Question

Consider the following three bonds of $1,000 face value. 1 1% Bond Maturity (year) Coupon Rate A 0.5 3.50% B 1.0 | 0.00% IC 1.5 L 4.90% Price 1002.84 957.24 1006.35 Table 03 (a) Describe and calculate the 0.5-year, 1.0-year and 1.5-year spot rates. (10 marks) (6) You form a portfolio by buying three shares of Bond A, five shares of Bond B and four shares of Bond C. Examine the yield to maturity of the portfolio. (10 marks)

Answer 1

The spot rate is simply YTM for these bonds , which will be calculated by use of formula below

$V=\sum_{i=1}^{n}\frac{C_i}{(1+r)^i}+\frac{Maturity\ value}{(1+r)^n}$

Answer A)

Bond	Maturity	Coupon rate	Coupon payment(half yearly)	Value	Spot rate
A	0.5	3.50%	17.5	1002.84	2.92%	RATE(1,17.5,-1002.84,1000)*2
B	1	0.00%	0%	957	4.47%	RATE(1,0,-957.24,1000)
C	1.5	4.90%	24.5	1006.35	4.46%	RATE(3,24.5,-1006.35,1000)*2

Answer b)

Bond	Share	Weight	Yield	W*YTM
A	3	0.25	2.92%	0.73%
B	5	0.416667	4.47%	1.86%
C	4	0.333333	4.46%	1.49%
Total share	12		Return yield	4.08%