Questions from Babbel

[Allacalander]

These are the first of many questions I'm sure to have from this book. I've read through the required readings once now, though understood very little or glazed over some sections that I didn't follow.

Chapter 1.
1. What is meant by the term "objective function concavity" as it relates to this chapter? I know what that means in a general sense, but I guess a different phrasing of the question is what is the objective function that they are considering? (pg 6)

2. There is a sentence I don't quite follow. It starts as "In addition, the idiosyncratic nature of some portion of these losses..." I'll let you look up the rest, since you'll need the context anyway. (pg 20)

3. "Credit risk that reveals itself as basis risk in the systematic risk." What does this mean? (pg 32)

Chapter 3
4. There are 6 bullets listed in subsection on the Level II Compensation Structure. I don't see how bullet #6 has anything to do with the other bullets. (pg 69-70)

Chapter 17
5. How is leverage equivalent to A/S? (pg 353)

Chapter 18
6. What is the "par bond" curve? I found references to a par yield curve and a bond yield curve and many other similar sounding curves. (pg 364)

7. The book states it is easy to check that one particular specification gives the same duration value as a directional model they provde. I can't figure out how to show this "easy to check" item. I think it might have to do with notation primarily. (pg 364)

8. Similarly, "it is not difficult to prove Eq (6)." Really? Because I couldn't figure it out. (pg 364)

9. How do they obtain Eq (7)? (pg 365)

10. I read "convexity" and, for simplicity, interpret that as "curvature." In doing so, I'm confused as to why "when convexity is relatively large, duration will decrease with increases in the factor." There are also two other similar conclusions they state here on similar agrumentative grounds. I know when they say convexity they are talking about the financial definition, but that doesn't help clear it up for me. (pg 365)

11. The last paragraph in this section begins with "beyond the formal mathematics" and then proceeds to use some more formal mathematics. Unfortunately, I don't follow starting from "Eq (6) is produced in the limit" (pg 365)

12. Does anyone know what a rectangular probability distribution is? Is that just another word from uniform? (pg 366)

I recognize that many of these are probably subtle details which aren't testable or even necessary, but every time I hit a spot I don't get, my attention and focus dwindles even more. Besides, how do I KNOW it isn't testable? This is probably a good number of questions to start with. The answers to these may well prompt others, and as I proceed through the chapter, I'll probably find more. Answer what you can; burn the rest.

[Laurelinda]

:wave: friend, I hope you don't mind my popping in here and checking up on y'all. I saw nobody replied to your post, so I thought I'd give it a go, with the caveat that I don't think Ch 18 was on the syllabus last year, so I'll be flying by the seat of my pants on that one.

First observation is, wow, I'd forgotten how obtuse B&F could be. It sure has some good stuff in it, though.

Chapter 1.
1. What is meant by the term "objective function concavity" as it relates to this chapter? I know what that means in a general sense, but I guess a different phrasing of the question is what is the objective function that they are considering? (pg 6)

I think they mean risk aversion. I think by "objective function" they mean what is more often called "utility function". The concavity means that you have dimishing desire to tolerate more and more risk. (Or you require more and more compensation for it.) It's the fundamental principle for implementing some kind of risk management to begin with, which seems to be the jist of the chapter.

2. There is a sentence I don't quite follow. It starts as "In addition, the idiosyncratic nature of some portion of these losses..." I'll let you look up the rest, since you'll need the context anyway. (pg 20)

They're basically saying that not only does diversification not get rid of systematic risk, but it often isn't even good enough for non-systematic, or idiosyncratic risk. Think of it this way: If you sell a lot of insurance policies, you can predict your claim payments a lot better and have less "risk" because you have less variation. And yet the diversification won't prevent you from getting the million-dollar claim you don't want to pay.

3. "Credit risk that reveals itself as basis risk in the systematic risk." What does this mean? (pg 32)

Let me try to break down the sentence into its clauses:
"In addition to the credit risk that reveals itself as basis risk
in the systematic risk factors above,
there is also the risk of default on significant firm investments."

This is saying that there are two kinds of credit risk: systematic and idiosyncratic. In its systematic or market-wide form, it shows up primarily in the level of credit spreads, which looks more like basis risk, meaning your assets are indexed to something slightly different from your liabilities. Imagine having a perfectly duration-matched portfolio, where changes in Treasuries affect your assets and liabilities in exactly the same way. You're safe! Oops, credit spreads just widened and devalued your assets, without devaluing your liabilities. Basis risk!

The idiosyncratic credit risk, on the other hand, is the risk of default on the specific assets in your portfolio. Oops, you invested in Lehman and WaMu.

