Six days after I blogged about political bias in our nation's colleges and universities, George Will published an interesting essay about this topic that I encourage all of you to read, entitled "The Left's last paradise."
Best wishes for a safe and happy Thanksgiving holiday. When you come back to campus, we'll obviously be finishing up Finance 4366. I have really enjoyed the class and wish all of you the best, whatever you are doing after this semester.
Here's my plan for the last two class sessions for Finance 4366.
1. Tuesday, November 30: We will pick up from where we left off today; specifically, we will work through the comparative statics analysis for call and put options (pages 24-37 of the lecture note entitled "The Black-Scholes Model". Time permitting, we will also work through my write-up on the solution to Problem 12.26 from the textbook.
2. Thursday, December 2: We will cover the lecture note entitled "Optimal Exercise Rules for American and European Options". The class will conclude with a review session for the final exam, and you will also complete the teacher evaluation form.
I have one more problem set assigned for Finance 4366. This consists of Hull, Chapter 12, p. 261, questions 12.24, 12.25, 12.27, 12.28, and it will be due on Thursday, December 2. At that time, I will make the solutions for the problem set available to you.
The final exam is scheduled for 2-4 p.m. on Friday, December 10 in HCB 408. It will be comprehensive in nature, and as I note in the course syllabus, the grade you receive on the final will also count for one of your midterm exams if it is higher than the scores on either of the midterms (anyone want to venture a guess as how one might use option pricing theory to compute the value of this option?).
I highly recommend two articles which have appeared recently on CollegeJournal:
1. "It's Never Too Early To Start Your Job Hunt"
2. "Up Next For Seniors: Compose a Resume"
Today's OpinionJournal features a very interesting and insightful article by John Fund entitled "High Bias". The basic premise of Fund's article is that political bias is alive and well in academia. Specifically, Fund claims that there is a "...lack of intellectual diversity on university campuses, whose faculties are overwhelmingly liberal."
Fund cites several studies which document the lack of intellectual diversity in academia. For example, one of the newest studies on this topic (by Swedish sociologist Charlotta Stern and Santa Clara University economist Daniel Klein) finds that in a random national sample of 1,678 responses from university professors, Democratic professors outnumber Republicans 3 to 1 in economics. 28 to 1 in sociology and 30 to 1 in anthropology. A particularly noteworthy quote comes from Robert Brandon, a Duke University philosophy professor, who offers a theory as to why conservatives are an endangered species on college and university campuses: "We try to hire the best, smartest people available. If, as John Stuart Mill said, stupid people are generally conservative, then there are lots of conservatives we will never hire. Mill's analysis may go some way towards explaining the power of the Republican Party in our society and the relative scarcity of Republicans in academia."
As we go through the mathematical details concerning the derivation of the Black-Scholes model, I think it is important to step back for a moment and think about the rationale/motivation behind "risk neutral valuation" and how this concept is related to very simple valuation concepts which were (hopefully) covered in the basic principles of finance course (i.e., Finance 3310).
Risk Neutral Valuation
Perhaps the most important insight in the theory of derivatives pricing involves the notion that a "risk neutral valuation relationship" exists between the price of a derivative security and its underlying asset. With some algebra, the Black-Scholes nonstochastic partial differential equation (see equation (8) on page 28 of http://129.62.162.249/ofod/fall2004/lecture14.ppt) can be solved for the current call option price ("C"). By inspection, the current option price depends upon the current price of the underlying stock along with other (deterministic) factors such as the rate of interest, the volatility of the underlying stock, and values of three (math) derivatives; specifically, the derivative of the call price with respect to time and the first and second derivatives of the call price with respect to the price of the underlying stock.
You may be thinking "so what?" The answer is that this result is huge. The Black-Scholes nonstochastic partial differential equation implies that for a given price of the underlying asset, a call option written against that asset must trade at the same price in a risk neutral economy as it would in a risk averse or risk loving economy. Since it is easiest to price the option as if investors are risk neutral (since this allows us to be completely agnostic concerning the nature of risk preferences), this is what we do.
Finance 3310 revisited (the "RADR" approach)
Most students' first exposure to pricing of risk comes in the Finance 3310 course, where they learn about the Capital Asset pricing model. Once this concept is introduced, students are taught to use the CAPM in order to determine the appropriate rate at which to discount the expected value of a future risky cash flow. This approach to pricing risk is commonly known as the risk adjusted discount rate, or RADR approach.
