Question

Suppose the historical standard deviation of a stock index has been 0.6% per day, and an investor has a $10,000 investment in the index. Calculate the 1-day, 5% VaR in dollars and provide two kinds of interpretation to your result.

Answer 1

Assuming that the Index values are normally distributed

5% VaR corresponds to z value of NORMSINV(0.05) = -1.64485 meaning that there is a 5% probability
that a normally distributed variable (returns in this case) will decrease in value by more than 1.64485
standard deviations.

So, 1 day 5% VaR = 1.64485 * 1 day standard deviation

= 1.64485* 0.6%*$10000

= $98.69

The meaning of $98.69 is that there is a 5% probability that the value of the portfolio will fall more than $98.69 in 1 day.

This also means that there is a 95% probability that the value of the portfolio will not fall by more than $98.69 in 1 day