CFA CFA Level 2 Convertible Bonds formulas explained

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Convertible Bonds formulas explained

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  • This topic has 4 replies, 4 voices, and was last updated 2w by cfyay.
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      I’ve got myself in a bit of a muddle over the convertible bond formulas.

      Is the conversion ratio static or always changing depending on the market price of the convert bond? In some questions I’ve come across, it seems that it is static, based on the following formula:

      par/initial conversion ratio = conversion price of the bond


      In other questions, it seems that the conversion ratio changes and the formula should be more:


      current market conversion ‘break even price’ = market price of convertible / conversion ratio


      and am I right in thinking that the breakeven price is the current market conversion price worked out using the above formula? i.e. it’s always changing and isn’t static? Or do you lock in an effective breakeven price based on the price you initially bought the bond at and the initial conversion ratio (or whatever is outlined in the indenture)?

      All the other formulas in the syllabus are clear to me on convertible bonds except the above ones, but given that you need to find out the current market conversion price or conversion ration before you work out premiums, I always get a bit stuck!

      I don’t think this stems from confusion over market convertible bond value and conversion value, which I understand to be defined as the following:

      Market convertible bond value = market price the convertible bond is currently selling for. Value here is equal to price as opposed to other definitions of value.

      Conversion value = conversion ratio x current stock price. (and you compare conversion value with straight value to get the current minimum value of the convert bond)

      Zee Tan voted up
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      Might be clearer to start from the beginning.

      A convertible bond is a bond that has an option to convert to a specified number of shares of common stock at a pre-defined conversion date.

      The conversion ratio = the number of shares each bond has the option to convert to.

      The bond has a par value, so the implied price per converted share is the conversion price. So if a bond can be converted into 10 shares, and the bond par value is $1,000:

      Conversion price = bond par value / conversion ratio

      = $1,000 / 10 shares

      = $100

      Conversion ratio does not change, its defined in the indenture, like the strike price of an option.

      I think the confusion here is that ‘conversion price’ is not as in ‘market price’, but more a ‘strike price’ equivalent.

      So if the market price of the underlying common stock increases beyond the conversion price, it is advantageous to convert the bond (hence the name ‘conversion price’ = the price where you convert).

      And because graphs help me see things better:

      Zee Tan voted up
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      Thank you! graph is very helpful

      Sophie Macon voted up
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      In the graph, is the reason why bond value is declining in the ‘distressed’ section because of credit risk?

    • Zee Tan

      In the graph, is the reason why bond value is declining in the ‘distressed’ section because of credit risk?

      As the share price approaches 0, the ability for the company to repay their bonds decreases, so bond value approaches 0.

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