21. Which of the following statements about American stock options is false?

A. American options can be exercised at or before maturity.

B. American options are always worth at least as much as European options.

C. American options can easily be valued with Monte Carlo simulation.

D. American options can be easily valued with binomial trees.

22. Which of the following is (are) true regarding the Black-Scholes model?

I. The Black-Scholes model assumes that stock returns are lognormally distributed.

II. The Black-Scholes model assumes that stocks are continuously traded.

III. The Black-Scholes model assumes that the risk-free interest rate is constant and the same for all maturities.

A. I only

B. III only

C. II and III

D. I, II and III

23. A bright quantitative analyst in your risk management department has developed a new risk measure that promises to be applicable to a wide set of risks across your firm. As a first step in your evaluation, you ask the analyst to demonstrate that it is a coherent risk measure. The results are listed below. Which equation shows that it is not a coherent risk measure?

Given:

l            x and y are state-contingent payoffs of two different portfolios

l            p(x) and p(y) are the risk measures of the two portfolios respectively

l            a and b are arbitrary constants (with a > 0)

l            r is the risk-free rate

A. p(x + y) = p(x) + p(y)

B. p(ax) = ap(x)

C. p(x) = p(y) if x = y

D. p(x + b(1 + r)) = p(x) ? b

24. A manager wants to swap a bond for a bond with the same price but higher duration. Which of the following bond characteristics would be associated with a higher duration?

I. A higher coupon rate

II. More frequent coupon payments

III. A longer term to maturity

IV. A lower yield

A. I, II and III

B. II, III and IV

C. III and IV

D. I and II

25. Consider an all-equity firm with equity capitalization of $2 billion. The firm's CFO considers the following three financing strategies:

I. Issue zero-coupon senior debt with principal amount of $1 billion payable in 10 years and purchase insurance for $100 million that will pay losses on the senior debt to investors in excess of $500 million.

II. Issue zero-coupon junior debt with principal amount of $500 million payable in 10 years and issue zero-coupon senior debt with principal amount of $500 million payable in 10 years.

III. Issue zero-coupon senior debt with principal amount of $1 billion payable in 10 years with a put option attached that gives the right to investors to put the debt to the firm at maturity for the principal amount.

Which of these strategies would have the most risky senior debt?

A. Strategy I

B. Strategy II

C. Strategy III

D. Senior debt is equally risky in all three strategies.

21. Which of the following statements about American stock options is false?

A. American options can be exercised at or before maturity.

B. American options are always worth at least as much as European options.

C. American options can easily be valued with ffice:smarttags" />Monte Carlo simulation.

D. American options can be easily valued with binomial trees.

Correct answer is C

C is correct. Since simulation methods cannot account for the possibility of early exercise, Monte Carlo simulation cannot easily value American options.fficeffice" />

Reference:  John Hull, Options, Futures, and Other Derivatives, 6th ed. Chapter 8.

A is incorrect. This statement is true - American options can be exercised at or before maturity.

B is incorrect. This statement is true - since one can hold an American option to maturity (and thereby replicate a European option), an American option is always at least as valuable as a European option.

D is incorrect. This statement is true - binomial trees can be used to value American options.

22. Which of the following is (are) true regarding the Black-Scholes model?

I. The Black-Scholes model assumes that stock returns are lognormally distributed.

II. The Black-Scholes model assumes that stocks are continuously traded.

III. The Black-Scholes model assumes that the risk-free interest rate is constant and the same for all maturities.

A. I only

B. III only

C. II and III

D. I, II and III

Correct answer is C

The Black-Scholes model does assume that stocks are continuously traded and that the risk-free interest rate is constant and the same for all maturities.

Further, the Black-Scholes model assumes that stock returns are normally distributed; stock prices are assumed to be lognormally distributed.

Reference:  John Hull, Options, Futures, and Other Derivatives, 6th ed. Chapter 13.

A is incorrect. The Black-Scholes model assumes that stock prices are lognormally distributed, and stock returns are normally distributed.

B is incorrect. The Black-Scholes model does assume that the risk-free interest rate is constant and the same for all maturities, but this is not the only true statement

D is incorrect. The Black-Scholes model assumes that stock prices are lognormally distributed, and stock returns are normally distributed.

23. A bright quantitative analyst in your risk management department has developed a new risk measure that promises to be applicable to a wide set of risks across your firm. As a first step in your evaluation, you ask the analyst to demonstrate that it is a coherent risk measure. The results are listed below. Which equation shows that it is not a coherent risk measure?

Given:

l            x and y are state-contingent payoffs of two different portfolios

l            p(x) and p(y) are the risk measures of the two portfolios respectively

l            a and b are arbitrary constants (with a > 0)

l            r is the risk-free rate

A. p(x + y) = p(x) + p(y)

B. p(ax) = ap(x)

C. p(x) = p(y) if x = y

D. p(x + b(1 + r)) = p(x) ? b

Correct answer is C

C is correct. This demonstrates that the risk measure does not satisfies the monotonicity property.  Monoticity property requires that:  p(x) = p(y).

Reference:  Philippe Jorion, Value At Risk, 3rd ed.  Chapter 5.

A is incorrect. This demonstrates that the risk measure satisfies the subadditivity property.

B is incorrect. This demonstrates that the risk measure satisfies the homogeneity property.

D is incorrect. This demonstrates that the risk measure satisfies the risk-free condition property.

24. A manager wants to swap a bond for a bond with the same price but higher duration. Which of the following bond characteristics would be associated with a higher duration?

I. A higher coupon rate

II. More frequent coupon payments

III. A longer term to maturity

IV. A lower yield

A. I, II and III

B. II, III and IV

C. III and IV

D. I and II

Correct answer is C

A higher coupon rate and more frequent coupon payments each decrease a bond's duration, so I and II would not be associated with higher duration.  Longer term to maturity and lower yield increase the bond's duration, given all other parameters remain the same.

Reference: Bruce Tuckman, Fixed Income Securities, 2nd ed. Chapter 6.

25. Consider an all-equity firm with equity capitalization of $2 billion. The firm's CFO considers the following three financing strategies:

I. Issue zero-coupon senior debt with principal amount of $1 billion payable in 10 years and purchase insurance for $100 million that will pay losses on the senior debt to investors in excess of $500 million.

II. Issue zero-coupon junior debt with principal amount of $500 million payable in 10 years and issue zero-coupon senior debt with principal amount of $500 million payable in 10 years.

III. Issue zero-coupon senior debt with principal amount of $1 billion payable in 10 years with a put option attached that gives the right to investors to put the debt to the firm at maturity for the principal amount.

Which of these strategies would have the most risky senior debt?

A. Strategy I

B. Strategy II

C. Strategy III

D. Senior debt is equally risky in all three strategies.

Correct answer is C

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