Why Convertible Bond Value Does Not Directly Give Bond Yield

Summary

The document raises a valuation question about a convertible bond: how to derive yield to maturity from a value calculated with an option valuation model. It considers treating the difference between the calculated value and the bond’s issue value as annualized growth over the bond’s term, then asks whether that internal-rate-of-return calculation is appropriate. It also asks whether an embedded option’s value can be translated into a separate contribution to yield.

No answer or worked method is included, so the document does not establish a standard conversion or provide evidence supporting the proposed calculation. Its useful point is the distinction it poses between valuing a convertible instrument, whose payoff includes an equity conversion feature, and calculating yield from contractual cash flows. Any yield measure would depend on specified cash flows, timing, and conventions; the document leaves those details unresolved. Treat it as a question framing a fixed-income and derivatives problem, rather than guidance for calculating a bond yield.

Key ideas

• The document asks how a model value for a convertible bond relates to yield to maturity.
• It questions whether annualizing the ratio of calculated value to issue value is appropriate.
• It also asks whether the embedded option’s value can be isolated as a yield contribution.
• No answer, calculation method, or supporting evidence is provided.
• Yield interpretation requires cash-flow and timing conventions that the document does not specify.

Tags

# Convertible Bond Option - Yield analyzis


# Convertible Bond Option - Yield analyzis












The following problem can be understood as an extension/modification of the textbook example of Hull (Options, Futures and other derivatives, chapter 27.4, 9th Edition), which is related to convertible bonds.

My questions is the following:

Based on the determination of the value of the convertible bond in t=0 (going from the end values to the left, in the example from Hull, this is 106.93), how do I calculate the yield to maturity of the bond? My initial guess is that, based on the term of the bond, the value would just be: (value of the bond/initial value)^(1/n)-1, where n is the term of the bond, the value of the bond is the calculated convertible bond in t=0, i.e. 106.93, and the initial value is the issue value of the bond, i.e. 100 in the example. Assuming a term of 1 year, the yield to maturity for the bond would be 6.93%, but somehow I'm really unsure whether this "internal rate of return calculation" is right for the case at hand.

Is there a "standard" method to convert the value of an option into its respective part of the yield to maturity of the underlying?

I hope my question is straight forward.

Thank you for your help.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.