Chapter 3
4. There are 6 bullets listed in subsection on the Level II Compensation Structure. I don't see how bullet #6 has anything to do with the other bullets. (pg 69-70)


I had to read that three times before I got it. The bullet points are addressing the question: "Why use Treasuries for a liability benchmark?" A companion question is, "Isn't the value of your liabilities affected by the risk that you might default on your own obligations? So why use default-free Treasuries?" The sixth bullet point is answering the companion question by saying that the risk of default is accounted for elsewhere, in the implicit put option held by the firm's shareholders. The put option is their right to default when the firm's value declines too far. Hence your own credit risk is considered part of equity, and including it in the valuation of your liabilities would be double counting.

Chapter 17
5. How is leverage equivalent to A/S? (pg 353)

I don't know, I figure it's one of many "measures of leverage". The D/E ratio is considered a "measure of leverage". I don't think you can define it as equal to leverage.

Chapter 18
6. What is the "par bond" curve? I found references to a par yield curve and a bond yield curve and many other similar sounding curves. (pg 364)

Good question! The par bond curve and the par yield curve are the same thing. A par curve is made up of rates that equal the yield to maturity on a conventional bond, usually paying coupons semiannually and expressed with semiannual compounding. A "par" curve is distinguished from a "spot" curve or a "forward" curve...and we can get in to those later if you'd like a follow-up post. :tup:

7. The book states it is easy to check that one particular specification gives the same duration value as a directional model they provde. I can't figure out how to show this "easy to check" item. I think it might have to do with notation primarily. (pg 364)

Gosh, I used to be so quantitative and I truly gave up energy on trying to figure that out. I know you already know it's an ignorable item for the exam and are just curious, so I'm sorry I can't help you. :shrug:

8. Similarly, "it is not difficult to prove Eq (6)." Really? Because I couldn't figure it out. (pg 364)

Repetition of my last response.

9. How do they obtain Eq (7)? (pg 365)

Ah, that one I can do! Recall from (3) that D(i) = -P'(i)/P(i) and C(i) = P"(i)/P(i). Also from (1), Q(j) = Q(i) + Q'(i)(j-i) + 0.5Q"(i)(j-i)^2..., which is just a Taylor series expansion.

Take the derivative of D(i) and get
D'(i) = -[P(i)P"(i) - P'(i)P'(i)]/[P(i)^2]
= -P"(i)/P(i) + [P'(i)/P(i)]^2
= -C(i) + D(i)^2,
or D(i)^2 - C(i).

So to use D instead of Q, we have from (1):

D(j) = D(i) + D'(i)(j-i) + ...
= D(i) + [D(i)^2 - C(i)](j-i) + ...

...and then they drop the remaining terms, which get small, as an approximation. Cool, huh?


10. I read "convexity" and, for simplicity, interpret that as "curvature." In doing so, I'm confused as to why "when convexity is relatively large, duration will decrease with increases in the factor."

Yeah, that's confusing me a little, too. By "relatively large" they mean larger than duration squared.

If you take the equation we derived above:

If C(i) > D(i)^2, then
D(i)^2 - C(i) < 0 and
[D(i)^2 - C(i)](j-i) goes further negative as (j-i) gets bigger,
so D(i) + [D(i)^2 - C(i)](j-i) = D(j) gets smaller. Hey it works! :toast:

11. The last paragraph in this section begins with "beyond the formal mathematics" and then proceeds to use some more formal mathematics. Unfortunately, I don't follow starting from "Eq (6) is produced in the limit" (pg 365)

Uhhh yeaaaaaaah. I think they're trying to get you to imagine (6) as the integral limit of a Riemann sum. My imagination doesn't want to go there right now.

12. Does anyone know what a rectangular probability distribution is? Is that just another word from uniform? (pg 366)

That would be my guess. Probably uniform in 2-dimensional space?

Answer what you can; burn the rest.

Hope you at least had fun with my answers, even if they didn't help, and even though I'm sure you've moved on by now!

Best of luck with APMV,
Laurelinda

[ckasady]

Without having done much in Babbel...

Convexity is techically the second derivative of the price function wrt interest (or that's what it is with some slight tweaks to the formula). Meaning duration (dP(i)/di) should increase with i if convexity is positive.

[Laurelinda]

Convexity is techically the second derivative of the price function wrt interest (or that's what it is with some slight tweaks to the formula). Meaning duration (dP(i)/di) should increase with i if convexity is positive.

Yeah, my bad. Must have been late last night.

[Allacalander]

Well, I had moved on to other texts, but was planning to come back to Babbel eventually.

Those responses will actually help a lot. At least I can figure out a few more things this way. Hopefully, they'll help some more people too.

I actually haven't had as much trouble understanding many of the other texts. Guess I'm just lucky. I'm afraid to open Crouhy though.