Question

Suppose that the current one-year rate and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:

1R1 = 1.88%, E(2r1) =2.99%, E(3r1) = 4.56%, E(4r1) = 5.65%

Using the unbiased expectations theory, calculate the current rate for three-year-maturity Treasury securities

(Write your answer in percentage not decimal for example 5.78%)

current rate for three-year-maturity =

Answer 1

The current rate for a 3 year maturity is :

( 1 year t bill) * ( 1 year rate in 2nd year) * ( one year rate in 3rd year ) = (3 year maturity) ^3

(1.088)* ( 1.0299)* (1.0456) = ( 1 + x) ^3

( 1.1716)^0.3333 = ( 1 + x)

1.0542 = ( 1 +x)

So, x = 5.42%

So, the current rate of 3 year maturity t bill is 5.42%.