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Old 07-01-2019, 03:39 PM
calculusjunkie calculusjunkie is offline
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Default 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.

Your comments are appreciated~
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Old 07-01-2019, 11:18 PM
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tkt tkt is offline
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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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Old 07-01-2019, 11:47 PM
calculusjunkie calculusjunkie is offline
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Thank you, makes sense. Completely forgot the fact that it was not a standard normal.
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