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[ 2009 FRM ] Long Practice Exam 1 Q16-20

 

16. All other things being equal, which of the following would you expect to increase the

yield-to-maturity (YTM) of a corporate bond ?

I. An increase in the risk-free interest rate

II. An increase in the company's business risk

III. An increase in the company's leverage ratio

A. III only

B. I and II only

C. I and III only

D. I, II and III

 

17. Which one of the following statements is incorrect regarding the properties of volatility smiles?

A. One possible reason for the smile in equity options is that people are concerned about stock market crashes.

B. Referring to the volatility smile of foreign currency options, implied volatility of at-the-money options is relatively low and it becomes higher for the deep in-the-money options and deep out-of-the-money options.

C. A volatility smile in foreign currency options exists because traders think that the lognormal distribution underestimates the likelihood of an extreme exchange rate movement.

D. The implied volatility of equity options increases as the strike price increases.

 

18. Consider a 2-year, 6% semi-annual coupon bond currently yielding 5.2% on a bond equivalent basis. If the Macaulay Duration of the bond is 1.92 years, its Modified Duration is closest to:

A. 1.97 years

B. 1.78 years

C. 1.87 years

D. 2.04 years

 

19. Which of the following divisions of a large multi-national bank would typically have the highest market risk?

A. Investment banking

B. Treasury management

C. Private banking

D. Retail brokerage

 

 

20.

l       The two-year risk-free rate in the United Kingdom is 8% per annum, continuously   compounded

l       The two-year risk-free rate in France is 5% per annum, continuously compounded

l       The current French Franc to the GBP currency exchange rate is that one unit of   GBP currency costs 0.75 units of French Franc's

If the observed two-year forward price of one unit of the GBP is 0.850 units of the French Franc, what is your strategy to make an arbitrage profit?

A. Borrow GBP, buy French Francs and enter a short forward contract on French Francs.

B. Borrow GBP, buy French Francs, and enter a short forward contract on GBP.

C. Borrow French Francs, buy GBP, and enter a short forward contract on French Francs.

D. Borrow French Francs, buy GBP, and enter a short forward contract on GBP.

 

16. All other things being equal, which of the following would you expect to increase the

yield-to-maturity (YTM) of a corporate bond ?

I. An increase in the risk-free interest rate

II. An increase in the company's business risk

III. An increase in the company's leverage ratio

A. III only

B. I and II only

C. I and III only

D. I, II and III

Correct answer is D

D is correct. As the risk-free rate increases, the yield on a corporate bond would increase.  Similarly, as the probability of default increases (as would happen with either an increase in the company's business risk or an increase in its leverage ratio), the yield on that company's bonds would increase.fficeffice" />

Reference:  Bruce Tuckman, Fixed Income Securities, 2nd ed. Chapter 3.

A is incorrect. An increase in the company's leverage ratio is not the only event that would increase the yield-to-maturity of a corporate bond.

B is incorrect. An increase in the risk-free rate and an increase in the company's business risk are not the only events that would increase the yield-to-maturity of a corporate bond.

C is incorrect. An increase in the risk-free rate and an increase in the company's leverage ratio are not the only events that would increase the yield-to-maturity of a corporate bond.

 

17. Which one of the following statements is incorrect regarding the properties of volatility smiles?

A. One possible reason for the smile in equity options is that people are concerned about stock market crashes.

B. Referring to the volatility smile of foreign currency options, implied volatility of at-the-money options is relatively low and it becomes higher for the deep in-the-money options and deep out-of-the-money options.

C. A volatility smile in foreign currency options exists because traders think that the lognormal distribution underestimates the likelihood of an extreme exchange rate movement.

D. The implied volatility of equity options increases as the strike price increases.

Correct answer is D

D is correct. This statement is false. Generally, the implied volatility of equity options decreases as the stock price increases.

Reference:  John Hull, Options, Futures, and Other Derivatives, 6th ed. Chapter 16.

A is incorrect.This statement is true. Particularly since the 1987 crash, market declines have produced more pronounced volatility skews, suggesting that "crashphobia" is one reason for volatility smiles.

