Actuarial Outpost
 
Go Back   Actuarial Outpost > Exams - Please Limit Discussion to Exam-Related Topics > SoA/CAS Preliminary Exams > Investment / Financial Markets
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions


Not looking for a job? Tell us about your ideal job,
and we'll only contact you when it opens up.
https://www.dwsimpson.com/register


Investment / Financial Markets Old Exam MFE Forum

Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 06-19-2017, 02:57 PM
mistersunnyd mistersunnyd is offline
Member
SOA
 
Join Date: Aug 2016
Studying for how to find a job
Posts: 104
Default Variance of weighted normal variables

I know this seems like a P question, but it appeared as a practice problem for MFE. Thus, I thought I'd ask here.
If I have two jointly normally distributed RVs, X and Y, with correlation rho, what is the variance of Z, with Z being aX - bY?
I always thought the formula for Var[aX-bY] = a^2Var[X]+b^2Var[Y] - 2abCov[X,Y], but the solution had a plus instead of a minus in front of 2abCov[X,Y]. Does anyone know why this is?
Reply With Quote
  #2  
Old 06-19-2017, 03:11 PM
jooni jooni is offline
Member
CAS
 
Join Date: Jan 2017
Posts: 76
Default

Which problem are you looking at?

I don't know about the formula for Var(aX-bY), but if you just use Var(aX + bY) with b being negative, then essentially you would get the minus sign before the 2abCov term, wouldn't you?
Reply With Quote
  #3  
Old 06-19-2017, 04:42 PM
Gandalf's Avatar
Gandalf Gandalf is offline
Site Supporter
Site Supporter
SOA
 
Join Date: Nov 2001
Location: Middle Earth
Posts: 30,911
Default

Quote:
Originally Posted by mistersunnyd View Post
I know this seems like a P question, but it appeared as a practice problem for MFE. Thus, I thought I'd ask here.
If I have two jointly normally distributed RVs, X and Y, with correlation rho, what is the variance of Z, with Z being aX - bY?
I always thought the formula for Var[aX-bY] = a^2Var[X]+b^2Var[Y] - 2abCov[X,Y], but the solution had a plus instead of a minus in front of 2abCov[X,Y]. Does anyone know why this is?
Your equation is right. As you have described the problem, the solution is wrong. Have you checked the errata, if errata exists?
Reply With Quote
  #4  
Old 06-19-2017, 04:48 PM
bujayherster bujayherster is offline
Member
CAS SOA
 
Join Date: May 2016
Location: Southbury, CT
Studying for MFE
College: Union Collge Alumnus
Posts: 64
Default

Quote:
Originally Posted by mistersunnyd View Post
I know this seems like a P question, but it appeared as a practice problem for MFE. Thus, I thought I'd ask here.
If I have two jointly normally distributed RVs, X and Y, with correlation rho, what is the variance of Z, with Z being aX - bY?
I always thought the formula for Var[aX-bY] = a^2Var[X]+b^2Var[Y] - 2abCov[X,Y], but the solution had a plus instead of a minus in front of 2abCov[X,Y]. Does anyone know why this is?

Isn't it because b = (-1), so with your equation:

Var[aX-bY] = Var[aX+(-b)Y]
= (a^2)Var[X]+(-b^2)Var[Y] - 2a(-b)Cov[X,Y]
= a^2Var[X]+b^2Var[Y] + 2abCov[X,Y]
__________________
1/P | 2/FM | 3F/MFE | 4/C | S | FAP | VEE-Economics | VEE-Corporate Finance | ERM Module | ERM Exam | APC | CFA | FRM |
Reply With Quote
  #5  
Old 06-19-2017, 05:09 PM
ToBeAnActuaryOrNotToBe ToBeAnActuaryOrNotToBe is offline
Member
SOA
 
Join Date: May 2014
Favorite beer: The ones in red solo cups.
Posts: 672
Default

Quote:
Originally Posted by bujayherster View Post
Isn't it because b = (-1), so with your equation:

Var[aX-bY] = Var[aX+(-b)Y]
= (a^2)Var[X]+(-b^2)Var[Y] - 2a(-b)Cov[X,Y]
= a^2Var[X]+b^2Var[Y] + 2abCov[X,Y]
Nope. Var[aX+bY] = a^2Var[X] +b^2Var[Y] + 2abCov[X,Y].
The original equation without a different b does not have a minus in front of the Covariance term. There is an error with the practice problem OP had.
Reply With Quote
  #6  
Old 06-19-2017, 05:23 PM
tkt's Avatar
tkt tkt is offline
Member
CAS SOA
 
Join Date: Jun 2011
Location: Des Moines
College: Drake University
Posts: 490
Default

Not sure if this post is referring to an Adapt problem. We have come across a similar forum post in Adapt's discussion forum today. What's in the Adapt solution (see the attached) is correct.

__________________
Tong Khon Teh, FSA, CFA
Product Manager, Actuarial
coachingactuaries.com
Reply With Quote
  #7  
Old 06-19-2017, 07:03 PM
mistersunnyd mistersunnyd is offline
Member
SOA
 
Join Date: Aug 2016
Studying for how to find a job
Posts: 104
Default

Ah never mind. It seems I made b negative while also putting a negative before the entire covariance term. Thanks for the help guys!
Reply With Quote
Reply

Tags
covariance, variance

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off


All times are GMT -4. The time now is 06:06 PM.


Powered by vBulletin®
Copyright ©2000 - 2018, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.21383 seconds with 11 queries