Convertible Bonds - Fixed Income

[rexthedog]

Evenin y’all,
CB’s are so dry… anyway, I’m trying to understand some essentials in the CB theory:
1) Why is CB = Straight V + V of equity Call option - V of call option on bond + V of put option on bond
2) Can someone explain the following two sentences:
a) Share price rises: bonds rise by less because of conversion premium paid for the bond
b) Share price falls: bonds fall by less, supported by the cushion of the bond’s straight value
Any explanations would be great.
Cheers,
Rex

 

[bfry]

Hey Rex - see if the following makes sense:
1. Convertibles are easiest (sometimes) to analyze by breaking down the components of the equation you posted:
A) The bond is a bond - it pays a coupon and is a debt obligation of the company. Nothing unusual here. Therefore the value of the convertible is always at least the same value as the straight bond.
B) The bond also has a long call option. If the underlying equity goes up you convert the bond and live happily ever after.
C and D) The equation you gave assumes some embedded optionality of the bond. For a callable bond you are short a call option on that bond and for a putable bond you are long a put option on that bond - reference the chapter where you value the bonds with embedded options. If the bond has no embedded options other than the call on the equity these two terms will go to 0 and you will just have a straight convertible made up of components A and B above.
For number 2:
A) Think about it - you are paying a premium for the convertible bond for the right to the stock if it appreciates. Say you pay $110 for a bond (with a conversion ratio of 18.33 shares per 1,000 of par value) from a firm that has another non-convertible bond that is priced at par (i.e. you are paying a $10 premium for the convertible). Lets also say the equity is selling for $50. If the equity goes up to $60 by holding the underlying equity you would have made $10. But by holding the underlying bond you are just now breaking even (because the market conversion price was $60/share when you originally bought the bond) - if you converted now you would be paying $60 a shares. Therefore if the bond went up by that same $10 the bond would never get converted because the market conversion price would always be above the current price of the equity. This is also why when equities are rising convertibles will (generally speaking) underperform there straight equity counterparts. Of course this assumes interest rates are held constant.
B) The bond can never go below its straight value as evidenced by the equation you put up in part 1. If the call option goes to 0 (and lets say so does their equity) they will still owe you the principal and coupon payments - at this point the call option is worth 0 and all you are left with from equation 1 is the straight bond value. This is why when markets are falling convertibles will (generally speaking) outperform their equity counterparts mainly because your downside risk is limited to the straight bond value and you will also be recieving the coupons when the equity is tanking.
Hope that helps.

 

[rexthedog]

Bfry you are the People’s Champion. One hundred thank you’s for your explanation.
Rex.