Math Camp, pt1

Math camp finally began yesterday, and has so far been void of sleeping bags, calculators, bow-ties, or witty jokes. The camp will be three weeks long, is not graded (but attendance is mandatory), and comprises 2 1/2 hours of lecture and 1 1/2 hours of application workshop each day.  The syllabus for the first half is as follows, and covers statistics for economics:

  1. Probability and random variables
    1. axioms
    2. conditional probability
    3. Bayes’ Theorem
  2. Probability distribution
    1. Probability mass functions
    2. Probability density functions
    3. Cumulative distribution functions
    4. Multivariate distributions (joint, marginal, conditional)
  3. Moments and the moment generating function
  4. Transformation of random variables and order statistics
  5. Inequalities and convergence
  6. Approximation (Taylor approximations and the delta method)
  7. Efficient estimation
    1. The Cramer-Rao Theorem
    2. The Rao-Blackwell Theorem
  8. Markov chains
  9. Methods of Moments
  10. Likelihood and maximum likelihood

I’m fairly familiar with everything on this list from previous classes except the following:

  • the delta method of approximation
  • Taylor approximations
  • Markov chains
  • multivariate distributions
  • the Rao-Blackwell Theorem

Part two of the camp will more directly cover mathematics, after part one treats statistics.

Sas vs. Stata update

I’ve been going through some UCLA tutorials on Sas for a couple of weeks now, and while I’m not yet an expert, there are some key differences between Stata and Sas on which I can comment.

  • Reading data files
    • Stata loads a data file into memory.  This means calculations are faster, but that the size of data file you can use is limited to the computer’s memory.
    • Sas uses “libraries” to reference files stored on the computer’s hard drive.  This means if you have 1TB of hard-drive space then you can use Sas to manipulate a 1TB dataset.  You would need 1,000GB of memory to do this with Stata.
    • The library system in Sas also makes it possible to reference multiple data files, even in the same step.  Stata, in contrast, can only work with one data file at a time.
  • Syntax & Interface
    • Sas’s data management syntax is more efficient that Stata’s.  For example, you can copy a data file and modify (add/drop/relabel) the variables all in one step.  However, Sas’s syntax is also more bulky at times, and always feels a little less intuitive than Stata’s.
    • Stata’s default delimiter is a RETURN.  Sas uses a semicolon, and those who aren’t used to typing semicolons on every tenth keystroke will get penalized for missing one somewhere.  Sas also requires “run;” at the end of each command, whereas Stata does not.
    • While Sas’s data management is more efficient, Stata’s econometrics (regressions, hypothesis tests, etc.) seem more intuitive.
    • Sas’s interface feels like something from the 1990s.  Stata’s interface is much better, and I especially like Stata’s side panel that shows all of the variables in the data set I have in memory.  In Sas, I have to either run a command to see the variable list or double-click on the file in the “library” panel to the left.
  • Graphics:  I think Sas produces much better graphics than Stata.
  • Help files:  Stata has done an extraordinary job of putting together detailed help files for all its commands.  They are also very easy to access, via internet as a .pdf or directly within Stata by typing “help _____”.  Sas has help files available, but they are less detailed and more difficult to find.

One of my professors from last semester uses Sas for all his data management and processing, and then transfers the data to Stata for the econometrics.  That may end up being my strategy, as well.

Ph.D. Prep – Programming

The two most common programs used for empirical data analysis are Stata and SAS.  If you do theoretical work, you might also use MatLab or you might just use a soap pencil on your dormitory window a la John Nash in “A Beautiful Mind.”  Other common programs/languages include SPSS, R, Python, and even Excel VBA.

Most of the younger finance faculty at my MBA school say to forget about SAS and just use Stata.  Stata is supposed to be better at the econometrics, and is more friendly to use since there are a ton of very thorough, official help files for Stata on the internet.

One of our younger faculty members uses Stata for the econometrics, but SAS for preparing the data.  The advantage to SAS is that it doesn’t load your entire data set into memory, like Stata, and just reads it from the hard drive.  This makes SAS better for getting very large data sets ready for the tests/regressions/whatever.

I’ve learned Stata fairly well through all my economics classes, and I also put together a self-study course on Stata, with the guidance of a professor, for my final MBA semester.  I plan to spend a lot of time this summer learning SAS, so I’ll probably have more to say on this subject later.

Ph.D. Prep – Application Process

Now, the application process:  this includes letters of recommendation, application forms/fees, test scores/transcripts, essays, interviews, and timeline.

Six of my applications wanted two letters of recommendation, and the other 16 wanted three letters.  The point of the letters is to vouch for your skills as a researcher and thinker, not for your character.  These should be from professors with whom you have worked on research.  At the time I applied, I had only researched with two professors, so my third letter was from a professor from whom I’d taken several classes and whom I knew well.

