Convertible bonds share price

Consider also that the relationship between convertible and share price depends on the degree of the convexity. In fact, if the security has high convexity, its sensitivity is high to the movements of the share price. While in falling share prices, the convertible bond will suffer less. 

Let us now consider the following example. ABC pic has issued a 5-year convertible bond with a market price of 112.2 and an underlying share with a market price of 0.65. The bond has also a coupon of 5.5%, while the dividend yield of the underlying stock is 2%. If an investor buys just 1 00 and the bond may be converted into 1 51.7 shares, the premium over a direct purchase of the ordinary shares expressed in basis points is equal to (112.2 - 98.6) or 1 3.6 per bond, in which 98.6 is obtained by multiplying the conversion ratio of 151.7 by the current stock price of 0.65. The compensation for this premium is the cash flow differential between the convertible and underlying shares, which is calculated as ( 1 00 x 5.5%) -(98.6 x 2%) or 3.5. The payback period measure is 13.6/3.5 or 3.86 years and the concept is similar to payback period used in corporate finance analysis. 

The first mie is one which maximises the value of the convertible bond at each instant in time . In practice, the definition starts from the Modigliani and Miller theorem asserting that the firm value is independent of the conversion strategy. Therefore, given the conversion value equal to the conversion ratio times the share price at conversion, the value of the outstanding equity after conversion is given by the pre-conversion firm value divided by the number of shares outstanding shares when the bond is converted. 

The embedded option component in convertible bonds makes the valuation sensitive from three main parameters share price, volatility and interest rate. These parameters affect the value of a convertible bond for both situations ... 

As noted, the share price is a key parameter of the option pricing model. An increase in the underlying share price will result in a rise of the convertible price, and a decrease in the share price will result in a fall of the convertible price. Figure 9.9 illustrates the comparison between the convertible bond price and share price of Intel Corporation. 

FIGURE 9.9 Comparison between the Intel s convertible bond price and Intel s share price. (Data source Bloomberg.)... 

Justifying the Conversion Premium at Issue The first important decision for pricing convertible bonds is to decide the conversion premium above the stock price at issue. The conversion premium at issue determines the conversion price, that is the point in which there is parity relationship between the underlying asset and the convertible bond. In fact bonds are often issued with a premium and the conversion price, also known as the strike price, is the actual price paid for the shares when conversimi occurs. 

Convertible instruments are usually issued with attached call or put options. Such features can be implemented into the valuation model. If a soft call feature has been implemented, it enables the issuer to force the conversion when the share price overcomes a percentage or trigger level above the conversion price. However, this option cannot be called in the first years hard call . Differently, after the protection period, the issuer can exercise the option. This second time is referred to soft call . Using the same example shown in Section 9.3.1, we assume that the bond may be redeemed in whole but not in part at their principal amount plus accrued interest on the last 2 years, in which the maturity date is at 20 February 2019. On and after this call date , if the share price exceeds 130% of the conversion price the issuer can force the conversion. Figure 9.23 shows the stock price tree in which at years 4 and 5 the stock price is above the threshold. 

The put option gives at the bondholder the right, but not the obligation to redeem the convertible bond to the issuer at the price defined in the indenture, hi this case, the value of the convertible bond is greater (the yield is lower) than the one without embedded put option. Usually, the issuer is required to redeem the convertible bond for cash, shares or both elements. 

The reverse convertible bonds have increased popularity in Europe and United States. This type of instrument gives to the issuer (not the bondholder) at maturity the right to exchange the bond into shares or to redeem it at par value plus accrued interests. In the first case, the bond is exchanged if the share price is less than conversion price, or if the conversion value is less than par value. Conversely, the issuer can redeem the bond. They typically have a domestic stock as underlying security, but they can also include foreign shares and indexes. 

The most important Greek for convertible bond valuation is the delta. Delta measures the sensitivity of the option price to changes in the price of the underlying share price as follows (Equation 9.19) ... 

For example, if an option has a delta of 50%, this means that if the share price or parity increases by one point, the option price or convertible bond price will rise by 0.5 points. 

Conversely, at the lowest node, the hedge ratio is 0 because the option is out of money or 0. This means that in the first case the bond trade like the equity, while in the second case like a conventional bond. Therefore when the share price increases the delta approaches unity, implying that the option is deeply in the money. In contrast, when the share price is low relative to the conversion price, the sensitivity of the convertible and therefore of the embedded option is low. 

The convertible bond will be more sensitive with the change of volatility when the option is at the money, or the share price is closed to the conversion price. 

A convertible bond is an issue giving the bondholder the right to exchange the bond for a specified amount of shares (equity) in the issuing company. This feature allows the investor to take advantage of favourable movements in the price of the issuer s shares. Exhibit 1.7 shows a Bloomberg Security Description screen of a convertible bond issued by Siemens Finance BV that matures in June 2010. This bond is convertible into 1,780.37 shares as can be seen in the upper left-hand corner of the screen in the box labeled Convertible Information. ... 

