Question

Use the following information to answer questions 13 through 17. Sawyer, Selbo and Shaw (SSS), an investment management firm, has compiled the following information concerning Treasury securities: Maturity Coupon Y-T-M Price 0.5 Years 0 8.0% $ 96.15 1.0 Year 0 8.3% $ 92.19 1.5 Years 8.5% 8.9% $ 99.45 2.0 Years 9.0% 9.2% $ 99.64 2.5 Years 11.0% 9.4% $103.49 3.0 Years 9.5% 9.7% $ 99.49 3.5 Years 10.0% 10.0% $100.00 4.0 Years 10.0% 10.4% $ 98.72 4.5 Years 11.5% 10.6% $103.16 5.0 Years 8.75% 10.8% $ 92.24

13. What is the one-year T-bill spot rate? (1 point)

14. What is the 1.5-year T-note theoretical spot rate? (4 points)

15. What is the two-year theoretical spot rate? (4 points)

16. What is the one-year implied forward rate six months from now? (3 points)

17. What is the one-year implied forward rate one-year from now? (3 points)

Answer 1

Ans 13) one year T - bill spot rate will be the same as YTM which is equal to 8.3%

Ans 14) T-note price = coupon/(1 + YTM at 6 month)^1 + coupon/(1 + YTM at 1 year)^2 + (face value + coupon)/(1 + YTM at 1.5 year)^3

we need to find YTM at 1.5 year

99.45 = 4.25/(1.04) + 4.25/(1.0415)^2 + 104.25/(1 + YTM)^3

YTM = 8.93%

Theoretical spot rate = 8.93%

Ans 15) T-note price = coupon/(1 + YTM at 6 month)^1 + coupon/(1 + YTM at 1 year)^2 + (coupon)/(1 + YTM at 1.5 year)^3 + (face value + coupon)/(1 + YTM at 2 year)^4

99.64 = 4.5/(1.04) + 4.5/(1.0415)^2 + 4.5/(1.0445)^3 + 104.5/(1 + YTM)^4

YTM = 9.25%

Ans 16) 1 year forward rate 6 month from now = (root(1 + YTM at year1.5/2)^3 /(1 + YTM at year 0.5) - 1) * 2

= (root((1.0445)^3/(1.04)) - 1) *2

= 9.35%

Ans 17) 1 year forward rate 1 year from now = (root(1 + YTM at year 2/2)^4 /(1 + YTM at year 1)^2 - 1) * 2

= (root((1.046)^4/(1.0415)^2) - 1) *2

= 10.1%