Question

1. Draw the yield curve of US Treasuries. US Treasuries Yield 3 Month 2.32% 2.46% 3 .37 3.17 3.01 2.88 265 6 Month 12 Month 2 Year 5 Year 2.65% 2.88% 3.01% 3.17% 10 Year 3.37% 30 Year 2.32 1o 3 3 G 1 month month month Year year year Year

Using the yield curve data in the image, calculate the expected future 5-year short rate for five years from now.

Answer 1

Using expectation hypothesis,

(1 + r10)^10 = (1 + r5)^5 x (1 + 5f5)^5

where, r10 - 10-year rate = 3.17%, r5 - 5-year rate = 3.01% and 5f5 - 5-year rate 5 year from now

=> (1 + 3.17%)^10 = (1 + 3.01%)^5 x (1 + 5f5)^5

=> 1.36626 = 1.1598 x (1 + 5f5)^5

=> 5f5 = (1.36626 / 1.1598)^(1/5) - 1 = 3.33%