Convertible Bonds

OK first things first — let’s nail down the terminology for convertible bonds. Price, premium, whatever — do NOT get these mixed up. Each one points at a very specific thing! We saw this stuff back in Level 1 too!

So this thing is a CB, which means there’s gonna be some clause like “one bond can be exchanged for X shares of stock,” and if that number of shares you can convert into is, say, 5 shares, we call that the conversion ratio.

OK now say I bought the bond at face value — $1,000. Asking to swap it for 5 shares is basically the same as asking the company to issue me new shares at $200 a pop, and that price is what we call the conversion price. So — the conversion price is locked in at issuance!

Now let’s say that stock is trading out there in the market. Say the market price right now is $300.

I’m holding one bond, but if you squint at it, I’m basically holding 5 shares of stock. Looked at that way, I’m sitting on $1,500 of value, and this number — conversion ratio × market price ⇒ is called the conversion value, which also goes by stock-equivalent value.

Thinking in value terms, a CB is basically the value of a straight bond (SB) ⨁ plus the value of the conversion option tacked on top.

CBs usually pay a smaller coupon than they would if issued as a plain straight bond (typically a coupon rate of around 1%). And the value when you look at JUST the straight-bond side of it is called the straight value.

OK now let’s see what the relationship between the CB and the stock price actually looks like on a chart.

Even if the stock price drops to 0, the SB part of the CB still has bond value sitting there, so the whole thing has a floor under it. And once the stock price climbs above the conversion price — that’s the moment bondholders go “yep, time to convert."

But in the real market, CBs tend to trade a little above these theoretical values.

i.e. CB value > Max(straight value, conversion value).

Sure, if the stock price collapses toward 0, the company’s basically on the verge of bankruptcy, so the CB price nosedives with it (this is called a busted convertible), but obviously that’s not something we need to sweat for CFA exam purposes.. heh

We said straight value = $950, and conversion value = 25 × $35 = $875.

So we can say this bond has at least $950 of value!

Now a few more terms coming at you here… Hold these tight and don’t get them mixed up (T_T)!!!

To buy this bond right now, you’d have to fork over $985.

And if you buy it at $985 and then convert it into 25 shares of that $35 stock, how much are you actually paying per share?

Same as buying at $985/25 = $39.40 a share, right?? → That’s the market conversion price!!

The CB is more expensive?!

Yeah, obviously — the CB protects your downside, so you could say it’s the price you pay for that downside protection… → that’s called the market conversion premium!!

market conversion premium per share = market conversion price - stock’s market price

You can also say it as “there’s an X% premium over the current stock price~” → that’s the market conversion premium ratio..

And then there’s another version that says “there’s this much extra over the straight value~"… (T_T) Premium over straight value

Summary

A little extra from the “net” material.

Callable Convertible Bonds

* Keep in mind a single bond can have multiple options stapled to it; treat this as one example of that.

Holding one CB is the same position as holding one SB ⨁ while simultaneously holding a conversion option,

* (conversion option: this has the same character as being long a call option on the stock)

So — if the volatility of the stock goes up → the call option’s value goes up → the value of the Convertible Bond goes up!!

OK then what about a Callable Convertible Bond…

Here “Callable” means the issuer can call the Convertible Bond itself back!! Same logic, just extended:

Callable Convertible Bond = SB + conversion option - call option (on CB)

*conversion option ≅ call option on stock

If stock price volatility goes up, CCB value goes up, and if interest rate volatility goes up, CCB value goes down!