$6.$ Pure expectations theory

The pure expectations theory, or the expectations hypothesis, asserts that long$-$term interest rates can be used to estimate future short$-$term interest rates.

Based on the pure expectations theory, is the following statement true or false?

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.

False

True

The yield on a one$-$year Treasury security is $5\mathrm{.}6100\%,$ and the two$-$year Treasury security has a $6\mathrm{.}7320\%$ 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? $($Note: Do not round your intermediate calculations.$)$

$6\mathrm{.}686\%$

$7\mathrm{.}8659\%$

$8\mathrm{.}9671\%$

$9\mathrm{.}9897\%$

Recall that on a one$-$year Treasury security the yield is $5\mathrm{.}6100\%$ and $6\mathrm{.}7320\%$ 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 $0\mathrm{.}45\%.$ What is the market$$s estimate of the one$-$year Treasury rate one year from now? $($Note: Do not round your intermediate calculations.$)$

$6\mathrm{.}9582\%$

$7\mathrm{.}9323\%$

$8\mathrm{.}8369\%$

$5\mathrm{.}9145\%$

Suppose the yield on a two$-$year Treasury security is $5\mathrm{.}83\%,$ and the yield on a five$-$year Treasury security is $6\mathrm{.}20\%.$ Assuming that the pure expectations theory is correct, what is the market$$s estimate of the three$-$year Treasury rate two years from now? $($Note: Do not round your intermediate calculations.$)$

$6\mathrm{.}45\%$

$6\mathrm{.}61\%$

$7\mathrm{.}10\%$

$6\mathrm{.}53\%$