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).
This exercise is part of the course
Intro to Computational Finance with R
Exercise instructions
- Assign to
mu_rthe mean of \(r\). - Assign to
sigma_rthe standard deviation of \(r\). - Assign to
W0the 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.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# r ~ N(0.04, (0.09)^2)
mu_r <-
sigma_r <-
# Initial wealth W0 equals $100,000
W0 <-
# The 1% value-at-risk
# The 5% value-at-risk