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1. [This classic value-at-risk question includes several key ideas. It is based on practice question 2010.P1.16, which is harder because it actually asks for a comparison between diversified and undiversified VaR!].

Question: Consider an equally-weighted portfolio with two bonds:

- Bond A: $50.00 price (exposure), 4.0% yield, 3.0 year duration, 3.0% annual yield volatility;
- Bond B: $50.00 price (exposure), 5.0% yield, 9.0 year duration, 7.0% annual yield volatility;

a. $8.15

b. $9.47

c. $10.90

d. $12.63

2. [This variation on practice question 2011.P1.24 is a nice way to quiz scaling VaR]

Question: Assume that portfolio daily returns are independently and identically normally distributed. Sam Neil, a new quantitative analyst, has been asked by the portfolio manager to calculate the portfolio Value-at-Risk (VaR) measure for 10, 15, 20 and 25 day periods. The portfolio manager notices something amiss with Sam’s calculations displayed below. Which one of following VARs on this portfolio is inconsistent with the others?

a. 1-day 99% VaR = $141.43

b. 10-day 95% VaR = $316.23

c. 20-day 99% VaR = $527.49

d. 25-day 95% VaR = $500.00

3. [variation on 2012.P1.1]

Question: You have been asked to estimate the VaR of a straddle option position in Big Pharma Inc. The company’s stock is trading at $100.00 and the stock has a daily volatility of 1.0%. The delta of the call option is +0.70. Using the delta-normal method, the VaR at the 95% confidence level of the straddle over a 1-day holding period is closest to which of the following choices?

a. Zero

b. $1.48

c. $1.97

d. $3.45

4. [variation on 2013.P2.2]

Question: The annual mean and volatility of a portfolio are 9.0% and 20.0%, respectively. The current value of the portfolio is USD 1,000,000. How does the 1-year 95% VaR that is calculated using a normal distribution assumption (normal VaR) differ from with the 1-year 95% VaR that is calculated using the lognormal distribution assumption (lognormal VaR)?

a. $26,409

b. $57,580

c. $83,333

d. $94,361

5. [variation on 2014.2.4]

Question: A risk manager is analyzing a 1-day 97.0% VaR model (an uncommon confidence level, you probably noticed). Assuming 250 days in a year, what is the maximum number of daily losses exceeding the 1-day

a. 7

b. 9

c. 12

d. 14

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