Financial Risk Manager Part 2
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A wealth management firm manages a portfolio valued at JPY 72 billion in assets under management. The portfolio manager calculates the daily Value at Risk (VaR) across various confidence levels, as presented in the table below:
Confidence Level VaR (USD) 95.0% 332,760,000 95.5% 336,292,500 96.0% 340,095,000 96.5% 350,332,500 97.0% 359,107,500 97.5% 367,882,500 98.0% 378,412,500 98.5% 392,452,500 99.0% 410,880,000 99.5% 439,252,500
What is the most accurate approximation of the daily Expected Shortfall (ES) at the 97.5% confidence level for the FRM examination?
A wealth management firm manages a portfolio valued at JPY 72 billion in assets under management. The portfolio manager calculates the daily Value at Risk (VaR) across various confidence levels, as presented in the table below:
| Confidence Level | VaR (USD) |
|---|---|
| 95.0% | 332,760,000 |
| 95.5% | 336,292,500 |
| 96.0% | 340,095,000 |
| 96.5% | 350,332,500 |
| 97.0% | 359,107,500 |
| 97.5% | 367,882,500 |
| 98.0% | 378,412,500 |
| 98.5% | 392,452,500 |
| 99.0% | 410,880,000 |
| 99.5% | 439,252,500 |
What is the most accurate approximation of the daily Expected Shortfall (ES) at the 97.5% confidence level for the FRM examination?
Explanation:
The correct answer is option C, which is JPY 405 million. The expected shortfall (ES) is an estimate of the potential loss that could be expected beyond the Value at Risk (VaR) threshold. In this case, the ES at the 97.5% confidence level is calculated by taking the average of the VaRs at confidence levels higher than 97.5%. The VaRs at 98.0%, 98.5%, and 99.0% confidence levels are JPY 378,412,500, JPY 392,452,500, and JPY 410,880,000 respectively. The average of these VaRs is calculated as follows:
This average value is rounded to JPY 405 million, which corresponds to option C. This method provides an estimate of the expected loss in the tail of the distribution beyond the VaR threshold, which is useful for assessing the potential impact of extreme market movements on a portfolio.