Assume that the yields to maturity for an 1-year 10% coupon bond and an 2-year 1
ID: 2813100 • Letter: A
Question
Assume that the yields to maturity for an 1-year 10% coupon bond and an 2-year 13% coupon bond are 12% and 15%, respectively. Both bonds have face values of $1,000. (Assume that the coupon payment is made annually.) (a) Calculate the price for each of the bonds. (Keep 2 decimal places, e.g. xx.12) 1-year bond: 2-year bond: (b) Calculate the 1-year and 2-year spot rates. (Keep your answer in decimal format 4 decimal places, eg. 01234 Do not give in percent format eg. 12.34%) 1-year spot rate s1 2-year spot rate s2 (a) Calculate the quasi-modified duration for each of the bonds. (Keep 2 decimal places, e.g. x.12) 1-year bond: 2-year bond:Explanation / Answer
(a) 1 year bond
Coupon C = 100
Yield to maturity, r = 12% = 0.12
Price1 = (1100/1.12)
= 982.14
2 year bond
Coupon = 130
YTM = 15% = 0.15
Price2= (130/1.15 ) + (1130/1.152)
= 113.043 + 854.442
= 967.49
(b) 1 year spot rate S1 = YTM of one year bond = 0.1200
2 year spot rate can be calculated using price of 2 year bond. If spot rates are applied to the cash flows of the bond each year , the present value should give the same price as given in (a)
That is;
967.49 = 130/(1+S1) + 1130/(1+S2)2
967.49 = 130/1.12 + 1130/(1+S2)2
(1+S2)2 = 1.3272
S2 = 0.1520
(c) Quasi modified duration is the duration using spot rates
Bond 1, Quasi modified duration is = 1.00
Bond 2,
Quasi modified duration = 1/967.49 [ (1* 130 / 1.12) + (2 * 1130 / 1.1522)]
=1/967.49 [ 116.07 + 1702.96]
= 1.88