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下列哪個陳述關(guān)于票面利率結(jié)構(gòu)是假的?
1. Which of the following statements concerning coupon rate structures is FALSE?
A. A. Zero-coupon bonds have only one cash inflow at maturity.
B. Accrual bonds, like zero-coupon bonds, always sell at a discount to face value.
C. Accrual bonds have only one cash inflow at maturity.
D. Step-up notes have coupon rates that increase over time at a pre-specified rate.
2. Consider the following 3-year currency swap, which involves exchanging annual interest of 2.75% on 10 million US dollars for 3.75% on 15 million Canadian dollars. The CAD/USD spot rate is 1.52. The term structure is flat in both countries. Calculate the value of the swap in USD if interest rates in Canada are 5% and in the United States are 4%. Assume continuous compounding. Round to the nearest dollar.
A. $152,000
B. $145,693
C. $131,967
D. $127,818
3. A 3-year, 8 percent semiannual coupon bond with $100 par value currently yields 8.50 percent. What would be the price of the bond?
A. $95.49.
B. $99.24.
C. $98.70.
D. $119.50.
4. Given that the dollar yen volatility is 12 percent and dollar peso volatility is 15 percent, and the correlation between dollar yen and dollar peso is 0.25, the best estimate of the yen peso volatility is:
A. 16.7%.
B. 19.2%.
C. 21.4%.
D. 23.1%.
5. Suppose the daily returns of a portfolio and a benchmark portfolio it is replicating are as follows:
Portfolio Return (bps) benchmark Portfolio Return(bps)
Day 1 34 30
Day 2 -89 -87
Day 3 108 102
Day 4 70 70
6. What is the tracking error over the four day period?
A. 3.16 bps
B. 2 bps
C. 10 bps
D. 2.39 bps
Answers:
1. Correct answer：B.
Accrual bonds, unlike zero-coupon bonds, do not always sell at a discount to face value. The interest accrues forward and thus the bonds are likely to sell for more than face value.
2. Correct answer: C
Vswap(USD) = BUSD ?(So ×BGBP) （So = spot rate in USD per GBP）
Bfixed = (PMTf.1year×e?(r×t)) + (PMTf.2year×e?(r×t)) + [(notional +PMTf ,3year)×e?(r× t )]
Step 1.calculate value of USD-denominated bond:
BUSD=275,000e?0.04×1+275,000e?0.04×2+10,275,000e?0.04×3=USD9,631,182 275,000 =10,000,000*2.75%
Step 2.calculate value of CAD-denominated bond
BCAD=565200e-0.05*1+565200e-0.05*2+15565200e-0.05*3=CAD14,438,805
565,200=15,000,000*3.75%
Step 3.calculate value of swap
Vswap(USD) = BUSD ?(So ×BCAD)（So = spot rate in USD per CAD）
=9,631,182-14,438,805/1.52=USD 131,967
3. Correct answer:C
I/Y = 8.50/2 = 4.25; FV = 100; N = 3x2 = 6; PMT = 0.08/2 x 100 = 4; PV = -98.70.
4. Correct answer: A
Here we use the * that: (Vol_A/B)^2 = (Vol_A)^2 + (Vol_B)^2 - 2 x Correlation x (Vol_A) x (Vol_B).
Therefore, yen/peso volatility = (0.12^2 + 0.15^2 - 2 x 0.25 x 0.12 x 0.15)^0.5 = 16.7%.
5. Correct answer: A
A. Correct. Tracking error is the standard deviation of the difference between the return of the managed portfolio and the benchmark portfolio.
tracking error =σep and E [RP - RB] = (4 + (-2) + 6 + 0) / 4 = 2.00 E [(RP - RB)]2 = (16 + 4 + 36 + 0) / 4 = 14.00 So, TE = (14.00 - 4.00)1/2 = 3.16 bps.
B. Incorrect. This solution incorrectly sets the tracking error equal to the average difference between the return of the managed portfolio and the benchmark portfolio. Tracking error is the standard deviation of the difference between the return of the managed portfolio and the benchmark portfolio.
C. Incorrect. This solution incorrectly sets the tracking error equal to the variance of the difference between the return of the managed portfolio and the benchmark portfolio. Tracking error is the standard deviation of the difference between the return of the managed portfolio and the benchmark portfolio.
D. Incorrect. This solution incorrectly sets the tracking error equal to the difference between the standard deviation of the return of the managed portfolio and the standard deviation of the return of the benchmark portfolio. Tracking error is the standard deviation of the difference between the return of the managed portfolio and the benchmark portfolio.
