Problem Set 2 helpful hints

Problem Set 2 is available from the course website at; its due date is Tuesday, September 5.

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. 13-19 of the lecture note for coverage of that topic.

On the importance of oversight, financial controls, and risk management in the real world – the case of FTX and Sam Bankman-Fried

I highly recommend that everyone tune in to Season 3, episodes 8 through 14 of the Michael Lewis podcast, “Against the Rules.” These seven episodes, each averaging around 35 minutes, delve into the extensive research conducted by Lewis for his upcoming book on the fascinating story of Sam Bankman-Fried, a 31-year-old entrepreneur who served as the founder and CEO of the cryptocurrency exchange FTX and its associated trading firm, Alameda Research. Both entities made headlines due to their dramatic collapse, culminating in Chapter 11 bankruptcy filings in late 2022. To access the podcast, you can visit Michael Lewis’s podcast homepage at

This podcast illustrates how a lack of oversight, financial controls, and risk management gave rise to spectacular business failures. The podcast host, Michael Lewis, is a well-known and highly regarded author whose books often become major motion picture productions; e.g., The Blind Side (2009), Moneyball (2011), and The Big Short (2015).

Gamma Iota Sigma Interest Meeting, August 31, 6:30-7:30 in Foster 322

The purpose of the Gamma Iota Sigma (GIS) at Baylor University is to promote, encourage, and sustain student interest in insurance, risk management, and actuarial science as professions, to promote high moral and academic excellence of chapter members, and to facilitate the interaction between Baylor University and the business community by fostering research activities, scholarship, and networking opportunities.

Visualizing Taylor polynomial approximations

On pp. 18-23 of the Mathematics Tutorial, I show how y = ex can be approximated with a Taylor polynomial centered at x=0 for \delta x 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 = ex 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.

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.