11. Imagine a stack-and-roll hedge of monthly commodity deliveries that you continue for the next five years. Assume the hedge ratio is adjusted to take into effect the mistiming of cash flows but is not adjusted for the basis risk of the hedge. In which of the following situations is your calendar basis risk likely to be greatest?

A. Stack and roll in the front month in oil futures.

B. Stack and roll in the 12-month contract in natural gas futures.

C. Stack and roll in the 3-year contract in gold futures.

D. All four situations will have the same basis risk

12. Given the following:

Current spot CHF/USD rate: 1.3680 (1.3680CHF = 1USD)

3-month USD interest rates: 1.05%

3-month Swiss interest rates: 0.35%

(Assume continuous compounding)

A currency trader notices that the 3-month forward price is USD 0.7350. In order to arbitrage, the trader should:

A. Borrow CHF, buy USD spot, go long Swiss franc forward

B. Borrow CHF, sell Swiss franc spot, go short Swiss franc forward

C. Borrow USD, buy Swiss francs spot, go short Swiss franc forward

D. Borrow USD, sell USD spot, go long Swiss franc forwards

13. Which of the following is NOT an assumption of the Black-Scholes options pricing model?

A. The price of the underlying moves in a continuous fashion

B. The interest rate changes randomly over time

C. The instantaneous variance of the return of the underlying is constant

D. Markets are perfect, i.e. short sales are allowed, there are no transaction costs or taxes, and markets operate continuously

14. Testing the fitness of the operational loss severity and frequency distributions to the data is fundamental. Which of the following is NOT a goodness-of-fitness test for severity distributions?

A. Kolmogorov-Smirnov

B. Anderson-Darling

C. Macaulay

D. Cramer-Von Mises

15. Suppose the face value of a three-year option-free bond is USD 1,000 and the annual coupon is 10%. The current yield to maturity is 5%. What is the Modified Duration of this bond?

A. 2.62

B. 2.85

C. 3.00

D. 2.75

11. Imagine a stack-and-roll hedge of monthly commodity deliveries that you continue for the next five years. Assume the hedge ratio is adjusted to take into effect the mistiming of cash flows but is not adjusted for the basis risk of the hedge. In which of the following situations is your calendar basis risk likely to be greatest?

A. Stack and roll in the front month in oil futures.

B. Stack and roll in the 12-month contract in natural gas futures.

C. Stack and roll in the 3-year contract in gold futures.

D. All four situations will have the same basis risk

Correct answer is A

Explanation:  The oil term structure is highly volatile at the short end, making a front-month stack-and-roll hedge heavily exposed to basis fluctuations. In natural gas, much of the movement occurs at the front end, as well, so the 12-month contract won't move as much. In gold, the term structure rarely moves much at all and won't begin to compare with oil and gas.fficeffice" />

Reference: McDonald, Chapter 6

12. Given the following:

Current spot CHF/USD rate: 1.3680 (1.3680CHF = 1USD)

3-month USD interest rates: 1.05%

3-month Swiss interest rates: 0.35%

(Assume continuous compounding)

A currency trader notices that the 3-month forward price is USD 0.7350. In order to arbitrage, the trader should:

A. Borrow CHF, buy USD spot, go long Swiss franc forward

B. Borrow CHF, sell Swiss franc spot, go short Swiss franc forward

C. Borrow USD, buy Swiss francs spot, go short Swiss franc forward

D. Borrow USD, sell USD spot, go long Swiss franc forwards

Correct answer is C

The spot is quoted in terms of Swiss Francs per USD.  To convert this into USD per Swiss Franc, we get: 1/1.3680 = 0.7310.  The theoretical futures price = 0.7310 * exp((0.0105 ? 0.0035) * 0.25) = 0.7323.  Therefore, the quoted futures price is too high.  Thus, one should sell the overvalued CHF futures contract. 

In order to arbitrage, one would do the following:

1)  Borrow 0.7310 * exp((-0.0035)*0.25) = 0.7304USD for 3 months.

2)  Buy spot exp((-0.0035)*0.25) = 0.9991CHF, invest at 0.35% for 3 months.

3)  Short a futures contract on 1 CHF.

At maturity,

1)  Pay back 0.7304 * exp((0.0105) * 0.25) = 0.7323USD.

2)  Receive 0.9991 * exp((0.0035) * 0.25) = 1 CHF.   

3)  Delivers 1 CHF on the futures contract, receives 0.7350USD.

An arbitrage profit of USD0.7350 - USD0.7323 = USD0.0027 would be realized in 3 months' time.

Reference: Options, Futures, and Other Derivatives, ffice:smarttags" />Hull, 2006.

13. Which of the following is NOT an assumption of the Black-Scholes options pricing model?

A. The price of the underlying moves in a continuous fashion

B. The interest rate changes randomly over time

C. The instantaneous variance of the return of the underlying is constant

D. Markets are perfect, i.e. short sales are allowed, there are no transaction costs or taxes, and markets operate continuously

Correct answer is B

The B-S model assumes:

The price of the underlying asset moves in a continuous fashion.

Interest rates are known and constant.

Variance of returns is constant.

Perfect liquidity and transaction capabilities

Thus, 'B' is the correct answer.

Reference: Options, Futures, and Other Derivatives, Hull, 2006.

14. Testing the fitness of the operational loss severity and frequency distributions to the data is fundamental. Which of the following is NOT a goodness-of-fitness test for severity distributions?

A. Kolmogorov-Smirnov

B. Anderson-Darling

C. Macaulay

D. Cramer-Von Mises

Correct answer is C

Macaulay duration (choice C) is a measure of interest rate sensitivity.  It is not a goodness-of-fitness test for severity distributions.

15. Suppose the face value of a three-year option-free bond is USD 1,000 and the annual coupon is 10%. The current yield to maturity is 5%. What is the Modified Duration of this bond?

A. 2.62

B. 2.85

C. 3.00

D. 2.75

Correct answer is A

Given the annual coupon is 10% and the current yield to maturity is 5%, the price of the bond is given by:

P = $100 * (1/1.05) + $100 * (1/1.05^2) + $1100 * (1/1.05^3) = $1136.16

and the duration is:

D = 1 * (100/1136.16) + 2 * (100/1136.16) + 3 * (1100/1136.16) = 2.75

The, modified duration is D/(1 + yield), or 2.75 / (1.05) = 2.62.

Reference: Fixed Income Securities, Tuckman, 2002.