11. If the daily, 95% confidence level value at risk (VaR) of a portfolio is correctly estimated to be USD 10,000, which of the following statements are correct: I. In 1 out of 20 days, the portfolio value will decline by USD 10,000 or less. II. In 1 out of 20 days, the portfolio value will decline by USD 10,000 or more. III. In 19 out of 20 days, the portfolio value will decline more than USD 10,000. IV. In 19 out of 20 days, the portfolio value will not decline by USD 10,000 or more. (a) I (b) II (c) I and III (d) II and IV

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**Question 11:**

If the daily, 95% confidence level value at risk (VaR) of a portfolio is correctly estimated to be USD 10,000, which of the following statements are correct:

I. In 1 out of 20 days, the portfolio value will decline by USD 10,000 or less.  
II. In 1 out of 20 days, the portfolio value will decline by USD 10,000 or more.  
III. In 19 out of 20 days, the portfolio value will decline more than USD 10,000.  
IV. In 19 out of 20 days, the portfolio value will *not* decline by USD 10,000 or more.

- (a) I  
- (b) II  
- (c) I and III  
- (d) II and IV  

**Question 12:**

Assume that portfolio daily returns are independently and identically normally distributed with mean zero. A new quantitative analyst has been asked by the portfolio manager to calculate portfolio VaRs for 10-, 15-, 20-, and 25-day periods. The portfolio manager notices something amiss with the analyst’s calculations. Assuming the annualized volatilities of daily returns for the four periods are equal, which of the following VaRs on this portfolio is inconsistent with the others?

- (a) VaR(10-day) = USD 316 million  
- (b) VaR(15-day) = USD 426 million  
- (c) VaR(20-day) = USD 447 million  
- (d) VaR(25-day) = USD 500 million  

**Question 13:**

A (possibly biased) coin is tossed twice. If the outcome is two heads, $5 is received. If *any* tail occurs a consolation prize of $1 is received. The fair price to play this game is $4. What is the implied probability of heads?

- (a) 0.87  
- (b) 0.61  
- (c) 0.71  
- (d) 0.80
Transcribed Image Text:**Question 11:** If the daily, 95% confidence level value at risk (VaR) of a portfolio is correctly estimated to be USD 10,000, which of the following statements are correct: I. In 1 out of 20 days, the portfolio value will decline by USD 10,000 or less. II. In 1 out of 20 days, the portfolio value will decline by USD 10,000 or more. III. In 19 out of 20 days, the portfolio value will decline more than USD 10,000. IV. In 19 out of 20 days, the portfolio value will *not* decline by USD 10,000 or more. - (a) I - (b) II - (c) I and III - (d) II and IV **Question 12:** Assume that portfolio daily returns are independently and identically normally distributed with mean zero. A new quantitative analyst has been asked by the portfolio manager to calculate portfolio VaRs for 10-, 15-, 20-, and 25-day periods. The portfolio manager notices something amiss with the analyst’s calculations. Assuming the annualized volatilities of daily returns for the four periods are equal, which of the following VaRs on this portfolio is inconsistent with the others? - (a) VaR(10-day) = USD 316 million - (b) VaR(15-day) = USD 426 million - (c) VaR(20-day) = USD 447 million - (d) VaR(25-day) = USD 500 million **Question 13:** A (possibly biased) coin is tossed twice. If the outcome is two heads, $5 is received. If *any* tail occurs a consolation prize of $1 is received. The fair price to play this game is $4. What is the implied probability of heads? - (a) 0.87 - (b) 0.61 - (c) 0.71 - (d) 0.80
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