Question

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 1

Answer

Using expectation hypothesis we have :

(i_1t + i_1t+1 + i_1t+2 ------------------------------ + i_1t+n)/n = i_nt

where n = number of period, i_nt = n period interest rate and i_1t+n = 1 year interest rate of nth period.

Now,

Here, The one-year interest rate is 4% in 2019 i.e. i_1t = 4%. The two year interest rate is 5% 2019 i.e. i_2t = 5 and we have to calculate The one-year interest rate in 2020 = i_1t+1.

Hence using above formula we have :

(i_1t + i_1t+1)/2 = i_2t => (4% + i_1t+1)/2 = 5%

=> i_1t+1 = 6%

Hence, The one-year interest rate in 2020 = i_1t+1 = 6%.

Now,

Here, The one-year interest rate is 4% in 2019 i.e. i_1t = 4%, The one-year interest rate in 2020 = i_1t+1.= 6%(calculate above) The three year interest rate is 5% 2019 i.e. i_3t = 6% and we have to calculate The one-year interest rate in 2021 = i_1t+2.

Hence using above formula we have :

(i_1t + i_1t+1 + i_1t+2)/3 = i_3t => (4% + 6% + i_1t+2)/3 = 6%

=> i_1t+2 = 8%

Hence, The one-year interest rate in 2021 = i_1t+2 = 8%.