Question

Suppose ABC Corporation has an obligation to pay $70,000 and $60,000 at the end of 4 years and 9 years respectively. In order to meet this obligation, it plans to invest money by selecting from the following three bonds:

	Coupon Rate	Maturity (years)	Yield
Bond 1	4%	2	7%
Bond 2	5%	4	7%
Bond 3	8%	10	7%

All bonds have the same face value $1000. Assume that the annual rate of interest to be used in all calculations is 7%. Consider semi-annual compounding.

(Keep your answers to 2 decimal places, e.g. xxx.12.)

(a) Find the present value and duration of the obligation.

     Obligation price: ________            Obligation duration: __________

(b) Find the price for each of these bonds.

     Bond 1: ________          Bond 2: ________         Bond 3: ________

(c) Determine Macaulay durations D1, D2, and D3 of these three bonds, respectively. (Keep 2 decimal places.)

     D1: ________                D2: ________               D3: ________

(d) Can the Corporation choose bonds 1 and 2 to construct its portfolio? Justify your answer.

(e) Suppose the Corporation decides to use bonds 2 and 3. Denote by V2 and V3 to be the amounts of money to be invested in the two bonds, respectively. To get an immunized portfolio, write down appropriate equations in V2 and V3 first, and solve for V2 and V3.

      V2: ________             V3: ________

Answer 1

Please refer to below spreadsheet for calculation and answer of (a to d). Cell reference also provided.

Cell reference -

e.

To immunized the portfolio we should invest in Bond-2 and Bond-3 in such a way that the average duration of this Bond Portfolio is equals to the average duration of obligation i.e 5.90 years.

Firstly, we need to calculate Portfolio weight to make its duration 5.90 years

where,

w1 = weight of Bond-2

w2 = weight of Bond-3

D2 = Duration of Bond-2 i.e 3.66

D3 = Duration of Bond-3 i.e 7.18

We Know,

w1+w2 =1

w2 = (1-w1)

Thus,

Amount invested in Bond-2 (V2) = PV of Obligation*w1

= 86,038.69*0.36

= $30,973.93

Amount invested in Bond-3 (V3) = PV of Obligation*w2

= 86,038.69*0.64

= $55,064.76

Hope this will help, please do comment if you need any further explanation. Your feedback would be appreciated.