Visualizing Taylor polynomial approximations

In his video lesson entitled “Visualizing Taylor polynomial approximations”, Sal Kahn replicates the tail end of yesterday’s Finance 4335 class meeting (beginning at the 1:06:13 mark in the Section 1 Zoom recording) in which we approximate y = ex with a Taylor polynomial centered at x=0.  Sal approximates y = ex with a Taylor polynomial centered at x=3 instead of x=0, but the same insight obtains in both cases, which is that the accuracy of Taylor polynomial approximations increases as the order of the polynomial increases (as also shown in pp. 18-23 of the Mathematics Tutorial lecture note).

Plans for next week’s Finance 4335 class meetings, along with a preview of future topics

We will devote next week in Finance 4335 to tutorials on probability and statistics. These tools are critically important in the measurement of risk and development of risk management strategies for individuals and firms alike. Next Tuesday’s class meeting will be devoted to introducing discrete and continuous probability distributions, calculating parameters such as expected value, variance, standard deviation, covariance, and correlation, and applying these concepts to measure expected returns and risks for portfolios comprising risky assets. The following Thursday will provide a deeper dive into discrete and continuous probability distributions, in which we showcase the binomial and normal distributions.

While I have your attention, let me briefly explain what the main “theme” will initially be in Finance 4335 (up to the first midterm exam on Tuesday, September 29). Starting on Tuesday, September 1, we will begin our discussion of decision theory. Decision theory addresses decision making under risk and uncertainty, which at the very heart of risk management. Initially, we’ll focus attention on variance as our risk measure. Most of the basic finance theories, including portfolio, capital market, and option pricing theories, define risk as variance. We’ll learn that while this is not necessarily an unreasonable assumption, circumstances may arise where it is not an appropriate assumption. Since individuals and firms encounter multiple sources of risk, we also need to take into consideration the portfolio effects of risk. Portfolio theory implies that risks often “manage” themselves by canceling each other out. Thus the risk of a portfolio is typically less than the sum of the individual risks which comprise the portfolio.

The decision theory provides a useful framework for thinking about concepts such as risk aversion and risk tolerance. The calculus comes in handy by providing an analytic framework for determining how much risk to retain and how much risk to transfer to others. Such decisions occur regularly in daily life, encompassing practical problems such as deciding how to allocate assets in a 401-K or IRA account, determining the extent to which one insures health, life, and property risks, whether to work for a startup or an established business and so forth. There’s also ambiguity when we have incomplete information about risk. This course will at least help you think critically about costs, benefits, and trade-offs related to decision-making whenever you encounter risk and uncertainty.

After the first midterm, the rest of the semester will be devoted to various other risk management topics, including the demand for insurance, asymmetric information, portfolio theory, capital market theory, option pricing theory, and corporate risk management.

Extended office hours tomorrow for help with Practice Quiz, “Faux” Problem Set, and Q&A related to online learning

I recommend that that everyone take the practice quiz listed as “Preparing for Online Instruction (Practice Quiz)” in the Quizzes section of Canvas and complete the “Test upload of ‘faux’ Finance 4335 Problem Set to Canvas” in the Assignments section of Canvas. Both assignments are listed and linked on the Finance 4335 home page, in the “To Do” section.

While neither assignment is for credit, I designed these assignments to familiarize (or perhaps, re-familiarize) students how to take quizzes and submit problem set assignments on Canvas. The “Test upload” assignment involves scanning a random document (preferably 2 or more pages) using the Adobe Scan app, creating a PDF file from the scan, and then uploading the PDF file to Canvas. Appendix C of “Finance 4335 Online – A Guide for Students” explains how to get and use this free software.

My office hours tomorrow will be from 3:30-5:30 (instead of the default 3:30-4:30) so that there will extra time for helping students with these assignments and provide Q&A time for addressing questions of a technical nature related to online learning.

