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Old 11-17-2017, 06:56 PM
Futon Futon is offline
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Default 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?
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Old 11-17-2017, 07:55 PM
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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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Old 11-17-2017, 08:01 PM
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And keep in mind they want Macaulay, not modified.
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Old 11-17-2017, 08:03 PM
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Quote:
Originally Posted by Colymbosathon ecplecticos View Post
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.

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Old 11-17-2017, 08:30 PM
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Quote:
Originally Posted by Breadmaker View Post
And keep in mind they want Macaulay, not modified.
That means the price of the stock is the modified duration. Why is that?
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Old 11-17-2017, 09:29 PM
Academic Actuary Academic Actuary is offline
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Quote:
Originally Posted by Futon View Post
Summation((v^t)*t*(1.02))/ Summation(v^t*1.02)

the 1.02 cancels out.

The 1.02 also has the exponent t.
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Old 11-17-2017, 09:31 PM
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Quote:
Originally Posted by Futon View Post
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.
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Old 11-17-2017, 10:58 PM
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Quote:
Originally Posted by Academic Actuary View Post
The 1.02 also has the exponent t.
And it still cancels out. According to another solution.



Quote:
Originally Posted by Academic Actuary View Post
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; 11-17-2017 at 11:05 PM..
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Old 11-17-2017, 11:21 PM
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Quote:
Originally Posted by Futon View Post
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
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Old 11-17-2017, 11:30 PM
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Quote:
Originally Posted by Academic Actuary View Post
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.
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