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  3. Intro to Computational Finance with R

Exercise

Determine the value-at-risk of continuously compounded monthly returns

Instead of the simple monthly return, now look at the continuously compounded monthly return \(r\) of the Microsoft stock. Assume that \(r\) is normally distributed with a mean \(0.04\) and a variance \((0.09)^{2}\). The initial wealth to be invested over the month is $100,000.

Determine the 1% and the 5% value-at-risk (VaR) over the month on the investment. That is, determine the loss in investment value that may occur over the next month with a 1% probability and with a 5% probability.

Use the fact that the continuously compounded return quantile can be transformed to a simple return quantile with the transformation \(R = e^{r} - 1\). The exponential \(e^{r}\) can easily be computed with exp(r).

Instructions

100 XP
  • Assign to mu_r the mean of \(r\).
  • Assign to sigma_r the standard deviation of \(r\).
  • Assign to W0 the initial wealth.
  • Compute the 1% value-at-risk and print the result to the console.
  • Compute the 5% value-at-risk and print the result to the console.