25503 Investment Analysis Tutorial 课堂作业 代写

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25503 Investment Analysis  Tutorial 课堂作业 代写


Finance Discipline Group

UTS Business School

25503 Investment Analysis

Tutorial 10

1. (a) What is meant by cash matching? Why is this not the most preferable method

for immunization?

(b) What does duration measure?

(c) What does immunization mean?

(d) What is immunization intended to accomplish? What is meant by the term

reimmunization?

(e) Consider a pure discount bond (no coupon payments) with a maturity of 4

years. The current yield-to-maturity is 9%. If the yield suddenly changes to

8.5%, how would the Macaulay duration respond to such a change?

(f) Suppose we have matched the maturity and present value of a single-payment

liability with the same characteristics of a coupon bond. When we make the

match, the yield curve is flat at 7%. Immediately after making the match, the

yield curve shifts to 8% (still flat).

i. What would be the result of such a change?

ii. Was the strategy appropriate to help you achieve an immunized position?

2. Assume you have a liability with three required payments: $3,000 due in 1 year;

$2,000 due in 2 years; and $1,000 due in 3 years.

(a) What is the Macaulay duration of this liability at a 20% (annually com-

pounded) rate of interest?

(b) What about at a 5% (annually compounded) rate of interest?

3. Assume the following characteristics for a particular bond: A face value of $1,000;

annual coupon payments of $60 (the first payment due in 1 year); an internal yield-

to-maturity of 7% (compounded annually); and a three year term.

(a) Compute the Macaulay duration of the bond.

(b) Given your answer above, compute the approximate change in the bond’s value

if the yield fell to 6.5%.

(c) Now compute the actually change in the bond’s value. Comment on the dif-

ference.

4. A 12% coupon paying bond with a face value of $100 and 2 years to maturity has a

yield of 8%. What is its duration? Assume semi-annual coupons and semi-annual

compounding.

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5. Suppose you are faced with a liability requiring the payment of $100,000 exactly two

years from now. The following two semi-annual coupon-paying bonds are available

for investment:

Bond Maturity Coupon Face Value

1 1 year 8% $100

2 3 years 10% $100

The market yield to maturity is a flat 12% per annum, with semi-annual compound-

ing.

(a) What is the duration of the liability, D L , and the duration of the two bonds,

D 1 and D 2 ?

(b) Suppose you want to invest now to meet the liability. How much money do

you need to put aside?

(c) Instead of randomly investing this amount into the two bonds, you decide

to form an immunizing portfolio that allows you to meet the liability even

if interest rates change. How many contracts of Bond 1 and Bond 2 do you

purchase for this portfolio?

(d) Assess the effectiveness of your immunizing portfolio if interest rates suddenly

decrease to 6%. Compare this to what would have happened had you only

invested in Bond 1.

6. You have an obligation to pay $1,000,000 ten years from now, and you would like to

make an investment that will enable you to meet this obligation. The investment

will be a portfolio containing the following two semi-annual coupon-paying bonds:

Bond Maturity Coupon Face Value

1 20 years 9% $100

2 30 years 6% $100

The market yield to maturity is a flat 9% per annum, with semi-annual compound-

ing.

(a) What is the duration of the liability and the two bonds: D L , D 1 , and D 2 ?

(Hint: Because the bonds in this question have very long maturities, com-

puting their durations is a lot of work if you do it by hand. So use Excel for

this.)

(b) How many contracts of Bond 1 and Bond 2 are in your immunizing portfolio?

(c) Analyze the effectiveness of your hedge if all yields change to 8% and to 10%,

respectively.

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