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

Besides monitoring the course calendar and “to do” list on the class Canvas page, also be sure to monitor due dates listed on the course website. See for the reading assignment due dates, and for the problem set due dates. Also, keep in mind that I will administer short quizzes in class on each of the dates shown for the required readings.

Lagrangian Multipliers

There is a section in the assigned “Optimization” reading due Thursday, August 27 on pp. 74-76 entitled “Lagrangian Multipliers” which (as noted in footnote 9 of that reading) may be skipped without loss of continuity. The primary purpose of this chapter is to re-acquaint students with basic calculus and how to use calculus to solve so-called optimization problems. Since the course only requires solving unconstrained optimization problems, there’s no need for Lagrangian multipliers.

Besides reading the articles entitled “Optimization” and “How long does it take to double (triple/quadruple/n-tuple) your money?” in preparation for this coming Thursday’s meeting of Finance 4335, make sure you have completed the student information survey, subscribed to the Wall Street Journal, and subscribed to the course blog (if you haven’t already done so).

Course Requirement: Obtain your email subscription to the Risk Management Course Blog Right Away!

A course blog has been established for Finance 4335 at the address; 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 now required to subscribe to the course blog via email. Students may also follow the course blog on Facebook or Twitter, but are not required to do so.

Email Subscription Instructions:

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

After clicking “Subscribe”, the following information will appear on the screen:

Next, check for an email from “Risk Management Blog <> ”:

Screen Shot 2016-06-16 at 7.15.43 PM
Next, simply click the “Confirm Follow” button. This will cause you to receive the following email:

Screen Shot 2016-06-16 at 7.21.17 PM

From that point forward, whenever I post to the course blog, you will immediately receive a nicely formatted version of the blog posting via email. Also, you can opt to change your delivery preferences, or even cancel your subscription.

Mea Culpa (email version sent yesterday evening)

Yesterday, I sent out invitations to students in both sections of Finance 4335 to become “followers” of the Finance 4335 course blog.  Here’s what the email invitation looked like: Around a couple of dozen of you dutifully clicked on the “Accept Invitation” button, which produced the following screen:

It appears that most of you filled in the 3 blanks and pushed the “Sign Up & Follow” button.  Those who took this action were then greeted by an email entitled “Welcome to”, making some of you proud owners of a free product called “My Website”.  While this is an interesting product (referred to by as a “custom magazine”), unfortunately, it is not an email subscription to the Finance 4335 course blog.

When I made this “invitation”, I mistakenly thought that it would convey an email subscription to the course blog, and the lucky handful of you who clicked on the “Follow by email subscription only” link at the bottom of the above form rather than the “Sign Up & Follow” button took the correct action.  Please accept my apology for not more carefully vetting this procedure before extending the invitation.  Upon realizing my error, I immediately rescinded everyone else’s “invitations”.

So here’s the workaround to obtaining an email subscription to the course blog – simply follow the instructions for subscribing by email as shown in the blog posting entitled “Instructions for subscribing to the Risk Management Course Blog”.  When you go to that blog posting, enter your email address in the form provided on the right-hand side of the page (like this):

Click the “SUBSCRIBE” button, you’ll receive an email from asking you to confirm the subscription.  When you complete this step, you will become the proud owner of an email subscription to the Finance 4335 course blog!

Once you have successfully subscribed to the Finance 4335 course blog, if you go to, your screen will look like this (this applies to those of you who inadvertently created a WordPress account prior to signing up for the email subscription):

You can get rid of “My Website” by clicking on the “Unfollow” link next to it and clicking on the blue “Save Changes” button.  When you do this,  “My Website” disappears from the screen.

Not that you would ever necessarily want to unsubscribe from your Risk Management email subscription, you always have the option to do so, and probably most of you will do this after this semester is over.  Whenever you receive an email from the Risk Management blog, the footer of that email provides links for unsubscribing and for managing your WordPress subscriptions.

In closing, I regret committing this error and any inconvenience it may have caused. Kudos to Chris Henle for helping me diagnose and figure out how to fix this problem.