Investment Management (Risk Measurement and Analysis)

Reference: [Hull]: John Hull, Risk Management and Financial Institutions, 4th Edition (John Wiley & Sons,

2015).

Questions:

1. [Lecture 3] Which of the following statements is correct?

a. Lower VaR indicates less expected loss for tail events.

b. The use of VaR may introduce agency problem.

c. An advantage of VaR is that it is free from model risk or implementation risk.

d. In VaR estimation, shorter holding period should be chosen if the firm operates in an illiquid market.

2. [Lecture 3] A large commercial bank is using VaR as its main risk measurement tool. Expected shortfall (ES) is suggested as a better alternative to use during market turmoil. What should be understood regarding VaR and ES before modifying current practices?

a. VaR is a coherent risk measure while ES is not.

b. ES is always greater than or equal to VaR.

c. While VaR ensures that the estimate of portfolio risk is less than or equal to the sum of the risks of that portfolio's positions, ES does not.

d. Both VaR and ES account for the severity of losses beyond the confidence threshold.

3. [Lecture 3] Assume an investor is very risk-averse and is creating a portfolio based on the mean-variance model and the risk-free asset. The investor will most likely choose an investment on the:

a. left-hand side of the efficient frontier.

b. right-hand side of the efficient frontier.

c. line segment connecting the risk-free rate to the market portfolio.

d. line segment extending to the right of the market portfolio.

4. [Lecture 3] A risk manager is comparing the use of parametric and non-parametric approaches for calculating VaR and is concerned about some of the characteristics present in the loss data. Which of the following conditions would make non-parametric approaches the favored method to use?

a. Scarcity of high magnitude loss event

b. Skewness in the distribution

c. Unusually high volatility during the data period

d. Unusually low volatility during the data period

5. [Lecture 3] The risk management group estimates the 1-day 99% VaR on a long-only, large-cap equity portfolio using a variety of approaches. A daily risk report shows the following information:

1-day 99% VaR Estimates (by approach):

Delta-normal VaR: 321,890

Monte Carlo Simulation VaR: 353,851

Historical Simulation VaR: 375,534

Which of the following is the most likely explanation for the variation in VaR estimates?

a. Data problems

b. Differences in model assumptions

c. Endogenous model risk (e.g., traders gaming the system to lower risk values)

d. Programming errors

6. [Lecture 3] Sam Neil, a new quantitative analyst, has been asked by the portfolio manager to calculate the portfolio 1-day 98% Value-at-Risk (VaR) measure based on the past 100 trading days. What will this be if worst 5 losses in the past 100 trading days are 316M, 385M, 412M, 422M and 485M in USD?

a. USD 385M

b. USD 412M

c. USD 422M

d. USD 485M

7. [Lecture 3] Which of the following is not a reason that expected shortfall (ES) is a more appropriate risk measure than value at risk (VaR)?

a. For normal distributions, only ES satisfies all the properties of coherent risk measurements.

b. ES gives an estimate of the magnitude of a loss, while VaR cannot tell the magnitude of the loss.

c. ES has less restrictive assumptions regarding risk/return decision rules than VaR.

d. ES satisfies all the properties of coherent risk measurements even for non-normal distributions.

8. [Lecture 3] Consider the following four statements about value at risk (VaR):

I. The choice of VaR confidence interval and time horizon should be uniform across users.

II. There is not much uniformity of practice as to confidence interval and time horizon; as a result, intuition on what constitutes a large or small VaR is underdeveloped.

III. There are a number of computational and modeling decisions that can greatly influence VaR results, such as the length of time series used for historical simulation or to estimate moments; and the technique used for estimating moments.

IV. There are a number of computational and modeling decisions that can greatly influence VaR results, such as mapping techniques and the choice of risk factors.

Which of the above statements is/are true?

a. None are true.

b. I and II are true.

c. II, III, and IV are true.

d. All are true.

9. [Lecture 3] Suppose () is a risk measure. (X+Y) (X) + (Y) is the mathematic equation for

a. monotonicity.

b. subadditivity.

c. positive homogeneity.

d. Translational invariance.

10. [Lecture 3] Assume that an operational process has a 5% probability of creating a material loss and, otherwise, no material loss is experienced. If the material loss occurs, the severity is normally distributed with a mean of $4 million and standard deviation of $2 million. What is the 95% expected shortfall?

a. $0.71 million

b. $3.29 million

c. $4.00 million

d. $7.29 million

11. [Lecture 3] After estimating the 99%, 1-day VaR of a bank's portfolio to be USD 1,484 using historical simulation with 1,000 past trading days, you are concerned that the VaR measure is not providing enough information about tail losses. You decide to re-examine the simulation results and sort the simulated daily P&L from worst to best giving the following worst 15 scenarios:

1 -$2,833

2 -$2,333

3 -$2,228

4 -$2,084

5 -$1,960

6 -$1,751

7 -$1,679

8 -$1,558

9 -$1,542

10 -$1,484

11 -$1,450

12 -$1,428

13 -$1,368

14 -$1,347

15 -$1,319

What is the 99%, 1-day ES of the portfolio?

a. USD 433

b. USD 1,285

c. USD 1,945

d. USD 2,833

12. [Lecture 3] Suppose each of two independent projects has a probability of 3% of a loss of $5 million and a probability of 97% of a loss of $2 million during a one-year period. When the projects are put in the same portfolio, how much would be the one-year, 96.5% ES for this portfolio?

a. $3.50 million

b. $4.57 million

c. $7.08 million

d. $10.00 million

13. [Lecture 3] If the weighting function in the general risk spectrum measure is set to 1/(1 - confidence level) for all tail losses, then the risk spectrum is a special case of:

a. value at risk.

b. mean-variance.

c. expected shortfall.

d. scenario analysis.