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On the ancient origin of the word “algorithm”

The August 29th assigned reading entitled “The New Religion of Risk Management” (by Peter Bernstein, March-April 1996 issue of Harvard Business Review) offers a concise overview of the same author’s 1996 book entitled “Against the Gods: The Remarkable Story of Risk“. An intriguing excerpt from page 33 of “Against the Gods” elucidates the historical roots of the term “algorithm.” An intriguing excerpt from page 33 of “Against the Gods” elucidates the historical roots 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.”

Note: The book cover shown above is a copy of a 1633 oil-on-canvas painting by the Dutch Golden Age painter Rembrandt van Rijn.
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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.

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On the relationship between the S&P 500 and the CBOE Volatility Index (VIX)

Besides going over the course syllabus during the first day of class on Tuesday, August 22, we will also discuss a particularly important “real world” example of financial risk. Specifically, we will study the relationship between realized daily stock market returns (as measured by daily percentage changes in the SP500 stock market index) and changes in forward-looking investor expectations of stock market volatility (as indicated by daily percentage changes in the CBOE Volatility Index (VIX)):
As indicated by this graph (which also appears in the lecture note for the first day of class), daily percentage changes in closing prices for the SP500 (the y-axis variable) and for the VIX (the x-axis variable) are strongly negatively correlated with each other. The blue dots are based on 8,470 contemporaneous observations of daily returns for both variables, spanning the 33-2/3-year period of time starting on January 2, 1990, and ending on August 15, 2023. When we fit a regression line through this scatter diagram, we obtain the following equation:

{R_{SP500}} = .00062 - .1147{R_{VIX}},

where {R_{SP500}} corresponds to the daily return on the SP500 index and {R_{VIX}} corresponds to the daily return on the VIX index. The slope of this line (-0.1147) indicates that on average, daily closing SP500 returns are inversely related to daily closing VIX returns.  Furthermore, nearly half of the variation in the stock market return during this time period (specifically, 48.87%) can be statistically “explained” by changes in volatility, and the correlation between {R_{SP500}} and {R_{VIX}} came out to -0.70. While a correlation of -0.70 does not imply that daily closing values for {R_{SP500}} and {R_{VIX}} always move in opposite directions, it does suggest that this will be the case more often than not. Indeed, closing daily values recorded for {R_{SP500}} and {R_{VIX}} during this period moved inversely 78% of the time.

You can also see how the relationship between the SP500 and VIX evolves prospectively by entering http://finance.yahoo.com/quotes/^GSPC,^VIX into your web browser’s address field.

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Calculus and Probability & Statistics recommendations…

Since many of the topics covered in Finance 4335 require a basic knowledge and comfort level with algebra, differential calculus, and probability & statistics, the second class meeting will include a mathematics tutorial, and the third and fourth class meetings will cover probability & statistics. I know of no better online resource for brushing up on (or learning for the first time) these topics than the Khan Academy.

So here are my suggestions for Khan Academy videos that cover these topics (unless otherwise noted, all sections included in the links which follow are recommended):

Finally, if your algebra skills are a bit on the rusty side, I would also recommend checking out the Khan Academy’s review of algebra.

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Important notice concerning Section III.C.16 of Baylor’s Honor Code Policy and Procedures document

According to Section III.C.16 of Baylor’s Honor Code Policy and Procedures, using, uploading, downloading, or purchasing any online resource that has been derived from material pertaining to a Baylor course without the written permission of the professor constitutes dishonorable conduct; i.e., an act of academic dishonesty.  Section IV.A. of the same document obligates faculty members who suspect that a student has engaged in dishonorable conduct of this sort to either handle the matter directly with the student or refer it to the Honor Council.

While you may use course-related documents that I distribute in class and on the course website for strictly personal academic purposes, anything other than your personal use of these documents is in violation of Section III.C.16 of Baylor’s Honor Code Policy and Procedures and therefore, expressly forbidden.  Examples include sharing course-related documents with students who are not enrolled in Finance 4335 and uploading such documents to so-called course-sharing websites such as Quizlet, Coursehero, and Chegg, etc.  Furthermore, the use of course-related documents (e.g., old problem sets and exams) from any other source other than me also represents an honor code violation.

I close by citing the “Academic Honesty and Integrity” section of the Finance 4335 course syllabus:

Plagiarism, or any form of cheating, involves a breach of student-teacher trust. This means that work on quizzes, problem sets, and exams submitted under your name is expected to be your own, neither composed by anyone else as a whole or in part, nor handed over to another person for complete or partial revision. Instances of plagiarism, or any other act of academic dishonesty, will be reported to the Honor Council and may result in failure of the course or expulsion from the University.

Baylor’s honor code and the Finance 4335 honor code are important resources for understanding various types of academic dishonesty, and I expect my students to be intimately familiar with both of these documents. The standards set forth in both of these honor codes will be applied to all of your work in Finance 4335.