# Shares Shorted for Convertible Bond

Hi, everyone,

I saw the following two ways to calculate the number of shares that need to be sold short to make the convertible bond delta neutral.

- Formula A: Conversion ratio x delta
- Formula B: Current bond price x delta / current stock price

Formula A is in CAIA’s textbook (P732). However, CAIA’s Workbook has both Formula A (P134) and Formula B (P159).

I use UpperMark that also has both formulas.

I don’t know which formula to use in the actual exam. Perhaps the one in the textbook?

What do you think?

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Hi everyone, am new here. Using Uppermark for CAIA Level 2.

Wanted to understand if anyone responded to this old post? Regarding the 2 seemingly conflicting formulas for Number of shares to short for conv arbitrage.

Now that I understand “Formula B” doesn’t appear in the textbook, should I just ignore it?

Cheers, any help at all appreciated

Isn’t Formula A and B the same with the substitution of the Conversion Ratio?

So, this is how I see it (please double check):

Conversion Ratio = current bond price/ current stock price

substitute into Formula A, you get formula B. in other words, re-written:

Formula A: (Current bond price/ current stock price) x delta is the same as

Formula B: (Current bond price x delta) / current stock price

Thanks for the reply.

I was under the impression (based on Uppermark’s definition) a conversion ratio was by definition strictly based on the bond’s face value (divided by a fixed conversion price). Hence I was confused when I saw market (or current prices) come into play

I’m familiar with the concept of convertibles, and always assumed convertibles had a fixed conversion price, and it didn’t make sense to me that the number of shares convertible (the conversion ratio) would fluctuate based on market prices of either the bond or the stock

Am I wrong in both paragraphs above? Again, replies to help me cement my understanding are greatly appreciated

You are correct. I was using the formula given in the original thread.

The conversion ratio is the Face Value (par)of convertible bond divided by the conversion price.

I use UpperMark as well, Thank you for clarifying.

No points on the exam for being correct on the forum, unfortunately =)

For now, I’ll just take it that I’ll ignore Formula B. Thanks for the input