# Fight Finance

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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. 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:

The 95% daily VaR corresponds to the result on the:

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 10,000 trading days from 4th August 1977 to 24 March 2017 based on closing prices. 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: