Consider stocks A and B whose annualised rate of return having the following characteristics Stock Standard Deviation
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- Consider stocks A and B whose annualised rate of return having the following characteristics
| Stock | Standard Deviation |
| A | 12% |
| B | 15% |
- Coefficient of correlation (r) between the two stocks is 0.3
- What is the daily 99% VaR of a portfolio consisting of $5 million of Stock A and $10 million of stock B? Given the 99% normal percentile is 2.33. Assume there are 252 trading days in a year
- What assumptions on the statistic model have you made in the calculation (i)?
- The following shows the return series of Stock C
| Day | Daily return of Stock C | Day | Daily Return of Stock C | |
| 1 | 12.0% | 16 | 9.0% | |
| 2 | 12.0% | 17 | 16.0% | |
| 3 | -8.0% | 18 | -1.0% | |
| 4 | -2.0% | 19 | 7.0% | |
| 5 | 2.0% | 20 | 19.0% | |
| 6 | 4.0% | 21 | 4.0% | |
| 7 | -2.0% | 22 | 14.0% | |
| 8 | 5.0% | 23 | 11.0% | |
| 9 | 9.0% | 24 | 6.0% | |
| 10 | 28.0% | 25 | 11.0% | |
| 11 | -50.0% | 26 | -1.0% | |
| 12 | 10.0% | 27 | -2.0% | |
| 13 | 6.0% | 28 | 2.0% | |
| 14 | 4.5% | 29 | 6.5% | |
| 15 | 1.0% | 30 | 3.2% |
- What are the procedures required to find the 90% daily Value-at-Risk (VaR) of stock C using historical simulation?
- What is the 90% daily Value-at-Risk of $1million investment in Stock C?
- What is the 90% daily Expected Shortfall of an $1million investment in stock C?
- Using the results in part ii) and iii), explain why the expected shortfall is more desirable than value-at-risk when used in regulatory requirement
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