## Value at risk

mayankmundhra30
Good Student
Posts: 23
Joined: Sat Jun 25, 2016 8:13 am

### Value at risk

Given the following 30 ordered simulated percentage returns of an asset, calculate the VAR and expected shortfall (both expressed in terms of returns) at a 90% confidence level.-16, -14, -10, -7, -7, -5, -4, -4, -4, -3, -1, -1, 0, 0, 0, 1, 2, 2, 4, 6, 7, 8, 9,11, 12, 12, 14, 18, 21, 23
a. VAR (90%) = 10, Expected shortfall = 14 Incorrect
b. VaR (90%) = 14, Expected shortfall = 15 Incorrect
c. VaR (90%) = 18, Expected shortfall = 22 Incorrect
d. VAR (90%) = 10, Expected shortfall = 15 Correct

Why the Var is 10 and not 7 as the 27th observation calculated as 90% of 30 observations

2) Why VaR for Fat tail is less than VaR for normal distribution?

edupristine
Finance Junkie
Posts: 964
Joined: Wed Apr 09, 2014 6:28 am

### Re: Value at risk

Hi Mayank

Ten percent of the observations will fall at or below the 3rd lowest observation of the 30 listed. Therefore, the VaR equals 10. The expected shortfall is the mean of the observations exceeding the VaR. Thus, the expected shortfall equals (16 + 14) / 2 = 15
The correct answer is: VAR (90%) = 10, Expected shortfall = 15.

mayankmundhra30
Good Student
Posts: 23
Joined: Sat Jun 25, 2016 8:13 am

### Re: Value at risk

Sir
There is a problem in the edupristine material.
Suppose we have an asset with ordered simulated price returns as below for sample of 500 days & is trading at 70. What is the VaR at 99% confidence interval if the returns for the last 500 days are:
-7%,-6.7%,-6.6%,-6.5%,-6.1%,5.9%.......4%,4.75%,5.1%,5.2%,5.3%.

The answer is -5.9%. but according to you it should be -6.1% ( the 1% of 500)
according to material the 495th data is -5.9%.
495=99% of 500.