Dear Professor Feingold,

Is there an easy way for me to figure out the size of common stock needed to be arbitraged versus a convert bond? For example: I was watching Newell Rubbermaid (NWL) convert trades the other day and witnessed large blocks of the common going up at the same time. Is there a way I could figure out, just by looking at the convert trade, what the estimated block would be on the common side? I know this entails knowing the delta -- which I don't think I could get to -- but maybe there's something else?

Thanks for any input.

Minyan Greg

Dear Minyan Greg,

Thanks for your letter.  Before I get to your question, I want to note that a couple of days ago, the Wall Street Journal ran a story about the rebirth of convertibles in 2009. The story pointed out that more traditional, unhedged investors are reassuming command of the market, with hedge funds losing a lot of their funding (both from investors and from their lenders, i.e. prime brokers). It cited one broker’s comment that while before September 2008, when the world as we know it changed, roughly two-thirds of its business was with hedge funds. Now more than two-thirds is with traditional outright investors.

This is good news for everyone - not the least of which are the remaining hedge funds!

Anyway, this relates directly to your question. Here’s how I usually go about estimating how much stock hedge funds will sell short against a new convertible issue. Think of this as a cookbook; a recipe, if you will.

Ingredients:
 

• Size of new convertible issue (in millions of dollars).
  
  
• Conversion premium (the amount by which the dollar amount of the issue exceeds its value if it were immediately converted, typically 20-30% these days, and usually given in the press releases: Often the releases will mention a conversion price, so just calculate the amount by which that price exceeds the stock’s closing price).
  
  
• Percentage of the issue to be owned by hedge funds (these days, let’s assume around 33%, as mentioned above).
  
  
• Theoretical delta (as you asked). As with call options, this is the degree (somewhere between 0 and 100%, theoretically) to which the convertible should participate in the move of the underlying stock. An excellent rule of thumb, though without any pure scientific merit, is that for a new issue, the delta is roughly 100% minus the conversion premium. Thus, the lower the premium, the more sensitive the convertible is to the moves in the stock.