I’ve received this question from a couple of students. Here is what I suggest:

I’d go through the videos, but at a faster pace than last time. Maybe do 2-3 lessons a day. Don’t spend a lot of time working problems while you are reviewing the lessons. The goal is to watch all the videos again as fast as possible so you can start working problems. Make sure you work every problem in the seminar. Work them twice if you can. For ones that you miss put them in a stack and rework them. Keep putting back in your stack untill you get them right. When you work problems do them in groups of 5 problems. Take 5 problems from different sections of the material (e.g. A.1, A.3, A.4, B.1, B.2) and work them under test conditions (give yourself 25 minutes for 5 problems).

Student Questions

Lots of students are confused about what the financial keys means. Let me define them here:

N – number of periods

I/Y – effective interest rate per period (assuming C/Y and P/Y is 1)

PV – cash flow at time 0

PMT – cash flow at time 1, 2, …, N (or 0, 1, …, N-1 for BGN mode)

FV – cash flow at time N

The sign of the cash flow is negative for a cash outflow and positive for a cash inflow. I hope that clears things up.

Student Questions

When the NAR is convertible less frequently than a year it seems to give lots of students trouble. Here is an email I sent recently to a student struggling with this idea. I hope it helps.

A nominal annual rate is an ANNUAL rate and a rate in NAME ONLY (that’s where the nominal comes). So when you have a nominal annual rate the first thing to do is convert it to an effective rate per the convertible period.

For example, if we have a nominal rate of 12% convertible semi-annually, then the first thing we do is divide by the number of compounding periods per year (since it is ANNUAL). Thus 12% / 2 = 6% effective per 6 months (the convertible period). Now we can actually use that 6% rate to move money around. To accumulate money for 6 months we simply multiply by 1.06. To move it for a year (which is 2 six-month periods) we multiply by (1.06)^2. To discount money for 10 years we would divide by (1.06)^20 since there are 20 six-month periods in 10 years.

Now assume that we are given a nominal rate of 12% convertible once every 4 years. Remember the 12% is an NOMINAL ANNUAL rate so first thing is to get the effective rate that we can use. 12% x 4 = 48% effective rate per 4 years (the convertible period). So if we want to accumulate money for 1 year then we multiply by (1.48)^(1/4) since 1 year is 1/4 of 4 years. If we want to accumulate money for 4 years then we multiply by 1.48. If we want to discount money for 40 years then we divide by (1.48)^10 since there are 10 four-year periods in 40 years.

Student Questions

At the end of the pyramid lesson I solve problem 106. A student sent me a better solution. The key thing to notice is the difference between the 12-year annuity and the 11-year annuity is just a level payment of 1 for 6 years. So the present-value of the 12 year annuity equals the present-value of the 11 year annuity plus a-angle-6. We find a-angle-6 = 5 just like I did in the lesson, then the present value of the 12-year annuity = 25 + 5 = 30.

Student Questions

Here is another great question I received.

I know that when we see simply “duration” on a question it is safe to assume that the question is asking for MacD (unless the interest rate is nominal, in which case we find ModD…) but are there any other things that we can assume? For example, if we simply see “annuity” in a problem, could we assume it was an annuity-immediate? Or would that not necessarily be the case? Are there any other wording things that are always specified or always implied to be one thing or the other?

If a problem says duration it means Macaulay duration, end of story. It doesn’t matter if they give you a nominal rate it still means Macaulay duration. If they want you to calculate modified duration, then they have to explicitly say Modified duration in the problem.

An annuity must tell you both the amount and the time the payments occur. You can assume neither. If the problem just says “An annuity pays 50 per year, calculate the present value.” Then you do not have enough information, b/c the time the payments are made is not given.

Student Questions

I received this great question from a student.

On this problem, why isn’t the MacD of the assets calculated as the duration of a portfolio?

It doesn’t look like it, but it really is b/c there are only two bonds:

Student Questions

This is a video response to this question on the AO.

Watch Video

Student Questions

I think there is some confusion about the decreasing annuities notation. The coefficient is the amount each payment decreases by. It is also the last payment. The first payment is the coefficient times the number of payments.

represents the present value of payments of 15, 10, and 5. Notice the first payment is 5 x 3 and the last payment is 5.

So if we have payments of 100, 90, 80 and 70. There are 4 payments and each payment decreases by 10. So we start with:

However, that only gives us 10×4, 10×3, 10×2, 10×1 => 40, 30, 20, 10.

So we need to add a level payment of 60 to each payment. So the present value is:

I hope that clears up some of the confusion.

Student Questions

A student asked the following:

I am reviewing No-Arbitrage Bounds with Transaction Costs. Could you please explain how the F- formula is derived?

Here is my response: Derivation of F-

Student Questions

I got this great question from a student:

I believe there is an error on problem 18 of Section B chapter 2.

The third choice in the true/false statements says:

A short put’s maximum loss is:

Strike price – FV (put premium)

The solution for this questions says that the above statement is true.

However, based on the notes from the 4th video of this chapter and the text book page 43, if the statement is going to be true it should be:

A long put’s maximum gain is:

Strike price – FV (put premium)

or

A short put’s maximum loss is:

FV (put premium) – Strike price

Please let me know if I am missing something.

Here was my response:

This is really just a difference in how you say you lost $X. Do you say I lost $X or I lost -$X. Hopefully the exam wouldn’t contain something like this.

If you short a put what is the worst case scenario? Well a put option has value when the stock price goes down, so the worst case scenario for a short put is a spot price at expiration of 0. You have to buy the stock at the strike price and you’ve accumulated the FV(premium). So FV(premium) – Strike price will be a negative number. Let’s say the FV(Premium) is $5 and the strike price is $100. Then according to the book you have a loss of $5 – $100 = -$95. To me it doesn’t make sense to say I lost -$95 (losing -$95 means winning $95 IMO). I would say I lost $95 = $100 – $5 = Strike Price – FV(premium).

Student Questions