Question

2. There is a portfolio whose current value is $10 million. Its monthly returns are normally distributed with a mean of 3.7% and a standard deviation of 0.5%.
   1. Compute the daily 99% and 95% VaRs of the portfolio
   2. Interpret the results of the VaRs above

Answer 1

We calculate VaR using the NORMINV function in Excel.

For the 99% VaR, the input arguments are :

probability = 0.01, which is 1% expressed as a decimal. We use 1% as the total is 100% and we are computing VaR at 99%

mean = 0.037, which is 3.7% expressed as a decimal

standard deviation = 0.005, which is 0.5% expressed as a decimal

The result of this function gives us a VaR of 0.025368261. Multiplying this with the portfolio value of $10 million, monthly VaR of the portfolio is $253,682.61

For the 95% VaR, the input arguments are :

probability = 0.05, which is 5% expressed as a decimal. We use 5% as the total is 100% and we are computing VaR at 95%

mean = 0.037, which is 3.7% expressed as a decimal

standard deviation = 0.005, which is 0.5% expressed as a decimal

The result of this function gives us a VaR of 0.028775732. Multiplying this with the portfolio value of $10 million, monthly VaR of the portfolio is $287,757.32

Interpretation :

99% VaR - It indicates that there is a 99% probability that the value of the portfolio will not decline by more than $253,682.61 over the next one month

95% VaR - It indicates that there is a 95% probability that the value of the portfolio will not decline by more than $287,757.32 over the next one month