Convertible Bond - Valuation

Valuation

See also Bond option: Embedded options, for further detail.

In theory, the market price of a convertible debenture should never drop below its intrinsic value. The intrinsic value is simply the number of shares being converted at par value times the current market price of common shares.

The 3 main stages of convertible bond behaviour are:

• In-the-money convertible bonds
• At-the-money convertible bonds
• Out-the-money

• In-the-money: Conversion Price is < Equity Price.
• At-the-money: Conversion Price is = Equity Price.
• Out-the-money: Conversion Price is > Equity Price.

• In-the-money CB's are considered as being within Area of Equity (the right hand side of the diagram)
• At-the-money CB's are considered as being within Area of Equity & Debt (the middle part of the diagram)
• Out-the-money CB's are considered as being within Area of Debt (the left hand side of the diagram)

From a valuation perspective, a convertible bond consists of two assets: a bond and a warrant. Valuing a convertible requires an assumption of

1. the underlying stock volatility to value the option and
2. the credit spread for the fixed income portion that takes into account the firm's credit profile and the ranking of the convertible within the capital structure.

Using the market price of the convertible, one can determine the implied volatility (using the assumed spread) or implied spread (using the assumed volatility).

This volatility/credit dichotomy is the standard practice for valuing convertibles. What makes convertibles so interesting is that, except in the case of exchangeables (see above), one cannot entirely separate the volatility from the credit. Higher volatility (a good thing) tends to accompany weaker credit (bad). In the case of exchangeables, the credit quality of the issuer may be decoupled from the volatility of the underlying shares. The true artists of convertibles and exchangeables are the people who know how to play this balancing act.

A simple method for calculating the value of a convertible involves calculating the present value of future interest and principal payments at the cost of debt and adds the present value of the warrant. However, this method ignores certain market realities including stochastic interest rates and credit spreads, and does not take into account popular convertible features such as issuer calls, investor puts, and conversion rate resets. The most popular models for valuing convertibles with these features are finite difference models such as binomial and trinomial trees.

• Binomial valuations Since 1991-92, most market-makers in Europe have employed binomial models to evaluate convertibles. Models were available from INSEAD, Trend Data of Canada, Bloomberg LP and from home-developed models, amongst others.

These models needed an input of credit spread, volatility for pricing (historic volatility often used), and the risk-free rate of return. The binomial calculation assumes there is a bell-shaped probability distribution to future share prices, and the higher the volatility, the flatter is the bell-shape. Where there are issuer calls and investor puts, these will affect the expected residual period of optionality, at different share price levels. The binomial value is a weighted expected value, (1) taking readings from all the different nodes of a lattice expanding out from current prices and (2) taking account of varying periods of expected residual optionality at different share price levels.

The three biggest areas of subjectivity are (1) the rate of volatility used, for volatility is not constant, and (2) whether or not to incorporate into the model a cost of stock borrow, for hedge funds and market-makers. The third important factor is (3) the dividend status of the equity delivered, if the bond is called, as the issuer may time the calling of the bond to minimise the dividend cost to the issuer.