Questions and responses are added here as they become "frequently asked." Check back for additional material.
Matrices
Q: Do we need to know how to work through matrices for the exam?
A: No. You do need to know some method for solving systems of linear
equations simultaneously. I use matrices because I find them easy to work
with and to represent in lecture settings.
Q: What's the logic behind augmenting the matrix with the identity matrix
in the Gauss-Jordan procedure for inverting?
A: Pretty much the same as the following: I want to invert the number
5. Whatever allowable row operations I perform on 5 to make it equal 1 is
what I would do to 1 to make it equal the inverse of 5. Thus, if we multiply
the pair [5:1] by .2, we obtain [1:.2]. We have [.2] as the inverse matrix
for [5].
Q: Isn't there an easier way to invert matrices?
A: Generally speaking, not really. However, there are many specific
instances where an easier way does exist. For example, to invert a diagonal
matrix, simply invert each of the elements in the principal diagonal. Similarly,
triangular and 2X2 (with determinants and co-factors) matrices are particularly
easy to invert. Unfortunately, these easy techniques do not generalize to
easy techniques for inverting larger matrices. For example, the method involving
determinants and cofactors is just as much work for 3X3 and larger matrices
as is the Gauss-Jordan method. Also, the Gauss-Jordan method is not difficult,
it is just time-consuming and repetitive.
Time Value of Money
Growth Models
Q: Why is the dividend amount in any year t equal to DIV(1+g)^(t-1)?
Why only t-1 years of growth for any year t?
A: The dividend in year 1 is DIV1. The dividend in year 2 is DIV1(1+g).
The dividend in year 3 is DIV1(1+g)^2. The dividend in year 4 is DIV1(1+g)^3.
The dividend in any year is DIV1(1+g)^(t-1).
Q: What if the company never pays a dividend?
A: Then use an earnings model. That is, substitute EPS for dividends in
the growth model.
The Efficient Frontier and Capital Market Line
Q: Is it really necessary to go through all the calculus steps to obtain
security weights in the Market Portfolio?
A: No. The calculus steps are shown so that you can see why the methodology
using the simultaneous equations works and so that you can more easily derive
a new methodology if the assumptions underlying the problem changes.
Options
Q: What is this e (the natural log function) that keeps turning up in
the pricing equations? Don't derive it, just express it in words.
A: Concerning a related topic, I'm sure that you understand 1/(1+r)^t,
the discrete time discount function. Now discount more than once per
year, say m times per year, and the discount function becomes 1/(1 + r/m)^(mt)
= (1 + r/m)^(-mt). Now, let m approach infinity so that the discount
function becomes continuous. Then, because e^(-rt ) is defined to be
(1 + r/m)^(-mt) as m approaches infinity, e^(-rt ) is the continuous time
discount function.
Snappy Answers to Stupid Questions
Q: Will this be on the exam?
A: I don't know. I haven't written it yet.
Q: What should we know for the exam?
A: Everything
Q: Do we have to answer all the questions on the exam?
A: Of course not. Answer as many as you like.
Q: Sorry I didn't make class last week. Did I miss anything?
A: No
Q: How come you took off more points from my exam than you did on his?
We made the same mistakes.
A: Sorry. Have him bring his exam back to me so I can fix it.
Q: Will the final be the same as the mid-term?
A: No. The final will have different questions.
Q: Can I turn in the project late?
A: Turn it in whenever you like.
Q: Can I re-take the exam?
A: Sure. Next semester.
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