Question

If you note the following yield curve in The Wall Street Journal, what is the one-year forward rate for the period beginning one year from today, 2f1 according to the unbiased expectations theory? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Maturity Yield One day 2.16 %

One year 2.38

Two years 2.62

Three years 2.73

Answer 1

Future expected rate or Forward rate:

Expectations theory attempts to predict what short-term interest rates will be in the future based on current long-term interest rates. The theory suggests that an investor earns the same interest by investing in two consecutive one-year bond investments versus investing in one two-year bond today.

Particulars	YTM	Values
YTM of 1 Year Bond Now	YTM 1	2.38%
YTM of 2 Year Bond Now	YTM 2	2.62%
YTM of 3 Year Bond Now	YTM 3	2.73%

1 Year after 1 year from Today Rate = [ [ (1 + YTM 2 ) ^ 2 / ( 1 + YTM 1 ) ^ 1 ] ^ ( 1 / 1 ) ] - 1
= [ [ ( 1 + 0.0262 ) ^ 2 / ( 1 + 0.0238 ) ^ 1 ] ^ ( 1 / 1 ) ] - 1
= [ [ ( 1.0262 ) ^ 2 / ( 1.0238 ) ^ 1 ] ^ ( 1 / 1 ) ] - 1
= [ [ 1.0531 / 1.0238 ] ^ ( 1 / 1 ) ] - 1
= [ [ 1.0286 ] ^ ( 1 / 1 ) ] - 1
= [ 1.0286 ] - 1
= 0.0286
= I.e 2.86 %