pure expectations theory:

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The pure expectations theory assumes that a one-year bond purchased today will have the same return as a one-year bond purchased five years from now. The yield on a one-year Treasury security is 5.8400%, and the two-year Treasury security has a 7.0100% yield. Assuming that the pure expectations theory is correct, what is the market's estimate of the one-year Treasury rate one year from now? Recall that on a one-year Treasury security the yield is 5.8400% and 7.0100% on a two-year Treasury security. Suppose the one-year security does not have a maturity risk premium, but the two-year security does and it is 0.1500%. What is the market's estimate of the one-year Treasury rate one year from now? Suppose the yield on a two-year Treasury security is 5.83%, and the yield on a five-year Treasury security is 6.20%. Assuming that the pure expectations theory is correct, what is the market's estimate of the three-year Treasury rate two years from now