Actuarial Outpost What is the Macaulay Duration of a stock?
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 Financial Mathematics Old FM Forum

#1
11-17-2017, 07:56 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128
What is the Macaulay Duration of a stock?

I've never seen this anywhere else. Is it safe to say that the duration of a stock is (1+i)*Price?
#2
11-17-2017, 08:55 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 5,984

The question says "stock", but ignore that.

What is the duration of an increasing perpetuity-immediate with payments growing 2%/year and interest rate = 5%?
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#3
11-17-2017, 09:01 PM
 Breadmaker Member SOA Join Date: May 2009 Studying for CPD - and nuttin' else! College: Swigmore U Favorite beer: Guinness Posts: 3,456

And keep in mind they want Macaulay, not modified.
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#4
11-17-2017, 09:03 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128

Quote:
 Originally Posted by Colymbosathon ecplecticos The question says "stock", but ignore that. What is the duration of an increasing perpetuity-immediate with payments growing 2%/year and interest rate = 5%?
Summation((v^t)*t*(1.02))/ Summation(v^t*1.02)

the 1.02 cancels out.

$\frac{\frac{1}{.05}+\frac{1}{.05^{2}}}{\frac{1}{.0 5}}=20$
#5
11-17-2017, 09:30 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128

Quote:
 Originally Posted by Breadmaker And keep in mind they want Macaulay, not modified.
That means the price of the stock is the modified duration. Why is that?
#6
11-17-2017, 10:29 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,256

Quote:
 Originally Posted by Futon Summation((v^t)*t*(1.02))/ Summation(v^t*1.02) the 1.02 cancels out. $\frac{\frac{1}{.05}+\frac{1}{.05^{2}}}{\frac{1}{.0 5}}=20$
The 1.02 also has the exponent t.
#7
11-17-2017, 10:31 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,256

Quote:
 Originally Posted by Futon That means the price of the stock is the modified duration. Why is that?
What material are you studying from? Read the section on Macaulay and modified duration.
#8
11-17-2017, 11:58 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128

Quote:
 Originally Posted by Academic Actuary The 1.02 also has the exponent t.
And it still cancels out. According to another solution.

Quote:
 Originally Posted by Academic Actuary What material are you studying from? Read the section on Macaulay and modified duration.
I'm studying from the SOA practice exam.

Breadmaker mentioned to keep in mind they want Macaulay not Modified. From the first solution, it's implied that (1+i)*Price is Macaulay. Since Modified = Macaulay/(1+i), Macaulay = Modified*(1+i). And the answer is Price*(1+i). Therefore Price=Modified.

Edit: Additionally, the solution called 100/3 a "duration" as well; and it can't be Macaulay duration since (1+i)(100/3) is the Macaulay duration.

Last edited by Futon; 11-18-2017 at 12:05 AM..
#9
11-18-2017, 12:21 AM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,256

Quote:
 Originally Posted by Futon And it still cancels out. According to another solution. I'm studying from the SOA practice exam.
If you can't afford a study manual I would recommend this.

http://faculty.atu.edu/mfinan/actuarieshall/mainf.pdf
#10
11-18-2017, 12:30 AM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128

Quote:
 Originally Posted by Academic Actuary If you can't afford a study manual I would recommend this. http://faculty.atu.edu/mfinan/actuarieshall/mainf.pdf
Thanks for referring.

Looks like I wasn't mistaken.