Krzysio's Weekly Practice Problems for FM/2

[krzysio]

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

Yours,
Krzys' Ostaszewski

[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.

[krzysio]

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'

[krzysio]

Originally Posted by yesactuary

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'

[krzysio]

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

Yours,
Krzys' Ostaszewski

[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!

[MyKenk]

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!

[hokensuri]

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.

[MyKenk]

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

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:

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.

[hokensuri]

Nice spreadsheet. Thanks!