Actuarial Outpost > SoA Question 1c) - Transistion question.
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#1
05-13-2003, 09:45 AM
 Toronto Member Join Date: Nov 2001 Posts: 513
Question 1c) - Transistion question.

I'm seeing alot of responses to question 1c) stating it was very difficult to calculate. The question stated it was a AAA 2 year bond. This implies, it was AAA during year 1, and moved to AAA, AA or A in year 2. What's so hard about this? (Recall transition occurs only at the END of the first year, not the beginning)

I think a lot of people treated it as a three bond.
#2
05-13-2003, 10:25 AM
 aces219 Member Join Date: Sep 2001 Location: Chicago Posts: 2,667
Re: Question 1c) - Transistion question.

Quote:
 Originally Posted by Toronto I'm seeing alot of responses to question 1c) stating it was very difficult to calculate. The question stated it was a AAA 2 year bond. This implies, it was AAA during year 1, and moved to AAA, AA or A in year 2. What's so hard about this? (Recall transition occurs only at the END of the first year, not the beginning) I think a lot of people treated it as a three bond.
'

I agree with you. When I first looked at it, it seemed like I had to run through a bunch of combinations, and then I realized that it would only change states once, which made it pretty easy.
#3
05-13-2003, 05:20 PM
 Ponderer Member Join Date: Oct 2001 Posts: 225

I don't know... The question did ask for a "expected TWO-YEAR horizon spread..." That sounds very much like 9 combinations (3 OVER first year X 3 OVER second year) is what they'll look for in the answer. But I'm sure doing it only for 1 year will get you at least half of the point values assigned to the part already.
#4
05-13-2003, 05:41 PM
 rl2 Member SOA Join Date: Jan 2002 Location: HKG / YVR Posts: 134

the spread for the first year is constant. its the AAA spread. only the spread for the second year is a random variable.

i did it the wrong way in the exam too. i dunno why. i really think i am becoming dumber and dumber. all the memorization in c5/c6 has made me think that every question is routine. if i've seen the question before, i just start regurgitating my heart out. i never bother to stop and think like in c1-4.

i am so disgusted with myself.
#5
05-13-2003, 07:25 PM
 Toonces Member Join Date: Nov 2001 Posts: 146

I disagree. It never says it's a 2-year bond. It is asking for the 2-year horizon spread, which seems to me to be the spread measured at a horizon of two years. Two years from now, the bond will experience two transitions.
#6
05-13-2003, 07:28 PM
 Dr T Non-Fan Member Join Date: Sep 2001 Location: Just outside of Nowhere Posts: 59,148

You did take the average of the 1-year and 2-year spreads, right?
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#7
05-13-2003, 08:55 PM
 Scrubby Member Join Date: Oct 2001 Posts: 62

I agree with Toonces. Just like an interest rate tree pricing caps...two years equals two transitions, the last transition occurs at the instant the observation period ends.
#8
05-13-2003, 09:21 PM
 phdmom Member SOA AAA Join Date: Nov 2001 Posts: 293

I also think there are 2 transitions. I squared the transition matrix and multiplied by the column of spreads. I got 25.4 as the answer.
#9
05-14-2003, 10:26 AM
 Toronto Member Join Date: Nov 2001 Posts: 513

The question specifically says a two year bond. Do you think they would allocate a single point for a question where you would have to take the square of a 3x3 matrix?

Just read the question. The question was worth 4 marks and both a and b were lists. So being question 1, which is always the easiest question, why would they make it the hardest.

The question, given a 2yr AAA bond what is its expected spread. Note that the Transition matrix States AT THE END OF THE YEAR. So what would it matter what the bond grade is at the end of year 2 since it would mature and be redeemed for Par. (no selling so price and grade would not matter)
#10
05-14-2003, 10:49 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 26,459

Quote:
 Originally Posted by Toronto The question specifically says a two year bond.
Where? Not the version posted by the SOA
Quote:
 Just read the question. The question was worth 4 marks
Worth 6 in the version posted by the SOA.

Is there any meaning to an average spread calculated during the first two years? You don't receive more spread if the bond changes categories.

Quote:
 The question, given a 2yr AAA bond what is its expected spread. Note that the Transition matrix States AT THE END OF THE YEAR.
Even with your interpretation of what the question is asking, why are year 2 transitions irrelevant? If you know the probability that an AAA bond at the start of year 2 will be AA at the end of year 2 is 0.1, why would you assume it has the AAA spread until the last day of the year? [Note that the timing within year is a non-issue for those interpreting the question as asking for the average spread at time 2 rather than the average spread in the interval (0,2)].

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