### Thank you!

and good luck with the rest of your program.

Here is the photo that Shu-Ai had taken in Rarig yesterday.

and good luck with the rest of your program.

Here is the photo that Shu-Ai had taken in Rarig yesterday.

The last assignment is nominally due in two weeks, but we can talk next week about how I can collect it since Bill's module is running on a different schedule this term.

I put my version of the MATLAB demonstration of the Michaud re-sampled allocation from the lab this evening in the docs folder for your reference.

The lab project yesterday consisted of -

- deriving an optimal mean-variance portfolio based on historical relative returns data, and
- augmenting the historical data to reflect a prior opinion

The historical data consists of five years of monthly relative returns on eleven sectors versus the Russell 3000 benchmark index.

The prior is to be represented by 12 months of pseudo-observations, with each sector return independent with mean 0% and standard deviation 2% per month.

For next week's lab, please write a script to produce 1,000 versions of the augmented data and the corresponding solutions for the SR (Sharpe Ratio) portfolio with unit expected objective.

Did anyone leave a pair of glasses in a red case in the MFM office? It is on the bookshelf.

The assignment is due at the beginning of the February 20 meeting.

I will be available for office hours on Sunday, February 3, from 7-9PM in the Vincent Hall MFM office. Please contact me for access to the building.

The lab project for this week is to put a version of the portfolio re-balance problem into the MATLAB standard form for linear programming. Find vectors $f$ and $b$ and a matrix $A$ such that the optimal trade list satisfies -

$argmin_x f'x$ s.t. $Ax\le b, x\ge 0$ where
$x=(buy_1,sell_1,buy_2,sell_2,...)'$ for assets 1, 2, 3, etc.

Initial allocations and prices and current prices for the assets are available in the file case9.dat. The object is to minimize transactions costs (0.05 per share) and capital gains taxes (20%) on gains or losses from sales. The constraints are that the new allocations must be positive, the new weights must be within 1% of initial weights, and cash must be raised through sales to cover purchases and costs.

Please work out the joint maximum likelihood estimates and standard errors for the location and scale of a Cauchy random variable given a sample of independent observations.

I would like to talk about office hours when we meet. In the fall term, I held office hours on Tuesdays evenings. Since this conflicts with Carlos' course, I want to discuss alternatives. One possibility would be for me to
hold office hours on Sunday afternoons or evenings.

Welcome to the second half of the data analysis, simulation, and portfolio optimization, which starts Wednesday and runs through March 5.

The schedule indicates that we have a different room in Ford Hall this term: FordH B10. I have not checked on it yet; but I assume there will be no problems. Let's plan to meet there at 5PM on Wednesday.

We will not need to use the Lind Hall lab in the first week.

I have posted a brief tutorial on the TGARCH model for timeseries conditional heteroskedasticity.

For the next four weeks, the topic will be fixed income markets, and Bill Barr will be your instructor.

Please see his course website for the reading assignment. Lectures will be in our lecture hall, FordH127.

I turned out the final assignment for Fall term, due 10/24.

Contact me if you have any questions.

Come to office hours on Tuesday, 6-8PM, if you want to see me in person.

I would like to change the scheduled topic for my module's last lecture this term, on 10/17, from CW's treatment of baskets to a review of the dominant conditional heteroskedasticity model, TGARCH.

The main reference for this is

Zakoin, Jean-Michel, *Threshold heteroskedastic models*, __Journal of Economic Dynamics and Control__, vol. 18, 1994, pp. 931-955

This journal is avaialble online through the library.

I have updated the case from yesterday to demonstrate the failure of the Cholesky method for simulating large vectors, and the alternate historical simulation method. I have also posted a note defining and justifying the method.

Use the projection formula (3.64) in analogy to the arguments leading to (3.74) to work out the time-scaling properties of a process with symmetric Levy-stable increments.

See (2.282) for the definition of a symmetric Levy-stable random variable.

I suggest you work these problems to check your understanding. These are appropriate for the material covered in Week 4. I will post problems for Week 5 tomorrow.

I will mark your solutions if you hand them in, but the scores will not count towards your grade.

I will mark your solutions if you hand them in, but the scores will not count towards your grade.

- Verify that the equations (2.176-7) in M for the gaussian copula in fact define a density by numerically integrating it over the domain for various values of the correlation paramter. Note that the integrand diverges in the corners, so you may want to use the
`eps`constant in MATLAB to truncate the integration bounds. You may also want to plot the function, for example using`ezsurfc()`. - Extend the regression analogy by using the equation (2.165) in M for the conditional mean of a normal dependent variable, X3, given values X2=x2 and X1=x1 for
__two__normal (but possibly correlated) independent variables. Interpreting this as a point estimator, compare what you get to the formulae for generized least squares.

I have posted two versions of the solutions I worked, one in Mathematica 6.0 and the other in MATLAB R2007b. If you need me to re-work the Mathematica solution for a previous version, please let me know. In both cases, I used trial and error to identify that the optimal portfolio was 55% risky asset and 45% riskless asset.

As was announced last week, until you hear otherwise assume that the Wednesday evening sessions will start at the classroom in FordH 127 at 5:00 and move to lab in LindH 024 after the break at 6:30.

The lab is scheduled to be open to the public prior to the lecture, so it should still be open after the break. If not, I can open it.

Here is the diagram that I shared in class from Casella & Berger that shows the relationships between the major classical distributions.

The files we use in the lab such as the M-file for `binomial()` will be kept in the directory http://www.math.umn.edu/~dodso013/fm503/docs/.

It is not required for success; but I encourage you to learn and use "functional" programming techniques in MATLAB (or Mathematica or whatever high-level programming language you use), especially when working with random variates.

You can load a sample of random variables into MATLAB using the command

sscanf(urlread('http://www.math.umn.edu/~dodso013/fm503/case1.dat'),'%f')

These are drawn uniformly between zero and some unknown upper bound. Please provide an interval estimate for the upper bound.

The objective is to have the narrowest interval that includes the true value. This is a contest; the winning team members will take home a Sven & Ole's bumper sticker!

There are readings due for the first session on 5 September. Please see the syllabus.

Orientation is 9 AM Monday, 27 August in Vincent Hall 120.

Feel free to leave comments for the instructor and other visitors.