Some convertibles are callable by the issuer, under prespecified conditions. These are known as convertible calk and remove one of the advantages of the straight convertible—that conversion is at the discretion of the bondholder—because by calling a bond the issuer is able to force conversion, on terms potentially unfavorable to the investor. There are two types of call option. Hardcall is nonconditional while soficall is conditional. If a bond is hardcall protected for any time after issue, then the issuer may not early-redeem the bond. During softcall protection, early redemption is possible under certain conditions, normally that the underlying share price must trade above a certain level for a specific period. This level is usually around 130 percent of the conversion price. 

Investors rarely convert voluntarily. They may during an event such as a call or a tender offer, or if the share price has risen by a considerable amount. The main reason why early redemption is not generally in the investors interest is because it will erode the time value of the option element, as well as remove the yield advantage of holding the convertible. It also removes the downside protection afforded by the bond. That is... 

Total return investment Most convertibles are issued as total return instruments, with the investor considering both the bond yield and the conversion premium on the equity. They will continue to trade like this unless the equity moves strongly either up or down. As a total return investment, the bond will exhibit roughly symmetrical conversion premiums. Its price is sensitive to both movements in the price of the underlying equity and market views on the credit outlook of the company. If the share price rises, the conversion option value increases as the conversion premium decreases, although at a slower rate compared to the equity itself. The reverse occurs if the share price falls, but the bond has downside protection, so as it approaches its bond floor, it outperforms the share and becomes less sensitive to movements in the share price. 

Consider a convertible bond issued by hypothetical borrower ABC PLC, which confers a right, but not the obligation, to the bondholder to convert into the underlying shares of ABC PLC at a specified price during the next ten years (see FIGURE 13.1). 

The ratio of exchange between the convertible bond and the ordinary shares can be stated either in terms of a conversion price or a conversion ratio. The conversion ratio is given hy (13-1),... 

Conversion terms for a convertible do not necessarily remain constant over time. In certain cases convertible issues will provide for increases or step ups in the conversion price at periodic intervals. A 1,000 denomination face value bond may be issued with a conversion price of say, 8.50 a share for the first three years, 10 a share for the next three years, and 12 for the next five years, and so on. Under this arrangement the bond will convert to fewer ordinary shares over time which, given that the share price is expected to rise during this period, is a logical arrangement. The conversion price is also adjusted for any corporate actions that occur after... 

Application of the binomial model requires a binomial tree detailing the price outcomes from the start period, which is shown at FIGURE 13.3. In the case of a convertible bond this will refer to the prices for the underlying asset, which is the ordinary share of the issuing company. 

P, is the price of the convertible bond is the price of the underlying equity C is the bond coupon r is the risk-free interest rate N is the time to maturity a is the annualized share price volatility c is the call option feature rd is the dividend yield on the underlying share... 

In the first instance, we wish to calculate the value of a call option on the underlying shares of a convertible bond. For Figure 13.3, if we state that the probability of a price increase is 50 percent, this leaves the probability of a price decrease as —p or 50 percent. If we were to construct a portfolio of b shares, funded by borrowing X pounds sterling, which mirrored the final payoff of the call option, we can state that the call option must be equal to the value of the portfolio, to remove any arbitrage possibilities. To solve for this, we set the following constraints ... 

We then take the analysis further for a convertible bond plus its embedded option. FIGURE 13.8 shows the price tree for the conventional bond where the share price and conversion price is equal to 100 in the current time period. Note how the conventional bond element of the convertible provides a floor for its price in later periods. 

The convertible price accounts for both the conventional bond element and the embedded option element. If we assume the share price in period t< is 97.01, then in period 6o the share can assume only one of two possible values, 106.25 or 92.24 (see Figure 13.6). In these cases, the value of the call option Ch and Cl will be equal to the higher of the bonds conversion value or its redemption value, which is 106.25 if there is a rise in the price of the underlying or 102.50 if there is a fall in the price of the underlying. This is the range of possible final values for the bond however, we require the current (present) value, so we discount this at the appropriate rate. 

The option element in a convertible cannot be stripped out of the bond element, and so is termed an embedded option. The valuation of the bond takes into account this embedded optionality. Note also that unlike a straight equity option, there is no additional payment to make on conversion the holder simply exchanges the bond for the specified number of shares. One could view the price paid for exercising the option as being the loss of the bond element, which is the regular coupon and redemption proceeds on maturity, but this should be viewed as more of an opportunity cost rather than a payment. This bond element is often referred to as the bond floor, which is the straight debt element of the convertible. The bond floor can be viewed as the level at which a vanilla bond issued by the same company would trade, that is, its yield and price. It generally accounts for between 50 percent and 80 percent of the total value. 

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