Comparison between Methods
- The best methods depend on speed required and whether the portfolio has non-linear elements.
- For large portfolios where non linearity is not a major factor, the delta normal method is fast
- and efficient.
- For portfolios with substantial non-linear elements full valuation may be necessary.
Visualizing WCS
- The worst case scenario (WCS) answers:
- What is the worst loss that can happen over a period of time?
- The probability of a “worst loss” is certain (100%); the timing is uncertain.
- Focuses on distribution of loss during the worse trading period:
- A worst case scenario can be simulated only using Monet Carlo Simulations
Visualizing WCS
- The area under the normal curve for confidence value is:
Confidence (x%) |
Z_{X%} |
90% |
1.28 |
95% |
1.65 |
97.5% |
1.96 |
99% |
2.32 |
Example
H = 100
Z < -2.33 ( 99% VaR ) -> 1 out of 100
Distribution of WCS mean = -2.51 and it’s 1st and 5th percentile are -3.1 and -3.9 resp.
What does this mean to a financial risk manager?
Solution
Mean of distribution of WCS = -2.51
It means that if the loss exceeds the VAR number(2.33), the average value of the loss would be 2.51 which is nothing but the expected shortfall (ES)
The 5st and 1st percentile of WCS is -3.1 and -3.9
It means that if the loss exceed the VAR, then probability of loss exceeding 3.9 is 1%
Similarly the probability of loss exceeding 3.1 would be 5%