The CEQ approach
An alternative approach to pricing risk which was probably not covered in Finance 3310 involves the certainty equivalent, or CEQ approach. This is a concept which I cover in some detail in the courses that I teach (i.e., FIN/RMI 4335 and FIN 4366). The CEQ approach involves discounting the certainty equivalent value of the risky cash flow at the risk free rate of interest. The certainty equivalent is determined by deducting the dollar value of the risk premium from the expected cash flow, and as we showed in class, can also be accomplished by summing the products of state-contingent cash flows multiplied by their corresponding "risk neutral" probabilities.
In summary, the two approaches to pricing risky assets are as follows:
Risk Neutral Valuation and the Integration approach to computing the value of an option
Derivatives pricing is better understood once one goes through some of the mathematical details. I realize that for most typical undergraduate (or even master's level) finance students, stochastic calculus is not a particularly familiar topic. Having said that, I (as well as your textbook author) believe that a basic introduction to concepts such as geometric brownian motion and Ito's Lemma make the underlying economics of the option pricing problem much more transparent; specifically, the notion of dynamic hedging. However, once we have established this concept, I believe that the integration approach to computing the Black-Scholes option price is easier to grasp than the differential equations approach, since it makes the link between risk neutral valuation and the CEQ approach to pricing risky assets much more transparent.
Conceptually, the integration approach to option pricing theory represents a calculus-based implementation of the CEQ approach. Specifically, we compute the certainty equivalent value of the expected payoff on the option, and then discount it back to the present time. The details of this are laid out in my paper entitled "Derivation and Comparative Statics of the Black-Scholes Call and Put Option Pricing Equations," as well as in the lecture note entitled "The Black-Scholes Model".
I have changed problem set 7 so that only questions 11.12, 11.13, and 11.16 will be due. Time permitting, I might try tackling 11.14 and 11.15 in class - no promises though!
Also, the new due date for the final problem set (#8) will be Tuesday, November 30. Problem set #8 consists of questions 12.24, 12.25, 12.26, 12.27, 12.28 from page 261 of Hull.
I am attaching a copy of a very interesting editorial about grade inflation at private universities. This appeared recently in Nature (October 14, 2004 issue).
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Call it Moore's law of US higher education: the quantity and quality of work that undergraduates must do to get top grades halves every decade. This is an exaggeration, of course, but many readers will recognize the sentiment. Is it just the jaded perception of cynical academics? On the contrary: the evidence suggests that there is a real problem of grade inflation in degree courses, especially at private universities. And the assessment of teachers by students, as well as parents' demands that they get what they think they've paid for, are making the problem worse.
Course evaluations were intended to give the instructor feedback about how well he or she was doing. But they rapidly became a favored tool of deans, tenure and promotion committees because they were quantifiable. Now there is an implicit understanding that if instructors give good grades, they will not be judged too severely by students. New faculty often grade more harshly than other members of the department, only to be 'punished' by students. Deans who believe that this doesn't happen are deluding themselves.
Also worrying is the idea - particularly evident at costly private universities - that students and their parents believe they are paying for a degree that will lead to a good job, rather than for a good education that will help them to think independently. The pressure on teachers to appease demanding students and parents by awarding high grades is obvious.
The consequences are all too clear. Anecdotal evidence suggests that there is a general unwarranted upward creep in grades (http://ctl.stanford.edu/Tomprof/postings/444.html). More objectively, the fact that graduate schools rely for admission criteria almost exclusively on the results of standardized tests, rather than on universities' individual grading, points to a systematic failure to ensure that grading standards are being maintained.
What to do? More universities should focus seriously on improving the instructional abilities of their faculty in programs - mandatory for new instructors - to videotape classes and analyze them with the faculty member to highlight strengths and weaknesses. And evaluations should take note of thoughtful individual comments by students, rather than relying on scores, or be abandoned.
Last month Edward C. Prescott and Finn E. Kydland won the 2004 Nobel Prize in Economic Sciences for two important papers they coauthored that advanced the field of "dynamic macroeconomics". As the Royal Swedish Academy of Sciences put it, Prescott and Kydland's work "has not only transformed economic research, but has also profoundly influenced the practice of economic policy in general, and monetary policy in particular." The Knowledge@Wharton website has an excellent article which explains the importance of Prescott's research to issues that confront our society today. The title of the article is: "What's Behind Edward C. Prescott's Nobel Prize?"
