Questions and responses are added here as they become "frequently asked." Check back for additional material.

Fixed Income
YTM
Q: Isn't there an easier way to get the Yield to maturity of a bond?
A: Generally, no. You have to substitute. There are some special cases where you can solve algebraicly for y, but this doesn't happen in most realistic scenarios.

Q: Then how does my calculator get y so fast?
A: Actually, you may notice that your calculator usually takes longer to calculate y than most anything else. It substitutes for y just as you do, though somewhat more efficiently.

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.

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 ) becomes the continuous time discount function.
Q:  Can you elaborate on the put-call parity relation?
A:  S + p = Xe^(-rt) + c  ;  On the left, we have a stock and a put.  The put protects the left side portfolio from downward stock price movement.  On the right, we have exercise money (allowed to grow at rate r until time t, when the options expire so that there is X to exercise the call) and a call.  If the stock goes down, we still have the exercise money even though the call is worthless.  So ask yourself what is the left-hand portfolio worth if the stock goes down.  Then ask what the right hand portfolio is worth if the stock goes down.  The two portfolios are worth the same if the options have the same exercise price X, right?  After this, ask yourself what is the left-hand portfolio worth if the stock goes up.  Then ask what the right hand portfolio is worth if the stock goes up.   The two portfolios are worth the same if the options have the same exercise price X, right?  So, no matter what happens, the two portfolios are going to be worth the same as each other; either they both go down the same amount or they both go up the same amount.  So, the two portfolios always have to be worth the same amount.  This is put call parity.  The really useful thing about this relation is that we can add or subtract terms from both sides of the equation, maintaining the equality and devise many useful interpretations.
 
 

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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