**Question 790** mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate, log-normal distribution, VaR, confidence interval

A risk manager has identified that their hedge fund’s continuously compounded portfolio returns are normally distributed with a mean of **10**% pa and a standard deviation of **30**% pa. The hedge fund’s portfolio is currently valued at $**100** million. Assume that there is no estimation error in these figures and that the normal cumulative density function at 1.644853627 is 95%.

Which of the following statements is **NOT** correct? All answers are rounded to the nearest dollar.

**Question 791** mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate, log-normal distribution, VaR, confidence interval

A risk manager has identified that their pension fund’s continuously compounded portfolio returns are normally distributed with a mean of **5**% pa and a standard deviation of **20**% pa. The fund’s portfolio is currently valued at $**1** million. Assume that there is no estimation error in the above figures. To simplify your calculations, all answers below use **2.33** as an approximation for the normal inverse cumulative density function at **99**%. All answers are rounded to the nearest dollar. Which of the following statements is **NOT** correct?

A company has a 95% daily Value at Risk (VaR) of $1 million. The units of this VaR are in:

**Question 948** VaR, expected shortfall

Below is a historical sample of returns on the S&P500 capital index.

S&P500 Capital Index Daily Returns Ranked from Best to Worst |
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10,000 trading days from 4th August 1977 to 24 March 2017 based on closing prices. |
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Rank | Date (DD-MM-YY) |
Continuously compounded daily return (% per day) |

1 | 21-10-87 | 9.23 |

2 | 08-03-83 | 8.97 |

3 | 13-11-08 | 8.3 |

4 | 30-09-08 | 8.09 |

5 | 28-10-08 | 8.01 |

6 | 29-10-87 | 7.28 |

… | … | … |

9980 | 11-12-08 | -5.51 |

9981 | 22-10-08 | -5.51 |

9982 | 08-08-11 | -5.54 |

9983 | 22-09-08 | -5.64 |

9984 | 11-09-86 | -5.69 |

9985 | 30-11-87 | -5.88 |

9986 | 14-04-00 | -5.99 |

9987 | 07-10-98 | -6.06 |

9988 | 08-01-88 | -6.51 |

9989 | 27-10-97 | -6.55 |

9990 | 13-10-89 | -6.62 |

9991 | 15-10-08 | -6.71 |

9992 | 29-09-08 | -6.85 |

9993 | 07-10-08 | -6.91 |

9994 | 14-11-08 | -7.64 |

9995 | 01-12-08 | -7.79 |

9996 | 29-10-08 | -8.05 |

9997 | 26-10-87 | -8.4 |

9998 | 31-08-98 | -8.45 |

9999 | 09-10-08 | -12.9 |

10000 | 19-10-87 | -23.36 |

Mean of all 10,000: | 0.0354 | |

Sample standard deviation of all 10,000: | 1.2062 | |

Sources: Bloomberg and S&P. | ||

Assume that the one-tail Z-statistic corresponding to a probability of 99.9% is exactly **3.09**. Which of the following statements is **NOT** correct? Based on the historical data, the 99.9% daily: