代写FINM7405 Financial Risk Management Tutorial 3 Questions代做留学生SQL语言程序

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FINM7405

Financial Risk Management

Tutorial 3 Questions

Note: Unless otherwise stated, assume in all of the questions below that for each bond, coupon is paid twice a year, interest rate is compounded semi-annually and the face value is $100.

Question 1

‘Zero coupon bonds are also known as discount bonds. ’ Do you agree with this statement? Why or why not?

Question 2

‘A 10% coupon, 2-year maturity bond is a discount bond. ’

Comment on whether the above statement is true, false or uncertain. Justify your answer.

Question 3

You bought a 2-year maturity, zero-coupon bond 2 months ago when the bond’s market yield was 8% p.a. compounded semi-annually. Will you obtain a gain or a loss if you sell the bond today and the current market yield of the bond increases to 9% p.a.?

a) Justify your answer without doing any calculations.

b) Now, calculate the gain/loss. Assume a face value of $100

Question 4

95 days ago, you bought a 180-day maturity BAB when the bill quoted price was $95.10. Earlier today, you manage to convince the bank to repurchase the BAB from you; the current bill quoted price is $96.50.

Without doing any calculations, will you obtain a gain or a loss if the bank agrees to repurchase the bill from you today? Justify your answer without doing any calculations.

Question 5

a) Go back to Question 4. Someone argues that you will obtain a gain equals to the quoted price difference of $96.50-95.10 = $1.40 per bill when you sell the bill back to the bank today. Do you agree with this calculation? Justify your answer.

b) Now, calculate the gain/loss for part (a). Assume a face value of $100,000 per bill.

Question 6

A 5% coupon-paying bond has a yield to maturity of 6% p.a. Calculate the bond’s clean price, accrued interest and dirty price under the following scenarios :

a) The bond still has 19 months to maturity

b) The bond still has 22 months to maturity

Question 7

A bond currently trades at $104, has a yield of 7% p.a. and a duration of 9. If the yield decreases to 6.6% p.a., approximate the new bond price using duration.

Question 8

A step-up bond still has 2 years to maturity. The annual coupon rate for the immediate next two coupons is 6% p.a. and the annual coupon rate for the final two coupons is 8% p.a.

i. If the yield is 5% p.a., what is the bond’s fair price ?

ii. Suppose the bond is trading in the market at $100. Construct a strategy to arbitrage from this situation.

iii. Ignore part (ii). Suppose now the bond is trading in the market at $110. Construct a strategy to arbitrage from this situation.

Question 9

A step-down bond still has 2 years to maturity. The annual coupon rate for the immediate next two coupons is 6% p.a. and the annual coupon rate for the final two coupons is 4% p.a. The following table shows some relevant spot rates :

Year	Spot rate
0.5	5% p.a.
1.0	5% p.a.
1.5	5.2% p.a.
2.0	5.5% p.a.

i. Calculate the fair price of the bond using the relevant spot rates shown in the table above.

ii. Compute the bond’s yield to maturity. You may want to use the Excel’s RATE function to obtain the YTM.

Question 10

A 5% p.a. coupon-paying bond has 3 years to maturity. Compute the bond values for the following scenarios:

i. Yield to maturity is 4% p.a.

ii. Yield to maturity is 5% p.a.

iii. Yield to maturity is 6% p.a.

Question 11

A 5% p.a. coupon-paying bond has a yield to maturity of 4% pa. Compute the bond values for the following scenarios:

i. The bond has 3 years to maturity

ii. The bond has 2 years to maturity

iii. The bond has 1 year to maturity

iv. The bond has 0 year to maturity.

What can you deduce from your answers above?

Question 12 (Multiple choice question)

Bond A is a 5% coupon bond with a yield of 8% p.a. Bond B is a 7.5% coupon bond with a yield of 6% p.a. The values of both bonds are likely to be … [Select the most likely solution, with no calculation is required to answer this question.]

a) $100 for A and $100 for B

b) $74 for A and $100 for B

c) $74 for A and $117 for B

d) $117 for A and $74 for B

e) $117 for A and $117 for B

Question 13 (Multiple choice question)

A 8% p.a. coupon-paying bond has a yield to maturity of 8% pa. and 20 years to maturity. The yield suddenly drops from 8% to 7.5%. As a result of the drop, the bond’s price will …

a) Increase

b) Stay the same

c) Decrease

Question 14 (Multiple choice question)

An advantage of the duration approach over the full valuation approach is …

a) its superior accuracy for nonparallel shifts in the yield curve.

b) it is not based on yield to maturity, which is a summary measure.

c) it saves considerable time when working with portfolios of bonds.

Question 15 (Multiple choice question)

A two-year spot rate of 8% is most likely the …

a) yield to maturity on a coupon-paying bond maturing at the end of year 4.

b) coupon rate in Year 2 on a coupon-paying bond maturing at the end of year 4.

c) yield to maturity on a zero-coupon bond maturing at the end of year 2.

Question 16 (Multiple choice question)

A bond matures in 10 years with a coupon of 4.5% pa. Its yield is 5.83% p.a. and it has a modified duration of 7.81. If the yield of the bond declines to 5.58%, the approximate percentage price change for the bond is closest to:

a) 1.95%

b) 3.91%.

c) 0.98%.

d) 1.20%

Question 17 (Multiple choice question)

Consider two bonds that are identical except for their coupon rates. The bond that will have the highest interest rate risk most likely has the:

a) highest coupon rate.

b) coupon rate closest to its market yield.

c) lowest coupon rate.

