Question

Suppose ABC Corporation has an obligation to pay $10,000 and $40,000 at the end of 5 years and 7 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%	3	6%
Bond 2	5%	6	6%
Bond 3	7%	10	6%

All bonds have the same face value $1000. Assume that the annual rate of interest to be used in all calculations is 6%. 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. (No need to key in 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:

I have no idea how to do (e).
My answers:
a) 33885.65, 6.56
b) 945.83, 950.23, 1074.39

c) 1.71, 3.07, 4.76

Please help! Thanks!

Answer 1

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

Cell reference -

e.

For immunization, the duration of Bond Portfolio consisting Bond-2 and Bond-3 should be equal to Duration of obligation i.e 6.56 years.

We can express Bond Portfolio duration in following manner-

where,

Dp = Duration of Portfolio i.e 6.56

W2 = Weight of Bond-2 in Portfolio

W3 = Weight of Bond-3 in Portfolio

W3 = (1-W2)

Putting the values

and,

Amount to be Invested in Bond-2 (V2)

Amount to be Invested in Bond-3 (V3)

Note-

If you need direct equation for calculation V2 and V3, please refer below

Where,

Dp = Duration of obligation(Portfolio)

D2 = Duration of Bond-2

D3 = Duration of Bond-3

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