Financial Risk Manager Part 1

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Tim Yang, FRM, is working on building a model using a Monte Carlo simulation. However, he is concerned about the accuracy of the simulation which is measured by its standard error. Tim initially runs a model with 81 simulations and the standard deviation was found to be 27%. He then runs the model with 144 simulations and the standard deviation is still 27%. What are the standard errors for the simulations?

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TTanishq

Standard error for the first simulation: 0.33%; Standard error for the second simulation: 0.19%

Standard error for the first simulation: 27%; Standard error for the second simulation: 27.00%

Standard error for the first simulation: 2.25%; Standard error for the second simulation: 3%

Standard error for the first simulation: 3%; Standard error for the second simulation: 2.25%

Explanation:

The standard error is calculated using the formula:

$\text{Standard error} = \frac{\text{Standard deviation}}{\sqrt{n}}$

For the first simulation (n = 81): $\text{Standard error} = \frac{27}{\sqrt{81}} = \frac{27}{9} = 3\%$

For the second simulation (n = 144): $\text{Standard error} = \frac{27}{\sqrt{144}} = \frac{27}{12} = 2.25\%$

Therefore, the standard errors are:

First simulation: 3%
Second simulation: 2.25%

This demonstrates that as the number of simulations increases, the standard error decreases, improving the accuracy of the Monte Carlo simulation.

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