Question 18

Consider the table below:

Bond	Price	Coupon rate	Yield
A	90	6%	9%
B	95	9%	8%
C	110	8%	6%
D	105	0%	5%
E	108	7%	9%
F	100	6%	6%

Without doing any calculations, select bonds that are incorrectly priced and explain why.

Question 19

Suppose you were an asset manager, and you invested your fund in one bond A and one bond B. The details of the respective bonds are given in the table below:

	Bond A	Bond B
Coupon rate	6%	7%
Yield to maturity	4%	5%
Years to maturity	2 yrs	3 yrs

What is the impact of a one basis point parallel shift (increase) of the term structure on the value of your portfolio?

Question 20

Bond	Description
(a)	10% $100 bond with 10 years to maturity and yield to maturity of 12% p.a.
(b)	10% $100 bond with 5 years to maturity and yield to maturity of 12% p.a.
(c)	10% $100 bond with 10 years to maturity and yield to maturity of 8% p.a.
(d)	5% $100 bond with 10 years to maturity and yield to maturity of 12% p.a.
(e)	$100 zero-coupon bond with 10 years to maturity and yield to maturity of 12% p.a.

Use the table above to answer the following questions:

i. Explain why bond (a) is priced at a discount.

ii. Explain why bond (b) is priced higher than bond (a).

iii. Explain why bond (c) is more attractive than bond (a).

iv. Explain why bond (d) is priced less than bond (a).

v. Without performing any calculations, which of the bonds listed in the above table is likely to be the most sensitive to interest rate changes? The least sensitive? Explain why.

vi. Estimate the DV01 for bond (b). [In the exam, if the question requires you to calculate the bond’s duration, then, the maturity of the bond is very unlikely to be more than 3 years.]

vii. Estimate (based on DV01) the impact of a 50 basis points increase in the yield to maturity on the price of a portfolio comprising of 200 bond (b).

viii. Estimate (based on the full valuation method) the impact of a 50 basis points increase in the

yield to maturity on the price of a portfolio comprising of 200 bond (b).

ix. Calculate the duration for bond (e). Note that “duration” means modified duration.

Question 21

The table below shows the abbreviated balance sheet of The Gap Bank. Calculate the weighted duration of both the bank’s assets and liabilities. What exposure if any does the bank have to a movement in interest rates?

The Gap Bank

Current Duration Economic (years) Value ($M)
Assets
Securities:
Liquid	150	0.5
Investments	100	3.5
Loans:
Floating	400	0
Fixed-rate	350	2
Total Assets	1000
Liabilities and net worth
Transaction deposits	400	0
CDs and other time deposits
Short-term	350	0.4
Long-term	150	2.5
Net worth	100
Total liabilities and net worth	1000

(Adapted from Hogan et al, ‘Management of Financial Institutions’, Wiley)

Question 22

(a) Calculate the modified duration of an 8% p.a. coupon bond that matures in 4 years if the bond’s YTM = 10% p.a.. [In the exam, if the question requires you to calculate the bond’s duration, then, the maturity of the bond is very unlikely to be more than 3 years.]

(b) Explain why modified duration is a better measure than maturity when calculating the bond’s sensitivity to changes in interest rates.

(d) Assuming the bond’s YTM decreases from 10% p.a. to 9.90% p.a., what is the bond’s price change under the ‘full valuation’ approach?

(e) How good is your approximation (derived in part (c)) compared to the price change estimated in part (d)?

(f) Going back to part (a). Would the modified duration increase or decrease if the coupon of the bond were 4%, not 8% (no calculation is required for this question).

(g) Going back to part (a). Would the modified duration increase or decrease if the maturity of the bond were 2 years, not 4 years (no calculation is required for this question).

Question 23

You expect interest rates to decline over the next few months. Given your interest rate outlook, would you prefer a long duration or a short duration bond portfolio? Justify your answer.

Question 24

This question illustrates the upward sloping yield curve under the pure expectations theory. Consider the followings:

• The current yield for 1-year bond is 5% p.a. compounded annually

• The market expects the future 1-year short-term yield (i.e., the forward rate between year 1 and year 2) is 6% p.a. compounded annually.

What is the 2-year long-term bond yield?

Question 25

This question illustrates the downward sloping yield curve under the pure expectations theory. Consider the followings:

• The current yield for 1-year bond is 5% p.a. compounded annually

• The market expects the future 1-year short-term yield (i.e., the forward rate between year 1 and year 2) is 4% p.a. compounded annually.

What is the 2-year long-term bond yield?

Question 26

This question illustrates the flat yield curve under the pure expectations theory. Consider the followings:

• The current yield for 1-year bond is 5% p.a. compounded annually

• The market expects the future 1-year short-term yield (i.e., the forward rate between year 1 and year 2) is remains at 5% p.a. compounded annually.

What is the 2-year long-term bond yield?

Question 27

The following table shows some spot rates :

Year	Spot rate
1	10% p.a.
2	11% p.a.
3	12% p.a.

For simplicity, assume all interest rates (including spot rates and forward rates) are compounded annually.

Based on the table above, what is

i. the 1-year forward rate between year 1 and year 2?

ii. the 2-year forward rate between year 1 and year 3?