## Assignments for Thursday, January 19 in Finance 4335

As indicated on the http://fin4335.garven.com/readings page of the course website, the readings assigned for the second day of class (Thursday, January 19) include

1. Calculating (Math) Derivatives, by James R. Garven
2. Optimization (chapter 2 from Managerial Economics, by W. Bruce Allen, Neil Doherty, Keith Weigelt, and Edwin Mansfield, 6th edition (2005))
3. How long does it take to double (triple/quadruple/n-tuple) your money?, by James R. Garven

Pages 74-76 of the “Optimization” reading  (entitled “Lagrangian Multipliers”)  may be skipped without loss of continuity. The primary purpose of this reading is to re-acquaint students with basic calculus and how to use calculus to solve (unconstrained) optimization (i.e., maximization and minimization) problems. Since none of our work in Finance 4335 requires solving constrained optimization problems, there’s no need (in this course, anyway) for Lagrangian multipliers.

Besides reading these three articles in preparation for the second day of class, Finance 4335 students are also required to complete Quiz 1 on Canvas,  fill in the Student information survey, and sign up for a free WSJ student membership at https://wsj.com/ActivateBaylor.

## 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, January 17, 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 on 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 8,315 contemporaneous observations of daily returns for both variables, spanning the 33-year period of time starting on January 2, 1990 and ending on December 30, 2022. 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 78.59% of the time.

## 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.

## Course Requirement: Email subscription to the Risk Management Course Blog (instructions given here)

A course blog has been established for Finance 4335 at the address http://risk.garven.com; it is also linked from the “Course Blog” button located on the course website. This resource provides a convenient means for Dr. Garven to distribute important announcements outside of class. Topics covered on the course blog typically include things like changes in the course schedule, clarifications, and hints concerning problem sets, information about upcoming exams, announcements concerning extra credit opportunities, and short blurbs showing how current events relate to many of the topics covered in Finance 4335.

All students enrolled in Finance 4335 are required to subscribe to the course blog via email.

Email Subscription Instructions:

In order to subscribe to the course blog via email, go to http://risk.garven.com and enter your email address in the form provided on the right-hand side of that webpage: