Course 6 2001 solutions #4

[FIOB]

Can someone please tell me how you know which rL to use in the solution?

[FIOB]

OK, let me try this again. In question #4 they give three different rL's. There should only be one. All three seem consistent with the other information they give. In the solution they use the first one, but they don't say why. Surely, there must be someone besides me who attempted this problem.

[Exam Slave]

see below.

<font size=-1>[ This Message was edited by: Exam Slave on 2002-02-12 12:49 ]</font>

[Exam Slave]

I attempted it and did very poorly, and I AM ENSLAVED TO TAKING THIS EXAM FOREVER!
Not that I'm bitter.

You need to choose one that makes the calculated bond price equal the given bond price. Most would choose the middle one, since it offers at most two iterations.

In summary, there is no way to determine in advance which one to choose.

[Songbird]

When I sat for this paper, I spent a lot of time trying to understand the question, but ended up with nothing. I just looked at it again, and I THINK I may have got it this time. (I can't find the solution though, so I don't know if I'm right. Where did you download it?) I suggest you have the Fabozzi textbook by your side, and flip to the chapter on valuation of bonds with embedded options.

The rL and rLL table seems confusing, probably because the sentence explaining it is a little hard to understand (at least to me). Anyway, for this part of the calculation you will need a numerical process (ie iteration) to find rL and rLL. Since that is not possible in the exam, they have simple given you 3 rLs and 3 rLLs along with their corresponding bond prices, so you need only pick the right ones from the list.

First, from the T-bonds table, use bootstrapping to get the forwards rates: 4%, 6.478% and 5.838%. Then, use these together with the credit spread table to calculate the bond prices for the 2-yr 5.5% coupon and 3yr 6.0% coupon bonds (credit spread is 0.5% and 0.6% respectively). I obtained 99.63 and 100.00 respectively, so I would take rL=6.369% and rLL=5.071%. (I'm only writing decimal places because my 3rd place did not match the table.) The rest you can refer to your textbook.

[FIOB]

Thanks, that makes sense. I guess I'll have to do a little more work myself.

The sample solutions came with the study notes.

[In England]

My problem when I took the 2001 exam is I didn't understand what the three rows in the table were since they weren't labeled. Did anyone else have that problem? Anyway, thanks for the post - it clarifies it for me.

[Songbird]

If you don't mind, could you post the answers (just the numbers) here?
I got $101.307 for (a) and $0.836 for (b), but not at all confident. I'm not sure how credit spread is applied onto the rLs. I tried to reproduce the rL table but could not even get close. The coupon is 6.75 and maturiy is 3 years, so do we assume credit spread is the same as the 6.00 coupon bond?

[Songbird]

In England:
Glad to know even a true English speaker could not understand it. :grin:
Just kidding. When I was doing it in the exam, I sweated it all out and was still totally confused. Yet, this time when I did it with the textbook opened by my side, everything was so smooth I had to think hard to recall what really caught me the first time!! I believe sometimes you don't even have to understand everything, so long as you know all the steps by heart (since no textbooks are allowed inside). I know a lot of us may dislike this but it is the truth: sometimes memorizing does help pass exams. Just my 2 cents for those who are really willing to "go all the way". :smile:

[Songbird]

Btw, could someone post the answers (numbers) to part (a) and (b) please? Thanks!

[In England]

I have the exam solution that came with the study notes, but I seem to be missing a page (although I have pages 42 and 43, so that doesn't make sense). All they give is the interest rate tree. They don't give the bond prices. I'll have to call the SOA. Does anyone else have the exam solution?

[actuary boy]

I agree. The society should receive a 3 on this question since they only answered one part out of three!

[Songbird]

That's odd. I have never encountered even one blunder in the SOA study notes. At least, they always posted me errata. :smile:

[Exam Slave]

"You are given the following information about on-the-run Treasuries:"

To do this problem, you need to know what "on-the-run" means.

"...about bonds issued by BIG corp. The credit spread is relative to Treasuries of the same maturity."

To do this problem, you'll need to know how to price bonds given the credit spread.

[llll]

In part b) of problem #4 it was given that call premium is 1%

Can anyone tell how to make use of this information in solving the problem?

Thanks.

[Exam Slave]

HOFIS, page 10.

[Songbird]

Call premium is applied to the face. Refer to the binomial tree chapter on valuing calls. Now, instead of 100, strike off V if it exceeds 101, and replace with 101.

[llll]

Thank you (Exam Slave & Songbird) for your help.

I forgot what is call premium and took it as the cost (to the bond issuer) of the call option as a percentage of premiums.

[llll]

My results for Part a) and b) are as follows:
a) VHH = 98.36
VHL = 100.16
VLL = 101.6
VH = 97.92
VL = 101.19
V = 102.02
b) for the callable bond
VHH = 98.36
VHL = 100.16
VLL = 101
VH = 97.92
VL = 100.9
V = 101.88
Call option value = $102.02 - $101.88 = $0.14
Do these numbers match anybody's?

[Songbird]

You forgot to add in the credit spread. Since the maturity is 3 years, 0.6% might be a good assumption. However, the coupon here is bigger than the one given in the table, you may suggest a reasonable adjustment.

[llll]

I think Credit spread is already accounted for in determining RL and RLL. The interest rate tree you got is for the corperate bond, not for Treasury, there is no need to add credit spread furthur.

[Songbird]

Sorry, my mistake. You're correct: that is how the textbook did it. I disagree with this method though: it's more like a "discount rate model" than an "interest rate model".

[llll]

May be I should use "discount rate tree" instead of "interest rate tree".

[In England]

The SOA says the course 6 committee is reviewing the solution (or lack thereof). I'll keep you posted.

[Songbird]

In England: are you close to the committee?
And what's the point of reviewing it now? The SOA said they only keep answer sheets for 6 months (if I remember correctly), so everything would have been destroyed by now.
Strictly speaking, there is nothing wrong with this question, and IIII has indeed given the correct annswers. However, I do find thie question rather unfair, for the following reasons:
1) The answers are "correct" only in the sense that they agree with the Fabozzi textbook. However, I feel that that particular chapter is flawed. Although we can't exactly say a model is "wrong", because there is really no such thing, the theory behind the model in the text is confusing and contradicts other practices. I am referring to this "interest" rate model including the credit spread. What it models is not the interest rate movement, but rather a discount rate movement. I do not know of any other practices that actually does this.
2) The rL and rLL table figures are not exactly correct. They are slightly off, but off enough to make me feel uncomfortable with them.
3) The wording of the question could have been clearer.
4) Too many marks awarded.

[Dr T Non-Fan]

I think iE is trying to say that the published solution is not the best example.

[Songbird]

I see 2 possibilities:
1) The SOA did not have a proper official solution. If so, what did they use for the marking guideline?
2) The SOA does not wish to publish their own solution, using a candidate's actual solution as a better example instead of a perfectly written solution. If so, why didn't they pick a better solution? Is it so hard to find a candidate who scored full marks for one question? Or maybe nobody scored full?

[In England]

No, I'm not close to the committee.

[llll]

I sent an e-mail to SOA Study Note Department. A representative said the table on page 42 of the solution would be the answer to a) and b). He/she also said they need to have an actuary to look at the answers.

[LightSwitch]

Didn't get the SoA solution yet, but isn't the problem flawed. I mean r_sub_0 = 0.04 + 0.002 = 0.042 does not discount the one-year 5% annual coupon to 100. 105/1.04 = 100.7677543 > 100. Doesn't this mean the the binomial interest rate tree is not calbrated correctly (starting with the root branch, r_sub_0). (HOFIS Ch. 34)

<font size=-1>[ This Message was edited by: LightSwitch on 2002-03-05 23:00 ]</font>

[LightSwitch]

On 2002-02-07 12:39, FIOB wrote:
Can someone please tell me how you know which rL to use in the solution?


Isn't it as simple as choosing the one with the price of the n+1 year bond equal to 100. This criterion ensures that the binomial interest rate tree is calibrated.

I think the practice problem #2 in JAM6 (page D-6,7) which covers HOFIS chapter 34, we verify that the interest rate tree is calibrated to the current yield curve. Here, in May2001SoA6#4, instead of doing it -- which is actually an iterative process that starts with guessing an initial r_sub_L -- they seem to be testing if we know the criteria.

<font size=-1>[ This Message was edited by: LightSwitch on 2002-03-05 23:06 ]</font>

[Dr T Non-Fan]

The problem is that you're given a choice of three rL's. The solution says which one does calibrate the bond, but it doesn't say WHY that particular one is chosen. There is no information about which one calibrates the tree. (That would make this discussion "moo." (J. Tribiani.))
To determine which one calibrates the tree, you have to guess, then solve for hL, then hope you're right. If you're wrong, you get to guess again.
In this problem, it appears that the question's creator knew that the candidate's best guess would be the middle rate. Therefore, he chose one of the others, so that the logically thinking candidate would, wild guesses excluded, have to do at most two calibrations.

[LightSwitch]

"There is no information about which one calibrates the tree. (That would make this discussion "moo." (J. Tribiani.))
To determine which one calibrates the tree, you have to guess, then solve for hL [you probably mean rL], then hope you're right. If you're wrong, you get to guess again." by Dr T Non-Fan.

Perhaps I am missing something, but let me ask, rhetorically, how do you determine which rL calibrates the binomial interest rate tree? I think it is just selecting the rL that price the bond at par (or 100). Which is done for you in the problem. Although the solution may not state, that this is the criterion, isn’t this the criterion used?

<font size=-1>[ This Message was edited by: LightSwitch on 2002-03-05 23:54 ]</font>

[Dr T Non-Fan]

No, not at all.
And it's confusing me as well.

The solution shows rL = 6.369%, not the 6.005% that you're (I think) pointing at.
Solution says, "99.632 (price of two-year 5.5%-coupon bond using rL=6.369%) = MV of BIG Co on-the-run issues given 5.5% coupon and 5.7% required YTM."

What seems to be required is that you must actually determine the price of BIG company's two- and three-year bonds according to their YTMs -- treasury YTM + credit spread.

THEN, the prices equate to the one rL you're supposed to use, and you create the elusive binomial tree.
The three-year/rLL relationship, I guess, is obvious, since BIG's required YTM = coupon. How one should believe that a three-year bond's price is determined only by the rLL is beyond the scope of this poster.

Anyone missing part b and the other half of part a of the answers? I'm borrowing these sheets and no pages are missing, according to the official page numbers (42 and 43).

[Dr T Non-Fan]

BTW, what a piece of crap question.
The exam question, I mean.
What a piece of crap answer, seeing as it's only half-there.

[FIOB]

OK, I get it now. It's way easier than I thought. It's all there in the solution. The YTM of a 2 year 5.5% coupon bond is .5% + 5.2% = 5.7%. So, the price of that bond must be 99.632. We can ignore the other two bonds, because they don't exist. Likewise, the price of the 3 year bond must be 100.00, so forget about the other two. That gives you the tree in the solution, and the rest is easy (although the solution should probably include the answer.) I get about 102.02 for (a) and 101.88 for (b).