Question

The cash prices of six-month and one-year Treasury bills are 95.0 and 90.0, respectively. A 1.5-year bond that will pay coupons of $5 every six months currently sells for $94. A two-year bond that will pay coupons of $6 every six months currently sells for $97.

Assume the principal of the bond is $100. 4 Calculate the six-month, one-year, 1.5-year, and two-year zero rates.

Answer 1

Current price = Princiapal value / ( 1+ spot rate )

Six month Treasury bill

95 = 100 / ( 1 + r0.5 )

r0.5 = 100 / 95 - 1 = 5.26% for 6 months

0ne year Trasury bill

90 = 100 / ( 1+ r1)

r 1 = 100 / 90 - 1 = 11.11%

1.5 year coupon bond

Price of bond = Coupon / ( 1+ r0.5 ) + coupon after 1 year / ( 1 + r1) + coupon for 1.5 yr / ( 1+ r1.5) + Principal / (1+r1.5)

94 = 5 / 1.0526 + 5 / 1.1111 + 105 / ( 1 + r1.5)

94 - 4.75 - 4.50= 105 / ( 1 + r1.5)

r1.5 = 105 / 84.75

r1.5 = 23.89%

2 year coupon bond

97 = 6 /1.0526 + 6 /1.1111 + 6 /1.2389 + 106 / ( 1 + r2)

97 - 5.70 - 5.4 - 4.84 = 106 / ( 1+r2)

r2 = 106/81.06 = 23.37%

Time period	Zero rates
0.5	5.26
1	11.11
1.5	23.89
2	23.37