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

Answer:

r4 = 3.66 %

r5 = 4.51 %

r6 = 4.61 %

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 = $\frac{(1+R_t)^t}{(1+R_{t-1})^{t-1}}-1$     ..................................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 = $\frac{(1+R_4)^4}{(1+R_{4-1})^{4-1}} -1$  

r4 = $\frac{(1+0.0260_4)^4}{(1+0.0225_{3})^{3}}-1$  

r4 = 0.0366

r4 = 3.66 %

and now put value for year 5  in equation 1

r5 = $\frac{(1+R_5)^5}{(1+R_{5-1})^{5-1}} -1$  

r5 = $\frac{(1+0.0298_5)^5}{(1+0.0260_{4})^{4}}-1$  

r5 = 0.0451

r5 = 4.51 %

and

now put value for year 6  in equation 1

r6= $\frac{(1+R_6)^6}{(1+R_{6-1})^{6-1}} -1$  

r6 = $\frac{(1+0.0325_6)^6}{(1+0.0298_{5})^{5}} -1$  

r6 = 0.0461

r6 = 4.61 %