Category: Math and Statistics

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Z Table Extra Credit Assignment (due at the start of class on Tuesday, January 30)

Here’s an extra credit opportunity for Finance 4335. Working on your own (i.e., this is not a group project; I will only give credit for spreadsheets that are uniquely your own), build your own “z” table in Excel (patterned after the table at http://fin4335.garven.com/stdnormal.pdf); the top row should have values ranging from 0.00 to 0.09, and the first column should have z values ranging from -3.0 to +3.0, in increments of 0.1).

Conveniently, Excel has the standard normal distribution function built right in; e.g., if you type “=normsdist(z)”, Excel returns the probability associated with whatever z value you provide. If you type “=normsdist(0)”, .5 is returned, since half of the area under the curve lies to the left of the expected value E(z) = 0. Similarly, if you type “=normsdist(1)”, then .8413 is returned because 84.13% of the area under the curve lies to the left of z = 1. Perhaps you recall from your QBA course that 68.26% of the area under the curve lies between z = -1; this “confidence interval” of +/- 1 standard deviation away from the mean (E(z)=0) is calculated in Excel with the following code: “=normsdist(1)-normsdist(-1)”, and so forth.

The grade you earn on this extra credit assignment will replace your lowest quiz grade; that is if your lowest quiz grade is lower than your extra credit grade. The deadline is the start of class on Tuesday, January 30.

You can turn your spreadsheet for this extra credit assignment in at the link labeled “Z Table Extra Credit Assignment” under the Assignment tab on Canvas.

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On the ancient origin of the word “algorithm”

The January 23rd 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 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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Visualizing Taylor Polynomials

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.

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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.