Unbiased Expectations Theory Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill...

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Unbiased Expectations Theory Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill...

Unbiased Expectations Theory Suppose that the current one-year rate (one-year spot 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=6.95%, E(₂r₁) =7.45%, E(₃r₁) =8.45% E(₄r₁)=8.95%

Using the unbiased expectations theory, what is the current (long-term) rate for four-year-maturity Treasury securities?

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Answer 1

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Answer #1

Assume Current (long term) rate for four -year-maturity Treasury Security =R

As per unbiased Expectation Theory,

(1+R)^4=(1+1R1)*(1+E(2r1)*(1+E(3r1)*(1+E(4r1)

1R1=6.95%=0.0695

E(2r1)=7.45%=0.0745

E(3r1)=8.45%=0.0845

E(4r1)=8.95%=0.0895

(1+R)^4=1.0695*1.0745*1.0845*1.0895

(1+R)^4=1.35783

1+R=1.35783^(1/4)=1.07947

R=0.07947

Current (long term) rate for four -year-maturity Treasury Security =0.07947=7.947%

Current (long term) rate for four -year-maturity Treasury Security =7.95%(rounded to two decimals)

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Answer 2

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