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Discussion (VaR Methodology)

  • Three value at risk (VaR) methods are reviewed: Delta-normal, historical simulation and Monte Carlo. Which are true of the following? Among the VaR methods, which:
  1. Efficient in terms of data use?
  2. Requires a (parametric) distributional assumption?
  3. Is LEAST appropriate for a portfolio that contains many embedded derivatives (e.g., options)?
  4. Is computationally fast?
  5. Handles fat tails?
  6. Suffers from sampling variation?

Example (Historical Simulations)

Suppose we have an asset with ordered simulated price returns as below for sample of 500 days and is trading at 70. What is the VaR at 99% confidence 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%

 

Solution

99% of 500 = 495th i.e. -5.9% = 0.059 x 70 = 4.13


 

Example (Historical Simulations)
We have an asset with ordered simulated price returns as below for sample of 400 days and is trading at 100. What is the VaR at 99% confidence if the returns for the last 400 days are:
-7%, -6.7%,-6.6%, -6.5%,-.6.1%,-5.9% … 4%, 4.75%,5.1%, 5.2%,5.3%
What is the expected shortfall?
 
Solution

VaR = 396th = -6.1% of 100 = -6.1
Expected shortfall = - (7 + 6.7 + 6.6 + 6.5)/4 = -6.7%

 

 
 

 

 

 
Expect atleast one direct question on the calculation of Expected Shortfall.

 





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