6. Suppose a portfolio consists of a USD 1 million investment in Euros and a USD 4 million investment in Mexican Pesos. Additional information is given below:

Portfolio beta of Euro = 0.90

Portfolio beta of Peso= 1.30

Diversified Portfolio VaR = USD 324,700

Based on the given information, the marginal VaR and the component VaR of the Euro position are closest to:

A. A

B. B

C. C

D. D

7. Which of the following is most accurate with respect to Delta-Normal VaR?

A. The delta-normal method provides accurate estimates of VaR for assets that can be expressed as a linear or non-linear combination of normally distributed risk factors.

B. The delta-normal method provides accurate estimates of VaR for options that are at-or-near-the-money and close to expiration.

C. The delta-normal method provides accurate estimates of VaR by generating a covariance (correlation) matrix and measuring VaR using relatively simple matrix multiplication.

D. The delta-normal method provides accurate estimates of VaR for options and other derivatives over ranges even if deltas are unstable.

8. Assume the continuously-compounded risk-free rate is 5% per annum, the appropriate discount rate for computing the present value of oil to be delivered one year in the future is 7% per annum (continuously compounded), the continuously compounded cost of storing oil for a year is 1% per annum, the continuously compounded convenience yield for owning oil for a year is 2% per annum, and the current price of oil is USD 75/bbl. What is the price the long would pay to the short today at time 0 to receive one barrel of oil in a year?

A. USD 49.01

B. USD 52.04

C. USD 47.56

D. USD 49.50

9. A market risk manager is monitoring a trader's portfolio which is currently solely long in a series of identical knock-out call options on JPY/USD. These are up-and-out European-style options that will expire in 1 month's time. The strike is at 110.00 JPY/USD and barrier at 120.00 JPY/USD. The current JPY/USD rate is at 119.50. The risk manager needs to decide on which Value-at-Risk (VaR) method will capture the risk of the portfolio most accurately. Which one of the following methods is the most appropriate?

A. The delta-normal method

B. The delta-gamma-vega method

C. Monte Carlo Simulation

D. The historical simulation method using vanilla JPY/USD option price time series

10. Which of the following best describes what we would normally expect to see in a seasonal agricultural market like wheat? Assume "the harvest" is normal and not unusually big or unusually small. Now consider the following statements about the market.

I. Prices fall at the harvest and rise after the harvest.

II. Prices are constant on average across the year regardless of seasonality.

III. Prices rise at the harvest and fall afterwards.

IV. The market is in contango when the harvest comes in.

V. The market is in backwardation when the harvest comes in.

VI. If the market goes into contango, it is most likely to do so right before a new harvest.

VII. If the market goes into backwardation, it is most likely to do so right before a new harvest.

Now choose the letter that best describes which of the above statements is true.

A. I and IV are the only true statements

B. I, IV, and VI are the only true statements

C. III, V, and VII are the only true statements

D. I, IV, and VII are the only true statements

6. Suppose a portfolio consists of a USD 1 million investment in Euros and a USD 4 million investment in Mexican Pesos. Additional information is given below:

Portfolio beta of Euro = 0.90

Portfolio beta of Peso= 1.30

Diversified Portfolio VaR = USD 324,700

Based on the given information, the marginal VaR and the component VaR of the Euro position are closest to:

A. A

B. B

C. C

D. D

Correct answer is A

A is correct.fficeffice" />

Marginal VaR of Euro = (USD 324,700 / USD 5,000,000) x 0.90 = USD 0.058

Component VaR of Euro = USD 324,700 x 0.90 x (1,000,000 / 5,000,000) = USD 58,446

B is incorrect. Because of the use of incorrect variable and/or incorrect formula.

C is incorrect. Because of the use of incorrect variable and/or incorrect formula.

D is incorrect. Because of the use of incorrect variable and/or incorrect formula.

Reference: Allen Boudoukh and Saunders, Chapter 1 and 3.

7. Which of the following is most accurate with respect to Delta-Normal VaR?

A. The delta-normal method provides accurate estimates of VaR for assets that can be expressed as a linear or non-linear combination of normally distributed risk factors.

B. The delta-normal method provides accurate estimates of VaR for options that are at-or-near-the-money and close to expiration.

