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#51
10-20-2006, 09:55 PM
 krzysio Member SOA AAA Join Date: Mar 2005 Location: Bloomington, Illinois Favorite beer: Tyskie Posts: 1,309
Exercise for October 21, 2006

It is posted at:
http://www.math.ilstu.edu/krzysio/KO-FM-Exercise75.pdf

Yours,
Krzys' Ostaszewski
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#52
10-20-2006, 10:26 PM
 yesactuary Member SOA Join Date: Nov 2005 Posts: 426
practice exam 6 #9

"the macaulay duration of the liabilities portfolio is 5"

how do you know the macaulay duration is 5 in this case? Thank you for your help.
#53
10-21-2006, 01:34 AM
 krzysio Member SOA AAA Join Date: Mar 2005 Location: Bloomington, Illinois Favorite beer: Tyskie Posts: 1,309

Quote:
 Originally Posted by yesactuary "the macaulay duration of the liabilities portfolio is 5" how do you know the macaulay duration is 5 in this case? Thank you for your help.
Macaulay duration of a single payment is its maturity.
Yours,
Krzys'
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#54
10-27-2006, 12:43 AM
 krzysio Member SOA AAA Join Date: Mar 2005 Location: Bloomington, Illinois Favorite beer: Tyskie Posts: 1,309
Option-free bond

Quote:
Originally Posted by yesactuary
Quote:
 Originally Posted by krzysio Just like sugar-free contains no sugar, option-free contains no options. Does that not make sense? Yours, Krzys' Ostaszewski

so it's same as non-callable bond?
I guess I am trying to use the most general terminology. A call option is one possible option that can be embedded in a bond. There are also puttable bonds. The option to default is also an option, although it is not discussed on exam FM. So I used the terminology "option-free" to indicate that there are no options, no calls, no puts, none.

Yours,
Krzys'
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#55
10-27-2006, 12:44 AM
 krzysio Member SOA AAA Join Date: Mar 2005 Location: Bloomington, Illinois Favorite beer: Tyskie Posts: 1,309
Exercise for October 28, 2006

It is posted at:
http://www.math.ilstu.edu/krzysio/KO-FM-Exercise76.pdf

Yours,
Krzys' Ostaszewski
__________________
Want to know how to pass actuarial exams? Go to:
http://smartURL.it/pass
#56
11-03-2006, 12:39 PM
 hokensuri Member Join Date: May 2006 Posts: 106
Exercise 5

A few questions regarding the problem below.

http://www.math.ilstu.edu/krzysio/KO-FM-Exercise5.pdf

1) Can someone explain why the first payment is invested a year from now? I thought this was an annuity-due.
2) Can someone explain how we can get 1.06 for the 5th payment?
3) A typo for the 4th payment? It should be 1.0725^2.

Thanks!
#57
11-03-2006, 12:56 PM
 MyKenk Note Contributor CAS AAA Join Date: Nov 2005 Location: twitter.com/mykenk College: Drake '06 Posts: 8,595

Quote:
 Originally Posted by hokensuri A few questions regarding the problem below. http://www.math.ilstu.edu/krzysio/KO-FM-Exercise5.pdf 1) Can someone explain why the first payment is invested a year from now? I thought this was an annuity-due. 2) Can someone explain how we can get 1.06 for the 5th payment? 3) A typo for the 4th payment? It should be 1.0725^2. Thanks!
1) I think that's a mistake, it looks like an annuity immediate to me!
2) Because you're investing for only 1 year, and by the time you make this investment, there have been 4 25 basis point parallel shifts in the yield curve, making the 1 year spot rate 7.00% - 4* .25% = 6.00%
3) Yes, this is a typo.

HTH!
#58
11-03-2006, 02:01 PM
 hokensuri Member Join Date: May 2006 Posts: 106

Quote:
 Originally Posted by mykenk 1) I think that's a mistake, it looks like an annuity immediate to me! 2) Because you're investing for only 1 year, and by the time you make this investment, there have been 4 25 basis point parallel shifts in the yield curve, making the 1 year spot rate 7.00% - 4* .25% = 6.00% 3) Yes, this is a typo. HTH!
Thanks, mykenk. But I am still a bit confused about (2). Let me think about it more though... I will ask you if I don't get it. Thanks again.
#59
11-03-2006, 03:32 PM
 MyKenk Note Contributor CAS AAA Join Date: Nov 2005 Location: twitter.com/mykenk College: Drake '06 Posts: 8,595

Here's a little chart of the spot rates. Notice that you're going to be using the last diagonal:

Code:
```n-year spot rate m years from now:

n      m=0      m=1      m=2      m=3      m=4
-      ----     ----     ----     ----     ----
1      7.00     6.75     6.50     6.25     6.00
2      8.00     7.75     7.50     7.25
3      8.75     8.50     8.25
4      9.25     9.00
5      9.50```
Now:
Code:
```Time     Yrs       Rate
of       to        to        Acc.
Pymt     Acc.      Acc.       Factor
-----    -----     -----      ------
0        5       1.0950     1.574239
1        4       1.0900     1.411582
2        3       1.0825     1.268480
3        2       1.0725     1.150256
4        1       1.0600     1.060000
--------
6.464557```
This assumes the typo is in the solution (first line, the first payment should be invested at the five year spot rate today, not a year from now, as a year from now the 5 year spot rate would be 9.25, and you'd only accumulate 4 years).

To correct the solution, if I'm right, change "a year from now" to "today", and everything else should be perfect.
#60
11-03-2006, 06:08 PM
 hokensuri Member Join Date: May 2006 Posts: 106