using the unbiased expectations theory what is the current long term rate for fo

Question

using the unbiased expectations theory what is the current long term rate for four year maturity treasury securities 5% Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill lates over the following three years (i.e, years 2, 3, and 4, respectively) are as follows: 23 iR1 500. E(2N).. 5.5%. EGri)-6.500 E(3M)-6.5% E(4,1) Earl) 7.00 o 7.000 Using the unbiased expectations theory, what is the current (long-term) rate for four-year-maturity Treasury securities? a 6.00 percent b 6.33 percent c 6.75 percent d 7.00 percent

Explanation / Answer

Answer

(1+ 4 year rate)4 = ( 1 + current spot rate)*(1 + forward rate year 2)* (1 + forward rate year 3)* (1 + forward rate year 4)

(1+ 4 year rate)4 = ( 1 + 0.05)*(1 + 0.055) * (1 + 0.065) * (1 + 0.07)

(1+ 4 year rate)4 = (1.05)*(1.055) *(1.065) * (1.07)

(1+ 4 year rate)4 = 1.262337

(1+ 4 year rate) = 4th root (1.262337)

(1+ 4 year rate) = 1.06

4 year rate= 1.06 – 1

4 year rate= 0.06

4 year rate= 6%

Answer : The current (long term) rate for four year maturity treasury securities is : (a) 6.00 percent

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