Financial Risk Manager Part 1
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Construct a 95% confidence interval for the future value of a pension fund where the number of simulations is 100, the mean ending value is $400,000, and the standard deviation is $23,300.
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TTanishq
A
($395,433.2, $404,566.8)
B
($400,000, $404,613)
C
($395,456, $404,456)
D
($395, $404)
Explanation:
Explanation
The confidence interval is constructed using the normal distribution, not the student's t-distribution because n is large (in line with the central limit theorem).
The interval is given by:
Thus,
CI = \`$400`,000 - 1.96\left(\frac{\`$23`,300}{\sqrt{100}}\right), \`$400`,000 + 1.96\left(\frac{\`$23`,300}{\sqrt{100}}\right)
= \`$400`,000 - 1.96(\`$2`,330), \`$400`,000 + 1.96(\`$2`,330)
= \`$400`,000 - \`$4`,566.8, \`$400`,000 + \`$4`,566.8
= (\`$395`,433.2, \`$404`,566.8)
Key points:
- For large sample sizes (n ≥ 30), we use the normal distribution (z-distribution)
- The 95% confidence level corresponds to z = 1.96
- The standard error is calculated as s/√n =
$23,300/√100 =$2,330 - The margin of error is 1.96 ×
$2,330 =$4,566.8
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