupons must be considered by the
From the issuer's point of view, conversion is a privilege granted to
the investor in return for a lower coupon. So when issuers are contemplating
coming to market, they must determine the minimal coupon and conversion
privilege that the market will bear. During times of low volatility, the
issuer can bring a deal that is similar to a deal done in the past. When
markets change rapidly, however, issuers must rely on theoretical pricing
Investors have a variety of convertibles that are continuously being
offered to them and look at converts differently. Money managers look at
the universe of convertibles. They only consider issuers whose stock seems
to be favorable. If they are bullish on the equity, they may purchase the
corresponding convertible. There are many subcategories: convertible fund
managers, fixed-income managers, risk-averse equity managers, income-oriented
equity managers and so on.
Arbitrage specialists, by contrast, attempt to lock in profits that result from misalignment between the equity market and the convertibles. They may
be long the convertible bond and short the corresponding equity or vice
versa. Since they maintain a close watch and a constant hedge, they are
less concerned about the positive outlook for the equity.
All of these investors must be able to determine whether a particular
deal is attractive. In addition, they must continuously monitor their portfolios.
In some cases, convertibles are illiquid instruments and it is difficult
to obtain a recent market quote. Thus, in many cases, investors wish to
"mark-to-model." Because of the illiquid nature of these instruments,
there is a premium on a trader's ability to execute a trade and get a fill.
It pays to be "connected to the market."
Convertible bond holders are exposed to a variety of risks, including
equity risks and the risks associated with fixed-income instruments. In
addition to continuously pricing their portfolios, investors also need to
determine risk measures and sensitivity parameters. Some of these risk measures
are associated with the equity markets (for example, Delta, Gamma or Vega).
Other measures are similar to the ones employed by fixed-income managers:
duration, convexity, key-rate duration and convexity, and so on.
There are four generations of convert models. The earliest compared the
relative advantages of owning the convert vs. owning the underlying shares
outright. By subtracting the dividend yield from the coupon, the method
computes a relative "yield advantage." Then, it computes the time
required for the yield differential to compensate for the initial "conversion
premium." During the 1970s several institutions manufactured a plastic
and carton circular slide rule that was used to compute relationships between
various factors. It was able to manipulate the "conversion value,"
"conversion premium," "conversion price" and "stock
A slightly more sophisticated approach considered the convertible as
a combination of a regular (nonconvertible) bond plus a call option on the
stock. The bond and call option are priced separately. Their prices are
then added to determine the price of the convertible. This method may work
reasonably well when the convertible is either an equity equivalent or a
bond equivalent. It is quite inaccurate in the hybrid region. This is unfortunate,
because most of the new issues are in that region, however. This is also
where most of the opportunity and value in the convertibles market are found.
In November 1994, Emanuel Derman's group at Goldman Sachs released a
paper entitled "Valuing Convertible Bonds as Derivatives." They
used the put-call parity and observed that you can think of a convertible
as a straight bond plus a call option that allows you to change the bond
for equity. Another way to think about the same convertible is as an equity
plus a put to exchange the equity onto a straight bond plus a swap to maturity
that gives you the bond's coupons in exchange for the equity's dividends.
In the paper, they also described a model that uses a binomial stock price
tree to price the convertible. They assume a constant risk-free rate, a
constant credit spread and a constant stock loan rate. A model that allowed
interest rates to change as a function of time would be more flexible.
The most advanced models consider the stochastic nature of both interest rates and share prices. This is the essence of a "two factor model."
Almost everyone agrees that "Convertible bonds, for example, should
be valued according to a model that considers both the behavior of interest
rates and the issuer's stock price" (see "The Problem with Black,
Scholes et al," Andrew Kalotay, Derivatives Strategy, November 1995).
However, two-factor models are quite sophisticated and much more difficult
Evaluating convert models
A good software system for converts and preferreds must do more than
compute accurate results.
- It should be based on the two-factor algorithm, and should be able
to cope with all the complications mentioned above and to accommodate some
new "wrinkles" that the market may come up with in the future.
- Since convertibles, by their very nature, depend on a lot of data,
the system should be well-organized, intuitable and user-friendly.
- Many models in this class suffer from "graininess" or "lack
of continuity." Often, a user makes a small change to one of the input
variables and discovers a large and inappropriate change in the value of
- A model should compute not only the price of the convertible, but also
all of the relevant risk and sensitivity parameters.
- A system must be in place to accommodate entire portfolios of convertible
bonds. Also, there must be a provision to compare and sort a universe of
bonds from an attractiveness standpoint. On the other hand, each individual
bond must be modeled correctly.
- An important advantage is to be able to connect to a database or a
data feed automatically. There is too much information to maintain all
the data manually. Even if the database does not provide 100 percent of
the required information, it will provide at least most of it.
- In the case of bonds that do not yet exist or are not covered by the
database, there should be a simple provision to add their details into
- Finally, the software must be able to handle nonconvertibles that are
callable and "putable" correctly. Therefore, it must have all
of the characteristics required from any standard bond-pricing algorithm:
it must be arbitrage-free, easy to calibrate and so on.
As financial instruments become more complex, less intuitable and less
liquid, market participants need to rely on complex mathematical models.
But mathematical models should only be used as a tool to assist the human
trader. It is up to traders to develop and hone their intuition, keep up
with the markets with constant education, and use the best tools to full
advantage. The old divisions between fixed income and equity are rapidly
being challenged by the amazing growth in hybrid instruments such as convertible
bonds, preferred shares and other types of mandatory converts.
For more information on convert and preferred models, see www.s-com-computer.com
A Converts & Preferreds Primer
Many investors feel that the market is in a cautious bull mode. These
investors see the equity market rising to an all-time record high and wish
to participate. On the other hand, they are scared of a market crash. Such
investors find convertible bonds and preferred shares to be very appealing.
Essentially, convertible are bonds that, at the holder's option, are
convertible into a prespecified number of shares. Usually, but not always,
the underlying shares are issued by the same entity that issued the convertible,
so when the stock rises, the convertible price rises in tandem with it and
it becomes an "equity equivalent." On the other hand, when the
stock declines, the convertible becomes equivalent to a normal bond and
its price will not suffer too much. If a convertible is held until its maturity
date, it matures just like a normal bond and the principal is paid back
to the holder.
Preferred shares are similar instruments. They pay a fixed dividend rate that cannot be changed. This is quite different than common stock, whose
dividend rate is determined periodically at the issuer's discretion. Preferreds
are also convertible into common stock. They have no maturity date and can
be held indefinitely. While the face value of a convertible bond is usually
$100, preferred shares typically have face values of $50 or $25.