Question

Question 3

a. A 10-year 5% coupon bond has a yield of 8% and a duration of 7.85 years. If the bond yield increases by 60 basis points, what is the percentage change in the bond price?

b. Alpha Insurance Company is obligated to make payments of $2 million, $3 million, and $4 million at the end of the next three years, respectively. The market interest rate is 8% per annum.

i. Determine the duration of the company’s payment obligations.

ii. Suppose the company’s payment obligations are fully funded and immunized using both 6-month zero coupon bonds and perpetuities. Determine how much of each of these bonds the company will hold in the portfolio.

I want to ask B2 ii

Answer 1

Answer to Qs. 3a

Yield (Y) = 8%

Change in Yield = 0.60%

Duration (D) = 7.85 yrs

P = Bond Price

% change in bond price = -D x Change in (1+Y)

                                                                (1+Y)                    

= -7.85 x 0.60%

                1.08

= - 4.36%

Due to increase in yield by 60 basis points, bond price will decrease by 4.36%

Answer to Qs. 3b (i)

Interest rate = 8% p.a.

Yrs (1)	Payment (2)	Discount factor @ 8% (3)	P.Value of Pmt di (4=2 x 3)	Weight of Payment (5)	Duration (1 x 5)
1	$ 2 mn	0.9259	$ 1.85 mn	0.2437	0.2437
2	$ 3 mn	0.8573	$ 2.57 mn	0.3384	0.6769
3	$ 4 mn	0.7938	$ 3.18 mn	0.4179	1.2536
TOTAL			$ 7.60 mn	1.000	2.1741

So, duration is 2.1741 yrs.

Answer to Qs. 3b (ii)

Let x = weight of zeroes

1 – x = weight of perpetuities

1x + (1-x) (1.04/ 0.04) = 2.1741

x = 0.9530

Place $7.6 mn x 0.9530 = $7.24 mn in zeroes and rest in perpetuities.