Var example explanation

[andrnev]

In the VaR section there are 3 examples given and I am struggling with understanding the second example. The text states

As a second simple example, assume the result of an investment with a uniform distribution where all outcomes between a profit of 30 and a loss of 20 are equally likely. In this case, the VaR with a 99% confidence level is 19.5. This is because the probability that the loss will lie between 19.5 and 20 is 0.5/50 = 1%. (Note that we divide the range of losses we are interested in (0.5) by the total range of losses (50) because all outcomes are equally likely.)


Question is how does one get a VaR of 19.5?

Is the following reasoning correct?

Since we want to estimate the 99% VaR level we want to see those losses which are at least upto 1% from the assumed extreme loss of 20. So we need to first find the X which corresponds to the 1% i.e.

X/50 = 1% where 50 is the full range of investment outcomes.

that comes to X = 0.5

and from the extreme loss of 20 we subtract 0.5 to get 19.5. This value can be interpreted in 2 ways
1. We have a 1% confidence that the range of losses lie between 19.5 to 20 or
2. The VaR of 19.5 signifies the loss that is not expected to be exceeded with a 99% confidence.

 

[gsarm1987]

Your interpretation is correct. The VaR 19.5 indicates that, with 99% confidence, the loss will not exceed 19.5. There is a 1% chance that the loss could be between 19.5 and 20.

Also, for a uniform distribution over a range of 50 units, the probability of any 0.5 unit interval (such as from 19.5 to 20) is 0.5/50, which is 1%. This explains why there is a 1% chance that the loss could fall within this interval.