Suppose we observe the following rates: 1R2= 8%, 1R2= 10%. If the unbiased expectations theory of the term structure of interest rates holds, what is the 1-year interest rate expected one year from now, E(2r1)?
According to the unbiased expectations theory of the term structure of interest rates, the 1-year interest rate expected one year from now (E(2r1)) will be equal to the current 2-year interest rate.
In this case, we have observed two rates: 1R2 = 8% and 1R2 = 10%. Since these are the rates for a 1-year bond in 2 years' time, the expected 2-year interest rate (E(2r1)) would be equal to the second rate we observed, which is 10%.
Therefore, based on the unbiased expectations theory, the 1-year interest rate expected one year from now is 10%.
To determine the 1-year interest rate expected one year from now, E(2r1), under the unbiased expectations theory of the term structure of interest rates, we need to consider the observed rates and apply the concept of expected future rates.
According to the unbiased expectations theory, the expected future rate should be equal to the current long-term rate. In this case, we have observed two rates, 1R2=8% and 1R2=10%.
Since 1R2 represents the 1-year interest rate observed 2 years from now, we can calculate the expected 1-year interest rate one year from now, E(2r1), by taking the average of the observed rates.
E(2r1) = (1R2 + 1R2) / 2
= (8% + 10%) / 2
= 9%
Therefore, based on the unbiased expectations theory, the expected 1-year interest rate one year from now is 9%.