C. The delta-normal method provides accurate estimates of VaR by generating a covariance (correlation) matrix and measuring VaR using relatively simple matrix multiplication.

D. The delta-normal method provides accurate estimates of VaR for options and other derivatives over ranges even if deltas are unstable.

Correct answer is C

A is incorrect. Accurate estimates only if the risks can be expressed as a linear combination.

B is incorrect. Accurate estimates only for deep out-of-the-money and deep in-the-money options (over ranges).

C is correct. This is the most accurate statement.

D is incorrect. Accurate estimates only if deltas are stable.

Reference: Philippe Jorion, Chapter 11.

8. Assume the continuously-compounded risk-free rate is 5% per annum, the appropriate discount rate for computing the present value of oil to be delivered one year in the future is 7% per annum (continuously compounded), the continuously compounded cost of storing oil for a year is 1% per annum, the continuously compounded convenience yield for owning oil for a year is 2% per annum, and the current price of oil is USD 75/bbl. What is the price the long would pay to the short today at time 0 to receive one barrel of oil in a year?

A. USD 49.01

B. USD 52.04

C. USD 47.56

D. USD 49.50

Correct answer is D

The correct prepaid forward price is the present value of the traditional forward price. The traditional forward price can be determined from the cost of carry formula as USD 50e(.05+.01-.02) = USD 52.04 (incorrect choice b). Discounting that back yields e(-.05) USD 52.04 = USD 49.50, which is the correct answer. Incorrect choice a is the spot price discounted at the difference between the risk-free rate and the asset discount rate, but this will only equal the discounted forward price if the expected future spot price is equal to the expected spot price. Finally, incorrect choice c is the spot price discounted at the risk-free rate ignoring storage costs and convenience yield.

Reference: McDonald, Chapter 6

9. A market risk manager is monitoring a trader's portfolio which is currently solely long in a series of identical knock-out call options on JPY/USD. These are up-and-out European-style options that will expire in 1 month's time. The strike is at 110.00 JPY/USD and barrier at 120.00 JPY/USD. The current JPY/USD rate is at 119.50. The risk manager needs to decide on which Value-at-Risk (VaR) method will capture the risk of the portfolio most accurately. Which one of the following methods is the most appropriate?

A. The delta-normal method

B. The delta-gamma-vega method

C. ffice:smarttags" />Monte Carlo Simulation

D. The historical simulation method using vanilla JPY/USD option price time series

Correct answer is C

A is incorrect as the options are very close to being knocked out and the change in the greeks like delta will be dramatically change (Delta will jump straight to zero once barrier is hit). This significant non-linearity in these types of barrier options makes the delta-normal method inappropriate.

B is incorrect. The same reason in (a) applies.

C is correct as the Monte Carlo Simulation is a full revaluation VaR method that takes into account the significant non-linearity in barrier options. For example, if one of the simulated scenarios indicates a JPY/USD level of 120.10, the options would have been knocked out and the MTM of the options will be zero.

D is incorrect as the vanilla JPY/USD option time series does not take into account the significant non-linearity of barriers option.

Reference: Hull, John, Options, Futures and Other Derivatives, Sixth Edition, Prentice Hall, New York, 2006, Chapter 22, Exotic Options

10. Which of the following best describes what we would normally expect to see in a seasonal agricultural market like wheat? Assume "the harvest" is normal and not unusually big or unusually small. Now consider the following statements about the market.

I. Prices fall at the harvest and rise after the harvest.

II. Prices are constant on average across the year regardless of seasonality.

III. Prices rise at the harvest and fall afterwards.

IV. The market is in contango when the harvest comes in.

V. The market is in backwardation when the harvest comes in.

VI. If the market goes into contango, it is most likely to do so right before a new harvest.

VII. If the market goes into backwardation, it is most likely to do so right before a new harvest.

Now choose the letter that best describes which of the above statements is true.

A. I and IV are the only true statements

B. I, IV, and VI are the only true statements

C. III, V, and VII are the only true statements

D. I, IV, and VII are the only true statements

Correct answer is D

Explanation:  The new harvest "resets" the storage market. For a while, consumption and production occur directly from the new harvest, and prices are low. Prices begin to rise as storage begins to occur. As the next harvest approaches, inventory may get tight, sending the market into backwardation.

Reference: McDonald, Chapter 6