Actuarial Outpost IFM Question: Investment Risk & Project Analysis
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

 DW Simpson Global Actuarial & Analytics Recruitment Download our Actuarial Salary Survey now with state-by-state salary information!

 Investment / Financial Markets Old Exam MFE Forum

#1
07-01-2019, 03:39 PM
 calculusjunkie CAS SOA Join Date: Mar 2014 College: University of Illinois, undergrad Posts: 23
IFM Question: Investment Risk & Project Analysis

I am having trouble understanding where the squared root in the denominator comes from in the solution for the question below:

Your firm purchased 100 units of equity-linked CDs which guarantees you the original principal \$1000 with effective annual interest 2%, plus 80% of the percentage increase in DJIA index price over the 2-year period.
The current DJIA price is 25669, and you model the DJIA index price at time tt using:
SDJIA(t)=25669e0.04t+0.12ZtSDJIA(t)=25669e0.04t+0. 12Zt, where ZtZt follows a normal distribution with mean 0 and variance tt.
Determine the Value-at-Risk at α=15%α=15% for your investment return.

The solution is attached.

Attached Files
 Investment Risk & Project Analysis.doc (100.0 KB, 50 views)
#2
07-01-2019, 11:18 PM
 tkt Member CAS SOA Join Date: Jun 2011 Location: Des Moines College: Drake University Posts: 539

Note that Z(t) is not a standard normal random variable; it is a normal random variable with mean 0 and variance t. Thus, Z(2) is normally distributed with mean 0 and variance 2.

To evaluate the probability involving a normal random variable, we subtract the mean and divide by the standard deviation. Thus, we subtract both the left and right sides of the inequality by 0 and divide both sides by sqrt(2). The left side becomes a standard normal random variable, Z. The right side becomes what's shown in the line with the yellow arrow.

Hope this helps!
__________________
Tong Khon Teh, FSA, CFA
Product Manager, Actuarial
coachingactuaries.com
#3
07-01-2019, 11:47 PM
 calculusjunkie CAS SOA Join Date: Mar 2014 College: University of Illinois, undergrad Posts: 23

Thank you, makes sense. Completely forgot the fact that it was not a standard normal.