Question

You purchase a 10 year bond with an annual fixed coupon rate of 7% and a par value of $1,000, when the yield to maturity on such bonds is 6%. You hold the bond for a year and then sell it. Assume the yield to maturity on the bond falls to 5.5% by the time you sell. What is your holding period return?

Answer 1

Value of Bond = PV of CFs from it.

Price of Bond Today:

Year	CF	PVF @6%	Disc CF
1	$      70.00	0.9434	$      66.04
2	$      70.00	0.8900	$      62.30
3	$      70.00	0.8396	$      58.77
4	$      70.00	0.7921	$      55.45
5	$      70.00	0.7473	$      52.31
6	$      70.00	0.7050	$      49.35
7	$      70.00	0.6651	$      46.55
8	$      70.00	0.6274	$      43.92
9	$      70.00	0.5919	$      41.43
10	$      70.00	0.5584	$      39.09
10	$ 1,000.00	0.5584	$    558.39
Price of Bond	$ 1,073.60

Price after 1 Year:

PV of CFc for remaining years

Year	CF	PVF @5.5%	Disc CF
1	$      70.00	0.9479	$      66.35
2	$      70.00	0.8985	$      62.89
3	$      70.00	0.8516	$      59.61
4	$      70.00	0.8072	$      56.51
5	$      70.00	0.7651	$      53.56
6	$      70.00	0.7252	$      50.77
7	$      70.00	0.6874	$      48.12
8	$      70.00	0.6516	$      45.61
9	$      70.00	0.6176	$      43.23
9	$ 1,000.00	0.6176	$    617.63
Price of Bond	$ 1,104.28

Holding Period return = [ Bond Price after 1 Year - Bond Price Today + Coupon amount ] / Bond Price Today

= [ $ 1104.28 - $ 1073.60 + 70 ] / 1073.60

= $ 100.68 / $ 1073.60

= 0.0938 i.e 9.38%