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21. Correct answer is B
22. Correct answer is B
The portfolio with 100% Stock P has a variance of return equal to 100 and a standard deviation of return equal to 10.ffice ffice" />
Moving the portfolio to 75% Stock P and 25% Stock Q changes the variance to:
Variance = (0.75)2 (100) + (0.25)2 (225) + 2(0.75)(0.25)(53.2) = 56.25 + 14.06 + 19.95 = 90.26
Standard deviation = (90.26)0.5 = 9.50
Hence, the percentage of risk reduced = (10 ? 9.5)/10 = 5.0%.
23. You are given the following information about an interest rate swap:
l 2-year Term
l Semi-annual payment
l Fixed Rate = 6 %
l Floating Rate = LIBOR + 50 basis points.
l Notional principal USD 10 million.
Calculate the net coupon exchange for the first period if LIBOR is 5% at the beginning of the period and 5.5% at the end of the period.
A. Fixed rate payer pays USD 0.
B. Fixed rate payer pays USD 25,000.
C. Fixed rate payer pays USD 50,000.
D. Fixed rate payer receives USD 25,000
Correct answer is B
A is incorrect. The candidate incorrectly uses the LIBOR rate at the end of the period.
B is correct. Fixed rate payer pays USD 25,000. See below for details.
C is incorrect. The candidate forgets to add the 50 basis points to the beginning LIBOR rate.
D is incorrect. The candidate is confused about the cash flow direction. A net positive payment is paid by the fixed rate payer, not receiving.
Computational Details for Numerical Answer:
Fixed rate payer pays 6%, therefore (0.06 / 2) x 10 million = USD 300,000.
Interest rate swaps have payments in arrears. Floating rate payer pays LIBOR rate at the beginning of period + 0.50%, i.e. 5 % + 0.50% = 5.5 %.
Therefore the floating rate payment = (0.055 / 2) x 10 million = USD 275,000.
The net payment of USD 25,000 is paid by the fixed rate payer.
Reference: Options, Futures, and Other Derivatives, by John Hull
24. Which of the following statements is false?
A. European-styled call and put options are most affected by changes in vega when they are at-the-money.
B. The delta of a European-styled put option on an underlying stock would move towards zero as the price of the underlying stock rises.
C. The gamma of an at-the-money European-styled option tends to increase as the remaining maturity of the option decreases.
D. Compared to an at-the-money European-styled call option, an out-of-the money European option with the same strike price and remaining maturity would have a greater negative value for theta.
Correct answer is D
A is true. Vega is highest for at-the-money options.
B is true. The delta for a European put option is negative, and the likelihood of exercise decreases, i.e., delta moves towards zero, as the price of the underlying stock increases.
C is true. Gamma increases as the time to maturity decreases. As time to maturity approaches zero, gamma approaches infinity.
D is false and therefore the correct answer. Theta is large and negative for an at-the-money European-styled option, whilst theta is close to zero when the price for the underlying stock is very low. Therefore the theta for an out-of-the-money European-styled call option would have a lower negative value compared to that of an at-the-money European-styled call option.
Reference: John Hull, Options Futures and Other Derivatives, 6th edition (ffice:smarttags" />New York: Prentice Hall, 2006), Chapter 15.
25. Bank Omega's foreign currency trading desk is composed of 2 dealers: dealer A, who holds a long position of 10 million CHF against the USD, and dealer B, who holds a long position of 10 million SGD against the USD. The current spot rates for USD/CHF and USD/SGD are 1.2350 and 1.5905 respectively. Using the variance/covariance approach, you worked out the 1 day, 95% VAR of dealer A to be USD77,632 and that of dealer B to be USD 27,911. If the correlation coefficient between the SGD and CHF is +0.602 and assuming that these are the only trading exposures for dealer A and dealer B, what would you report as the 1 day, 95% VAR of Bank Omega's foreign currency trading desk using the variance/covariance approach?
A. USD 97,027
B. USD 105,543
C. USD 113,932
D. Cannot be determined due to insufficient data
Correct answer is A
A. Note that the question asks for the VAR number to be expressed in USD. Therefore, the first step is to convert the foreign currency positions in terms of USD.
Dealer A's position in USD: 10,000,000/1.2350 = USD 8,097,166
Dealer B's position in USD: 10,000,000/1.5905 = USD 6,287,331
Given that the VAR of dealer A is USD 77,632, we first work the daily volatility for the USD/CHF, denoted here by sCHF .
By definition we get 8,097,166 x 1.645 x sCHF = 77,632
Therefore, sCHF = 77,632/(8,097,166 x 1.645) = 0.005828 or 0.5828%
Similarly, the daily volatility for the USD/SGD, denoted here by sSGD is worked out as follows: sSGD = 27,911/(6,287,331 x 1.645) = 0.002699 or 0.2699%
By definition, the standard deviation of the change in the portfolio which comprises of both the currency pairs over a 1-day period is given by:
[(0.005828 x 8,097,166)2 + (0.002699 x 6,287,331)2 + 2 x 0.602 x (0.005828 x 8,097,166) x (0.002699 x 6,287,331)]0.5 = [(46,963.56)2 + (16,975)2 + 959,881,479.22]0.5 = [3,453,608,072.09]0.5 = 58,983
Therefore, The 1-day, 95% VAR is 1.645 x 58,983 = USD97,027
C is incorrect. This would overstate the VAR. Summing up the VARs would be correct only if the correlation coefficient is 1. Here the correlation coefficient is 0.602
B is incorrect. By inspection, this can be eliminated straight away as the VAR of the combined positions cannot exceed the sum of the VAR of the individual positions.
D is incorrect. Given the VARs of the individual positions, one can obtain the daily volatilities of the USD/CHF and the USD/SGD. The correlation of the SGD and CHF is also given. Therefore, there is sufficient data to work out the standard deviation of the change of the combined positions and hence arrive at VAR.
Note: the volatilities and correlation coefficients for this question are actual numbers as at 22 June 06, extracted from Bloomberg's database.
Reference: Saunders & Cornet, Financial Institutions Management, 4th ed. (New York: McGraw-Hill, 2003), Chapter 10. | 
发表于 2009-6-13 14:47
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