As I promised, here are some reminders and "hints" that you might find helpful as you prepare for and take the second midterm exam in FIN 4366:
I will not be on campus on Tuesday, so my office hours for that day are canceled. My graduate assistant, Mr. Derek Fay, will administer the exam at the scheduled time and place.
I have decided to make problem set 6 optional. If you turn it in and your grade is higher than on a previous problem set, I'll use the higher grade from problem set #6 to substitute for the lower problem set grade. In addition to completing the Introduction to Binomial Trees (Part 2) lecture note, I plan to go through the problem set in class in some detail. This will help you learn the material even better!
Tomorrow (Thursday, November 4) we'll be completing our study of chapter 10 and starting on chapter 11, so please try to read chapter 11 prior to coming to class. Also, I updated the Introduction to Binomial Trees (Part 2) lecture note somewhat to be more complete in terms presenting binomial pricing formulas.
We'll complete the Introduction to Binomial Trees (Part 2) lecture note tomorrow and time permitting, move on to another lecture note based upon Chapter 11. I'll let you know as soon as the chapter 11 lecture note is available.
p = probability of an "up" move (1 - p corresponds to the probability of a "down" move);
p' = "risk neutral" probability of an "up" move;
u = 1 plus the rate of return on the underlying asset when there is an "up" move;
d = 1 plus the rate of return on the underlying asset when there is an "down" move;
dt = a discrete time interval, or "timestep" over which the price of the underlying asset changes;
m = the annualized "drift" of the underlying asset; this corresponds to the annualized expected return;
s = the annualized "volatility" of the underlying asset; this corresponds to the annualized standard return;
D = the number of shares of the underlying asset that you sell short when you put together a hedge portfolio which also consists of a long position in one option;
V = the current market value of a call option;
P = the current market value of your hedge portfolio;
V+ = the value of a call option one timestep from now when it makes an "up" move;
V- = the value of a call option one timestep from now when it makes a "down" move;
The 2:1 Kerry advantage indicated on Tuesday evening at 5 p.m. on Tradesports.com was apparently driven by market participants acting on faulty data (specifically, faulty exit polling). Even though the media networks have not yet (as of 2:30 a.m. on Thursday, November 3) called the election, the only "Bush wins" state contracts that are still trading are Iowa ($97), Nevada ($95), Ohio ($95), New Mexico ($90), Wisconsin ($5.70), Minnesota ($1.20), New Hampshire ($0.50), and Michigan ($0.10). Assuming that Iowa, Nevada, Ohio, and New Mexico go to Bush and Wisconsin, Minnesota, New Hampshire and Michigan go to Kerry, the "most likely" final Electoral College tally should be 286 for Bush and 252 for Kerry.
As of 5:00 p.m. this evening, the prediction markets data suggest that the odds now favor a Kerry victory, with the Republican Party maintaining control of both houses of Congress. As late as 2 p.m. today, the market was still pricing a marginally higher probability of a Bush victory; the PRESIDENT.GWBUSH2004 contract was selling at the time for $55, and the BUSH.OHIO and BUSH.FLORIDA contracts were selling for similar prices. However, the market dynamics changed significantly starting around 2:30 p.m., with the release of exit polling data which appeared to favor Kerry. As of 5:00 p.m., the last trade on the PRESIDENT.GWBUSH2004 contract occurred at a price of $32.20, whereas the last trade on the PRESIDENT.KERRY2004 contract occurred at a price of $67.60, and BUSH.OHIO and BUSH.FLORIDA were selling for $39 and $43 respectively. Although PRESIDENT.GWBUSH2004 is selling off and PRESIDENT.KERRY2004 is rallying, the HOUSE.GOP.2004 contract (which pays off $100 in the event that Republicans maintain control of the US House of Representatives) is selling for $90 and the SENATE.GOP.2004 contract (Republicans maintain control of the US Senate) is selling for $86.80.
While it may be a bit premature to call the election, as I noted earlier it would appear that the most likely outcome at this point is a Kerry presidency coupled with a GOP controlled Congress.
Based upon the pricing this morning (at 9:30 a.m. CST) of the state by state contracts, I am projecting a "most likely" 272-266 Bush win today. This assumes that Bush wins Florida ($54) and Ohio ($55), but loses Iowa (the latter contract is currently priced at $50). If Bush picks up Iowa, it will be 279-259.
The most sane polling-based website I have found is www.realclearpolitics.com. (I call this a "sane" site because it averages polling results, whereas many other websites (e.g., http://www.electoral-vote.com) simply allocate votes in a given state based upon the latest poll in that state.) There, you'll find an electoral college map of the United States, which currently has Bush leading Kerry 227-203. The "toss-up" states are New Hampshire (4 electoral votes), Pennsylvania (21 electoral college votes), Ohio (20 electoral college votes), Florida (27 electoral college votes, Wisconsin (10 electoral college votes), Minnesota (10 electoral college votes), Iowa (7 electoral college votes), and New Mexico (5 electoral college votes). The prediction markets result reported above assumes that Kerry picks up New Hampshire ($33.70), Pennsylvania ($22), Wisconsin ($42), Minnesota ($21.50), and Iowa, whereas Florida, Ohio, and New Mexico ($59.80) go to Bush.
As of 8:30 a.m. this morning, the PRESIDENT.GWBUSH2004 contract was trading for $56, whereas the PRESIDENT.KERRY2004 contract was trading for $43.60. If you look "under the hood" at the state-specific "Bush Wins" contracts, it would appear that Ohio ($52), Iowa ($54.20), and Wisconsin ($42) are the most "in play" at this point in time. The lowest price "Bush Wins" contract going for Bush at this point is Florida (at $61.50), and the lowest price "Bush Wins" contract going for Kerry at this point is New Hampshire (at $33). If Bush wins Ohio and Iowa, while Kerry wins Wisconsin, the Electoral College total would be 279-259 in favor of Bush. Furthermore, the BUSH.ELECTORALVOTES contract is currently pricing a 276-262 margin in favor of Bush. If you look at page 7 of my "Decision Making under Risk and Uncertainty, part 2" lecture note (which we covered during our class session on September 14), I was predicting an Electoral College margin then of 278-260 in favor of Bush.
While I expect Bush to win reelection on the basis of the prediction markets' estimates, the election would appear to be quite close, and could really go either way. However, regardless of whether Bush or Kerry win, it appears that the GOP will continue to retain control of Congress. Currently, the HOUSE.GOP.2004 contract is selling for $95, whereas the SENATE.GOP.2004 contract is selling for $84.50. These prices are not far off earlier all-time high's set for both contracts.
One final point - if you haven't already voted, please be sure to vote on Tuesday (although I do not recommend missing class because it will be a particularly important lecture)!