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#1




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 equitylinked 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 2year 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 ValueatRisk at α=15%α=15% for your investment return. The solution is attached. Your comments are appreciated~ 
#2




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! 
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