From: John Conover <john@email.johncon.com>
Subject: Bush/Kerry optimal wagers
Date: 21 Sep 2004 05:08:20 -0000
I swore after the 2K election that I would not do this again, but here
is the way you model the outcome of an election based on poll data; I
got beat up when I predicted-5 days before the election-that the 2K
Presidential Election would have an inconsistent popular and electoral
vote:
http://www.johncon.com/john/correspondence/001103172714.28588.html
See:
http://www.johncon.com/john/correspondence/020508170137.5425.html#appendixIII
for details of the methodology, (using the California Gubernatorial
recall as an example.)
The recent polls say 46% of the voters, (in the popular vote,) would
vote for Bush, 43% for Kerry. There are 43 days left to the election,
and the polls move at about 1% per day, and are a zero-sum game, (in
the simple/lay sense-what Bush gets in a poll on one day, Kerry loses,
and vice verse.)
What that means is that sqrt (43) = 6.5574385243% is the standard
deviation of the popular vote poll data on election day-43 days from
now-or there is a 14% chance that Bush's poll data will be above 46 +
6.5574385243 = 52.6%, and a 14% chance of being below 46 -
6.5574385243 = 39.4%. The numbers for Kerry on election day is a 14%
chance of being above 43 + 6.5574385243 = 49.6% and a 14% chance of
being below 43 - 6.5574385243 = 36.4.
Since it is a zero-sum game, the winner of the popular vote will have
to have more than 43 + ((46 - 43) / 2 ) = 44.5%, or a 1.5 /
6.5574385243 = 0.228747855 standard deviations.
Referring to the CRC tables for the standard deviation, 0.228747855
corresponds to about a 59% chance for Bush, and a 41% chance for
Kerry, to win-call it a 60/40 chance, 43 days from now.
So, going long on Bush, one would optimally bet a fraction (2 * 0.6) -
1 = 20% of one's capital, (be it political, money, whatever,) on Bush
winning. And, the expected returns would be 2%, per election, iterated
over elections with similar statistical characteristics, from:
http://www.johncon.com/john/correspondence/020213233852.26478.html#equation1.20
which is a 10% ROI in 43 days-not too bad, (that's equivalent to about
2X per year.)
Of course, there is uncertainty in the poll numbers, and a strategy of
watching the numbers to do a stop-limit, (e.g., betting on Kerry later
to go short on the Bush wager,) may be advisable-just like in options,
and possibly set up a no risk wager, (working backward on implied
volatility.)
John
--
John Conover, john@email.johncon.com, http://www.johncon.com/