There still seems to be confusion around the convertible notes, so I'll try another analogy. I'll leave out details and the analogy won't be perfect but it's to get the idea across.
Buying a convertible note is like buying Super Shares with special powers. So, when the market price for common shares was $92/share, you decided to buy Super Shares for $125/share. The reason you paid the extra money was because of the special powers of Super Shares.
The main power of Super Shares is that it comes with a built-in put (hedge) of sorts. Meaning, if the stock price goes under $125, then you'll still get your full $125 you paid for it. So, if the stock goes to $50 (or even $1) you can still get $125 for each share. That's the main Super Share power. Conversely, if the stock price for shares goes above $125, for example to $500, then your Super Shares can get the full market price of $500. The downside is limited but the upside is not.
The reason you bought Super Shares (and not regular shares) was because you wanted to invest in the company but also didn't want to lose money if things didn't work out. So the Super Shares were perfect because you're guaranteed not to lose the $125/share you put in, and yet you can still realize all the gains above $125/share.
Now Super Shares have their special powers for 5 years, and then they lose their super powers and become regular shares (ie., full exposure to downside).
You can sell your Super Shares at anytime to another person. You'll get what a regular share is worth plus extra for the special powers of a Super Share.
Now, there's another way you can get rid of your Super Shares. You can (if certain criteria is met) convert your Super Shares into regular shares and then sell your regular shares. But by doing this, you don't get any money for the special powers of the Super Shares. (It would be better to just sell your Super Shares to another person and get more money for them.)
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That may be, but you are talking about the "option premium" on September 9th...not what it will be and what will impact it if the conversion criteria is met. I personally have called away stock instead of selling the underlying, more valuable option because of the tax consequences of exercising vs calling away. A fund manager, who is behind for the year and needs short term performance to attract and retain investors may want a short-term paper profit of 30+ percent 70+ percent annualized rather than holding the bond for the duration or trading it if there is a premium on Oct. 1. I don't disagree with your well reasoned and well presented arguments, I am not convinced the numbers you are using are as static as you believe.
I don't think early conversion ability will affect note premiums much, if at all. The reason being is that the note premium is based on the value of the convertible note which is mainly it's downside risk protection (vs common share).
Liquidity is already achieved through the notes being openly traded, thus added an undesirable liquidity option like early conversion provides no benefit to the note holders.
Now, I'll admit that there might be some added perception benefit that the notes are more liquid and that might increase the note premium, but if so it will likely do so only in a trivial manner (ie., less than 1% of note value) since liquidity is already present and the bulk of the note premium is it's built-in hedge.
I thought about possible tax benefits to early conversion but couldn't think of any, especially because the notes are 5 years in length.
Lastly, for the fund manager wanting to increase his short-term performance, his best bet is to sell the convertible notes (if he wants to) when the stock price is the highest to gain maximum profit, whether it's before or after Oct 1 it doesn't really matter.