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Observe the three year treasury rate (1r3) to be 5.2 percent, expected 1 year rate next...

Observe the three year treasury rate (1r3) to be 5.2 percent, expected 1 year rate next year -E(2r1)-to be 6.2%, and theexpect one year rate the following year-E(3r1)- to be6.8 percent. If unbiased theory of the term structure of interest rates hold, whats the one year Treasury security rate?

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Answer #1

Based on unbiased expectations theory,

(1 + 3 Yr Rate)3 = (1 + 1 Yr rate) * (1 + 1 Yr rate 1 Yr from now) * (1 + 1 Yr rate 2 Yr from now)

(1 + 5.2%)3 = (1 + 1 Yr rate) * (1 + 6.2%) * (1 + 6.8%)

1.164253 = (1 + 1 Yr rate) * (1.062) * (1.068)

1.164253 = (1 + 1 Yr rate) * 1.134216

(1 + 1 Yr rate) = 1.0265

1 Yr rate = 0.0265 = 2.65%

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