Actuarial Outpost Immunization question
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 Financial Mathematics Old FM Forum

#1
11-08-2017, 11:08 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128
Immunization question

So I don't really understand the solution. How is the cost H/1.1 + I/1.2321 + J?

Why is it 1.2321 and not 1.1^2? Why is J not multiplied by anything?
#2
11-09-2017, 12:29 AM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,340

Quote:
 Originally Posted by Futon So I don't really understand the solution. How is the cost H/1.1 + I/1.2321 + J? Why is it 1.2321 and not 1.1^2? Why is J not multiplied by anything?
1.2321 = 1.11^2. J is selling at par so the cost of face amount J is J.

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#3
11-10-2017, 03:14 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128

Quote:
 Originally Posted by Academic Actuary 1.2321 = 1.11^2. J is selling at par so the cost of face amount J is J. -
Thanks.

Yea sorry looks like I tripped up. I don't see a use of this equation either, so what is the point of it?

And what exactly is being minimized and why?

Last edited by Futon; 11-10-2017 at 03:37 PM..
#4
11-10-2017, 04:05 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,340

Quote:
 Originally Posted by Futon Thanks. Yea sorry looks like I tripped up. I don't see a use of this equation either, so what is the point of it? And what exactly is being minimized and why?
You are minimizing the cost of the cash flow matching portfolio. It is something actually done in the real world although it is accomplished with large scale linear programming.
#5
11-10-2017, 04:14 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128

Quote:
 Originally Posted by Academic Actuary You are minimizing the cost of the cash flow matching portfolio. It is something actually done in the real world although it is accomplished with large scale linear programming.
Okay so what do people look for when solving for the smallest amount? In other words, why does the problem desire the biggest amount of J?
#6
11-10-2017, 04:35 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,340

Quote:
 Originally Posted by Futon Okay so what do people look for when solving for the smallest amount? In other words, why does the problem desire the biggest amount of J?
J has the highest yield, so it would provide the lowest cost asset. Now in the real world it would have the higher yield due to things like credit risk which is ignored on the fm exam.
#7
11-10-2017, 04:40 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128

Quote:
 Originally Posted by Academic Actuary J has the highest yield, so it would provide the lowest cost asset. Now in the real world it would have the higher yield due to things like credit risk which is ignored on the fm exam.
So I would pick the two highest yields of each year right? I has bigger yield than H but picking I and J would be impossible?