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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.

Convert behavior

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 involved.

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 investor.

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 models.

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.

Model convertibles

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 price."

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 to build.

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 the output.
  • 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 the model.
  • 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 (or www.miint.net/~sccc).

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.