Question

3. An investor decides to buy USD 10,000,000 of an annual bond with a coupon of 1.75%, with exactly 3 years to maturity and giving a yield to maturity of 1.68%.

(a) Firstly, calculate the price of the bond. Do all your calculations to 2 decimal places. (10%)

(b) Now from this price calculate the Macaulay duration of the bond.

(c) Next, you should calculate the Modified duration and explain what this is telling you.

(d) And finally, calculate the BPV of the bond and explain what this is telling you. Remember for this one the market convention is to quote to 4 decimal places. Maximum word count: 100 words

Answer 1

Solution:

a)Calcultaion of price of bond

Price of bond is the present value of all coupon and redemption or par value.

Annual coupon=$10,000,000*1.75%=$175,000

YTM=1.68% or 0.0168

Price of bond=Coupon/(1+YTM)^n+Coupon+Par value/(1+r)^n

=$175,000/(1+0.0168)^1+$175,000/(1+0.0168)^2+($175,000+$10,000,000)/(1+0.0168)^3

=$172,108.58+$169,264.93+$9678,940.17

=$10,020,313.68

b)Calculation of Macaulay duration of bond

Macaulay duration=PV1/PV*N1+PV2/PV*N2+PVN/PV*N

Where,

N refers to no. of period

PV1,PV2 and PVN refers to present value of cash flows that occur at N1,N2 and N

PV is price of bond

Coupon No.	1	2	3	Price of bond
Present value of cash flows	$172,108.58	$169,264.93	$9678,940.17	$10,020,313.68
PV/Price	0.0172	0.0169	0.9659

Duration of bond=0.0172*1+0.0169*2+0.9659*3

=2.9488 years

c)Modified duration of bond

Modified duration=Macaulay duration/(1+YTM)

=2.9488 years/(1+0.0168)

=2.90 years

d)Calculation of BPV

Price of bond when YTM is 1.68%=$10,020,313.68

Price of bond when YTM decrease by 1basis point i.e 0.01%(1.67%)

=$10023,220.17

Price of bond when YTM Increase by 1 basis point(1.69%)=10017,408.31

BPV=(Aboslut price change with +1bp)-(Absolute price change with -1bp)/2

=($10017,408.31-$10,020,313.68)-($10023,220.17-$10,020,313.68)/2

=$2905.55+2906.49/2

=$2906.02

Basis point value represents the change in the value of an assets due to change in 0.01% change in the yield.It is commonly used to measure the risk in a bond position or a portfolio and can be effectively used while hedging the portfolio.