Assuming the pure expectations theory is correct, which of the following statements is CORRECT?

Group of answer choices

Reinvestment rate risk is higher on long$-$term bonds, and interest rate $($price$)$ risk is higher on short$-$term bonds.

If $2-$year Treasury bond rates exceed $1-$year rates, then the market must expect interest rates to rise.

If $1-$year rates are $6\%$ and $2-$year rates are $7\%,$ then the market expects $1-$year rates to be $6\mathrm{.}5\%$ in one year.

Interest rate $($price$)$ risk and reinvestment rate risk are relevant to investors in corporate bonds, but these concepts do not apply to Treasury bonds.

If both $2-$year and $3-$year Treasury rates are $7\%,$ then $5-$year rates must also be $7\%.$