B is incorrect. This statement is true. The implied distribution for foreign currency options is more peaked with heavier tails than the assumed lognormal distribution, which means implied volatility increases as the strike price moves away from the exchange rate.

C is incorrect. This statement is true. The implied distribution for foreign currency options is more peaked with heavier tails than the assumed lognormal distribution, which means implied volatility increases as the strike price moves away from the exchange rate.

 

18. Consider a 2-year, 6% semi-annual coupon bond currently yielding 5.2% on a bond equivalent basis. If the Macaulay Duration of the bond is 1.92 years, its Modified Duration is closest to:

A. 1.97 years

B. 1.78 years

C. 1.87 years

D. 2.04 years

Correct answer is C

C is correct. Let m be the compounding frequency.  The modified duration is calculated as follows:

Macaulay Duration  = Modified Duration * (1 + y/m)

1.92 = Mod. Dur. * (1 + 0.052/2) = Mod. Dur. * 1.026

Therefore, Modified Duration = 1.92 / 1.026 = 1.87 years.

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

A is incorrect. This answer incorrectly uses (1 - y/m) in the formula above.

B is incorrect.

D is incorrect. This answer incorrectly uses (1 - y/m) in the formula above, sets y to 0.06 (0.052 is correct) and sets m to 1 (2 is correct).

 

19. Which of the following divisions of a large multi-national bank would typically have the highest market risk?

A. Investment banking

B. Treasury management

C. Private banking

D. Retail brokerage

Correct answer is B

B is correct. Treasury management faces high market risk since any unfavorable market movement is absorbed directly by the company.

Reference:  Anthony Saunders, Financial Institutions Management, 5th ed. Chapter 10.

A is incorrect. Investment banking is primarily exposed to credit risk of default, such as a bad loan.

C is incorrect. Private banking is primarily exposed to operational risk and takes no market risk since it act as agents for investors.

D is incorrect. Retail brokerage is primarily exposed to operational risk and takes no market risk since it act as agents for investors.

 

20.

l       The two-year risk-free rate in the ffice:smarttags" />United Kingdom is 8% per annum, continuously   compounded

l       The two-year risk-free rate in France is 5% per annum, continuously compounded

l       The current French Franc to the GBP currency exchange rate is that one unit of   GBP currency costs 0.75 units of French Franc's

If the observed two-year forward price of one unit of the GBP is 0.850 units of the French Franc, what is your strategy to make an arbitrage profit?

A. Borrow GBP, buy French Francs and enter a short forward contract on French Francs.

B. Borrow GBP, buy French Francs, and enter a short forward contract on GBP.

C. Borrow French Francs, buy GBP, and enter a short forward contract on French Francs.

D. Borrow French Francs, buy GBP, and enter a short forward contract on GBP.

Correct answer is D

D is correct. Borrowing 1 FF means in two years we owe exp(0.05 * 2) FF, which is 1.11 FF.

Converting the FF today gives 1.33 GBP which grows to 1.33 exp(0.08 * 2) GBP in two years. 

Entering a short forward contract on GBP means the 1.33 exp(0.08 * 2) GBP is exchanged for (1.33 exp(0.08 * 2) * 0.85) FF, which is 1.32 FF.  Since 1.11 FF is owed, this strategy guarantees a profit.

Reference:  John Hull, Options, Futures, and Other Derivatives, 6th ed. Chapter 4.

A is incorrect. Borrowing 1 GBP means in two years we owe exp(0.08 * 2) GBP, which is 1.17GBP.

Converting the GBP today gives 0.75 FF which grows to 0.75 exp(0.05 * 2) FF in two years. 

Entering a short forward contract on FF means the 0.75 exp(0.05 * 2) FF is exchanged for (0.75 exp(0.05 * 2) * (1/0.85)) GBP, which is 0.98 GBP.  Since 1.17 GBP is owed, this strategy guarantees a loss.

B is incorrect. This strategy does not guarantee a profit.

C is incorrect. This strategy does not guarantee a profit.

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