Most of my application forms were practically identical.  A few made me type in all the course information from my transcripts by hand.  My average application fee was $85, but many schools will waive that fee if you can demonstrate special financial need.  I just paid the fees.

Almost all of my schools wanted official GMAT scores and transcripts, sent directly from Pearson and the schools.  A few just wanted self-reported information, with official scores and transcripts to be required upon admission.

Ph.D. essays were not as demanding as MBA essays.  Most schools’ essay prompts were very similar, so I just had to tweak my master copy a little to explain what I liked about that school and with which professors I’d like to work.  Only the University of Michigan and U.C. Berkeley required truly unique essays.

I interviewed with only three schools before I made my decision.  One school flew me to campus for a big interview day.  The other two interviews were about 15 minutes long over Skype (I chose one of the Skype schools).  One program accepted me without any interview at all.  The purpose of the interview is to see if you “check out” and speak English.  If you get to the interview stage, your skills and background have likely already passed the test.  Now, two or three professors just want to talk with you to see if you seem sociable and articulate enough.  Here are some of the questions I got in interviews:

  • When did you decide you wanted to get a Ph.D.?
  • Tell us a little about your research.
  • What did you do in (class) _____?
  • Where else are you applying? i.e. If we admit you, are you likely to actually come here?
  • What are your professional goals?  i.e. Do you want to be an academic (good), or are you headed to Wall Street (bad)?
  • only one school asked technical questions, like “find the determinant of this 2×2 matrix” or “explain OLS regression”

My application timeline started December 1 and ended mid-March.  Application deadlines ran from December 1 to February 1.  I did my first interview at the end of January, and got my first offer in mid-February.  If you receive an offer, the program is obligated to hold your spot until April 15.  However, if you make someone wait until April 15 and then turn down their offer, they then have to scramble to fill your spot at the last minute.  It’s unprofessional, and can burn bridges.

Next post:  Ph.D. Prep – Programming

Ph.D. Prep – Selecting Programs

This post will outline what I’ve learned about program rankings & selecting programs.

As a rule of thumb, you want to go the most prestigious program to which you can get accepted.  Schools hire professors from peer schools or better, so if you get your Ph.D. at the University of Colorado, you will not teach at Stanford.  If, however, you graduate from Stanford and want to be a small-town teacher, you can always go the College of Southern Idaho.

Here’s the other reason why getting into a good school helps:  each finance program graduates maybe 3-5 Ph.D.s per year, but each university’s finance department only hires maybe 1-2 per year.  The top five schools’ graduates, then, tend to meet the hiring needs of the top 15 finance departments.  Job prospects get a lot harder for the middle-of-the-pack graduates of the #45 program.  If you do go to the #45 program, however, isn’t the end of the world.  You can end up teaching at a solid state school, make a good salary with limited publishing pressure, and even run a nice local consulting business on the side.

Ph.D. programs aren’t ranked separately from their business schools in the same way as MBA programs, though most of the highest-ranked MBA schools also have the best doctoral programs in finance.  Arizona State University maintains a Ph.D. Finance Program Ranking based on the number of papers published in top journals (though not all of these schools actually have doctoral programs).  The most helpful source I used was the faculty at my university–especially the youngest professors.  The reputation of your Ph.D. program will follow you to some degree throughout your life, and so it is an important consideration.  Professors will be able to tell you which programs are gaining prestige, which are considered top-notch, and which are heading downhill.

The other criteria that matters is subject of interest.  A few of the top schools like Harvard will have faculty focusing on just about anything you might care about, but most schools lean in one direction or another.  Professors can tell you what each school’s specialty is, and can often even tell you the names of the most productive researchers.  Those are the ones you’ll want to work with.

I applied to four or five programs I thought I’d really enjoy, plus another 15 of the the top-20 schools, plus 3-4 “backup” schools.  One of my MBA classmates shot himself in the foot by only applying to the top five programs.  He didn’t get into any of them, and now has to scramble to find a job during the last few weeks before graduation.

Next post:  Ph.D. Prep – Application Process

Ph.D. Prep – Reading

Reading existing finance literature is important for two reasons:

One, exposure to varied ideas helps you discover what interests you.  Nobody does their dissertation on “finance;” they do dissertations on “liquidity in off-the-run treasury bond auctions,” or “mortgage-backed securities trading spreads and implied default risk.”  You don’t need to choose a dissertation area before applying, and your interests will evolve during the Ph.D. anyway.  The professors who are considering admitting you to their program want to know that you’ve at least thought intelligently about what you want to research.

