How do you value a convertible bond for an interview?
Hi there I was recently asked this question in an interview for an EB:
A convertible bond is like a call option and a regular bond. How do you value it? Face value = $100 Current price = $110 Coupon = 5% Matures in 1 year
I was asked to find YTM for the debt portion first and then given the call option value at 15? Also have $95 scrawled on my notes. Could someone try and work through this? I'm lost
A common method is to value the bond as the independent sum of the raw bond and the call option using usual pricing methods.
is this for SA? which round was this?
Full time first round
Interested as well. My approach would have been the following: for the debt proportion the CP or = 5%.
Given the fact that the call option is valued at 15, the bond part is valued at 95. Hence the YTM is roughly equal to 10% (5 + 100-95). I checked for a CP at $95 the YTM = 10.256%
Not sure if this is correct but this is how I would have tried to solve this.
Hi this looks pretty close to how the interviewer described it! Thanks!
A little confused though: what does CP stand for and theoretically shouldn't the coupon rate > YTM when something is trading at a premium?
Also could you explain your calculation in "Hence the YTM is roughly equal to 10% (5 + 100-95)"
Thanks again!
CP = Current price
The YTM should always be >= Coupon Rate. The explanation is you buy a bond for $100 dollars with a coupon rate of 5% and a Face Value of $100. Say it matures in 1year. Your 'profit' will be FV-buy in price (current price)+interests but FV=CP so your only profit comes from your interests. Hence your yield will only come from the coupon rate. I have never heard of a case where the CP > FV, hence your profit can only be higher than the interests (coupon rate), your YTM = annualised profit (simplified version).
-My second point is 10% = CR+FV-CP
with all the infos you gave above, the bigger FV-CP is the higher the YTM will be compared to this simplified formula. For instance: For a CP of $80 the YTM=5%+100-80=25% (simplified formula that I use in inteviews) and using the YTM formula you get 27.778%.
The bond is trading at a premium, so YTW cannot ever be greater than 5%. Because this bond matured in 1 year, you can use a simple calculation - [PV/(Face + Coupon Payment)] - 1 = YTW. So in this case you’d have 110/105 - 1 = which equals 4.76%, this isn’t completely correct just a rough approximation due to the nature of the way YTW is calculated (No interviewer will penalize you for doing this). Next you have to value the option, which should be very simple. It’s just the PV of the bond (Which is 110) minus the strike which is 15, so it should be 95.
Variation of Black-scholes
Convertible bond valuation (Originally Posted: 12/01/2010)
For those trading convertible securities, what valuation software do you use? Proprietary or third party?
Just use Bloomberg's corp bond calculator. I think the command is YSE.
Monis
Yeah seems like Monis is pretty much industry standard. Thanks guys
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