… are available at http://fin4335.garven.com/spring2023/statclassproblem.pdf and http://fin4335.garven.com/spring2023/statclassproblemsolutions.pdf respectively.

### Problem Set 2 helpful hints

Problem Set 2 is available from the course website at http://fin4335.garven.com/spring2023/ps2.pdf; its due date is Tuesday, January 31.

Problem Set 2 consists of two problems. The first problem requires calculating expected value, standard deviation, and correlation, and using this information as inputs into determining expected returns and standard deviations for 2-asset portfolios. The second problem involves using the standard normal probability distribution to calculate the probabilities of earning various levels of return by investing in risky securities and portfolios; see pp. 15-21 of the http://fin4335.garven.com/spring2023/lecture4.pdf lecture note for coverage of that topic.

### Formula Sheet for today’s class problem in Finance 4335

As promised, I have posted the formula sheet for today’s statistics class problem in Finance 4335 at http://fin4335.garven.com/spring2023/statformulasheet.pdf. I highly recommend that everyone work through the class problem with the help of this formula sheet prior to Thursday’s Finance 4335 class meeting.

### The 17 equations that changed the course of history (spoiler alert: we use 3 of these equations in Finance 4335!)

Equations (2), (3), and (7) from this list play particularly important roles in Finance 4335!

From Ian Stewart’s book, these 17 math equations changed the course of human history.

### Solutions for Problem Set 1…

… are available at http://fin4335.garven.com/fall2022/ps1solutions.pdf.

### On the ancient origin of the word “algorithm”

The January 24th assigned reading entitled “The New Religion of Risk Management” (by Peter Bernstein, March-April 1996 issue of *Harvard Business Review*) provides a succinct synopsis of the same author’s 1996 book entitled “Against the Gods: The Remarkable Story of Risk“. Here’s a fascinating quote from page 33 of “Against the Gods” which explains the ancient origin of the word “algorithm”:

“The earliest known work in Arabic arithmetic was written by alKhowarizmi, a mathematician who lived around 825, some four hundred years before Fibonacci. Although few beneficiaries of his work are likely to have heard of him, most of us know of him indirectly. Try saying “alKhowarizmi” fast. That’s where we get the word “algorithm,” which means rules for computing.”

### Visualizing Taylor polynomial approximations

On pp. 18-23 of the Mathematics Tutorial, I show how *y = **e*^{x} can be approximated with a Taylor polynomial centered at *x*=0 for values ranging from -2 to +2. In his video lesson entitled “Visualizing Taylor polynomial approximations”, Sal Kahn essentially replicates my work; the only difference between Sal’s numerical example and mine is that Sal approximates *y = **e*^{x} with a Taylor polynomial centered at *x*=3 instead of *x*=0. The important insight provided in both cases is that the accuracy of Taylor polynomial approximations increases as the order of the polynomial increases.

### Rules for calculating (math) derivatives

### How to know whether you are on track with Finance 4335 assignments

At any point in time throughout this semester, you can make sure that you are on track with Finance 4335 assignments by monitoring due dates on Canvas and on the course website. Links for future class meetings, quizzes, problem sets, and exams appear on the Canvas “To Do” list. Links for readings (along with their due dates) appear on http://fin4335.garven.com/readings/, and links for problem sets (along with their due dates) appear on http://fin4335.garven.com/problem-sets/. In the case of assigned readings, students are required to complete a short (10-minute) readings quiz prior to the start of class for each reading assignment due date; the window for completing this task begins 24 hours prior to the start of the class meeting for which the reading assignment is due.