The one-year interest rate is 4% in 2019. The two year interest rate is 5% 2019 and the
three-year interest rate is 6% in 2019. According to the expectation hypothesis, what is
your expectation of one-year interest rate in 2020 and 2021 respectively? Explain your
calculation.
Answer
According to Expectation hypothesis :
Rnt = (R1t + R1t + 1 + R1t + 1 + ---------------R1t + n - 1)/n
where, Rnt = n periods interest rate and R1t + n - 1 = one year expected interest rate of nth period.
Now, Here The one-year interest rate is 4% in 2019. The two year interest rate is 5%
i.e. R2t = 2 year interest rate = 5%, R1t = one year interest rate in 2019 = 4% and R1t + 1 = one-year interest rate in 2020 is what we have to calculate.
Using above formula we have :
R2t = (R1t + R1t + 1)/2
=> 5% = (4% + R1t + 1)/2
=> R1t + 1 = 6%
Hence, expectation of one-year interest rate in 2020 = 6%
Now, Here The one-year interest rate is 4% in 2019. The three year interest rate is 6% 2019
i.e. R3t = 3 year interest rate = 5%, R1t = one year interest rate in 2019 = 4%, R1t + 1 = one year interest rate in 2020 = 6% , R1t + 2 = one-year interest rate in 2021 is what we have to calculate.
Using above formula we have :
R3t = (R1t + R1t + 1 + R1t + 2)/3
=> 6% = (4% + 6% + R1t + 2)/3
=> R1t + 1 = 18% - 4% - 6% = 8%
Hence, expectation of one-year interest rate in 2021 = 8%
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