"Struggling under a cascade of bankruptcy filings in the airline and steel industries, the government's pension insurance agency (aka the Pension Benefit Guaranty Corporation, or PBGC) said yesterday that its deficit has more than doubled in the past year -- to $23.3 billion," according to The Washington Post. In "How to Reduce the Cost of Federal Pension Insurance," Richard A. Ippolito, former chief economist at the PBGC, warns that the agency is poised for a taxpayer bailout similar to the 1980s savings and loan crisis. He recommends transforming the PBGC into a private insurance program that sets premiums according to the amount of risk plan sponsors add to the program.
The second midterm scores are in. Here are the descriptive statistics:
| Midterm 2 | |
| Mean | 77.40 |
| Median | 76.00 |
| Mode | 73.00 |
| Standard Deviation | 7.93 |
| Range | 27.00 |
| Minimum | 66.00 |
| Maximum | 93.00 |
The course grade distribution after the first exam is as follows:
| Course | |
| Mean | 81.21 |
| Median | 80.16 |
| Standard Deviation | 8.75 |
| Range | 28.59 |
| Minimum | 64.47 |
| Maximum | 93.05 |
If letter grades had to be assigned today, based upon this distribution I would use the following curve (which would generate a class GPA of 3.17):
| A | 87.0 |
| B+ | 81.0 |
| B | 74.0 |
| C+ | 68.0 |
| C | 61.0 |
| D | 48.0 |
The due date for problem set #7 will be Thursday, November 18 rather than tomorrow. I figured that y'all might be interested in knowing this before unduly torturing yourselves this evening.
I have posted the lecture notes that we will be using for the next few meetings: Also, a problem set based upon Chapter 11 will be due on November 16. See http://129.62.162.249/4366problem_sets/ for more details.
Dr. Martin F. Grace makes some very insightful comments concerning Rand's just released study entitled "Compensating the Victims of 9/11". Dr. Grace links to Figure 2 of the Rand study, which shows how compensation is distributed according to who (e.g., charity, government, private insurers) paid what to whom (e.g., civilians and emergency responders killed or seriously injured during the attacks on the twin towers), and he notes that charity picked up 7% of the tab, private insurers paid 51% of total losses, and the government picked up the remainder.
An obvious public policy implication is whether ex post victim compensation by charity and government may "crowd out" private insurance. As Dr. Grace notes, "public policy should be designed to encourage people to have more insurance rather than rely upon prospective government payments." I made similar points two months ago concerning the effect of public disaster relief on the risk management incentives of firms and individuals. The prospect of public disaster relief creates a serious moral hazard problem by reducing consumers' demand for private insurance, which in turn incentivizes them to underinvest in loss prevention and mitigation.
The 2nd midterm exam (blank exam booklet and key) is now available from the class website!
On Thursday, we will continue our study of option pricing. The chapters coming up will be chapters 11 and 12. I will also post the lecture notes as well as information concerning problem sets fairly soon. Besides reading chapters 11-12, my paper entitled "Derivation and Comparative Statics of the Black-Scholes Call and Put Option Pricing Equations" will also be required reading.
For a highly literate, non-emotional, fact/science-based perspective on the outsourcing debate, go no further than today's Econoblog entry entitled "The Rise of Outsourcing"!
Following up on Dr. Seward's RMI@Baylor posting entitled "Social Security Reform: When will it come?", there are a couple of Social Security-related articles appearing in the blogosphere which are definitely worth a read. For starters, check out Alex Tabarrok's posting on marginalrevolution.com entitled "The Social Security Inversion". The basic premise of this article is that current (and past) retirees have gotten the best deal from Social Security; indeed, many of them did far better than they could have done in any other investment (Tabarrok cites the (spectacular) example of the first known Social Security recipent, Ida May Fuller, who received a nominal payoff equal to 925 times her total contribution into the system). Unfortunately (as both Seward and Tabarrok point out), for today's workers and their children, Social Security (as it is currently configured) is a raw deal; even if the Social Security system does not become insolvent, current workers will receive a very poor return on their "investment".
The second article appears in yesterday's online version of the Wall Street Journal. Entitled "Social Security: What's Next", this article provides both liberal and conservative views concerning reforming the Social Security system.
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)!