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CBOT/CME Merger: An Arithmetical Subplot

I've been thinking again, for no very compelling reason, about the merger of the two great Chicago exchanges in 2007. In form, it was an acquisition of the Chicago Board of Trade by the Chicago Mercantile Exchange, after the CME won a bidding war with the Intercontinental Exchange (ICE),

I'm looking at Erika Olson's book about the behind-the-scenes maneuvering that ended in that result. One of the many subplots involves ERPs, the "exercise right privileges" possessed by many CBOT members with regard to yet another Chicago institution, the Chicago Board Options Exchange.
This takes some explaining. First, neither the CBOT nor the CBOE is a mere set of initials. Each is a true acronym, "see-bot" and "see-bow" respectively. Second, the CBOE, established in 1973, does what the name implies. It provides a forum for the trade in options. It was initially a spin-off from the CBOT, and they had a close continuing relationship. One part of that: everyone with at least 27,338 shares in the CBOT had the privilege of trading on the CBOE, an ERP.

Once a CME bid was announced, even before ICE became involved, the question arose: what happens to the ERPs?

The CEO of CBOT, Bernie Dan, was all in favor of the deal with CME. At one critical meeting, he explained to the members that every share of their equity in the exchange was going to be worth .3006 shares (that is, a little less than one third of a share) of the new entity, called The CME Group. So: how many shares of The CME Group would one need to qualify for an ERP? That is a straightforward mathematical question, what is .3006 of 27,338?

Well, straightforward in that one can easily enter it into a calculator. Personally I wouldn't want to try to do that in my head: !

Apparently, at the meeting when Dan announced the .3006-to-1 ratio, one of the members/traders did try to do it in his head.

As Olson writes, he "attempted to figure the numbers out loud and got it totally wrong." She gives the impression that she's doing him a solid by not naming him and subjecting him to innumeracy-shaming. "I heard other traders grumble in disapproval of the colleague's inability ... 'This is fucking embarrassing."

Really? Whoever he is, he need fear no disapproval from me. I admire anyone who would TRY to do that off the cuff sans calculator.

The answer, by the way, is that 8,217.8028 shares of CME stock were necessary to keep an ERP in the CBOE.

But I bet my bright readers have already figured that out.

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