Two, the hardest thing for students to do is to make the transition from learners to contributors.  Ph.D. students enter as classroom pupils; they are expected to leave as critical and original thinkers.  Scientific breakthroughs very rarely come ex nihilos–out of nowhere–but rather as incremental but important progress.  To become a contributor (and to pass your Ph.D. classes) you will be required to understand the important ideas that have contributed to the field of financial economics over the past 40 years, and also to be aware of what current discoveries are being made.  This means doing a lot of reading.

There are two kinds of papers that are most useful to read:

Classic papers are the seminal ideas that constitute the foundations of finance research.  These are the “shoulders of giants” on which you’ll stand.

Working papers are the cutting edge ideas on the frontier of the science.  By the time a paper is actually published, its ideas have already been discussed for perhaps 1-3 years.

 

One of my primary motivations for starting this blog was to have somewhere to outline and discuss the papers I read.

I’ve read maybe a couple dozen working papers, and I’ll read more over the summer.  Many working papers are available with a free SSRN account.  Look for papers submitted by good researchers at respected universities.

One of my professors kept the lists of “classic papers” he was expected to read during his Ph.D. program.  I have those lists of over 200 papers, and I hope to get through 30-40 of them this summer.  These papers usually appeared in top journals (esp. Journal of Finance and Journal of Financial Economics), won major awards, and/or have the most citations on Google Scholar.

Next post:  Ph.D. Prep – Selecting Programs

Ph.D. Prep – Research Assisting

If math/econ background and high test scores are the first two pillars of good preparation, research assisting is the third.  I worked with three different finance professors, and even though I didn’t do anything flashy or award-winning, the work helped a lot in my applications.

Finance faculty members make the final admissions decisions, and they basically want to know two things:  Are you smart enough to be a successful academic researcher? and Do you want to be a successful academic researcher?  They also want to know that you speak English well enough to teach, but that’s a topic for another day.

Research assisting helps you in three ways.  First, it lets you find out if research is something you really enjoy.  A lot of research assisting is simply data gathering and processing, but that represents a huge part of the professor’s work, as well.  You also learn a lot more about the overall research & publishing process by spending some time and building a relationship with a professor.  Second, research assisting gives you credibility when you say in your applications and interviews that you know what you’re getting into.  There are many cases of bright young students who end up dropping out of doctoral school because they discover they don’t like research.  Since most Ph.D. Finance programs only accept 4-6 students each year, even one dropout is a huge cost.  Third, research assisting lets you build relationships.  The academic world is very small.  If you research with Dr. _____ and he puts a good word in for you with a friend at the University of _____, it could make all the difference.

I once had a professor explain it to me this way:  “Research assisting works a bit like an apprenticeship.  You need to learn the trade of academic research before you can be successful on your own, and that means you need to find someone who will work with you and give you an opportunity to learn.”

Next post:  Ph.D. Prep – Reading

Ph.D. Prep – Test Scores

One more quick aside before I continue with my Ph.D. preparation:  test scores.

I finished my undergrad in 2009, and I was still considering perhaps doing some kind of math or statistics Masters Degree en route to a Ph.D.  I took the GRE in January 2010 and then, because I was also considering an MBA, I took the GMAT two months later.  My GRE score was about the 95th percentile, and my GMAT was in the 99th.

I applied to 22 of the top 30 Ph.D. Finance programs, and all of them accepted either test.  I used the GMAT, since my score was relatively better.  I did not take the GRE-Math subject test, and none of the programs to which I applied specifically asked for it.  The subject test may be more useful for Economics Ph.D. programs.

Next post:  Ph.D. Prep – Research Assisting

Ph.D. Prep – Math Summer

I had a lot of work to do to get ready for Ph.D. applications.  I worked as a research assistant during the summer of my MBA program, and spent every remaining daylight hour in the Math Lab.  The Math Lab at my school is in the heavily air-conditioned room where they used to keep the main-frame computer in the 1970s.  It’s about 59 degrees around the clock.  So, I spent 12-14 hours of each summer day dressed like Christmas, writing matrices and solving differential equations.

I was on campus working from about 7am to 8pm, Monday-Saturday, eating a quick lunch while walking to class or working out a homework problem.  That translates to about an 80-hour work week, which is actually fairly light by some standards.  Some of that was overkill, since the main reason I was taking the classes was to show I could get A’s.  An A-minus or B-plus would have rendered the time spent a failure.  I think I averaged 98% in the classes I took.

The point is, getting through a Ph.D. program is a lot of work.  I’ve talked to professors who said they regularly spent 100 hours/week on school.  Preparing for a Ph.D. program is also a lot of work.  Some people just can’t continue working that hard and concentrating for that many hours each day.  That’s also another reason why you have to really enjoy coursework and research–you’ll literally be doing it all day, every day.  I do, and I do.