Question

Suppose you just started at a prestigious fixed-income investment fund. Your supervisor asked you to do a few quick calculations for a bond that the firm might invest in. This bond has the following terms:

• Face value = $1000

• Coupon rate = 8% (coupons paid semi-annually)

• Yield to maturity = 10% (annual rate, compounded semi-annually)

• Time-to-maturity = 7 years

Calculate the price of the bond. Round to six digits after the decimal.

The bond price calculated in part 1.1 is the (flat/full) price

Calculate the modified duration of the bond based on annual yields. (i.e. use the approximation formula with 10% as y, 10.1% as y + ∆y, and 9.9% as y − ∆y.) Round to four digits after the decimal

Calculate the convexity of the bond based on annual yields. (i.e. use the approximation formula with 10% as y, 10.1% as y + ∆y, and 9.9% as y − ∆y.) Round to four digits after the decimal

Answer 1

a)
Face value =	$1,000
Coupon rate = 8% (coupons paid semi-annually)	4.00%
Yield to maturity = 10% (annual rate, compounded semi-annually)	5.00%
Time-to-maturity = 7 years x 2	14
Price of the Bonds	$901.013591
b)
Face value =	$1,000
Coupon rate =	8.00%
Yield to maturity =	10.00%
Time-to-maturity =	14
Payment frequency	2
Basis	0
Settlement Date	1-Jan-20
Maturity Date	1-Jan-27
Modified Macaulay Duration	5.1419

Par Value (M)	$1,000
Coupon Rate (C)	4%
Year to Maturity (T)	14
Yield to Maturity (Y)	5.0%
Period (t)	Coupon Payment (CF)	Discounted (CF)	Weightage = (CF/[P*(1+Y)^2])	Weightage*t*(1+t)/(1+Y)^t
1	$40	$38.10	0.0383	0.07
2	$40	$36.28	0.0365	0.20
3	$40	$34.55	0.0348	0.36
4	$40	$32.91	0.0331	0.55
5	$40	$31.34	0.0316	0.74
6	$40	$29.85	0.0300	0.94
7	$40	$28.43	0.0286	1.14
8	$40	$27.07	0.0273	1.33
9	$40	$25.78	0.0260	1.51
10	$40	$24.56	0.0247	1.67
11	$40	$23.39	0.0235	1.82
12	$40	$22.27	0.0224	1.95
13	$40	$21.21	0.0214	2.06
14	$1,040	$525.27	0.5288	56.08
Bond Price is calculated as
Bond Price (P)	$901.01
Convexity is calculated as
Convexity	70.41