James has estimated an annual standard deviation of $750,000 on one of its projects, based on a normal distribution of returns. The average annual return is $2,400,000.
Estimate the value at risk (VAR) at a 95% confidence level for one year and over the project’s life of six years.
For 95% confidence, VAR is 1.645 standard deviations from the mean.
i.e. for one year = 1.645 x $750,000 = $1,233,750
This means that James can be 95% certain that the returns will be $1,166,250 or more every year ($2,400,000 – $1,233,750).
Over six years, the total standard deviation is square root of ( 6 x ($750,000 squared)) = $1,837,117
Therefore the VAR = 1.645 x 1,837,117 = $3,022,057
This means that James can be 95% certain that the returns will be $11,377,943 or more in total over the six year period ($14,400,000 – $3,022,057).