Question

A recent edition of The Wall Street Journal reported interest rates of 2.25 percent, 2.60 percent, 2.98 percent, and 3.25 percent for three-year, four-year, five-year, and six-year Treasury note yields, respectively. According to the unbiased expectations theory of the term structure of interest rates, what are the expected one-year rates during years 4, 5, and 6?

Answer 1

r4 = 3.66 %

r5 = 4.51 %

r6 = 4.61 %

Step-by-step explanation:

given data

interest rates = 2.25 %

interest rates = 2.60 %

interest rates = 2.98 %

interest rates = 3.25 %

time = 3 year

time = 4 year

time = 5 year

time = 6 year

to find out

expected one-year rates during years 4, 5, and 6

solution

we will apply here formula of unbiased expectations theory for expected interest rate that is

r =
`((1+R_t)^t)/((1+R_(t-1))^(t-1))-1` ..................................1

here r is expected one yea rate of interest

t is denoted year

and R is reported rate of interest

so put here value for 4 year

r4 =
`((1+R_4)^4)/((1+R_(4-1))^(4-1)) -1`

r4 =
`((1+0.0260_4)^4)/((1+0.0225_(3))^(3))-1`

r4 = 0.0366

r4 = 3.66 %

and now put value for year 5 in equation 1

r5 =
`((1+R_5)^5)/((1+R_(5-1))^(5-1)) -1`

r5 =
`((1+0.0298_5)^5)/((1+0.0260_(4))^(4))-1`

r5 = 0.0451

r5 = 4.51 %

and

now put value for year 6 in equation 1

r6=
`((1+R_6)^6)/((1+R_(6-1))^(6-1)) -1`

r6 =
`((1+0.0325_6)^6)/((1+0.0298_(5))^(5)) -1`

r6 = 0.0461

r6 = 4.61 %